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Activity 1. Designing a Roller Coaster (Teacher’s Notes)

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

OBJECTIVE: The objective of this activity is to motivate the significance of the product of force and distance to lift an object through a given height. This is done by having the student discover that this product is invariant when several alternatives are considered. The invariance of the product of force and distance motivates giving it the special name of work and considering the work done to result in an increase of gravitational potential energy.

IDEA: The work done to lift an object from a tabletop to a given height above the tabletop is the same, regardless of the slope of the incline along which it is pulled. This invariance of the work done motivates equating it to the gravitational potential energy acquired by the object: Work = ΔPEg. The inclined plane is also one of the basic simple machines known in ancient times. Like all simple machines, it allows objects to be lifted with less force, provided that the force acts through a greater distance. In all cases, the product of the force and the distance through which it acts is the same, if friction is negligible.

LEVEL: middle level (7, 8, and 9)

DURATION: approximately 60 minutes (5 minutes setup, 30 minutes data gathering, 20 minutes data analysis, 5 minutes take down)

STUDENT BACKGROUND: Students must be able to measure with a meterstick and a spring scale, also make and interpret linear and simple inverse graphs.

ADVANCE PREPARATION: Assemble a spring scale, cart, incline, and supports for the incline for each group of students. Check spring scale for accuracy.

MANAGEMENT TIPS: Elicit student responses to the Reflective Question before proceeding on to the activity.

Emphasize that the height of the first hill is to be kept constant, and that distances measured along the slope should extend only as far as the height of this hill. The transparency on page 181 can be used to illustrate this. Inform students that they themselves will need to support the incline for steep slopes.

After step 7, elicit from students that the relationship between the force and distance is inverse and that making a graph of force vs. reciprocal of distance may give a straight line. This can be facilitated by reasoning that (0,0) is a logical point on the graph. (As the force gets infinitesimally small, the distance becomes infinitely large, and its reciprocal becomes infinitesimally small as well.)

RESPONSES TO SOME QUESTIONS:Reflective Question. Some students may seek to minimize the force needed to pull the cart up the incline. Others may seek to maximize the amount of time in order to minimize the rate at which work is done to lift the cart (“power”) or to increase the dread of the ride. Arguments for a steep slope result from space limitations, materials costs, and the desire to increase the number of riders per hour.

The following sample data were gathered:

Force (N) Distance (m) 1/distance (m-1(Force) (distance) (J) 
4.3 0.28 3.57 1.20 
2.8 0.48 2.08 1.34 
2.0 0.66 1.52 1.32 
1.6 0.92 1.09 1.47 
1.3 1.21 0.83 1.57 
Force (N) Distance (m) 1/distance (m-1(Force) (distance) (J) 
4.3 0.28 3.57 1.20 
2.8 0.48 2.08 1.34 
2.0 0.66 1.52 1.32 
1.6 0.92 1.09 1.47 
1.3 1.21 0.83 1.57 

6. A graph of force vs. distance along the incline should indicate an inverse relationship between these two variables. This motivates making a graph of the force vs. the reciprocal of the distance along the incline in step #8.

8. The graph of force vs. reciprocal of distance along the incline should be a straight line through the origin:

9 and 10. The product of the force and the distance along the incline is about the same for all slopes. Thus the work done to pull the cart along the incline is about the same for all slopes.

12 and 13. The work done to pull the cart to the top of the first hill and the gravitational potential energy acquired as a result can be calculated by multiplying the weight of the cart (force required to pull it straight up) by the vertical distance from the tabletop to the top of the first hill. In the sample data, a force of 4.3 N was used to raise the cart a vertical distance of 0.28 m. The work done, and gravitational potential energy acquired, is (4.3 N)(0.28 m) = 1.20 J.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: The work done to pull the cart from the tabletop to the top of the first hill is about the same for all slopes of the incline. This suggests that it is a fundamental quantity, which is also called the gravitational potential energy acquired by the cart (more correctly, by the system of the Earth and the cart), depending only on its weight and the height through which it has risen. The importance of considering the system to include the Earth in establishing the concept of gravitational potential energy is emphasized by Alan Van Heuvelen and Xueli Zou, “Multiple Representations of Work-Energy Processes,” Am. J. Phys.69(2), 184–194 (Feb. 2001), reproduced in Appendix G. Otherwise, gravity is an external force, and one can consider only the work that it does.

POSSIBLE EXTENSIONS: Have students calculate gravitational potential energies in question 11 relative to the floor rather than relative to the tabletop and show that the gravitational energy increase in question 13 is the same as if the gravitational potential energy is calculated relative to the tabletop.

One can measure the force of friction (f ) between the cart and the inclined plane by measuring the minimum force to pull the cart up the incline (F + f, where F is the force needed to pull the cart in the absence of friction) and the minimum force for the object to slide down the incline (Ff ), then finding the sum and dividing by two.

If a wood block instead of a frictionless cart is pulled up an incline, friction will play a major role, and the work done to pull the block up the incline to a given height will clearly be more than that required for a direct lift (increase in gravitational potential energy). The ratio of the increase in gravitational potential energy to the work done is known as the efficiency. Thinking of the incline as a simple machine, one can also calculate the ideal mechanical advantage (IMA) (slant distance/vertical distance) and actual mechanical advantage (AMA) (force exerted/weight).

The following sample data were gathered for pulling a wood block up on incline:

Angle (deg)1020304090
Force (N) 0.5 0.75 0.95 1.1 1.35 
Distance (m) 0.427 0.212 0.158 0.132 0.068 
Work (J) 0.21 0.16 0.15 0.15 0.09 
Efficiency (%) 43.00 57.74 61.16 63.22 100.00 
IMA 6.28 3.12 2.32 1.94 1.00 
AMA 2.70 1.80 1.42 1.23 1.00 
Angle (deg)1020304090
Force (N) 0.5 0.75 0.95 1.1 1.35 
Distance (m) 0.427 0.212 0.158 0.132 0.068 
Work (J) 0.21 0.16 0.15 0.15 0.09 
Efficiency (%) 43.00 57.74 61.16 63.22 100.00 
IMA 6.28 3.12 2.32 1.94 1.00 
AMA 2.70 1.80 1.42 1.23 1.00 

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

Suppose you were called upon to design a roller coaster. The first part of your design would be to move the passengers to the top of the first hill. How steep would you make the incline? How fast would you have the passengers move up the incline? What are some of the other considerations you would need to take into account?

__________

  • inclined plane (e.g., 1” × 6” (or 8”) × 4’ boards from building supply company, or a table with one side propped up with books or bricks)

  • meterstick

  • low-friction cart (e.g., PASCO, Hall’s)

  • supports for inclined plane (e.g., books or bricks)

  • spring scale, to measure force in newtons (0-5 N)

In answering the reflective question, you may have listed the force to pull the passengers (in the roller coaster cars) to the top of the first hill as one of the considerations you would need to take into account. In this activity you will investigate how this force depends on the slope of the incline. To do this, set up an inclined plane on a table, with means to support it at one end to provide a wide range of slopes.

With the tabletop representing the ground, select a position above the tabletop to represent the height of the first hill. Measure and record the vertical distance (in meters) from the tabletop to this point. See Diagram #1.

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Connect a spring scale (measuring force in newtons) to a cart (representing the roller coaster) and place the cart on the incline. For a variety of slopes of the incline, measure the force needed to pull the cart up the incline with a slow constant speed. Pull in the direction parallel to that of the incline.

For each slope, measure the distance (in meters) along the incline from the tabletop (ground) to the point representing the height of the first hill. Remember to keep the point representing the height of the first hill constant. As you slide the base of the incline toward this point to make the slope steeper, the other end of the incline will extend beyond this point; however, remember to measure to the point representing the height of the first hill, not to the end of the incline. Record your measured forces and distances along the plane in a table similar to the following (the blank column is reserved for the addition of future calculations):

Data Table #1

Type of slope (e.g., gentle, steep) Distance along incline (m)  (Force) (N) 
    
    
    
    
    
Type of slope (e.g., gentle, steep) Distance along incline (m)  (Force) (N) 
    
    
    
    
    

Diagram #1

Measure and record the force needed to pull the cart straight up, vertically. Include this measurement and the vertical distance from the tabletop to the top of the first hill (from step #2) in your data.

Make a graph of the force required to pull the cart vs. (as a function of) the distance along the incline the cart needed to travel to reach the top of the first hill.

What kind of relationship do you see between the force required to pull the cart and the distance it must move along the incline to reach the top of the first hill? Explain.

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__________

Note: Stophere until directed to continue by your teacher.

In the blank column of Data Table #1 calculate the reciprocal of the distance along the incline. Make a graph of the pulling force vs. the reciprocal of the distance along the incline.

What kind of relationship do you see between the force required to pull the cart and the reciprocal of the distance it must move along the incline to reach the top of the first hill?

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__________

What do you conclude about the product of the force required to pull the cart and the distance it must move along the incline to reach the top of the first hill?

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__________

The product of the force exerted to pull the cart parallel to the incline and the distance the cart moved along the incline is defined as the work done to pull the cart. What can you conclude about the work done to pull the cart up the incline to the top of the first hill for various slopes?

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__________

One of the ways you measured the work done to pull the cart was to multiply the force required to pull it straight up (its weight) by the vertical distance through which it was pulled (data from step #4). The result of doing this work is known as an increase in potential energy of the cart (at the top of the first hill). Because this increase in potential energy resulted from opposing a gravitational force, it is more specifically an increase in gravitational potential energy, and some would call it simply gravitational energy. Furthermore, because the gravitational force is exerted by the Earth, the potential energy is more correctly considered to be possessed by the system of the Earth and the cart rather than by the cart alone. In general, this gravitational potential energy relative to a given point is found as follows:

gravitational potential energy = (weight)(height above a given reference point).

In symbols, PEg = mgh.

Note, however, that this given reference point is arbitrary. It has been chosen to be the height of the tabletop in this case. The reason that the reference point for gravitational potential energy is arbitrary is that only changes in potential energy are significant.

How much work did you do to lift the cart from the tabletop to the top of the first hill?

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__________

How much gravitational potential energy did the cart acquire in rising to the top of the first hill? (Note: The unit for energy, which comes from multiplying force in newtons times distance in meters, is the joule. A joule is a newton times a meter. The symbol for joule is J.)

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__________

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

OBJECTIVE: The objective of this activity is to motivate the idea that energy can exist in kinetic as well as potential form and that it is possible to convert one form to the other. If the amount of gravitational potential energy decrease is matched by a kinetic energy increase, the sum of the two forms of energy will remain the same, and the total energy obtained from this sum becomes a conserved quantity.

IDEA: The increase in an object’s gravitational potential energy from being lifted is offset by a decrease as the object falls down again. The farther it falls, the more its gravitational potential energy decreases, the faster it goes, and the more its kinetic energy increases. The process of falling can be viewed as a conversion from gravitational potential to kinetic energy, so that the sum of the two forms of energy remains constant:

ΔPEg + ΔKE = 0

PEg + KE = constant.

LEVEL: high school (10-12)

DURATION: approximately 80 minutes (10 minutes setup, 30 minutes data gathering, 30 minutes data analysis, 10 minutes take down)

STUDENT BACKGROUND: Students must be able to measure with a meterstick, a spring scale, a balance, and a photogate, also make and interpret graphs.

ADVANCE PREPARATION: Assemble a cart with a flag, an incline and supports for the incline, a meterstick, and a photogate for each group of students. Assemble a few spring scales and balances to be used as needed to measure the weight and mass of the cart. Teach students how to measure velocities with a photogate. (Also note that the speed so measured is actually the average speed of the cart during the time it passes through the photogate, but that the small width of the flag ensures that this average speed is the closest we can measure to the instantaneous speed at the photogate. Instructions for measuring speeds with a photogate using a CBL and TI-83, a CBL2 or LabPro and TI-83+, a LabPro and a computer, or a PASPORT Xplorer Datalogger are provided on separate pages.)

MANAGEMENT TIPS: Elicit student responses to the Reflective Question before proceeding on to the activity.

It is important in this activity to have carts that have not only minimal friction but also minimum wheel mass in order to minimize rotational inertia and energy.

Emphasize the need to start the cart rolling down the incline at the same position every time without pushing and to measure the position of the cart by the location of the front of the cart. How well students are doing this can be checked by the consistency of several measurements of the speed of the cart at each point along the incline.

After step 6 elicit that the gravitational potential energy decrease is varying as the square of the speed and that making a graph of gravitational potential energy decrease vs. speed squared should give a straight line. This can be facilitated by reasoning that (0,0) is a logical point on the graph.

RESPONSES TO SOME QUESTIONS:Reflective Question: It is hoped that students will realize that as the roller coaster’s gravitational potential energy decreases, its speed increases. Some students who may already have been introduced to the concept of kinetic energy will give this as their answer. Those who have not been introduced to the concept of kinetic energy will be introduced to it in this activity, and it is intended that all students will be introduced to kinetic energy in a quantitative sense.

The following sample data were gathered:

Final dist. above tabletop (m)Final PE (J)Vert. dist. fallen (m)decrease in PE (J)speed (m/s)speed squared(m2/s2)
0.045 0.23 0.235 1.18 2.12 4.49 
0.105 0.53 0.175 0.88 1.82 3.31 
0.15 0.75 0.13 0.65 1.57 2.46 
0.187 0.94 0.093 0.47 1.32 1.74 
0.227 1.14 0.053 0.27 1.00 
Final dist. above tabletop (m)Final PE (J)Vert. dist. fallen (m)decrease in PE (J)speed (m/s)speed squared(m2/s2)
0.045 0.23 0.235 1.18 2.12 4.49 
0.105 0.53 0.175 0.88 1.82 3.31 
0.15 0.75 0.13 0.65 1.57 2.46 
0.187 0.94 0.093 0.47 1.32 1.74 
0.227 1.14 0.053 0.27 1.00 

6 and 7. The graph of the gravitational potential energy decrease vs. the speed of the cart should look like a parabola of the form y = cx2. This suggests that the gravitational potential energy decrease will vary linearly with the square of the cart’s speed, and it does.

8 and 9. The units of the slope of the graph of gravitational potential energy decrease vs. square of the cart’s speed must be J divided by (m2/s2), or kg, since J = N.m = kg.m2/s2. The slope therefore must be the mass of the cart (the only mass in the experiment) divided by some number. In the sample data provided, the weight of the cart was measured as 5.0 N, its mass measured as 0.502 kg, and the slope of the graph of gravitational potential energy decrease vs. square of the cart’s speed is 0.263 kg, very close to half the mass of the cart. Therefore,

decrease in gravitational potential energy = increase in (mass/2)(square of speed)

decrease in gravitational potential energy = increase in kinetic energy.

The kinetic energy expressed by mv2/2 is only the kinetic energy of linear motion; it does not include kinetic energy due to rotation, say, of the wheels of the cart. For this reason, the best results are obtained for this experiment with low-friction carts with small wheels.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: The gravitational potential energy decrease as an object’s height decreases is marked by a corresponding increase in kinetic energy. Being able to equate the decrease in one quantity, which depends only on position, to the increase in another, which depends on motion, suggests that these quantities are all forms of an “overall” quantity, which we call energy, and which can be converted among several forms, two of which are called “potential” and “kinetic.” It should be stressed, though, that both potential and kinetic energy are forms of energy, just as dollars and Euros are both forms of money.

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

In the activity “Designing a Roller Coaster” you have seen that a roller coaster acquires gravitational potential energy upon rising to the top of the first hill. After that, the roller coaster rolls down the hill; and, in doing so, it gives up some, if not all, of the gravitational potential energy it had acquired. What happens to the gravitational potential energy that is given up?

__________

  • inclined plane (e.g., 1” × 6” (or 8”) × 4’ boards from building supply company, or table with one side propped up with books or bricks)

  • meterstick

  • low-friction cart (e.g., PASCO, Hall’s) with flag (e.g., business card)

  • photogate

  • supports for inclined plane (e.g., books or bricks)

  • spring scale, to measure force in newtons

  • balance, to measure mass in grams or kilograms

The farther down the hill the coaster rolls, the faster it goes. Is there something related to its motion that can be equated to the gravitational potential energy that it gives up? If so, what?

You can answer the above reflective question by measuring the decrease in gravitational potential energy and comparing it to the motion of the coaster at various points along an incline as it rolls down the incline. To do this, mount an inclined plane and mark the highest point on the incline from which the front of the cart can be released. This is the starting position from the top of the first hill in this activity. Measure and record the vertical distance from the tabletop to this point.

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Position a photogate so that the flag on the low-friction cart just barely passes through it when the front of the cart reaches a lower point on the incline (see diagram 1). Measure the vertical distance from the tabletop to the point on the incline by the front of the cart at this point. Release the cart from its starting position and measure the time for the flag to pass through the photogate. Calculate the cart’s speed as it passes through the photogate by dividing the width of the flag by the measured time, and record it in a data table like the one on the next page. (This speed is actually the average speed of the cart during the time it passes through the photogate, but the small width of the flag ensures that this average speed is the closest we can measure to the instantaneous speed at the photogate. If you have a CBL and TI-83, a CBL2 or LabPro and TI-83+, a LabPro and a computer, or are using a PASPORT Xplorer Datalogger, directions are provided on separate pages.)

Reposition the photogate to determine the speed of the cart released from the same starting position as it passes other points along the incline. Also make sure in all cases to measure and record the vertical distance from the tabletop to the point on the incline by the front of the cart at the point in question. (An alternative is to position several photogates along the incline and make several measurements of speed simultaneously.) Record all measurements of final vertical distance from the tabletop and calculations of speed in a data table like the one on the next page.

Diagram #1

Measure the weight of the cart or look up its value from Activity #1, “Designing a Roller Coaster,” so that you can calculate the cart’s gravitational potential energy at each point along the incline, according to the formula:

gravitational potential energy = (weight)(height above a given point),

PEg = mgh,

with the tabletop considered to be the reference point, as in the “Designing a Roller Coaster” activity.

__________

What is the gravitational potential energy of the cart at the starting position, measured in question #1?

__________

Record your measurements and calculations in a data table like the following:

Data Table #1

Final distance above tabletop (m)Final gravitational potential energy (J)Vertical distance fallen (m)Decrease in gravitational potential energy (J)Speed (m/s)
Enter final vertical distance above tabletop (from question #3) Multiply vertical distance in first column by weight of cart Subtract final vertical distance above tabletop from vertical distance above tabletop to starting position (question #1) Subtract final gravitational potential energy from gravitational potential energy at starting position (calculated in question #4) Enter value of speed measured with photogate 
     
     
     
     
     
Final distance above tabletop (m)Final gravitational potential energy (J)Vertical distance fallen (m)Decrease in gravitational potential energy (J)Speed (m/s)
Enter final vertical distance above tabletop (from question #3) Multiply vertical distance in first column by weight of cart Subtract final vertical distance above tabletop from vertical distance above tabletop to starting position (question #1) Subtract final gravitational potential energy from gravitational potential energy at starting position (calculated in question #4) Enter value of speed measured with photogate 
     
     
     
     
     

Make a graph of the decrease in gravitational potential energy vs. the speed of the cart. What kind of relationship do you see between the decrease in gravitational potential energy and the speed of the cart?

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Note: Stophere until directed to continue by your teacher.

Calculate the square of the speed of the cart at each position and make a graph of the gravitational potential energy decrease vs. the square of the cart’s speed. What kind of relationship do you see in this graph? What does this suggest as a possible answer to the question raised at the outset of this activity about the roller coaster (or anything else that falls after acquiring gravitational potential energy): Is there something related to its motion that can be equated to its decrease in gravitational potential energy?

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__________

What are the units of the slope of the graph of the gravitational potential energy decrease vs. the square of the cart’s speed?

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How does the slope of the graph of gravitational potential energy decrease vs. the square of the cart’s speed relate to the mass of the cart? From the equation of the best straight line fit for the gravitational potential energy decrease vs. the square of the cart’s speed, what can you infer about the relationship among the cart’s decrease in gravitational potential energy, its speed, and its mass? (You will need to measure the mass of the cart to answer this question.)

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__________

The quantity related to the gravitational potential energy decrease and depending on the mass and square of the speed is called kinetic energy (energy of motion). We consider that as the cart’s gravitational potential energy decreases, its kinetic energy increases. Another way to say this is that the cart’s gravitational potential energy is transformed into kinetic energy. The amount of kinetic energy depends on the square of the cart’s speed and a constant, which can be determined from the slope of the graph of the gravitational potential energy decrease vs. the square of the cart’s speed. This slope has units of kg, and its magnitude equals the cart’s mass divided by a number. If 2 is the whole number closest to the number the mass is divided by to get the slope of the graph of gravitational potential energy decrease vs. square of cart’s speed, then the equation relating kinetic energy, mass, and speed is

kinetic energy = (mass/2)(square of speed) = half the mass times the square of the speed.

In symbols, KE = (1/2)mv2,

where “v” represents speed rather than velocity.

As in the case of gravitational potential energy, the units for kinetic energy are joules.

If the cart’s gravitational potential energy is transformed into kinetic energy, what can you say about the sum of the cart’s gravitational potential and kinetic energy as it rolls down the incline?

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__________

If the sum of the cart’s gravitational potential and kinetic energy is called the cart’s total energy, in what way is total energy a more significant concept than gravitational potential energy or kinetic energy alone?

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__________

We can represent the amounts of kinetic and gravitational potential energy in a bar graph. Since the amount of gravitational potential energy varies directly as the height above a specific point, the amount of gravitational potential energy can be represented by a bar of the same height. Since the amount of kinetic energy equals the gravitational potential energy decrease, the height of the bar representing kinetic energy will be the difference in heights of the bars representing gravitational potential energy at the top of the hill and at subsequent positions along the incline, as displayed in the following diagram:

Many activities require measuring the speed of a vehicle or object. This can be done by measuring the time the object or a flag mounted on it takes to pass through a photogate and dividing the length of the object or flag by that time. To measure that time with a photogate and a TI-83+ and CBL2/LabPro using the “DATAGATE” program, do the following:

Mount the photogate(s) so that the object or flag on the vehicle whose speed is to be measured will intercept the photogate(s).

Connect the photogate probe(s) to the DIG/SONIC port of the CBL2/LabPro unit. CBL2 units can accommodate only one photogate.

Make sure that the link cord is connected between the calculator and the CBL2/LabPro unit (link ports are on the bottom of each unit).

Turn on the CBL2/LabPro unit and calculator.

Press the <PRGM> key on the calculator.

Select <DATAGATE> and press <ENTER>.

Press <ENTER>. Connected photogates will be listed, with an “X” if blocked, “O” if unblocked.

Press <1: SETUP>.

Press <2: GATE>.

Press <2: TWO PHOTOGATES> (LabPro only) or <1: ONE PHOTOGATE>, depending on the number of photogates you are using.

Enter the “flag width in meters” and press <ENTER>.

Press <1: OK>.

Press <2. START>.

Let the flag pass through the photogates (in numerical order, if two gates are used). The trial number and time each gate is intercepted will be displayed on the calculator screen. In order to read the times and velocities from the “GRAPH” option, at least two trials must be measured.

Press <STO->> to Stop.

Press <3: GRAPH> to see either times or velocities displayed vs. trial number. Choose <DELTA TIME> to see the times displayed or <VELOCITY> to see the corresponding velocities. Values can be read by moving the cursor with arrow keys. When finished with either “GRAPH” option, press <ENTER>.

Press <1: Return to Main Screen>.

Press <4: Quit>.

Many activities require measuring the speed of a vehicle or object. This can be done by measuring the time the object or a flag mounted on it takes to pass through a photogate and dividing the length of the object or flag by that time. To measure that time with a photogate and a TI-83+ and CBL2/LabPro using the “PHYSICS” program, do the following:

  1. Mount the photogate so that the object or flag on the vehicle whose speed is to be measured will intercept the photogate.

  2. Connect the photogate probe to the DIG/SONIC port of the CBL2/LabPro unit.

  3. Make sure that the link cord is connected between the calculator and the CBL2/LabPro unit (link ports are on the bottom of each unit).

  4. Turn on the CBL2/LabPro unit and calculator.

  5. Press the <APPS> key on the calculator.

  6. Use the arrow keys on the calculator to highlight the program PHYSICS. Press <ENTER>.

  7. When the program title screen appears, press <ENTER>, as prompted on the screen.

  8. If it is not already highlighted, highlight 1:SET UP PROBES and press <ENTER>.

  9. At prompt, “NUMBER OF PROBES,” press <1> or highlight 1:ONE and press <ENTER>.

  10. At prompt, “SELECT PROBE,” select <7.MORE> twice, then <3.PHOTOGATE>. (This can be done by pressing the number or using the arrow keys to select the desired alternative and pressing <ENTER>.)

  11. If directed to connect the photogate probe to DIG1, press <ENTER>, because you have already done this in step 2.

  12. You should now be at the “TIMING MODES” menu. Choose <5.CHECK GATE>. This allows you to read on your TI-83+ screen whether the gate is blocked (an object is blocking the beam) or unblocked. After you have finished testing the gates, press “+” to QUIT and return to the “TIMING MODES” menu.

  13. Choose <2.GATE>.

  14. Choose the number of gates (“one”).

  15. When directed, let the object whose speed is to be measured pass through the photogate. At the conclusion of the data gathering, the “SAMPLING” on the CBL2 screen should change to “DONE.” Press <ENTER>.

  16. Repeat time measurements as desired.

  17. To calculate speeds, divide the length of the flag intercepting the photogates by the measured time.

Many activities require measuring the speed of a vehicle or object. This can be done by measuring the time the object or a flag mounted on it takes to pass through a photogate and dividing the length of the object or flag by that time. To measure that time with a photogate and a TI-83 and CBL using the “PHYSICS” program, do the following:

  1. Mount the photogate so that the object or flag on the vehicle whose speed is to be measured will intercept the photogate.

  2. Connect the photogate probe to CH 1 of the CBL unit.

  3. Connect the link cord between the calculator and CBL unit (link ports are on the bottom of each unit). Make sure that the link cord is firmly inserted into each unit (a twisting motion helps to ensure this).

  4. Turn on the CBL unit and calculator.

  5. Press the <PRGM> key on the calculator.

  6. Use the arrow keys on the calculator to highlight the program PHYSICS. Press <ENTER>. At this point the calculator screen should have “prgmPHYSICS” showing; press <ENTER> again.

  7. When the program title screen appears, press <ENTER>, as prompted on the screen.

  8. If it is not already highlighted, highlight 1:SET UP PROBES and press <ENTER>.

  9. At prompt, “NUMBER OF PROBES,” press <1> or highlight 1:ONE and press <ENTER>.

  10. At prompt, “SELECT PROBE,” select <7.MORE> twice, then <3.PHOTOGATE>. (This can be done by pressing the number or using the arrow keys to select the desired alternative and pressing <ENTER>.)

  11. If prompted to select a channel, press <1> and <ENTER>. If directed to connect the photogate probe to CH 1, press <ENTER>, because you have already done this in step 2.

  12. You should now be at the “TIMING MODES” menu. Choose <5.CHECK GATE>. This allows you to read on your TI-83 screen whether the gate is blocked (an object is blocking the beam) or unblocked. After you have finished testing the gates, press “+” to QUIT and return to the “TIMING MODES” menu.

  13. Choose <2.GATE>.

  14. Choose the number of gates (“one”).

  15. When directed, follow the instructions to move your hand through the gate to arm it. At this point, the “READY” on the CBL screen should change to “SAMPLING.” Press <ENTER>.

  16. When directed, let the object whose speed is to be measured pass through the photogate. The “SAMPLING” on the CBL screen should change to “DONE.” Press <ENTER>.

  17. Repeat time measurements as desired.

  18. To calculate speeds, divide the length of the flag intercepting the photogates by the measured time.

Many activities require measuring the speed of a vehicle or object. This can be done by measuring the time the object or a flag mounted on it takes to pass through a photogate and dividing the length of the object or flag by that time. To measure that time with a photogate and a PASPORT Xplorer Datalogger, do the following:

  1. Mount the photogate so that the object or flag on the vehicle whose speed is to be measured will intercept the photogate.

  2. Connect the photogate probe to a PASPORT Photogate Port (PASCO PS-2123A).

  3. Plug the Photogate Port into a PASPORT Xplorer Datalogger (PASCO PS-2000).

  4. Press the Start / Stop button on the Xplorer Datalogger. When the photogate is intercepted, the time of interception will be displayed on the screen (and will remain on the screen until it is replaced by a subsequent time measurement).

  5. The object’s speed can be determined by dividing the width of the flag by the interception time as measured on the screen of the Datalogger. (The most recent time measurement will be displayed on the screen.)

  6. The speed can also be determined by connecting the Datalogger to the USB port of a computer equipped with DataStudio software. This connection will automatically call up DataStudio and display the interception times of all trials stored in the Datalogger. The speed can then be calculated by clicking on “Calculate” and “New,” then defining speed as the flag width (a constant assigned a numerical value) by the time (a variable whose values have been input as data).

Many activities require measuring the speed of a vehicle or object. This can be done by measuring the time the object or a flag mounted on it takes to pass through a photogate and dividing the length of the object or flag by that time. To measure that time with a photogate and a LabPro using a computer and Logger Pro, do the following:

  1. Connect a photogate to Dig/Sonic 1 on a LabPro, and connect the LabPro to a computer. Connect the AC adapter for the LabPro unit to a wall outlet.

  2. Open Vernier Logger Pro on the computer. Version 3.4.2 or a newer version is recommended because of greater ease of use. If you are working with an older version of Logger Pro, it is recommended that you upgrade to the most recent version.

  3. Pull down the File menu and choose “Open.” Open the Probes & Sensors folder. Now choose “Photogates” and then choose “One Gate Timer.”

  4. On the left of the screen use the Photogate Distance control to set the width of the flag or length of the object in meters. (This distance will be divided by the time intervals measured by the photogates to calculate the speeds.)

  5. To measure and record the speed of an object passing through the photogate, click “Collect.”

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

OBJECTIVE: The objective of this laboratory activity is to measure the potential energy of an elastic system and determine its dependence on the system’s deformation. This is done by the reverse of the strategy of Activity 2, in which the concept of kinetic energy is developed by equating its increase to the decrease in potential energy of a descending cart. Here the total energy is equated to the maximum kinetic energy of an elastic system, with a decreased kinetic energy relative to this value equated to a corresponding increase in the system’s potential energy. In this way the elastic potential energy is measured, and its dependence on the deformation of the system is investigated.

In the “low-tech” version of this activity, the elastic potential energy is found by calculating the work done to stretch a spring, as measured by the area under the graph of the stretching force vs. amount of stretch. How the elastic potential energy so determined depends on the amount of stretch is then investigated.

IDEA: When work is done to stretch an elastic material, the force needed to stretch the material increases with the amount of stretch. Thus, the work done by stretching an elastic material is not done by a constant force, and the resulting potential energy does not depend linearly on the stretch, as gravitational potential energy depends linearly on the distance through which an object is lifted. In this activity the dependence of potential energy on the stretch of an elastic object is investigated by measuring the position and motion of an object hanging from an oscillating spring. Recall that the gravitational potential energy of a roller coaster is found to convert to kinetic energy when the coaster rolls down a hill, only to have it reconvert to gravitational potential energy upon ascending the next hill. In the same way, this activity will measure potential energy according to how much kinetic energy has been converted, with this potential energy being reconverted to kinetic energy as the object on the spring oscillates up and down.

LEVEL: High school (most likely grade 12, as this topic is on the AP syllabus but not a necessary part of many typical high school courses. Moreover, the level of mathematical analysis required in this activity is significantly more sophisticated than that of the other activities.) The “low-tech” version (Activity 3e) is suitable for high school students in grades 10-12.

DURATION: approximately 80 minutes (10 minutes setup, 30 minutes data gathering, 30 minutes data analysis, 10 minutes take down)

STUDENT BACKGROUND: Students must be able to measure with a metric scale and a motion sensor and to analyze data gathered by a motion sensor on a graphing calculator or the equivalent. For the “low-tech” version students must be able to calculate the areas under graphs, using the numbers on the graph axes.

ADVANCE PREPARATION: Assemble a spring and stand with metric scale, masses, and mass hanger for each group of students. Teach students how to measure with the motion sensor.

Springs can be purchased from hardware stores and from scientific equipment companies (separately or as part of a Hooke’s Law apparatus). The most suitable spring will stretch about 0.10 m when 0.30 kg is hung from it.

MANAGEMENT TIPS: Elicit student response to the Reflective Question before proceeding on to the activity.

Emphasize the need to start the object oscillating directly up and down (with no sideward motion) just before the motion sensor makes its measurements. Emphasize to students the need for a “clean” sinusoidal curve for the position of the mass hanger vs. time.

After step 13 (generic version)/step 34 (CBL version)/step 25 (LabPro version)/step 10 (“low-tech” version), elicit that the graph of potential energy vs. displacement shows that the potential energy varies as the square of the displacement from equilibrium and that graphing potential energy vs. the square of the displacement from equilibrium will yield a straight line.

In the “low-tech” version, elicit after step 6 that the work done to stretch the spring can be calculated from the area under the graph of the external gravitational force stretching the spring vs. the distance the spring is stretched. This area has the shape of a triangle. Make sure that students measure its base and altitude correctly, according to the numbers on the graph axes.

RESPONSES TO SOME QUESTIONS: Reflective Question: Stretching a spring does work on it, which increases the spring’s potential energy. The amount of potential energy might be expected to depend on the stiffness of the spring and the amount by which it is stretched. Student Sam Weinig measured the following data for the stretching of a spring by the following masses; they show a spring constant of 2.94 N/0.108 m = 27.2 N/m.

Data Table #1

Added mass (kg) Added weight (N) Position along scale (m) Displacement (position along scale – equilibriumposition) (m) 
0.00 0.0  
0.05 0.49 0.019  
0.10 0.98 0.036  
0.15 1.47 0.054  
0.20 1.96 0.072  
0.25 2.45 0.089  
0.30 2.94 0.108  
Added mass (kg) Added weight (N) Position along scale (m) Displacement (position along scale – equilibriumposition) (m) 
0.00 0.0  
0.05 0.49 0.019  
0.10 0.98 0.036  
0.15 1.47 0.054  
0.20 1.96 0.072  
0.25 2.45 0.089  
0.30 2.94 0.108  

Where in the cycle of oscillations do you expect the kinetic energy to be the greatest?

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ANS:at the midpoint, between the highest and lowest position of the vibrating object.

Where in the cycle of oscillations do you expect the kinetic energy to be the least?

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ANS:at the highest and lowest positions of the vibrating object, where it reverses direction, and therefore has zero velocity.

Where in the cycle of oscillations do you expect the potential energy to be the greatest?

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ANS:at the highest and lowest positions of the vibrating object, where the spring is stretched or compressed the most and the kinetic energy is least.

Where in the cycle of oscillations do you expect the potential energy to be the least?

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ANS:at the midpoint, where the kinetic energy is greatest and the spring is not deformed from its equilibrium position.

Student Weinig then gathered the following data with a TI-83+/LabPro for a 300-g object added to a 34.2-g mass hanger for time, position, and velocity, with 50 samplings separated by 0.045 second. From these data he calculated the kinetic and potential energies, displacement from equilibrium, and displacement squared:

Data Table #2

time (s) KE (J) PE (J) displacement (m) displacement2 (m2position (m) velocity (m/s) 
0.000 0.103 0.027 0.064 0.004 0.691 -0.784 
0.045 0.130 0.000 0.029 0.001 0.656 -0.882 
0.090 0.001 0.129 -0.015 0.000 0.612 -0.065 
0.135 0.000 0.130 0.023 0.001 0.650 0.043 
0.180 0.090 0.040 -0.011 0.000 0.616 -0.734 
0.225 0.064 0.066 -0.043 0.002 0.584 -0.620 
0.270 0.028 0.102 -0.067 0.004 0.560 -0.407 
0.315 0.002 0.128 -0.080 0.006 0.547 -0.120 
0.360 0.006 0.124 -0.078 0.006 0.549 0.188 
0.405 0.035 0.095 -0.063 0.004 0.564 0.457 
0.450 0.071 0.059 -0.037 0.001 0.590 0.651 
0.495 0.088 0.042 -0.004 0.000 0.623 0.725 
0.540 0.075 0.055 0.028 0.001 0.655 0.669 
0.585 0.043 0.087 0.056 0.003 0.683 0.509 
0.630 0.011 0.119 0.074 0.006 0.701 0.259 
0.675 0.000 0.130 0.080 0.006 0.706 -0.028 
0.720 0.014 0.116 0.072 0.005 0.699 -0.293 
0.765 0.044 0.086 0.053 0.003 0.680 -0.515 
0.810 0.073 0.057 0.025 0.001 0.652 -0.660 
0.855 0.079 0.051 -0.006 0.000 0.621 -0.688 
0.900 0.060 0.070 -0.037 0.001 0.590 -0.602 
0.945 0.028 0.102 -0.060 0.004 0.566 -0.410 
0.990 0.004 0.126 -0.073 0.005 0.553 -0.154 
1.035 0.003 0.127 -0.074 0.006 0.553 0.126 
1.080 0.025 0.105 -0.062 0.004 0.565 0.386 
1.125 0.055 0.075 -0.030 0.001 0.597 0.574 
1.170 0.074 0.057 -0.010 0.000 0.616 0.663 
1.215 0.068 0.062 0.020 0.000 0.647 0.639 
1.260 0.044 0.086 0.047 0.002 0.674 0.512 
1.305 0.017 0.113 0.066 0.004 0.693 0.318 
1.350 0.000 0.130 0.076 0.006 0.702 0.052 
1.395 0.010 0.120 0.071 0.005 0.698 -0.247 
1.440 0.037 0.093 0.053 0.003 0.680 -0.469 
1.485 0.060 0.070 0.029 0.001 0.656 -0.602 
1.530 0.071 0.059 -0.001 0.000 0.626 -0.651 
1.575 0.058 0.072 -0.030 0.001 0.597 -0.589 
1.620 0.031 0.099 -0.054 0.003 0.573 -0.432 
1.665 0.007 0.123 -0.069 0.005 0.558 -0.201 
1.710 0.001 0.129 -0.072 0.005 0.555 0.071 
1.755 0.018 0.112 -0.062 0.004 0.564 0.327 
1.800 0.048 0.082 -0.042 0.002 0.584 0.534 
1.845 0.068 0.062 -0.014 0.000 0.613 0.639 
1.890 0.066 0.064 0.015 0.000 0.642 0.629 
1.935 0.046 0.084 0.042 0.002 0.669 0.524 
1.980 0.018 0.112 0.062 0.004 0.689 0.330 
2.025 0.001 0.129 0.072 0.005 0.699 0.083 
2.070 0.005 0.125 0.070 0.005 0.697 -0.179 
2.115 0.028 0.102 0.056 0.003 0.683 -0.411 
2.160 0.056 0.074 0.033 0.001 0.659 -0.580 
2.205 0.069 0.061 0.004 0.000 0.631 -0.645 
2.250 0.070 0.060 -0.025 0.001 0.601 -0.648 
time (s) KE (J) PE (J) displacement (m) displacement2 (m2position (m) velocity (m/s) 
0.000 0.103 0.027 0.064 0.004 0.691 -0.784 
0.045 0.130 0.000 0.029 0.001 0.656 -0.882 
0.090 0.001 0.129 -0.015 0.000 0.612 -0.065 
0.135 0.000 0.130 0.023 0.001 0.650 0.043 
0.180 0.090 0.040 -0.011 0.000 0.616 -0.734 
0.225 0.064 0.066 -0.043 0.002 0.584 -0.620 
0.270 0.028 0.102 -0.067 0.004 0.560 -0.407 
0.315 0.002 0.128 -0.080 0.006 0.547 -0.120 
0.360 0.006 0.124 -0.078 0.006 0.549 0.188 
0.405 0.035 0.095 -0.063 0.004 0.564 0.457 
0.450 0.071 0.059 -0.037 0.001 0.590 0.651 
0.495 0.088 0.042 -0.004 0.000 0.623 0.725 
0.540 0.075 0.055 0.028 0.001 0.655 0.669 
0.585 0.043 0.087 0.056 0.003 0.683 0.509 
0.630 0.011 0.119 0.074 0.006 0.701 0.259 
0.675 0.000 0.130 0.080 0.006 0.706 -0.028 
0.720 0.014 0.116 0.072 0.005 0.699 -0.293 
0.765 0.044 0.086 0.053 0.003 0.680 -0.515 
0.810 0.073 0.057 0.025 0.001 0.652 -0.660 
0.855 0.079 0.051 -0.006 0.000 0.621 -0.688 
0.900 0.060 0.070 -0.037 0.001 0.590 -0.602 
0.945 0.028 0.102 -0.060 0.004 0.566 -0.410 
0.990 0.004 0.126 -0.073 0.005 0.553 -0.154 
1.035 0.003 0.127 -0.074 0.006 0.553 0.126 
1.080 0.025 0.105 -0.062 0.004 0.565 0.386 
1.125 0.055 0.075 -0.030 0.001 0.597 0.574 
1.170 0.074 0.057 -0.010 0.000 0.616 0.663 
1.215 0.068 0.062 0.020 0.000 0.647 0.639 
1.260 0.044 0.086 0.047 0.002 0.674 0.512 
1.305 0.017 0.113 0.066 0.004 0.693 0.318 
1.350 0.000 0.130 0.076 0.006 0.702 0.052 
1.395 0.010 0.120 0.071 0.005 0.698 -0.247 
1.440 0.037 0.093 0.053 0.003 0.680 -0.469 
1.485 0.060 0.070 0.029 0.001 0.656 -0.602 
1.530 0.071 0.059 -0.001 0.000 0.626 -0.651 
1.575 0.058 0.072 -0.030 0.001 0.597 -0.589 
1.620 0.031 0.099 -0.054 0.003 0.573 -0.432 
1.665 0.007 0.123 -0.069 0.005 0.558 -0.201 
1.710 0.001 0.129 -0.072 0.005 0.555 0.071 
1.755 0.018 0.112 -0.062 0.004 0.564 0.327 
1.800 0.048 0.082 -0.042 0.002 0.584 0.534 
1.845 0.068 0.062 -0.014 0.000 0.613 0.639 
1.890 0.066 0.064 0.015 0.000 0.642 0.629 
1.935 0.046 0.084 0.042 0.002 0.669 0.524 
1.980 0.018 0.112 0.062 0.004 0.689 0.330 
2.025 0.001 0.129 0.072 0.005 0.699 0.083 
2.070 0.005 0.125 0.070 0.005 0.697 -0.179 
2.115 0.028 0.102 0.056 0.003 0.683 -0.411 
2.160 0.056 0.074 0.033 0.001 0.659 -0.580 
2.205 0.069 0.061 0.004 0.000 0.631 -0.645 
2.250 0.070 0.060 -0.025 0.001 0.601 -0.648 

The graphs of potential energy vs. displacement from equilibrium and displacement squared are as follows:

The best straight line fit to the second graph (linear regression on a TI-83+) is

Potential energy = (11.510)(displacement squared) + 0.05774.

In symbols, PE = my2 + b,

where “y” is the object’s displacement from equilibrium.

The units of the slope are J/m2, or N/m, which are the units of the spring constant k. Since the value of the spring constant has already been determined to be 27.2 N/m, the slope is approximately half the spring constant. Thus, within a constant, which is arbitrary in defining potential energy, the potential energy of the object equals approximately half the spring constant times the square of its displacement from equilibrium.

In symbols, PE = (1/2)ky2.

The equilibrium position of the object is its position when the downward gravitational force balances the upward spring force. Because the weight of the object stretches the spring by distance mg/k, it hangs a distance mg/k lower than it would in a zero-gravity environment. Thus the position of the object, y, as measured relative to its equilibrium position, is related to the position relative to equilibrium in a zero-gravity environment, y’, as follows:

Therefore we can express the object’s potential energy as

PE = (1/2)k(y′ + mg/k)2 = (1/2)ky2 + mgy′ + (1/2)m2g2/k.

The first term is half the spring constant times the square of its stretch in a gravity-free environment (the elastic potential energy in the absence of gravity), the second term is gravitational potential energy, and the last term is a constant. This is also displayed on the transparency on page 187.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: The value of ky2/2 experimentally obtained for elastic potential energy can also be theoretically derived by showing that it is equal to the work done by the stretching force ky—namely the area of the triangle that is the area under the graph of the stretching force vs. displacement. This approach is used in the “low-tech” version of this activity, Activity 3e.

POSSIBLE EXTENSIONS: This investigation could be performed with elastic materials other than springs.

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

A force is required to stretch a spring. Does this force do work? If so, does this work increase the potential energy of the spring? If so, what does this potential energy depend on?

__________

  • spring

  • stand to mount spring with metric scale (or equivalent)

  • hooked masses or mass hanger with assorted masses – several 50-g masses are suggested

  • motion sensor

A spring is an example of an elastic substance, so named because it returns to its original length after a force stretching it is no longer applied. When an external force stretches an elastic material, the material in return exerts what is called an elastic force to oppose the external stretching force, so that the net result of the elastic force and the external stretching force is zero, leaving the elastic material in static equilibrium. The external force stretching a piece of elastic also does work to stretch it. The result of this work is a form of potential energy called elastic potential energy. You can see the conversion of this elastic potential energy to kinetic energy by stretching a rubber band to store potential energy and then releasing the rubber band—the moving rubber band has kinetic energy.

You have probably noticed that the force needed to stretch an elastic object depends on how much the elastic object is stretched. For example, the force to stretch a rubber band a lot is more than the force needed to stretch it a little. In this laboratory activity you will first investigate the relationship between the external gravitational force needed to stretch a spring and the amount it is stretched and then the relationship between the elastic potential energy of the spring and the amount the spring is stretched.

The external gravitational force stretching the spring is the weight hanging from it. To investigate the relationship between this stretching force and the amount the spring is stretched, hang a spring from a stand equipped with a metric distance scale, and suspend a mass hanger or hooked mass from the bottom of the spring. Measure the position of the bottom of the mass hanger or where the hooked mass attaches to the spring along the scale, and call this the initial equilibrium position. Then add at least four additional masses (50-g masses are suggested), one at a time, and record the position of the bottom of mass hanger along the scale.

Enter your measurements in the following table:

Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     
Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     

Plot a graph of the added weight (external gravitational force stretching the spring, in newtons) vs. the distance the spring is stretched (in meters). Although the distance the spring is stretched is the dependent variable, it is customary to plot the distance stretched along the horizontal axis in this case.

What relationship do you see between the added weight (external gravitational force) and the distance the spring is stretched?

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__________

If you do not observe a linear relationship between the added weight and the distance the spring is stretched, find a relationship between these variables that is linear when you make a graph. Carry out a best straight line fit to your linear graph. (For a TI-83 or TI-83+, see Appendix B, “Using the TI-83 to Analyze Data.”) The slope of this straight line is known as the “spring constant,” denoted by the symbol k. The spring constant is a measure of the stiffness of the spring. The greater the spring constant, the stiffer the spring.

What is your experimentally determined value of k? What are its units?

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__________

Now that you have measured the spring constant, you are ready to investigate how the spring’s potential energy depends on how much it is stretched. To do this, you will trace the motion of the maximum mass you had placed on your spring as it oscillates up and down, treating the oscillating object like the car on a roller coaster, in which there is a continual exchange of kinetic and potential energy.

Where in the cycle of oscillations do you expect the kinetic energy to be the greatest?

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__________

Where in the cycle of oscillations do you expect the kinetic energy to be the least?

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__________

Where in the cycle of oscillations do you expect the potential energy to be the greatest?

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__________

Where in the cycle of oscillations do you expect the potential energy to be the least?

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__________

Place the motion sensor on the floor and mount the oscillating spring so that the conical pattern of ultrasonic waves emitted by the motion sensor will be intercepted and reflected only by the base of the mass hanger hanging from the oscillating spring.

Measure the time, position, and velocity of the oscillating object for two or three oscillations. There should be at least 10 data samples for each cycle.

Set up a spreadsheet with your time measurements in column A, your position measurements in column B, and your velocity measurements in column C.

Calculate the kinetic energy of the oscillating object in column D. (Important Note: Don’t forget to include the mass of the mass hanger in the total mass!)

Scan column C for the maximum absolute value of velocity; this corresponds to the maximum kinetic energy. In column G calculate the maximum kinetic energy minus kinetic energy (in column D). Note that this corresponds to a decrease in kinetic energy, which we also consider to be the increase in elastic potential energy.

Scan column B for the maximum and minimum values of the position of the oscillating object. Find the average of the average maximum and minimum positions; this represents the equilibrium position of the object. In column E calculate the displacement of the object from its equilibrium position by subtracting the equilibrium position from the values of the position in column B.

Plot a graph of elastic potential energy (column G) vs. displacement of the object on the spring (column E). What is the shape of the graph?

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__________

Note: Stophere until directed to continue by your teacher.

Calculate the square of the displacement of the object (column E) in column F.

Plot a graph of the elastic potential energy (column G) vs. square of the displacement from equilibrium of the object (column F). Although you may still see a considerable scatter of points (remember that you have a point on your graph for each sample your motion sensor took!), you should notice that the scatter is about a straight line with positive slope.

Obtain the best straight line fit for the graph of the elastic potential energy vs. the square of displacement from equilibrium, using the same procedure that you used to get the best straight line fit for the weight added vs. spring stretch above.

What are the units of the slope of elastic potential energy vs. square of displacement from equilibrium? How do they compare to the units of the spring constant? From the equation of the best straight line fit for the elastic potential energy vs. square of displacement from equilibrium, what can you infer about the dependence of the elastic potential energy of the spring on the spring constant and how much it is stretched?

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__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

A force is required to stretch a spring. Does this force do work? If so, does this work increase the potential energy of the spring? If so, what does this potential energy depend on?

__________

  • spring

  • stand to mount spring with metric scale (or equivalent)

  • hooked masses or mass hanger with assorted masses – several 50-g masses are suggested

  • TI-83+ graphing calculator

  • Vernier LabPro unit

  • motion sensor

A spring is an example of an elastic substance, so named because it returns to its original length after a force stretching it is no longer applied. When an external force stretches an elastic material, the material in return exerts what is called an elastic force to oppose the external stretching force, so that the net result of the elastic force and the external stretching force is zero, leaving the elastic material in static equilibrium. The external force stretching a piece of elastic also does work to stretch it. The result of this work is a form of potential energy called elastic potential energy. You can see the conversion of this elastic potential energy to kinetic energy by stretching a rubber band to store potential energy and then releasing the rubber band—the moving rubber band has kinetic energy.

You have probably noticed that the force needed to stretch an elastic object depends on how much the elastic object is stretched. For example, the force to stretch a rubber band a lot is more than the force needed to stretch it a little. In this laboratory activity you will first investigate the relationship between the external gravitational force needed to stretch a spring and the amount it is stretched and then the relationship between the elastic potential energy of the spring and the amount the spring is stretched.

The external gravitational force stretching the spring is the weight hanging from it. To investigate the relationship between this stretching force and the amount the spring is stretched, hang a spring from a stand equipped with a metric distance scale, and suspend a mass hanger or hooked mass from the bottom of the spring. Measure the position of the bottom of the mass hanger or where the hooked mass attaches to the spring along the scale, and call this the initial equilibrium position. Then add at least four additional masses (50-g masses are suggested), one at a time, and record the position of the bottom of mass hanger along the scale.

Enter your measurements in the following table:

Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     
Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     

Plot a graph of the added weight (external gravitational force stretching the spring, in newtons) vs. the distance the spring is stretched (in meters). Although the distance the spring is stretched is the dependent variable, it is customary to plot the distance stretched along the horizontal axis in this case.

What relationship do you see between the added weight (external gravitational force) and the distance the spring is stretched?

Show answer Hide answer

__________

If you do not observe a linear relationship between the added weight and the distance the spring is stretched, find a relationship between these variables that is linear when you make a graph. Carry out a best straight line fit to your linear graph. (For a TI-83 or TI-83+, see Appendix B, “Using the TI-83 to Analyze Data.”) The slope of this straight line is known as the “spring constant,” denoted by the symbol k. The spring constant is a measure of the stiffness of the spring. The greater the spring constant, the stiffer the spring.

What is your experimentally determined value of k? What are its units?

Show answer Hide answer

__________

Now that you have measured the constant of your spring, you are ready to investigate how the spring’s potential energy depends on how much it is stretched. To do this, you will trace the motion of the maximum mass you had placed on your spring as it oscillates up and down, treating the oscillating object like the car on a roller coaster, in which there is a continual exchange of kinetic and potential energy.

Where in the cycle of oscillations do you expect the kinetic energy to be the greatest?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the kinetic energy to be the least?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the potential energy to be the greatest?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the potential energy to be the least?

Show answer Hide answer

__________

The instructions below are for a TI-83+ graphing calculator connected to a Vernier LabPro unit with a Vernier motion sensor, using the DataMate application.

Place the motion sensor on the floor and mount the oscillating spring so that the conical pattern of sound waves emitted by the motion sensor will be intercepted and reflected only by the base of the mass hanger hanging from the oscillating spring.

Connect the motion sensor to the Dig/Sonic 1 port of the LabPro unit.

Make sure that the link cord is connected between the calculator and the LabPro unit (link ports are on the bottom of each unit).

Turn on the calculator and connect the AC adapter for the LabPro unit to a wall outlet.

Press the <APPS> key on the calculator.

Use the arrow keys on the calculator to highlight the application DataMate. Press <ENTER>, then press the <CLEAR> key to reset the program. At this point the LabPro automatically checks for and identifies the probes connected to it. The calculator monitors and displays readings from the probe(s).

Press <1.Setup>.

Move cursor to “Mode” and press <ENTER>.

Press <2.Time Graph>. If you wish to change the time settings, press <2.Change time settings> and enter desired time settings as needed. (An interval of .04 to .05 seconds seems to work well; shorter intervals lead to more “jagged” graphs of distance and velocity vs. time. The number of samples combined with the interval between samples should give time enough for between two and three oscillations of the spring. Too many samples could exceed the memory capacity of the system.)

Press <1.OK>.

Press <1.OK>.

Press <2.Start> to begin gathering data. A “beep” will indicate the onset and conclusion of sampling. At the conclusion of the period for measuring, a menu of available graphs will appear. Use the arrow key to move the cursor to the left of the name of the graph you wish to view and press <ENTER>. After you view each desired graph, press <ENTER> in order to return to the menu.

When you have finished with the graphs of the data that have been taken, press <1.Main Screen>.

If you wish to make further measurements with the same time settings, press <2.Start>. If you wish to make further measurements with different time settings, repeat steps 13–17 and then press <2.Start>. If you wish to select only a portion of your graph, press <4.Analyze> and select the statistics option. If you wish to quit, press <6.Quit>. The time data will be stored in L1, distance data in L6, velocity data in L7, and acceleration data in L8.

After you have quit the DataMate application, press <STAT> and press <ENTER> to select <EDIT> from the resulting menu. This will show the lists of data you have collected, as noted in steps 18–20 above.

Calculate the kinetic energy of the oscillating object in column L2 by moving your cursor up to the L2 cell and entering .5*[mass of oscillating object, in kg]*L7*L7 and then pressing <ENTER>. (Important Note: L7 can be entered via “LIST” or “CATALOG” functions of the TI-83+. Don’t forget to include the mass of the mass hanger in the total mass!)

Scan the L7 column for the maximum absolute value of velocity; this corresponds to the maximum kinetic energy. In column L3 calculate the maximum kinetic energy minus kinetic energy by moving your cursor up to the L3 cell and entering .5*[mass of oscillating object, in kg]* [max abs velocity]*[max abs velocity] - L2. Note that what you have calculated in column L3 is the elastic potential energy.

Scan the L6 column for the maximum and minimum values of the position of the object oscillating on the spring. Find the average of the average maximum and minimum positions; this represents the equilibrium position of the object. In column L4 calculate the displacement of the object from its equilibrium position by moving your cursor up to the L4 cell and entering L6—[equilibrium position of object].

Press <2nd> and <Y=> to activate <STAT PLOT>. Program one of the plotting routines to plot L4 (displacement from equilibrium) on the x-axis and L3 (potential energy) on the y-axis. Press <ZOOM> and <9> or press <WINDOW> and select values of Xmin, Xmax, Ymin, and Ymax to accommodate your values in L4 and L3 and press <GRAPH> to see how the elastic potential energy depends on the displacement from equilibrium. What is the shape of the graph?

Show answer Hide answer

__________

__________

Note: Stophere until directed to continue by your teacher.

Program column L5 to calculate the square of the displacement from equilibrium and repeat step 25, but with L5 (square of the displacement from equilibrium) on the x-axis. Although you may still see a considerable scatter of points (remember that you have a point on your graph for each sample your motion sensor took!), you should notice that the scatter is about a straight line with positive slope.

Obtain the best straight line fit for the graph of the elastic potential energy vs. square of displacement from equilibrium, using the same procedure that you used to get the best straight line fit for the weight added vs. spring stretch above.

What are the units of the slope of the elastic potential energy vs. square of displacement from equilibrium? How do they compare to the units of the spring constant? From the equation of the best straight line fit for the elastic potential energy vs. square of displacement from equilibrium, what can you infer about the dependence of the elastic potential energy of the spring on the spring constant and how much it is stretched?

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

A force is required to stretch a spring. Does this force do work? If so, does this work increase the potential energy of the spring? If so, what does this potential energy depend on?

__________

  • spring

  • stand to mount spring with metric scale (or equivalent)

  • hooked masses or mass hanger with assorted masses — several 50-g masses are suggested

  • TI-83 graphing calculator

  • TI CBL unit

  • motion sensor

A spring is an example of an elastic substance, so named because it returns to its original length after a force stretching it is no longer applied. When an external force stretches an elastic material, the material in return exerts what is called an elastic force to oppose the external stretching force, so that the net result of the elastic force and the external stretching force is zero, leaving the elastic material in static equilibrium. The external force stretching a piece of elastic also does work to stretch it. The result of this work is a form of potential energy called elastic potential energy. You can see the conversion of this elastic potential energy to kinetic energy by stretching a rubber band to store potential energy and then releasing the rubber band—the moving rubber band has kinetic energy.

You have probably noticed that the force needed to stretch an elastic object depends on how much the elastic object is stretched. For example, the force to stretch a rubber band a lot is more than the force needed to stretch it a little. In this laboratory activity you will first investigate the relationship between the external gravitational force needed to stretch a spring and the amount it is stretched and then the relationship between the elastic potential energy of the spring and the amount the spring is stretched.

The external gravitational force stretching the spring is the weight hanging from it. To investigate the relationship between this stretching force and the amount the spring is stretched, hang a spring from a stand equipped with a metric distance scale, and suspend a mass hanger or hooked mass from the bottom of the spring. Measure the position of the bottom of the mass hanger or where the hooked mass attaches to the spring along the scale, and call this the initial equilibrium position. Then add at least four additional masses (50-g masses are suggested), one at a time, and record the position of the bottom of mass hanger along the scale.

Enter your measurements in the following table:

Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     
Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     

Plot a graph of the added weight (external gravitational force stretching the spring, in newtons) vs. the distance the spring is stretched (in meters). Although the distance the spring is stretched is the dependent variable, it is customary to plot the distance stretched along the horizontal axis in this case.

What relationship do you see between the added weight (external gravitational force) and the distance the spring is stretched?

Show answer Hide answer

__________

If you do not observe a linear relationship between the added weight and the distance the spring is stretched, find a relationship between these variables that is linear when you make a graph. Carry out a best straight line fit to your linear graph. (For a TI-83 or TI-83+, see Appendix B, “Using the TI-83 to Analyze Data.”) The slope of this straight line is known as the “spring constant,” denoted by the symbol k. The spring constant is a measure of the stiffness of the spring. The greater the spring constant, the stiffer the spring.

What is your experimentally determined value of k? What are its units?

Show answer Hide answer

__________

Now that you have measured the constant of your spring, you are ready to investigate how the spring’s potential energy depends on how much it is stretched. To do this, you will trace the motion of the maximum mass you had placed on your spring as it oscillates up and down, treating the oscillating object like the car on a roller coaster, in which there is a continual exchange of kinetic and potential energy.

Where in the cycle of oscillations do you expect the kinetic energy to be the greatest?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the kinetic energy to be the least?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the potential energy to be the greatest?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the potential energy to be the least?

Show answer Hide answer

__________

The instructions below are for a TI-83 graphing calculator connected to a CBL unit with a Vernier motion sensor, using the PHYSICS program.

Place the motion sensor on the floor and mount the oscillating spring so that the conical pattern of sound waves emitted by the motion sensor will be intercepted and reflected only by the base of the mass hanger hanging from the oscillating spring.

Connect the motion sensor to the SONIC channel of the CBL unit.

Connect the link cord between the TI-83 and CBL unit (link ports are on the bottom of each unit). Make sure that the link cord is firmly inserted into each unit (a twisting motion helps to ensure this).

Turn on the CBL unit and calculator.

Press the <PRGM> key on the calculator.

Use the arrow keys on the calculator to highlight the program PHYSICS. Press <ENTER>. At this point the calculator screen should have “prgmPHYSICS” showing; press <ENTER> again.

When the program title screen appears, press <ENTER>, as prompted on the screen.

If it is not already highlighted, highlight 1:SET UP PROBES and press <ENTER>.

At prompt, “NUMBER OF PROBES,” press <1> or highlight 1:ONE and press <ENTER>.

At prompt “SELECT PROBE,” select 1:MOTION. (If the cursor is there, press <ENTER>; an alternative is to press <1>.)

You should now be back at the main menu screen. Select 2.COLLECT DATA and press <ENTER> or press <2>.

From the data collection menu, select 1:MONITOR INPUT and press <ENTER> (or press <1>. From the distance measurements read on both the calculator and the CBL unit for various positions of the object to be measured you can determine whether the positioning of the motion sensor will allow it to make reliable measurements of the object in its various positions. When you are satisfied that the motion sensor is positioned correctly, press “+” to return to the data collection menu.

Press <2> or highlight 2:TIME GRAPH and press <ENTER>.

“ENTER TIME BETWEEN SAMPLES IN SECONDS” when prompted to do so, and press <ENTER>. (An interval of .04 to .05 seconds seems to work well; shorter intervals lead to more “jagged” graphs of distance and velocity vs. time.)

“ENTER NUMBER OF SAMPLES” when prompted to do so, and press <ENTER>. (The number of samples combined with the interval between samples should give time enough for between two and three oscillations of the spring. Too many samples could exceed the memory capacity of the system.)

The calculator will then display the EXPERIMENT LENGTH and prompt you to press <ENTER>.

On the CONTINUE menu select 1:USE TIME SETUP and press <ENTER> or press <1>.

From the TIME GRAPH menu select 1:NON-LIVE DISPLAY and press <ENTER> or press <1>.

You will be prompted to press <ENTER> to begin collecting data. Make sure to set the spring into oscillation before you press <ENTER>. The time data will be stored in L1, distance data in L4, velocity data in L5, and acceleration data in L6.

Press <ENTER> after the data are collected to get to the SELECT GRAPH menu. To select additional graphs from this menu, press <ENTER>.

After you have finished examining the graphs, press <ENTER> and <4> (or select 4:NEXT and press <ENTER>).

If you wish to REPEAT the measurement with the same time interval and number of samples, press <2> or select 2:YES and press <ENTER>. Otherwise, press <1> or select 1:NO and press <ENTER>.

Upon returning to the main menu, you can choose among the alternatives, including 2:COLLECT DATA (with a different time interval and/or number of samples), 3:ANALYZE, and 7:QUIT. If you wish to select only a portion of your graph for further analysis, you can do this with the “ANALYZE” option. But the ultimate analysis of your data will be done on the TI-83 after you have quit the application of the CBL.

After you have quit the CBL application, press <STAT> and press <ENTER> to select <EDIT> from the resulting menu. This will show the lists of data you have collected, as noted in step 25 above.

Calculate the kinetic energy of the oscillating object in column L2 by moving your cursor up to the L2 cell and entering .5*[mass of oscillating object, in kg]* L5*L5 and then pressing <ENTER>. (Important Note: Don’t forget to include the mass of the mass hanger in the total mass!)

Scan the L5 column for the maximum absolute value of velocity; this corresponds to the maximum kinetic energy. In column L3 calculate the maximum kinetic energy minus kinetic energy by moving your cursor up to the L3 cell and entering .5*[mass of oscillating object, in kg]* [max abs velocity]*[max abs velocity] –L2. Note that what you have calculated in column L3 is the elastic potential energy.

Scan the L4 column for the maximum and minimum values of the position of the oscillating object. Find the average of the average maximum and minimum positions; this represents the equilibrium position of the object. In column L6 calculate the displacement of the object from its equilibrium position by moving your cursor up to the L6 cell and entering L4—[equilibrium position of object].

Press <2nd> and <Y=> to activate <STAT PLOT>. Program one of the plotting routines to plot L6 (displacement from equilibrium) on the x-axis and L3 (potential energy) on the y-axis. Press <ZOOM> and <9> or press <WINDOW> and select values of Xmin, Xmax, Ymin, and Ymax to accommodate your values in L6 and L3 and press <GRAPH> to see how the elastic potential energy depends on displacement from equilibrium. What is the shape of the graph?

Show answer Hide answer

__________

Note: Stophere until directed to continue by your teacher.

Reprogram column L6 to calculate the square of the displacement from equilibrium and repeat step 34. Although you may still see a considerable scatter of points (remember that you have a point on your graph for each sample your motion sensor took!), you should notice that the scatter is about a straight line with positive slope.

Show answer Hide answer

__________

Obtain the best straight line fit for the graph of the elastic potential energy vs. the square of displacement from equilibrium, using the same procedure that you used to get the best straight line fit for the weight added vs. spring stretch above.

What are the units of the slope of elastic potential energy vs. square of displacement from equilibrium? How do they compare to the units of the spring constant? From the equation of the best straight line fit for the elastic potential energy vs. square of displacement from equilibrium, what can you infer about the dependence of the elastic potential energy of the spring on the spring constant and how much it is stretched?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

A force is required to stretch a spring. Does this force do work? If so, does this work increase the potential energy of the spring? If so, what does this potential energy depend on?

__________

  • spring (PASCO SE-8749 or the equivalent) with mounting stand and scale or

  • stand with spring and metric scale (PASCO ME-9827 or the equivalent)

  • hooked masses or mass hanger with assorted masses — several 50-g masses are suggested

  • DataStudio software (PASCO CI-6870E)

  • PASPORT Xplorer Datalogger (PASCO PS-2000)

  • PASPORT motion sensor (PASCO PS-2103)

A spring is an example of an elastic substance, so named because it returns to its original length after a force stretching it is no longer applied. When an external force stretches an elastic material, the material in return exerts what is called an elastic force to oppose the external stretching force, so that the net result of the elastic force and the external stretching force is zero, leaving the elastic material in static equilibrium. The external force stretching a piece of elastic also does work to stretch it. The result of this work is a form of potential energy called elastic potential energy. You can see the conversion of this elastic potential energy to kinetic energy by stretching a rubber band to store potential energy and then releasing the rubber band—the moving rubber band has kinetic energy.

You have probably noticed that the force needed to stretch an elastic object depends on how much the elastic object is stretched. For example, the force to stretch a rubber band a lot is more than the force needed to stretch it a little. In this laboratory activity you will first investigate the relationship between the external gravitational force needed to stretch a spring and the amount it is stretched and then the relationship between the elastic potential energy of the spring and the amount the spring is stretched.

The external gravitational force stretching the spring is the weight hanging from it. To investigate the relationship between this stretching force and the amount the spring is stretched, hang a spring from a stand equipped with a metric distance scale, and suspend a mass hanger or hooked mass from the bottom of the spring. Measure the position of the bottom of the mass hanger or where the hooked mass attaches to the spring along the scale, and call this the initial equilibrium position. Then add at least four additional masses (50-g masses are suggested), one at a time, and record the position of the bottom of mass hanger along the scale.

Enter your measurements in the following table:

Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     
Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     

Plot a graph of the added weight (external gravitational force stretching the spring, in newtons) vs. the distance the spring is stretched (in meters). Although the distance the spring is stretched is the dependent variable, it is customary to plot the distance stretched along the horizontal axis in this case.

What relationship do you see between the added weight (external gravitational force) and the distance the spring is stretched?

Show answer Hide answer

__________

If you do not observe a linear relationship between the added weight and the distance the spring is stretched, find a relationship between these variables that is linear when you make a graph. Carry out a best straight line fit to your linear graph. (For a TI-83 or TI-83+, see Appendix B, “Using the TI-83 to Analyze Data.”) The slope of this straight line is known as the “spring constant,” denoted by the symbol k. The spring constant is a measure of the stiffness of the spring. The greater the spring constant, the stiffer the spring.

What is your experimentally determined value of k? What are its units?

Show answer Hide answer

__________

Now that you have measured the constant of your spring, you are ready to investigate how the spring’s potential energy depends on how much it is stretched. To do this, you will trace the motion of the maximum mass you had placed on your spring as it oscillates up and down, treating the oscillating object like the car on a roller coaster, in which there is a continual exchange of kinetic and potential energy.

Where in the cycle of oscillations do you expect the kinetic energy to be the greatest?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the kinetic energy to be the least?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the potential energy to be the greatest?

Show answer Hide answer

__________

Where in the cycle of oscillations do you expect the potential energy to be the least?

Show answer Hide answer

__________

The instructions below are for a PASCO PASPORT motion sensor connected to a PASPORT Xplorer Datalogger

Place the motion sensor on the floor and mount the oscillating spring so that the conical pattern of sound waves emitted by the motion sensor will be intercepted and reflected only by the base of the mass hanger hanging from the oscillating spring.

Plug the motion sensor into a PASPORT Xplorer Datalogger. Adjust the sampling rate on the Datalogger to be 20 Hz, using the “+” and “-” buttons. Press the “check” button to accept the new value of sampling rate.

Set the spring into oscillation. Press the “play” button on the Datalogger to begin recording data. Allow data to collect for three cycles of oscillations and press the “play” button again to stop the recording of data.

Connect the Datalogger to the USB port of a computer equipped with DataStudio software. This connection will automatically open DataStudio and display the position vs. time graph measured as the mass hanger oscillated up and down.

Click on the “Smart Tool.” This will introduce a set of coordinate axes with the coordinates of each point indicated at its origin. Use the “Smart Tool” to identify the maximum and minimum values of the position. Calculate their average—this is the equilibrium position of the hanging object—and record this value:

Maximum position: __________

Minimum position: __________

Average (= equilibrium position): __________

To obtain a graph of the velocity of the hanging object vs. time, click on “Setup” and choose “Velocity” to activate this measurement. To add velocity to the existing graph, drag “Velocity” from the Summary window to the center of the position vs. time graph. Use the “Smart Tool” to identify the maximum absolute value of the velocity and record it:

Maximum absolute value of velocity: __________

Minimize the position and velocity vs. time graphs.

Click on “Calculate” and “New.” Define PE (potential energy) as “0.5*mass*vmax^2 – 0.5*mass*velocity^2.” Enter the previously measured values of “mass” (include the mass of the hanger along with the masses hanging on it!) and “vmax” (maximum absolute value of velocity), and identify “velocity” as already entered data. Also define “disp” (displacement from equilibrium) as “position – eqpos,” entering the calculated value of “eqpos” (equilibrium position) and identifying “position” as already entered data.

Make a graph of the potential energy vs. displacement from equilibrium. One way to do this is to drag “Graph” from the display menu onto PE as listed on the data menu on the upper left of the screen. This gives a graph of PE vs. time. Then drag the data symbol for displacement from equilibrium onto “time” on this graph to cause displacement from equilibrium to replace time on the x-axis. Another way to change variables on a graph axis is to hover over the desired axis and click. A choice of all available measurements and calculations will be available. What is the shape of the graph?

Show answer Hide answer

__________

Note:Stop here until directed to continue by your teacher.

Make a graph of the potential energy vs. the square of the displacement from equilibrium. To do this, click on “Calculate” and “New.” Define “dispsq” as “disp^2” and drag the data symbol for the square of the displacement from equilibrium onto “disp” on the graph to cause the square of the displacement from equilibrium to replace displacement from equilibrium on the x-axis.

Obtain the best straight line fit for the graph of the potential energy vs. the square of the displacement from equilibrium.

What are the units of the slope of the potential energy vs. square of displacement from equilibrium? How do they compare to the units of the spring constant? From the equation of the best straight line fit for the potential energy vs. square of displacement from equilibrium, what can you infer about the dependence of the potential energy of the spring on the spring constant and how much it is stretched?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

A force is required to stretch a spring. Does this force do work? If so, does this work increase the potential energy of the spring? If so, what does this potential energy depend on?

__________

  • spring

  • stand to mount spring with metric scale (or equivalent)

  • hooked masses or mass hanger with assorted masses – several 50-g masses are suggested

  • computer

  • Logger Pro software

  • Vernier LabPro unit

  • motion sensor (Vernier Go! Motion sensor does not require a LabPro unit)

A spring is an example of an elastic substance, so named because it returns to its original length after a force stretching it is no longer applied. When an external force stretches an elastic material, the material in return exerts what is called an elastic force to oppose the external stretching force, so that the net result of the elastic force and the external stretching force is zero, leaving the elastic material in static equilibrium. The external force stretching a piece of elastic also does work to stretch it. The result of this work is a form of potential energy called elastic potential energy. You can see the conversion of this elastic potential energy to kinetic energy by stretching a rubber band to store potential energy and then releasing the rubber band—the moving rubber band has kinetic energy.

You have probably noticed that the force needed to stretch an elastic object depends on how much the elastic object is stretched. For example, the force to stretch a rubber band a lot is more than the force needed to stretch it a little. In this laboratory activity you will first investigate the relationship between the external gravitational force needed to stretch a spring and the amount it is stretched and then the relationship between the elastic potential energy of the spring and the amount the spring is stretched.

The external gravitational force stretching the spring is the weight hanging from it. To investigate the relationship between this stretching force and the amount the spring is stretched, hang a spring from a stand equipped with a metric distance scale, and suspend a mass hanger or hooked mass from the bottom of the spring. Measure the position of the bottom of the mass hanger or where the hooked mass attaches to the spring along the scale, and call this the initial equilibrium position. Then add at least four additional masses (50-g masses are suggested), one at a time, and record the position of the bottom of mass hanger along the scale.

Enter your measurements in the following table:

Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     
Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     

Plot a graph of the added weight (external gravitational force stretching the spring, in newtons) vs. the distance the spring is stretched (in meters). Although the distance the spring is stretched is the dependent variable, it is customary to plot the distance stretched along the horizontal axis in this case.

What relationship do you see between the added weight (external gravitational force) and the distance the spring is stretched?

Show answer Hide answer

__________

If you do not observe a linear relationship between the added weight and the distance the spring is stretched, find a relationship between these variables that is linear when you make a graph. Carry out a best straight line fit to your linear graph. (For a TI-83 or TI-83+, see Appendix B, “Using the TI-83 to Analyze Data.”) The slope of this straight line is known as the “spring constant,” denoted by the symbol k. The spring constant is a measure of the stiffness of the spring. The greater the spring constant, the stiffer the spring.

What is your experimentally determined value of k? What are its units?

Show answer Hide answer

__________

Now that you have measured the constant of your spring, you are ready to investigate how the spring’s potential energy depends on how much it is stretched. To do this, you will trace the motion of the maximum mass you had placed on your spring as it oscillates up and down, treating the oscillating object like the car on a roller coaster, in which there is a continual exchange of kinetic and potential energy.

Where in the cycle of oscillations do you expect the kinetic energy to be the greatest?

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__________

Where in the cycle of oscillations do you expect the kinetic energy to be the least?

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__________

Where in the cycle of oscillations do you expect the potential energy to be the greatest?

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Where in the cycle of oscillations do you expect the potential energy to be the least?

The instructions below are for a computer with Logger Pro software connected to a Vernier LabPro unit with a Vernier motion sensor, or connected to a Vernier Go! Motion sensor.

Place the motion sensor on the floor and mount the oscillating spring so that the conical pattern of sound waves emitted by the motion sensor will be intercepted and reflected only by the base of the mass hanger hanging from the oscillating spring.

Connect the motion sensor to the Dig/Sonic 1 port of the LabPro unit, and connect the AC adapter for the LabPro unit to a wall outlet. If you are using a Vernier Go! Motion sensor, connect it directly to the computer.

Open Vernier Logger Pro on the computer.

If the motion sensor is not recognized by Logger Pro, select “Set Up Sensors” and “Show All Interfaces” from the “Experiment” menu, then click on Dig/Sonic 1 and select “Motion Sensor” if you are using a LabPro unit. Then click “Close.” Whether you are using a LabPro unit or a Go! Motion sensor, you should now have a table displaying time, position, and velocity and axes for graphs of position and velocity vs. time.

Click the icon with the graph and stopwatch to select the frequency of data sampling. Select a time period of 5 seconds and 30 samples/second. Click “Done.”

Click “Collect” and start the mass in oscillation.

After the data are collected, select the velocity graph (by clicking on it) and click the “A” icon to autoscale it. Then click on the “Examine” button (the one with an “X” on it), and scroll across to locate when the velocity is greatest. Record this time.

From the Data menu select “New Calculated Column.” In the Name field, enter Kinetic Energy. In the Short Name field, enter KE. In the Units field, enter J. In the Equation field enter 0.5*mass* “velocity”^2, where “mass” is the actual mass (including the mass of the mass hanger!), not the word “mass.” Enter the word “velocity” by pulling down the list of Variables and choosing “velocity.” This action will paste “velocity” into the equation, including the quotation marks.

Note the value of the kinetic energy at the time the velocity is greatest. This is also the time of greatest, or maximum, kinetic energy.

The difference between the maximum kinetic energy and kinetic energy at other times is the elastic potential energy. Follow the procedure in step 14 above to create another “New Calculated Column,” this one called elastic potential energy and defined as the kinetic energy subtracted from the maximum kinetic energy, as determinted in step 15.

Now select the position graph (by clicking on it) and click the “A” icon to autoscale it. Then click on the “Examine” button (the one with an “X” on it), and scroll across to locate when the position is a maximum and minimum. Determine the maximum and minimum values of the position of the object oscillating on the spring and find their average; this represents the equilibrium position of the object.

Create yet another “New Calculated Column” to display the displacement from equilibrium, defined as the equilibrium position subtracted from the position of the object.

Now use Logger Pro to create a graph of elastic potential energy vs. displacement from equilibrium. What is the shape of the graph?

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__________

Note: Stophere until directed to continue by your teacher.

Create a final “New Calculated Column” to calculate the square of the displacement from equilibrium, and create a graph of elastic potential energy vs. the square of the displacement from equilibrium. Although you may still see a considerable scatter of points (remember that you have a point on your graph for each sample your motion sensor took!), you should notice that the scatter is about a straight line with positive slope.

Obtain the best straight line fit for the graph of the elastic potential energy vs. square of displacement from equilibrium, using the same procedure that you used to get the best straight line fit for the weight added vs. spring stretch above.

What are the units of the slope of the elastic potential energy vs. square of displacement from equilibrium? How do they compare to the units of the spring constant? From the equation of the best straight line fit for the elastic potential energy vs. square of displacement from equilibrium, what can you infer about the dependence of the elastic potential energy of the spring on the spring constant and how much it is stretched?

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

A force is required to stretch a spring. Does this force do work? If so, does this work increase the potential energy of the spring? If so, what does this potential energy depend on?

__________

  • spring

  • stand to mount spring with metric scale (or equivalent)

  • hooked masses or mass hanger with assorted masses—several 50-g masses are suggested

A spring is an example of an elastic substance, so named because it returns to its original length after a force stretching it is no longer applied. When an external force stretches an elastic material, the material in return exerts what is called an elastic force to oppose the external stretching force, so that the net result of the elastic force and the external stretching force is zero, leaving the elastic material in static equilibrium. The external force stretching a piece of elastic also does work to stretch it. The result of this work is a form of potential energy called elastic potential energy. You can see the conversion of this elastic potential energy to kinetic energy by stretching a rubber band to store potential energy and then releasing the rubber band—the moving rubber band has kinetic energy.

You have probably noticed that the force needed to stretch an elastic object depends on how much the elastic object is stretched. For example, the force to stretch a rubber band a lot is more than the force needed to stretch it a little. In this laboratory activity you will first investigate the relationship between the external gravitational force needed to stretch a spring and the amount it is stretched and then the relationship between the elastic potential energy of the spring and the amount the spring is stretched.

The external gravitational force stretching the spring is the weight hanging from it. To investigate the relationship between this stretching force and the amount the spring is stretched, hang a spring from a stand equipped with a metric distance scale, and suspend a mass hanger or hooked mass from the bottom of the spring. Measure the position of the bottom of the mass hanger or where the hooked mass attaches to the spring along the scale, and call this the initial equilibrium position. Then add at least four additional masses (50-g masses are suggested), one at a time, and record the position of the bottom of mass hanger along the scale.

Enter your measurements in the following table:

Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     
Added mass (g) Added mass (kg) Added weight (N) Position along scale (m) Stretch (Position along scale – equilibrium position) (m) 
     
     
     
     
     
     

Plot a graph of the added weight (external gravitational force stretching the spring, in newtons) vs. the distance the spring is stretched (in meters). Although the distance the spring is stretched is the dependent variable, it is customary to plot the distance stretched along the horizontal axis in this case.

What relationship do you see between the added weight (external gravitational force) and the distance the spring is stretched?

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__________

If you do not observe a linear relationship between the added weight and the distance the spring is stretched, find a relationship between these variables that is linear when you make a graph. Carry out a best straight line fit to your linear graph. (For a TI-83 or TI-83+, see Appendix B, “Using the TI-83 to Analyze Data.”) The slope of this straight line is known as the “spring constant,” denoted by the symbol k. The spring constant is a measure of the stiffness of the spring. The greater the spring constant, the stiffer the spring.

What is your experimentally determined value of k? What are its units?

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__________

Now that you have measured the constant of your spring, you are ready to investigate how the spring’s potential energy depends on how much it is stretched. To do this, recall how the concepts of work and potential energy are related in Activity 1. There you found that, regardless of the slope, the product of the force required to pull a cart along the incline and the distance along the incline to reach a given height is the same, and that this product is called the work done on the cart. The work done on the cart to lift it in opposition to Earth’s gravitational force is the gravitational potential energy acquired by the cart. Draw a graph showing the force exerted on the cart on the vertical axis and the distance the cart is lifted on the horizontal axis.

How is the work done to lift the cart (which also equals the increase in gravitational potential energy) represented on the graph?

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__________

How is the graph of the external gravitational force stretching the spring vs. the distance the spring is stretched different from the graph of the force lifting the cart vs. the distance the cart is lifted?

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__________

How can the work done to stretch the spring be calculated from the graph of the external gravitational force stretching the spring vs. the distance the spring is stretched?

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__________

Note: Stophere until directed to continue by your teacher.

Divide the horizontal axis of your graph of the external gravitational force stretching the spring vs. the distance the spring is stretched into five equal sections. Draw vertical lines perpendicular to the horizontal axis at the section boundaries. What shape does each vertical line make with the graph and the horizontal axis?

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__________

Measure the area enclosed by the shapes formed by each vertical line with the graph and the horizontal axis. Remember to use the numbers on the graph axis (and their units) to calculate the areas, not measurements you make with a ruler. Record values in a data table like the one below:

Amount of stretch (m)

 

Area under “Force vs. stretch” graph from origin to the amount of stretch (N.m = J)

 
  
  
  
  
  

Amount of stretch (m)

 

Area under “Force vs. stretch” graph from origin to the amount of stretch (N.m = J)

 
  
  
  
  
  

Make a graph of the area under the “Force vs. stretch” graph vs. the amount of stretch. Again keep the distance stretched on the horizontal axis.

What relationship do you see between the area under the “Force vs. stretch” graph vs. the amount of stretch?

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__________

Note: Stophere until directed to continue by your teacher.

Calculate the square of the amount of stretch for each of the above values and make a graph of the area under the “Force vs. stretch” graph vs. the square of the amount of stretch. What kind of relationship do you see in this graph? What does this suggest about the relationship between the work done to stretch a spring and the amount the spring is stretched?

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__________

How is the work done to stretch a spring related to the spring’s elastic potential energy?

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__________

What are the units of the slope of the graph of the area under the “Force vs. stretch” graph vs. the square of the amount of stretch? How do they relate to the units for the spring constant?

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__________

What does the slope of the graph of the area under the “Force vs. stretch” graph and the square of the amount of stretch represent? How do you know?

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__________

From the equation for the best straight line fit for the graph of area under the “Force vs. stretch” graph vs. the square of the amount of stretch, what can you infer about the dependence of the elastic potential energy of the spring on the spring constant and how much it is stretched?

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__________

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain, Calculate

OBJECTIVE: This activity demonstrates the conversion of gravitational potential energy to thermal energy. Coupled with Activity 6, which demonstrates the conversion of electrical energy to thermal energy, this activity relates energy in three major forms: mechanical (kinetic and potential), electrical, and thermal.

IDEA: The difficulty in showing the conversion from mechanical to thermal energy is that amounts of mechanical energy in our daily lives are typically small while amounts of thermal energy in our daily lives are typically large. The key to this experiment is the use of electronic temperature measurements, which can be made to the nearest hundredth of a degree. As with other activities investigating the conversion of energy into thermal form, this activity culminates in the measurement of a specific heat.

LEVEL: high school (10, 11, and 12)

DURATION: approximately 40 minutes (5 minutes setup, 20 minutes data gathering, 10 minutes data analysis, 5 minutes take down)

STUDENT BACKGROUND: Students must be able to measure with a ruler and operate a temperature probe, following a set of instructions. They also need to be reliable and patient about counting to 100.

ADVANCE PREPARATION: Assemble a container of copper shot, a ruler, and temperature probes. Acquaint students with the temperature probe if they are not familiar with it.

Cooling the copper shot in advance would allow the range of temperatures to center on ambient temperature and minimize heat escape to surroundings. This was not done for the sample data presented in these notes.

MANAGEMENT TIPS: Elicit student responses to the Reflective Question before proceeding on to the activity.

Advise students against two practices that could adversely affect their data: 1) Jerking the container upon inverting it could impart more energy to the copper shot than it acquires from the energy of natural fall. 2) Waiting too long for the temperature readings to stabilize after every 100 inversions could allow the shot to cool off too much. A suggested method to avoid jerking the container while inverting it is provided in the student handouts.

A way to minimize unwanted cooling is to minimize the difference between the temperatures of the shot and the ambient environment. One way to do this is to cool the shot slightly so that its beginning and ending temperatures differ equally from the ambient temperature.

RESPONSES TO SOME QUESTIONS: Responses to the Reflective Question could include the following: the kinetic energy 1) goes into your hand, 2) becomes noise, 3) is converted to mass, 4) stays inside the shot, 5) dents the lid, 6) goes into the air, 7) disappears, 8) converts to heat, 9) compresses other shot, 10) pushes other shot out of the way.

The following data and calculations were obtained with a TI-83+/LabPro system:

Number of inversions Temperature (deg C) 
26.49 
100 26.72 
200 26.93 
300 27.21 
400 27.33 
500 27.47 
Number of inversions Temperature (deg C) 
26.49 
100 26.72 
200 26.93 
300 27.21 
400 27.33 
500 27.47 

The best linear regression fit to these data had the form

T = 0.0020 n + 26.52, where T = temperature

and

n = number of inversions.

Thus the temperature increase per inversion is 0.0020°C.

The distance fallen by the shot in the container was 6 cm = 0.06 m. The corresponding decrease in potential energy per unit mass for each inversion is therefore mgh/m = gh = 10 N/kg × 0.06 m = 0.6 J/kg. Dividing this by the temperature increase for each inversion gives 0.6 J/kg/0.002°C = 300 J/kg. °C. The accepted specific heat of copper is 385 J/kg . °C.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: As is also the case of the conversion of electric energy to thermal energy, this activity results in a measurement of specific heat, the amount of energy to increase the thermal energy of a kilogram of a substance by one degree Celsius. Rather than confirming the conversion of another form of energy to thermal energy, this measurement of specific heat actually assumes that all the gravitational potential energy from the falling copper shot is converted to thermal energy. What ultimately substantiates the idea of conservation of energy in energy conversions is the consistence of the values of specific heat measured in this type of experiment and other experiments in which thermal energy is transferred from one material to another.

POSSIBLE EXTENSIONS: The approach of this activity can be used to measure the specific heat of other elements. It has historically been performed with lead shot, because of the especially low specific heat of lead (130 J/kg . °C), but the recognized toxicity of lead now makes this a metal to avoid in the laboratory, especially since the dust created by collisions of lead shot could be inhaled or ingested. Other metals that could be used are aluminum, iron, and zinc. Their specific heats are given as follows:

Element Specific heat (J/kg. °C) 
Aluminum 903 
Iron 450 
Zinc 388 
Element Specific heat (J/kg. °C) 
Aluminum 903 
Iron 450 
Zinc 388 

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

When a jar of copper shot is inverted, the falling copper shot experiences a transformation of gravitational potential energy to kinetic energy. But what happens to the kinetic energy after the shot lands on the other end?

__________

  • temperature probe (precision greater than 0.01°C)

  • ruler

  • jar (or tube) of copper shot

  • three finger clamp

In this activity you will investigate the change in the copper shot’s temperature after its container has been inverted. The temperature of a given amount of copper shot can be measured after its container has been inverted a given number of times with a temperature probe, as follows:

Connect the temperature probe and record the initial temperature of the copper shot in the container (before you invert it). Make sure that the end of the probe is covered with shot.

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__________

Remove the temperature probe from the copper shot and seal the container.

Invert the container of copper shot 100 times. Be careful not to jerk the container. One way to invert the container without jerking is to clamp the container near its center, hold the clamp in one hand with the clamp resting on the fingers of the other, then roll the clamp back and forth across your finger.

After 100 inversions, record the temperature of the copper shot as you did in step 1.

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__________

Repeat steps 3 and 4 for four additional sets of 100 inversions. Make an appropriate data table and record the respective values.

After the last temperature measurement you will need to make a graph of temperature of the copper shot vs. number of inversions. You may view this graph on the computer or calculator to which your temperature probe is interfaced.

You can facilitate the analysis of your data by answering the following questions:

What type of relationship does your graph indicate between the temperature of the copper shot and the number of inversions?

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__________

What is the average temperature change for a single inversion?

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__________

Overturn the container of copper shot (with the lid on) and measure the distance from the surface level of the shot to the bottom of the container.

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__________

Because the temperature of the copper shot has increased, we see that gravitational potential energy has been transformed to thermal energy. What is the gravitational potential energy transformed to thermal energy in each inversion? Show how you calculated this.

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__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion? Show how you calculated this.

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__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion divided by the temperature increase for each inversion? Note that the units for this are J/kg · °C and that this is the amount of energy required to change the temperature of 1 kg of substance by 1°C, or specific heat.

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__________

Compare your experimental results to the accepted value of the specific heat of copper: 385 J/kg · °C. What is your percent error? If your measured value is greater than the accepted value, what could explain this result? If the measured value is less than the accepted value, what could explain this result?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

When a jar of copper shot is inverted, the falling copper shot experiences a transformation of gravitational potential energy to kinetic energy. But what happens to the kinetic energy after the shot lands on the other end?

__________

  • Vernier LabPro unit

  • TI-83+ graphing calculator

  • temperature probe

  • ruler

  • jar of copper shot

  • three finger clamp

In this activity you will investigate the change in the copper shot’s temperature after its container has been inverted. The temperature of a given amount of copper shot can be measured after its container has been inverted a given number of times with a temperature probe interfaced to a TI-83+/LabPro system, using the DataMate application, as follows:

Connect the temperature probe to CH 1 of the LabPro unit.

Make sure that the link cord is connected between the calculator and the LabPro unit (link ports are on the bottom of each unit).

Turn on the calculator and connect the AC adapter for the LabPro unit to a wall outlet.

Press the <APPS> key on the calculator.

Use the arrow keys on the calculator to highlight the application DataMate. Press <ENTER>, then press the <CLEAR> key to reset the program. At this point the LabPro automatically checks for and identifies the probes connected to it. The calculator monitors and displays readings from the probes.

Press <1.Setup>.

Move the cursor to “Mode” and press <ENTER>.

Press <3.Events With Entry>.

Press <1.OK>.

Place the temperature probe into the copper shot.

Press <2.Start>. You will then be asked to press <ENTER> to collect data. Press <ENTER> when the reading on the calculator screen is stable, in order to register the temperature of the copper shot.

The calculator will now prompt you to input a value. Input 0 <ENTER> to indicate that this reading corresponds to the temperature of the copper shot after no inversions have been performed on its container.

Remove the temperature probe from the copper shot, reclose the cover of the container, and invert the container of copper shot 100 times. In doing this it is important not to jerk the container. One way to invert the container without jerking is to clamp the container near its center, hold the clamp in one hand with the clamp resting on the fingers of the other, then roll the clamp back and forth across your finger. After 100 inversions, replace the temperature probe in the copper shot. Press <ENTER> after the temperature has risen to a stable value, in order to register the temperature of the copper shot after 100 inversions have been performed on the copper shot container. When prompted to input a value, input 100 <ENTER> to indicate that this reading corresponds to the temperature of the copper shot after 100 inversions have been performed on its container.

Repeat step 13 for four additional sets of 100 inversions, entering, respectively, values of 200, 300, 400, and 500.

After your last measurement, press <STO->> to see a graph of the temperature of the copper shot vs. number of inversions of the copper shot container (the window for the x-axis will match the range of values you have input). When you are finished with the graph, press <ENTER>.

Press <6.Quit>. You will be told that the number of inversions will be displayed in L1 and the temperatures in L2. This can be verified by pressing <ENTER> (to exit the DataMate application), then pressing <STAT> and selecting EDIT.

The temperatures are measured in units of degrees Celsius. Enter the temperatures in the following data table:

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

To display your data graphically, activate a plot by pressing <2nd> and <Y=> to get <STAT PLOT>, then press <ZOOM> and <9> or press <WINDOW> and select appropriate values of Xmin, Xmax, etc., and finally press <GRAPH>.

If the same temperature increase has occurred for each set of 100 inversions, your graph of temperature vs. number of inversions should be a straight line of positive slope. To determine the best straight line fit to your data, press <STAT> and select <CALC> from the menu with the arrow keys. Use the arrow keys to select “4.LinReg,” which will give you the best fit in the form y = ax + b, which translates to

[temperature] = a*[number of inversions] + b.

From the relationship you have established between the temperature and the number of inversions, what is the average temperature change for a single inversion?

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__________

Overturn the container of copper shot (with the lid on) and measure the distance from the surface level of the shot to the bottom of the container (in meters). This is the vertical distance fallen by the shot in each inversion.

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__________

Because the temperature of the copper shot has increased, we see that gravitational potential energy has been transformed into thermal energy. What is the gravitational potential energy transformed to thermal energy in each inversion? Show how you calculated this.

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__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion? Show how you calculated this.

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__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion divided by the temperature increase for each inversion? Note that the units for this are J/kg · °C. and that this is the amount of energy required to change the temperature of 1 kg of substance by 1°C, or specific heat.

Show answer Hide answer

__________

Compare your experimental results to the accepted value of the specific heat of copper: 385 J/kg · °C What is your percent error? If your measured value is greater than the accepted value, what could explain this result? If the measured value is less than the accepted value, what could explain this result?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

When a jar of copper shot is inverted, the falling copper shot experiences a transformation of gravitational potential energy to kinetic energy. But what happens to the kinetic energy after the shot lands on the other end?

__________

  • TI CBL unit

  • TI-83 graphing calculator

  • temperature probe

  • ruler

  • jar of copper shot

  • three finger clamp

In this activity you will investigate the change in the copper shot’s temperature after its container has been inverted. The temperature of a given amount of copper shot can be measured after its container has been inverted a given number of times with a temperature probe interfaced with a TI-83/CBL system, using the PHYSICS program, as follows:

Connect the temperature probe to CH 1 of the CBL unit.

Connect link cord between calculator and CBL unit (link ports are on the bottom of each unit). Make sure that the link cord is firmly inserted into each unit (a twisting motion helps to ensure this).

Turn on the CBL unit and calculator.

Press the <PRGM> key on the calculator.

Use the arrow keys on the calculator to highlight the program PHYSICS. Press <ENTER>. At this point the calculator screen should have “prgmPHYSICS” showing; press <ENTER> again.

When the program title screen appears, press <ENTER>, as prompted on the screen.

If it is not already highlighted, highlight 1:SET UP PROBES and press <ENTER>.

At prompt, “NUMBER OF PROBES,” press <1> or highlight 1:ONE and press <ENTER>.

Select <6.TEMPERATURE>. (This can be done by pressing <6> or using the arrow keys to select <6.TEMPERATURE> and pressing <ENTER>.)

If prompted to select a channel, press <1> and <ENTER>. If directed to connect the temperature probe to CH1, press <ENTER>, because you have already done this in step 1.

You should now be back at the main menu screen. Select <2. COLLECT DATA>.

From the data collection menu choose <3. TRIGGER PROMPT>. The TI-83/CBL pair is now prepared to gather data.

Place the temperature probe in the copper shot and press <TRIGGER> on the CBL unit when the temperature reading is stable. The calculator will not prompt you to input a value. Input 0 <ENTER> to indicate that this reading corresponds to the temperature of the copper shot after no inversions have been performed on its container.

Remove the temperature probe from the copper shot, reclose the cover of the container, and invert the container of copper shot 100 times. One way to invert the container without jerking is to clamp the container near its center, hold the clamp in one hand with the clamp resting on the fingers of the other, then roll the clamp back and forth across your finger. After 100 inversions, replace the temperature probe in the copper shot. Monitor the CBL and press <TRIGGER> on the CBL unit when the temperature reading is stable. The calculator will not prompt you to input a value. Input 100 <ENTER> to indicate that this reading corresponds to the temperature of the copper shot after 100 inversions have been performed on its container.

Repeat step 14 for four additional sets of 100 inversions, entering, respectively, values of 200, 300, 400, and 500.

After your last measurement choose <2. STOP AND GRAPH> from the data collection menu. The calculator will display a graph of temperature (in L2) vs. number of inversions (in L1).

After you have finished viewing your graph, press <ENTER> and respond to the prompt “REPEAT?” If you wish to collect more data input <2. YES>; otherwise <1. NO>, and <7. QUIT> from the main menu.

The temperatures are measured in units of degrees Celsius. Enter the temperatures in the following data table:

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

To display your data graphically, activate a plot by pressing <2nd> and <Y=> to get <STAT PLOT>, then press <ZOOM> and <9> or press <WINDOW> and select appropriate values of Xmin, Xmax, etc., and finally press <GRAPH>.

If the same temperature increase has occurred for each set of 100 inversions, your graph of temperature vs. number of inversions should be a straight line of positive slope. To determine the best straight line fit to your data, press <STAT> and select <CALC> from the menu with the arrow keys. Use the arrow keys to select “4.LinReg,” which will give you the best fit in the form y = ax + b, which translates to

[temperature] = a*[number of inversions] + b.

From the relationship you have established between the temperature and the number of inversions, what is the average temperature change for a single inversion?

Show answer Hide answer

__________

Overturn the container of copper shot (with the lid on) and measure the distance from the surface level of the shot to the bottom of the container (in meters). This is the vertical distance fallen by the shot in each inversion.

Show answer Hide answer

__________

Because the temperature of the copper shot has increased, we see that gravitational potential energy has been transformed to thermal energy. What is the gravitational potential energy transformed to thermal energy in each inversion? Show how you calculated this.

Show answer Hide answer

__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion? Show how you calculated this.

Show answer Hide answer

__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion divided by the temperature increase for each inversion? Note that the units for this are J/kg · °C and that this is the amount of energy required to change the temperature of 1 kg of substance by 1°C, or specific heat.

Show answer Hide answer

__________

Compare your experimental results to the accepted value of the specific heat of copper: 385 J/kg · °C. What is your percent error? If your measured value is greater than the accepted value, what could explain this result? If the measured value is less than the accepted value, what could explain this result?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

When a jar of copper shot is inverted, the falling copper shot experiences a transformation of gravitational potential energy to kinetic energy. But what happens to the kinetic energy after the shot lands on the other end?

__________

  • ruler

  • jar of copper shot (For better results, place the copper shot in a PASCO Energy Transfer Calorimeter ET-8499 or container from PASCO Basic Calorimetry Set TD-8557.)

  • DataStudio Software (PASCO CI-6870F)

  • PASPORT Xplorer Datalogger (PASCO PS-2000)

  • temperature sensor [PASCO PS-2125; for faster response the PASCO Fast Response Temperature Sensor (PS-2135) can be connected to the PS-2125]

  • three finger clamp

In this activity, you will investigate the change in the copper shot’s temperature after its container has been inverted. The temperature of a given amount of copper shot can be measured after its container has been inverted a given number of times with a temperature probe, as follows:

Turn on the Xplorer datalogger, then plug in the temperature sensor. Click the → button until the temperature can be seen on the display.

Place the temperature probe into the copper shot in the jar. Allow the temperature measurement to stabilize, then record the temperature of the copper shot (before you invert it) in a data table like the one following:

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

Remove the temperature probe from the copper shot and seal the container.

Invert the container of copper shot 100 times. Be careful not to jerk the container. One way to invert the container without jerking is to clamp the container near its center, hold the clamp in one hand with the clamp resting on the fingers of the other, then roll the clamp back and forth across your finger.

Record the temperature of the copper shot as you did in steps 1-2.

Repeat steps 4 and 5 for four additional sets of 100 inversions. Record the respective values in the same data table.

Using DataStudio, follow steps 8-16 below to create a graph with number of inversions on the horizontal axis and temperature on the vertical axis.

Open DataStudio and choose the Enter Data option.

Click the Summary button on the main toolbar.

Double-click on Editable Data to open the data properties.

Click on the X under Variable Name and type “# of inversions.”

Click on the triangle at the right side of the Variable Name box and choose Y.

Type “temperature” and enter “deg C” in the Units box and click the OK button.

Click the Summary button again to close the window.

Enter your data into the table.

Observe your graph of temperature vs. # of inversions and look for patterns.

You can facilitate the analysis of your data by answering the following questions:

What type of relationship between the temperature of the copper shot and the number of inversions does your graph indicate?

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__________

What is the average temperature change for a single inversion?

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__________

Overturn the container of copper shot (with the lid on) and measure the distance from the surface level of the shot to the bottom of the container.

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__________

Because the temperature of the copper shot has increased, we see that gravitational potential energy has been transformed to thermal energy. What is the gravitational potential energy transformed to thermal energy in each inversion? Show how you calculated this.

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__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion? Show how you calculated this.

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__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion divided by the temperature increase for each inversion? Note that the units for this are J/kg · °C and that this is the amount of energy required to change the temperature of 1 kg of substance by 1°C, or specific heat.

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__________

Compare your experimental results to the accepted value of the specific heat of copper: 385 J/kg · °C. What is your percent error? If your measured value is greater than the accepted value, what could explain this result? If the measured value is less than the accepted value, what could explain this result?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

When a jar of copper shot is inverted, the falling copper shot experiences a transformation of gravitational potential energy to kinetic energy. But what happens to the kinetic energy after the shot lands on the other end?

__________

  • computer with USB port

  • Go! Temp probe

  • Logger Lite version 1.2 or later

  • ruler

  • jar of copper shot

  • three finger clamp

In this activity you will investigate the change in the copper shot’s temperature after its container has been inverted. The temperature of a given amount of copper shot can be measured after its container has been inverted a given number of times with a temperature probe interfaced to a computer, as follows:

Connect the Go! Temp probe to the computer.

Launch Logger Lite.

Choose Data Collection from the Experiment menu.

Change the Mode to Events with Entry.

Locate the Column Name field and enter “Inversions.”

Locate the Short Name field, and enter “n.”

Locate the Units field, and enter “#.”

Click “Done” to close the dialog box.

Place the temperature probe into the copper shot.

Click “Collect” to prepare for data collection. No values will be recorded just yet.

When the reading on the computer screen is stable, click “Keep” to record temperature of the copper shot.

Logger Lite will now prompt you to enter a value for the number of inversions. Enter “0” and click “OK.”

Remove the temperature probe from the copper shot, reclose the cover of the container, and invert the container of copper shot 100 times. In doing this it is important not to jerk the container. One way to invert the container without jerking is to clamp the container near its center, hold the clamp in one hand with the clamp resting on the fingers of the other, then roll the clamp back and forth across your finger. After 100 inversions, replace the temperature probe in the copper shot. Click “Keep” after the temperature reading has stabilized, in order to register the temperature of the copper shot after 100 inversions have been performed on the copper shot container. Enter “100” and click “OK” to indicate that this reading corresponds to the temperature of the copper shot after 100 inversions have been performed on its container.

Repeat step 13 for four additional sets of 100 inversions, entering, respectively, values of 200, 300, 400, and 500.

After your last measurement press “Stop.”

The temperatures are measured in units of degrees Celsius. Enter the temperatures in the following data table:

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

Number of inversions

 

Temperature (deg C)

 

0

 
 

100

 
 

200

 
 

300

 
 

400

 
 

500

 
 

Inspect your graph of temperature vs. number of inversions. Choose “Autoscale → Autoscale” from the Analyze menu if you need to rescale the graph. What kind of pattern do you see in your graph?

Show answer Hide answer

__________

You can facilitate the analysis of your data by answering the following questions:

What type of relationship between the temperature of the copper shot and the number of inversions does your graph indicate?

Show answer Hide answer

__________

What is the average temperature change for a single inversion?

Show answer Hide answer

__________

Overturn the container of copper shot (with the lid on) and measure the distance from the surface level of the shot to the bottom of the container.

Show answer Hide answer

__________

Because the temperature of the copper shot has increased, we see that gravitational potential energy has been transformed to thermal energy. What is the gravitational potential energy transformed to thermal energy in each inversion? Show how you calculated this.

Show answer Hide answer

__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion? Show how you calculated this.

Show answer Hide answer

__________

What is the gravitational potential energy transformed to thermal energy per unit mass for each inversion divided by the temperature increase for each inversion? Note that the units for this are J/kg · °C and that this is the amount of energy required to change the temperature of 1 kg of substance by 1°C, or specific heat.

Show answer Hide answer

__________

Compare your experimental results to the accepted value of the specific heat of copper: 385 J/kg · °C. What is your percent error? If your measured value is greater than the accepted value, what could explain this result? If the measured value is less than the accepted value, what could explain this result?

Show answer Hide answer

__________

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

OBJECTIVE: The objective of this activity is to motivate the concept of power, or rate at which energy is transformed, and to apply it to the rate at which students do work to increase their gravitational potential energy in climbing a flight of stairs.

IDEA: Students are asked to measure their increase in gravitational potential energy as they climb a flight of stairs, then to calculate the rate at which this potential energy increases. This is followed by asking students to calculate their body’s energy needs for a day, both to perform various physical activities (including the climbing of stairs) and to maintain internal body functions.

LEVEL: middle level (7, 8, and 9)

DURATION: approximately 40 minutes

STUDENT BACKGROUND: Students must be able to measure time with a stopwatch, measure distance with a meterstick, and enter data into and calculate with a spreadsheet.

ADVANCE PREPARATION: Gather metersticks and stopwatches, arrange for use of computers and convenient staircase.

MANAGEMENT TIPS: Elicit student responses to the Reflective Question before proceeding on to the activity.

In checking student plans to measure and calculate the work they do climbing the stairs, make sure that students measure the distance walked up the stairs vertically, not along the slant of the stairs. They can determine their mass in kilograms by dividing their weight in pounds by 2.2 and their weight in newtons by multiplying their mass (in kg) by the Earth’s gravitational field, approximately 10 N/kg. Students reluctant to reveal their weight can be allowed to use the weight of a friend or family member but should answer all questions in terms of the daily activities of that other person. One way to administer the time measurements is to line up students on the landing at the foot of the staircase to be climbed. Have the last student time the first student, then have all other students timed by the student who has just climbed the stairs. (This allows all the timing by a single stopwatch, transferred among student timers at the top of the stairs.)

SAFETY: Require students to step on each step in order to reduce risk of injury.

RESPONSES TO SOME QUESTIONS: In general, student answers to questions will vary, with differences in weight and in physical activities performed during the day. For example, a 175-lb. male of average build needs 175 × 12 = 2100 Calories per day to maintain internal body functions. The energy requirement for physical activity will vary greatly from student to student but probably be no more than 1000 Calories. An 80-kg student walking up a flight of stairs with a vertical height of 3.0 m does 2400 Joules of work, which corresponds to 14.4 kJ/min or 240 watts, if it is done in 10 seconds. The vertical average velocity is thus 0.3 m/s, and the student’s kinetic energy in climbing the stairs is 3.6 J, using vertical velocity only, far less than the potential energy acquired.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: One outcome of this activity is a calculation of the amount of energy used by each student from food each day, both to maintain internal body functions and to perform physical activities.

POSSIBLE EXTENSIONS: Once students have determined their need of energy from food for a day, students could be asked to inventory the energy content of the food they eat in a typical day and see how closely their consumption of energy from food matches their use of energy for internal body functions and physical activities.

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

When you climb a flight of stairs, do you ever stop to think that you are pushing down on the stairs to lift yourself? By exerting this force to lift yourself, you are doing work on yourself, which shows up as an increase in your gravitational potential energy. The rate at which you do work is calledpower.Like the rate at which electric appliances transform electrical energy to other forms, power is expressed injoules/sec, orwatts. With how many watts of power can you climb the stairs?

__________

  • meterstick

  • stopwatch

  • bathroom scale (optional)

Devise a plan to make the measurements and calculate the work you must do to climb a flight of stairs as well as the rate at which you do it (your power). Use standard metric units. After your teacher approves your plan, carry it out under your teacher’s direction.

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__________

Create an organized data chart showing the data you measured as you climbed the flight of stairs.

Create a detailed, step-by-step data analysis sheet showing what you did to calculate the power (in watts) with which you climbed the stairs.

Climbing stairs is only one activity in which you do work—either on yourself or something else—during the day. This work is made possible because of the energy you acquire from the food you eat. In fact, most of the energy from the food you eat goes to maintain your internal body functions, like maintaining your internal body temperature at 37° Celsius.

The energy from the food you eat is rated on nutrition labels in terms of Calories, and each Calorie of energy can increase the temperature of one kilogram of water by one degree Celsius. One Calorie is equal to 4180 joules (J), or 4.18 kilojoules (kJ). The number of Calories per day needed to maintain your internal body functions can be found by multiplying your weight (in pounds) by 12 (if you are male of average build) or 11 (if you are female of average build), adding 5% if you are skinny, subtracting 5% if you are plump, or subtracting 10% if you are more than plump.*

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__________

According to the preceding paragraph, how many Calories do you need per day to maintain your internal body functions?

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__________

In addition to energy for maintaining your internal body functions, you also need energy to perform various physical activities. The rates at which men and women use energy to perform these activities* are given in the following tables in terms of Calories per minute and kilojoules per minute

Table I.
Activity # Cal/min (man) # min # cal # kJ/min # kJ 
driving a car 0.47   1.96  
washing dishes by hand 0.59   2.47  
typing quickly 0.59   2.47  
playing musical instrument at moderate rate 1.1   4.60  
walking, normal rate 1.8   7.52  
bicycling, easy rate 2.3   9.61  
skating, moderately 3.5   14.63  
swimming, moderate speed 3.5   14.63  
walking, briskly 3.5   14.63  
Ping Pong, brisk game 4.6   19.23  
walking upstairs, moderate rate 5.3   22.15  
tennis, average rate 5.6   23.41  
running, moderate speed 7.6   31.77  
bicycling, racing speed 8.3   34.96  
swimming, hard 8.7   36.37  
dancing, very vigorously   27.62  
running, cross country 9.8   40.96  
Activity # Cal/min (man) # min # cal # kJ/min # kJ 
driving a car 0.47   1.96  
washing dishes by hand 0.59   2.47  
typing quickly 0.59   2.47  
playing musical instrument at moderate rate 1.1   4.60  
walking, normal rate 1.8   7.52  
bicycling, easy rate 2.3   9.61  
skating, moderately 3.5   14.63  
swimming, moderate speed 3.5   14.63  
walking, briskly 3.5   14.63  
Ping Pong, brisk game 4.6   19.23  
walking upstairs, moderate rate 5.3   22.15  
tennis, average rate 5.6   23.41  
running, moderate speed 7.6   31.77  
bicycling, racing speed 8.3   34.96  
swimming, hard 8.7   36.37  
dancing, very vigorously   27.62  
running, cross country 9.8   40.96  
*

Rates of Calories used are taken from Gerald Slutsky, “I Didn’t Know It Was Loaded,” in Energy: Options for the Future (Food and Energy), Stony Brook University, NY, p. F-17.

Table II.
Activity # Cal/min (woman) # min # cal # kJ/min # kJ 
driving a car 0.43   1.7974  
washing dishes by hand 0.52   2.1736  
typing quickly 0.52   2.1736  
playing musical instrument at moderate rate 0.91   3.8038  
walking, normal rate 1.5   6.27  
bicycling, easy rate   8.36  
skating, moderately 2.9   12.122  
swimming, moderate speed 2.9   12.122  
walking, briskly 2.9   12.122  
Ping Pong, brisk game 3.8   15.884  
walking upstairs, moderate rate 4.4   18.392  
tennis, average rate 4.7   19.646  
running, moderate speed 6.3   26.334  
bicycling, racing speed 6.9   28.842  
swimming, hard 7.2   30.096  
dancing, very vigorously 7.6   31.768  
running, cross country   33.44  
Activity # Cal/min (woman) # min # cal # kJ/min # kJ 
driving a car 0.43   1.7974  
washing dishes by hand 0.52   2.1736  
typing quickly 0.52   2.1736  
playing musical instrument at moderate rate 0.91   3.8038  
walking, normal rate 1.5   6.27  
bicycling, easy rate   8.36  
skating, moderately 2.9   12.122  
swimming, moderate speed 2.9   12.122  
walking, briskly 2.9   12.122  
Ping Pong, brisk game 3.8   15.884  
walking upstairs, moderate rate 4.4   18.392  
tennis, average rate 4.7   19.646  
running, moderate speed 6.3   26.334  
bicycling, racing speed 6.9   28.842  
swimming, hard 7.2   30.096  
dancing, very vigorously 7.6   31.768  
running, cross country   33.44  
*

Rates of Calories used are taken from Gerald Slutsky, “I Didn’t Know It Was Loaded,” in Energy: Options for the Future (Food and Energy), Stony Brook University, NY, p. F-17.

Enter the number of minutes per day you perform each activity, then calculate the number of Calories used by multiplying the #Cal/min by the number of minutes. The number of kilojoules per minute is obtained by multiplying the #Cal/min by 4.18, and the number of kilojoules is obtained by multiplying the #kJ/min by the number of minutes. Enter your values into a spreadsheet like the one above and calculate the total number of Calories and kilojoules.

How does the total number of Calories or kilojoules for physical activity compare with the number of Calories or kilojoules needed for internal body functions (question 4)?

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__________

How does the rate of using energy (in kJ/min) to climb stairs at a moderate rate in the table above compare with the value you calculated in step 3 above? In the space provided, calculate and show how you change your answer from joule/second to kilojoules/minute before answering.

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__________

Could a difference between your measured value of energy rate (in kJ/min) to climb stars at a moderate rate and the value given in the table depend on the amount of kinetic energy you “gave yourself” in order to climb the stairs? Find out by measuring your average vertical speed. You may use the height you climbed on the stairs and the time you took to climb the stairs. Then use this speed to find your kinetic energy. You may look up the equation for kinetic energy if you need to do that. Show your calculations in the space provided.

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__________

How does your kinetic energy climbing the stairs compare with your potential energy increase?

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__________

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

OBJECTIVE: This activity demonstrates the conversion of electrical to thermal energy, using the known power of an immersion coil, which gives the rate at which it converts electrical energy into thermal form.

IDEA: The increase in thermal energy needed to increase the temperature of a substance by a given amount depends on not only the temperature increase but also the mass of the substance and its thermal properties in the form of specific heat, the amount of energy needed to increase the temperature of 1 kg of a substance by 1.0°C. This is shown by investigating the dependence of the temperature increase of given masses of water on 1) the amount of electrical energy converted to thermal energy and 2) the mass of the water. The equation relating temperature increase to mass and amount of energy converted to thermal energy is then inverted to look at how the amount of energy converted to thermal energy depends on the mass and the temperature increase. The amount of energy converted to thermal energy is seen to vary directly as the mass and the temperature increase, and the constant of proportionality shows up as the specific heat.

LEVEL: high school (10, 11, and 12)

DURATION: approximately 80 minutes (10 minutes setup, 30 minutes data gathering, 30 minutes data analysis, 10 minutes take down)

STUDENT BACKGROUND: Students must be able to measure time with a stopwatch and temperature with a thermometer and to make and interpret graphs.

ADVANCE PREPARATION: Assemble immersion heaters, beakers, thermometers, and stopwatches. Caution students emphatically on safe handling of immersion heaters (immersing them in water before turning them on, never immersing the cords or plugs, never leaving them unattended, and disconnecting them when not in use). Digital or Enviro-Safe® thermometers may be used instead of spirit-filled thermometers, but mercury thermometers should not be used.

MANAGEMENT TIPS: Elicit student responses to the Reflective Question before proceeding on to the activity.

Point out the reason that the immersion heaters should be on a minute before actual timing begins—that it takes this long for energy to convert from electrical to thermal form in the coil and then to thermal form in the water. Students wishing to witness this firsthand can measure the temperature of the water at 30-second or one-minute intervals, beginning with the time the heater is plugged into the wall outlet. A graph of water temperature vs. time will show a constant slope (constant rate of temperature change) after about the first minute but a much lower initial rate of temperature change. This can also be seen if the temperatures are measured with an electronic probe. The reason that the water temperature should not exceed 60°C is that at significantly higher temperature than that of ambient air, the cooling of water in the beaker (which varies as the difference between the water temperature and that of ambient air) will counteract the heating of the water too much. Although this activity is written for a 200 W immersion coil, coils with other power ratings can be used if the times are scaled inversely—e.g., only 2/3 as great for a 300 W immersion coil.

Students should be instructed to cool their beakers to room temperature before beginning another set of measurements.

RESPONSES TO SOME QUESTIONS: Responses to the Reflective Question could include the following: mass of the water, shape of container, stuff in water, isotopic composition, nature of container, transfer of energy to environment, initial temperature of water, effect of heating the heater, mass of the heater, composition of the heater, and altitude.

To determine how the water temperature increase depends on the amount of electrical energy converted to thermal energy, what measurements would you need to make?

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ANS:Measure the temperature increase, with the amount of water constant, when the immersion heater is on for different amounts of time and therefore converts different amounts of electrical energy to thermal energy.

Averaging three trials measuring temperature changes for a 200-W immersion heater for 2.0 minutes in the listed masses of water yielded the following results:

Time* (min) Electrical Energy converted (J) Initial Temperature (°C) Final Temperature (°C) Temperature Change (°C) Energy/ (mass . temp change) (J/kg · °C) 
1.0 12000 27 39.3 12.3 4891 
1.5 18000 27 43.9 16.9 5336 
2.0 24000 27 49.3 22.3 5389 
2.5 30000 27 55.1 28.1 5332 
3.0 36000 27 60.5 33.5 5378 
Time* (min) Electrical Energy converted (J) Initial Temperature (°C) Final Temperature (°C) Temperature Change (°C) Energy/ (mass . temp change) (J/kg · °C) 
1.0 12000 27 39.3 12.3 4891 
1.5 18000 27 43.9 16.9 5336 
2.0 24000 27 49.3 22.3 5389 
2.5 30000 27 55.1 28.1 5332 
3.0 36000 27 60.5 33.5 5378 
*

time measured after a minute had already elapsed on the stopwatch

2.

Make a graph of the temperature change vs. energy converted. What does this tell you about the relationship between the temperature change and the energy converted (from electrical to thermal form)?

ANS:The temperature change varies linearly with the amount of energy converted from electrical to thermal form.

3.

How do you expect the temperature change should be related to the mass of the water, if the amount of energy converted (from electrical to thermal form) is kept constant?

ANS:The greater the mass of water, the smaller the temperature increase should be.

4.

To find out how the temperature change relates to the mass of the water (with a constant amount of energy converted), what kind of measurements would you need to make?

ANS:Measure the temperature increase, with the amount of energy converted constant, when different masses of water are heated.

Averaging three trials measuring temperature changes for a 200-W immersion heater for 2.0 minutes in the listed masses of water yielded the following results:

Volume of water (mL) Mass of water (kg) 1/mass of water (kg-1) Initial Temperature (°C) Final Temperature (°C) Temperature Change (°C) Energy/ (mass.temp change) (J/kg · °C) 
150 0.150 6.67 31.1 61.4 30.3 5281 
175 0.175 5.71 28.2 53.8 25.6 5364 
200 0.200 5.00 30.2 50.5 20.3 5911 
225 0.225 4.44 26.7 47.8 21.1 5047 
Volume of water (mL) Mass of water (kg) 1/mass of water (kg-1) Initial Temperature (°C) Final Temperature (°C) Temperature Change (°C) Energy/ (mass.temp change) (J/kg · °C) 
150 0.150 6.67 31.1 61.4 30.3 5281 
175 0.175 5.71 28.2 53.8 25.6 5364 
200 0.200 5.00 30.2 50.5 20.3 5911 
225 0.225 4.44 26.7 47.8 21.1 5047 

Make a graph of the temperature change vs. mass of water. What does this tell you about the relationship between the temperature change and the mass of the water (when the same amount of energy is converted)?

Show answer Hide answer

ANS:The temperature change varies inversely as the mass of the water.

Make a graph of the temperature change vs. the reciprocal of the mass of the water. What does this tell you about the relationship between the temperature change and the mass of the water (when the same amount of energy is converted)?

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ANS:The temperature change varies inversely as the mass of the water.

It is now expected that you have found that the temperature change varies directly as the amount of energy converted and inversely as the mass of the water:

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ANS:ΔT = (constant)(Q)/m, where

ΔT = temperature change (in °C)

Q = energy converted (from electrical to thermal form, in J)

m = water mass (in kg).

This equation can be “inverted” into the following form:

Q = (1/constant)(m)(ΔT).

(1/constant) = (new constant)

Q = (new constant)(m)(ΔT), or (C)(m)(ΔT).

The “new constant” can be determined by dividing the energy converted by the product of the water mass and the temperature change. This can be done by adding an additional column to the right of the data tables.

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ANS:This is done using the tables on student sheets.

What are the units of this “new constant”? What is the significance of this “new constant”?

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ANS:The units are joules per kg per degree Celsius. The “new constant” tells the number of joules required to increase thermal energy for every kg and degree Celsius.

How do your values of the “new constant” compare with the specific heat of water?

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ANS:Most of the values of Energy/(mass) (temperature change) compare favorably with the accepted value of the specific heat of water: 4180 J/(kg · °C). Because the size of the degree on the Kelvin scale is the same as on the Celsius scale, some sources quote values of specific heat in units of J/(kg · K).

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: This activity is another example of investigating how one variable depends on other variables in the system. Experimentally the temperature change seems to be the “natural” dependent variable, with water mass and amount of energy converted (equal to power times time) as the independent variables. Later the amount of energy converted emerges as the dependent variable, and the dependence of energy converted on mass and temperature change is deduced.

POSSIBLE EXTENSIONS: Because there are no other substances safe to use with immersion heaters, this approach cannot be used to measure the specific heat of other substances directly. However, once the specific heat of water is established, one can calculate how much thermal energy a given mass of water acquires when it is heated by immersing a hot mass of another subtance in it, and from this the specific heat of the other substance. Suppose that 0.200 kg of a “mystery substance” in boiling water (initial temperature 100°C ) is added to 0.200 kg water initially at 20°C and that the final temperature of the combined masses is 35°C. Then the specific heat of the “mystery” substance could be calculated as follows:

Thermal energy given up by “mystery” substance =

Thermal energy acquired by water.

(Specific heat of “mystery” substance)(mass of “mystery” substance)(temperature decrease of “mystery” substance) =

(Specific heat of water)(mass of water)(temperature increase of water).

(Specific heat of “mystery” substance) (0.200 kg)(100°C – 35°C) = (4180 J/(kg · °C))(0.200 kg)(35oC – 20°C).

Specific heat of “mystery” substance = 965 J/(kg °C)

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

If you submerge an immersion heater in water and then connect it to an electric outlet, you will cause the temperature of the water to increase. Electric current from the wall outlet flows through the coil of the heater in the water, the coil gets hot, and the water gets warmer. What is going on in terms of energy?

In everyday language, you might say that “The electricity heats the water.” In more specific energy terms you might say that “Electrical energy is used to produce heat energy.” Scientists would prefer to say that “Electrical energy is converted to thermal energy.”

Just as one can measure the conversion of potential energy to kinetic energy on a roller coaster, and vice versa, so also can one measure the conversion of electrical energy to thermal energy. We can calculate the electrical energy converted from the power rating of the heater and the time it is turned on. Power is expressed in watts, which are joules per second (J/s). In this case power is the rate at which electrical energy is converted to thermal energy by the heater. The energy converted by a 200-W heater in 2.0 minutes is

(200 J/s)(120 s) = 2.4 × 104 J,

since a watt is a joule per second and there are 120 seconds in 2.0 minutes.

You might expect that the temperature increase of the water might depend on the amount of electrical energy converted to thermal energy. What other variable in this system might the temperature increase of the water depend on?

__________

  • stopwatch

  • 200-W immersion coil

  • spirit thermometer (-10°C to 110°C)

  • 250-mL beaker

  • source of water

  • 100-mL graduated cylinder

To determine how the water temperature increase depends on the amount of electrical energy converted to thermal energy, what measurements do you need to make?

Show answer Hide answer

__________

NOTE: Stophere until directed to continue by your teacher.

For reasons of safety and reliable scientific measurements, we do not want the water temperature to exceed 60°C. Therefore, it is suggested that for 200 mL water a 200-W immersion heater not be turned on for more than three minutes. Accordingly, the following specific directions are suggested:

IMPORTANT SAFETY NOTE:The immersion heater mustNEVERbe plugged in unless its coil is immersed in water. The cord and plug areNEVERto be immersed in water.NEVERleave a plugged-in immersion heater unattended. Always disconnect an immersion heater when it is not being used.

Pour 200 mL water into a 250-mL glass beaker, and place an immersion heater and thermometer in it. Put the plug from the immersion heater into a wall outlet and start the stopwatch at the same time. Energy is not converted from electrical to thermal form in the coil of the heater instantaneously. Therefore, the immersion heater should be on for a minute before the actual timing begins. When one minute appears on the stopwatch, observe and record the initial temperature of the water. After the required number of additional minutes has elapsed, read the thermometer and record the result. Disconnect the immersion heater plug when you are finished taking readings.

You can record your data in a table like the following:

Time on stop-watch (min.) (measured) Time on stop-watch – 1 min. (min) (calculated) Electrical energy converted (J) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      
Time on stop-watch (min.) (measured) Time on stop-watch – 1 min. (min) (calculated) Electrical energy converted (J) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      

Make a graph of the temperature change vs. electrical energy converted. What does this graph tell you about the relationship between the temperature change and the energy converted (from electrical to thermal form)?

Show answer Hide answer

__________

How do you expect the temperature change should be related to the mass of the water, if the amount of energy converted (from electrical to thermal form) is kept constant?

Show answer Hide answer

__________

To find out how the temperature change relates to the mass of the water (with a constant amount of energy converted), what kind of measurements would you need to make?

Show answer Hide answer

__________

Again, for reasons of safety and reliable scientific measurements, we do not want the water temperature to exceed 60°C. Moreover, we need to provide enough water in the beaker to keep the immersion heater immersed in water. Accordingly, the following specific directions are suggested:

Pour between 150 and 225 mL water into a 250-mL glass beaker, and place an immersion heater and thermometer in it. Put the plug from the immersion heater into a wall outlet and start the stopwatch at the same time. Because the immersion heater needs about a minute to start the heating process, it should be on for a minute before the actual timing begins. When one minute appears on the stopwatch, observe and record the initial temperature of the water. After two additional minutes have elapsed, read the thermometer and record the result. Disconnect the immersion heater plug.

You can record your data in a table like the following:

Time on stop-watch (min.) (measured) Time on stop-watch … 1 min. (min) (calculated) Electrical energy converted (J) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      
Time on stop-watch (min.) (measured) Time on stop-watch … 1 min. (min) (calculated) Electrical energy converted (J) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      

Make a graph of the temperature change vs. mass of water. What does this tell you about the relationship between the temperature change and the mass of the water (when the same amount of energy is converted)?

Show answer Hide answer

__________

Make a graph of the temperature change vs. the reciprocal of the mass of the water. What does this tell you about the relationship between the temperature change and the mass of the water (when the same amount of energy is converted)?

Show answer Hide answer

__________

It is now expected that you have found that the temperature change varies directly as the amount of energy converted and inversely as the mass of the water:

ΔT = (constant)(Q)/m, where

ΔT = temperature change (in °C),

Q = energy converted (from electrical to thermal form, in J),

m = water mass (in kg).

This equation can be “inverted” into the following form:

Q = (1/constant)(m)(ΔT).

(1/constant) = (new constant)

Q = (new constant)(m)(ΔT), or (C)(m)(ΔT).

The “new constant” can be determined by dividing the energy converted by the product of the water mass and the temperature change. This can be recorded in an additional column to the right of the data tables.

What are the units of this “new constant”? What is the significance of this “new constant”?

Show answer Hide answer

__________

The units for the “new constant” are J/(kg · °C). The numerical value of this “new constant” is the number of joules needed to increase the temperature of a kg of a substance (in this case, water) by 1°C. This quantity is known as the specific heat. For water its measured value is 4180 J/(kg · °C).

How do your values of the “new constant” compare with the specific heat of water? Calculate the percent error and explain why your answer to question 8 is higher or lower than the specific heat of water.

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

If you submerge an immersion heater in water and then connect it to an electric outlet, you will cause the temperature of the water to increase. Electric current from the wall outlet flows through the coil of the heater in the water, the coil gets hot, and the water gets warmer. What is going on in terms of energy?

In everyday language, you might say that “The electricity heats the water.” In more specific energy terms you might say that “Electrical energy is used to produce heat energy.” Scientists would prefer to say that “Electrical energy is converted to thermal energy.”

Just as one can measure the conversion of potential energy to kinetic energy on a roller coaster, and vice versa, so also can one measure the conversion of electrical energy to thermal energy. We can calculate the electrical energy converted from the power rating of the heater and the time it is turned on. Power is expressed in watts, which are joules per second (J/s). In this case power is the rate at which electrical energy is converted to thermal energy by the heater. The energy converted by a 200-W heater in 2.0 minutes is

(200 J/s)(120 s) = 2.4 × 104 J,

since a watt is a joule per second and there are 120 seconds in 2.0 minutes.

You might expect that the temperature increase of the water might depend on the amount of electrical energy converted to thermal energy. What other variable in this system might the temperature increase of the water depend on?

__________

  • 200-W immersion coil

  • computer with USB port

  • Go! Temp probe

  • Logger Lite software version 1.2 or newer

  • 250-mL beaker

  • source of water

  • 100-mL graduated cylinder

To determine how the water temperature increase depends on the amount of electrical energy converted to thermal energy, what measurements do you need to make?

Show answer Hide answer

__________

NOTE: Stophere until directed to continue by your teacher.

For reasons of safety and reliable scientific measurements, we do not want the water temperature to exceed 60°C. Therefore, it is suggested that for 200 mL water a 200-W immersion heater not be turned on for more than three minutes. Accordingly, the following specific directions are suggested:

IMPORTANT SAFETY NOTE: The immersion heater mustNEVERbe plugged in unless its coil is immersed in water. The cord and plug areNEVERto be immersed in water.NEVERleave a plugged-in immersion heater unattended. Always disconnect an immersion heater when it is not being used.

Connect the Go! Temp probe to the computer.

Launch Logger Lite.

Choose Data Collection from the Experiment menu.

Change the Experiment Length to “n,” where n is one more than the number of minutes for which you want to time the temperature increase. (The reasons for this are given in step 10 below.) Change the time units to minutes using the drop-down menu.

Change the sampling rate to “100” samples/minute.

Click “Done” to close the dialog box.

Pour 200 mL water into a 250-mL glass beaker, and place an immersion heater and thermometer into the water. Be sure the probe and immersion heater are not in contact.

Put the plug from the immersion heater into a wall outlet and click “Collect” in Logger Lite at the same time.

Energy is not converted from electrical to thermal form in the coil of the heater instantaneously. Therefore, the immersion heater should be on for a minute before the actual timing begins. Observe and record the initial temperature of the water after the first minute has passed. Observe and record the temperature of the water after the additional number of desired minutes has passed, and then disconnect the immersion heater plug.

You can record your data in a table like the following:

Time (min.) (measured) Time – 1 min. (min) (calculated) Electrical energy converted (J) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      
Time (min.) (measured) Time – 1 min. (min) (calculated) Electrical energy converted (J) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      

Make a graph of the temperature change vs. electrical energy converted. What does this graph tell you about the relationship between the temperature change and the energy converted (from electrical to thermal form)?

Show answer Hide answer

__________

How do you expect the temperature change should be related to the mass of the water, if the amount of energy converted (from electrical to thermal form) is kept constant?

Show answer Hide answer

__________

To find out how the temperature change relates to the mass of the water (with a constant amount of energy converted), what kind of measurements would you need to make?

Show answer Hide answer

__________

Again, for reasons of safety and reliable scientific measurements, we do not want the water temperature to exceed 60°C. Moreover, we need to provide enough water in the beaker to keep the immersion heater immersed in water. Accordingly, the following specific directions are suggested:

Pour between 150 and 225 mL water into a 250-mL glass beaker, and place an immersion heater and temperature probe into the water. Be sure the probe and immersion heater are not in contact.

Put the plug from the immersion heater into a wall outlet and click “Collect” in Logger Lite at the same time.

Because the immersion heater needs about a minute to start the heating process, it should be on for a minute before the actual timing begins. Observe and record the initial temperature of the water after the first minute has passed. Observe and record the initital temperature of the water after two additional minutes have passed, and then disconnect the immersion heater plug.

You can record your data in a table like the following:

Volume of water (mL) (measured) Mass of water (kg) (calculated) 1/mass of water (kg-1) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      
Volume of water (mL) (measured) Mass of water (kg) (calculated) 1/mass of water (kg-1) (calculated) Initial Temperature (°C) (measured) Final Temperature (°C) (measured) Temperature change (°C) (calculated) 
      
      
      
      

Make a graph of the temperature change vs. mass of water. What does this tell you about the relationship between the temperature change and the mass of the water (when the same amount of energy is converted)?

Show answer Hide answer

__________

Make a graph of the temperature change vs. the reciprocal of the mass of the water. What does this tell you about the relationship between the temperature change and the mass of the water (when the same amount of energy is converted)?

Show answer Hide answer

__________

It is now expected that you have found that the temperature change varies directly as the amount of energy converted and inversely as the mass of the water:

ΔT = (constant)(Q)/m, where

ΔT = temperature change (in °C)

Q = energy converted (from electrical to thermal form, in J)

m = water mass (in kg).

This equation can be “inverted” into the following form:

Q = (1/constant)(m)(ΔT).

(1/constant) = (new constant)

Q = (new constant)(m)(ΔT ), or (C)(m)(ΔT).

The “new constant” can be determined by dividing the energy converted by the product of the water mass and the temperature change. This can be done by adding an additional column to the right of the data tables.

What are the units of this “new constant”? What is the significance of this “new constant”?

Show answer Hide answer

__________

The units for the “new constant” are J/(kg · °C). The numerical value of this “new constant” is the number of joules needed to increase the temperature of a kg of a substance (in this case, water) by 1°C. This quantity is known as the specific heat. For water its measured value is 4180 J/(kg · °C).

How do your values of the “new constant” compare with the specific heat of water? Calculate the percent error and explain why your answer to question 8 is higher or lower than the specific heat of water.

Show answer Hide answer

__________

PROCESS SKILLS: Measure, Observe, Calculate

OBJECTIVE: The objective of this activity is to measure the energy transferred by burning a chemical fuel such as paraffin (in a candle) or diethylene glycol (in Sterno®).

IDEA: The energy transferred by burning a chemical fuel is measured by exposing a known mass of water to the flame from the burning fuel, then multiplying the known specific heat of water [4180 J/(kg · °C), as obtained in Activity 6] by the mass of the water and its increase in temperature.

LEVEL: middle level (7, 8, and 9)

DURATION: approximately 40 minutes (5 minutes setup, 15 minutes data gathering, 15 minutes data analysis, 5 minutes take down)

STUDENT BACKGROUND: Students need to be able to measure volume (of water) in a graduated cylinder, measure mass (of chemical fuel) to the nearest 0.1 g on a balance, and measure temperature with a thermometer.

ADVANCE PREPARATION: Gather equipment together beforehand and ensure that students have the necessary measurement skills. Digital or Enviro-Safe® thermometers may be used instead of spirit-filled thermometers, but mercury thermometers should not be used.

MANAGEMENT TIPS: Elicit student response to the Reflective Question before proceeding on to the activity.

An acceptable plan to measure the energy transferred from the combustion of a chemical fuel is measuring the mass of the chemical fuel and the temperature of 100 mL of water (100 g) before igniting the fuel, placing the water just above the flame, extinguishing the flame after the water temperature rises by, say 30°C, measuring the highest value to which the water temperature rises and the remaining mass of the chemical fuel.

To measure the energy transferred from burning paraffin in a candle, take a short household candle, about 1.5 cm in diameter, light it and drop some melted wax onto a small square of corrugated cardboard to serve as a base on which to stand the candle. Measure the mass of the candle and its corrugated base before and after it is burned, and measure the temperature of a known mass of water before and after the heating is done. From this calculate the candle mass burned and the increase in the water’s thermal energy. The thermal energy from the candle can be channeled upward by a “chimney” formed by removing both ends from a large juice can. The water to be heated can be contained in a soup can with the top end removed and suspended from a glass rod lying across the top of the juice can.

The thermal energy transferred to the water, which is also the energy transferred from burning the chemical fuel, can be measured by the relationship developed in Activity 6, “Converting Electrical to Thermal Energy”:

Q = (4180 J/(kg · °C))(m)(ΔT), where

4180 J/(kg · °C) is the specific heat of water, m is the mass of the water, and

ΔT is the change in water temperature.

The energy yield (in J/g) can be calculated by dividing the energy transferred by the mass of the fuel.

The data can be collected in a data table like the following:

 Fuel mass (g) Water temperature (°C) 
Initial value   
Final value   
Difference   
 Fuel mass (g) Water temperature (°C) 
Initial value   
Final value   
Difference   

SAFETY: The most important piece of equipment to manage from the safety point of view is the matches. Students need to strike only one match and ignite their chemical fuel only once. You can control this by bringing the matchbox to each student group as they need to use it. Never allow a student to carry a chemical fuel that is aflame. Flammable materials such as books and extra clothing must be removed from the laboratory table on which chemical fuels are burned. Make sure that students are wearing safety goggles before they ignite the chemical fuel and that they continue to wear them until the flame is extinguished. While the fuel is burning, students must also tie long hair back and tuck in loose clothing so that it doesn’t make contact with the flame. Also, make sure that the chemical fuel is in a stable position and located near the center of the laboratory table so it is less likely to be knocked over.

If students receive burns to their skin, relief can be obtained by promptly cooling the affected area with cold water.

RESPONSES TO SOME QUESTIONS: Reflective Question: An acceptable plan to measure the energy transferred from the combustion of a chemical fuel is given under “Management Tips” above.

The following data were reported for paraffin by Jane Nelson for 321 g water in an 80-g can:

 Candle mass (g) Water temperature (°C) 
Initial value 32.48 10.2 
Final value 31.23 40.2 
Difference 1.25 30.0 
 Candle mass (g) Water temperature (°C) 
Initial value 32.48 10.2 
Final value 31.23 40.2 
Difference 1.25 30.0 

Therefore, the thermal energy acquired by the water is

(30°C)(4180 J/kg · °C)(0.321 kg) = 40300 J

Thus the energy yield in joules per gram is 40300 J/1.25 g = 32.2 kJ/g.

The accepted value is 41.5 kJ/g.

If students use Sterno® (diethylene glycol) instead of paraffin, the value of the energy yield provided by the manufacturer is 22.4 kJ/g.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: Emphasize that measuring the thermal energy acquired by water is a standard way to measure the “heating” value of chemical fuels. Also emphasize that the thermal energy transferred to the environment by burning the chemical fuel came not from the fuel alone but from the system of the fuel molecules and oxygen molecules in the air, with which the fuel molecules reacted. This is true of the release of thermal energy from burning any fuel. Further examples are considered in Activity 14, “Problems Related to Energy ‘Sources.’”

Why the measured energy yield is less than the accepted value can be the basis of a good discussion of experimental procedures. Polling students as to why their measured energy yield was less than the accepted value should produce suggestions that include inaccuracy in measurement of fuel mass (before or after combustion), inaccuracy in measuring water volume, inaccuracy in measuring temperature (either before or after), and, most importantly, the fact that much of the energy from the flame was transferred out into the air and not directly to the water.

POSSIBLE EXTENSIONS: In addition to measuring and calculating the energy yield of solid petroleum-based fuels, this approach can be used to measure the energy yield of easily ignited foods, such as mini-marshmallows and nuts. Be fore-warned, though, that a burning nut emits a very offensive odor.

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

Energy is provided to most living organisms from the chemical reaction between food or fuel and oxygen in the air. Cars, buses, and planes receive their energy from the chemical reaction of oxygen in the air with fuels made from petroleum. Substances that bring about an energy transfer from a chemical reaction are called chemical fuels. How can the amount of energy transferred be measured?

__________

  • balance, able to measure to the nearest 0.1 g

  • candle (with corrugated cardboard for base) or Sterno® (in container)

  • 250-mL beaker

  • stand for beaker (at height of fuel flame)

  • water

  • 100-mL graduated cylinder

  • spirit thermometer (-10°C to 110°C)

  • matches (safety)

  • safety goggles

  • stirring rod

IMPORTANT SAFETY NOTE: Flammable materials such as books and extra clothing must be removed from the laboratory table on which chemical fuels are burned. Make sure that you are wearing safety goggles before you ignite the chemical fuel and that you continue to wear them until the flame is extinguished. While the fuel is burning, you must also tie long hair back and tuck in loose clothing so that it doesn’t make contact with the flame. Also, make sure that the chemical fuel is in a stable position and located near the center of the laboratory table so it is less likely to be knocked over. Never carry a chemical fuel that is aflame in your hand.

What makes petroleum-based fuels so convenient for transportation is that their energy yield (in joules per kilogram) is large and that they can be carried safely and easily on the vehicles that use them. To measure the energy yield of paraffin from a candle or of diethylene glycol from Sterno®, begin by answering the following questions:

When a chemical fuel is burned by reacting chemically with oxygen in the air and energy is transferred to its surroundings, what is the form of this energy?

Show answer Hide answer

__________

If you are given the equipment listed under “Materials” above, how could you measure the amount of energy transferred from burning a chemical fuel?

Show answer Hide answer

__________

What measurements would you need to make? Devise a plan to measure and calculate the number of joules transferred by burning a kg of a chemical fuel such as paraffin (in a candle) or diethylene glycol (in Sterno®).

Show answer Hide answer

__________

Create an organized data chart showing the data you measured as you measured the energy transferred from burning a measured mass of a chemical fuel.

Create a detailed, step-by-step data analysis sheet showing what you did to calculate the energy transferred from burning a measured mass of a chemical fuel.

Divide the energy transferred from burning the measured mass of a chemical fuel by the mass of the chemical fuel in order to calculate its energy yield.

PROCESS SKILLS: Measure, Observe, Compare, Test, Explain

OBJECTIVE: The objective of this activity is to measure the efficiency with which electrical energy is converted into light energy by a light bulb by using a light probe to measure the rate at which light energy is emitted by the bulb (light power) and dividing it by the rate at which electrical energy is supplied to the bulb (electric power). The electric power is specified (in watts) on the light bulb. The probe measures the intensity of the light (power per unit area), and this is multiplied by the area of a sphere whose radius is the distance from the light bulb to calculate the light power.

IDEA: The concept of efficiency is “what you get out” relative to “what you put in.” The efficiency of a conversion from one form of energy to another is the ratio of the amount of energy converted to the “new” form to the amount of energy converted from the “old” form. This could also be expressed as a ratio of power (rate at which energy is converted to the “new” form divided by rate at which it is converted from the “old” form). The efficiency of an energy conversion is often expressed as a percentage.

While, according to the First Law of Thermodynamics, energy can be converted from one form to another without changing the total amount of energy, the Second Law of Thermodynamics makes it likely that the conversion will not proceed with 100% efficiency to the desired “new” form. Most, if not all, of the electrical energy not converted to the desired final form is converted to thermal energy.

LEVEL: high school (10, 11, and 12)

DURATION: approximately 80 minutes (10 minutes setup, 30 minutes data gathering, 30 minutes data analysis, 10 minutes take down)

STUDENT BACKGROUND: Students must be able to measure with a meterstick and make measurements with a device that measures light intensity. Students also need to understand how the concept of intensity is related to energy and power.

ADVANCE PREPARATION: Assemble a meterstick, 40-W incandescent bulb in fixture, and a device that measures light intensity for each group of students. Acquaint students with the device that measures light intensity if they are not familiar with it.

MANAGEMENT TIPS: Elicit student responses to the Reflective Question before proceeding on to the activity.

Make sure that, unless they follow the zeroing procedure in the LabPro version, students point their light intensity measuring device directly toward the light bulb and away from any other light sources, such as daylight and other students’ bulbs.

RESPONSES TO SOME QUESTIONS: An oft-quoted efficiency for conversion from electrical energy to light energy in an incandescent bulb (Reflective Question) is 5%.

Some light probes measure light intensity in mW/cm2. The conversion to W/m2 is as follows:

mW/cm2 = 10-3W/(10-2m)2 =

10 W/m2. Multiply the number of

mW/cm2 by 10 to get the number of W/m2.

The following data and calculations were obtained with a TI-83+/LabPro system:

Distance from center of bulb (m) Light intensity (W/m2Light power (W) Efficiency of conversion 
0.4 4.5265 9.10 0.227 
0.5 4.4366 13.93 0.348 
0.6 2.7715 12.53 0.313 
0.7 2.2618 13.92 0.348 
0.8 1.7302 13.91 0.348 
0.9 1.3297 13.53 0.338 
1.0 1.0554 13.26 0.331 
Distance from center of bulb (m) Light intensity (W/m2Light power (W) Efficiency of conversion 
0.4 4.5265 9.10 0.227 
0.5 4.4366 13.93 0.348 
0.6 2.7715 12.53 0.313 
0.7 2.2618 13.92 0.348 
0.8 1.7302 13.91 0.348 
0.9 1.3297 13.53 0.338 
1.0 1.0554 13.26 0.331 

The following data and calculations were obtained with a TI-83/CBL system:

Distance from center of bulb (m) Light intensity (W/m2Light power (W) Efficiency of conversion 
0.4 4.6559 9.36 0.234 
0.5 3.4764 10.91 0.273 
0.6 2.1411 9.68 0.242 
0.7 1.874 11.53 0.288 
0.8 1.2175 9.79 0.245 
0.9 1.0061 10.24 0.256 
1.0 0.9727 12.22 0.305 
Distance from center of bulb (m) Light intensity (W/m2Light power (W) Efficiency of conversion 
0.4 4.6559 9.36 0.234 
0.5 3.4764 10.91 0.273 
0.6 2.1411 9.68 0.242 
0.7 1.874 11.53 0.288 
0.8 1.2175 9.79 0.245 
0.9 1.0061 10.24 0.256 
1.0 0.9727 12.22 0.305 

Note that the conversion efficiency is essentially independent of distance. It is greater than the 5% efficiency of conversion from electrical energy to visible light energy because the TI light probe is sensitive to wavelengths ranging from 300 nm to 1100 nm. Only 400-700 nm represent visible light; the range of 700-1100 nm represents a considerable amount of infrared radiation, which is felt as heat.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: That less than 100% of the energy used by the bulb is detected by the light probe is not a violation of the First Law of Thermodynamics principle that a system acquires or gives up energy only when work is done on it or it does work on something else, respectively. While the First Law of Thermodynamics guarantees that the amount of energy remains the same after it has been converted from one form to another, the effect of the Second Law of Thermodynamics is that when energy is converted from one form to another, some of it is converted into a less useful form, typically thermal energy.

POSSIBLE EXTENSIONS: Repeat the above procedure with an incandescent bulb of a different power rating or with a compact fluorescent bulb that fits a standard socket. What differences do you observe? (Note: A 100-W incandescent bulb is found to “overload” a TI light probe at distances closer than 0.50 m.)

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

The First Law of Thermodynamics tells us that energy can be converted from one form to another, without changing the total amount of energy. The Second Law of Thermodynamics tells us that after conversion the forms of energy may not be as useful as they were before the conversion took place. The incandescent light bulb is a good example of this, because only some of the energy it converts from electrical energy becomes visible light energy; the rest becomes thermal energy. What percentage of the electrical energy converted by an incandescent light bulb becomes visible light energy?

__________

  • meterstick

  • 40-W incandescent light bulb, fixture, and cord

  • light probe or other device to measure light intensity in W/m2

The amount of energy converted from electrical energy to visible light energy by an incandescent light bulb can be measured with a light probe or other device to measure light intensity, as follows:

Place a 40-W incandescent light bulb on a table and a meterstick with the “0” end at the center of the light bulb. Position the light probe 40 cm from the center of the bulb so that it points directly to the light bulb and away from any other light but with the light bulb off.

Turn on bulb. Measure and record the intensity of the light at a distance of 40 cm from the bulb in a table like the one below.

Reposition the light probe so that it is 50 cm from the center of the bulb. Measure and record the intensity of the light at this distance in a table like the one below.

Repeat step 3 for distances of 60 cm, 70 cm, 80 cm, 90 cm, and 100 cm.

Enter the light intensities (in watts per square meter) and the distances from the light probe to the center of the light bulb (in meters) in the following data table:

Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     
Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     

The light intensity you have measured is received in all directions from the bulb, passing through a sphere concentric with the bulb and having a radius equal to the distance from the bulb. To find the rate at which light energy is received from the bulb (in watts), multiply this intensity (in W/m2) by the area of the sphere (4πr2, where r is the distance from the center of the bulb in meters). This is the light power received from the bulb. Calculate its value for each distance from the bulb and enter it into the data table (this can be facilitated by using a spreadsheet).

To find the efficiency with which the light bulb converts electrical energy into visible light, divide the measured light power provided by the bulb by the electrical power supplied to it (40 W). (Again, this can be facilitated by using a spreadsheet.)

Question

How does the conversion efficiency depend on the distance from the light bulb to the probe?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

The First Law of Thermodynamics tells us that energy can be converted from one form to another, without changing the total amount of energy. The Second Law of Thermodynamics tells us that after conversion the forms of energy may not be as useful as they were before the conversion took place. The incandescent light bulb is a good example of this, because only some of the energy it converts from electrical energy becomes visible light energy; the rest becomes thermal energy. What percentage of the electrical energy converted by an incandescent light bulb becomes visible light energy?

__________

  • meterstick

  • 40-W incandescent light bulb, fixture, and cord

  • TI-83+ graphing calculator

  • Vernier LabPro unit

  • TI light probe

The amount of energy converted from electrical energy to visible light energy by an incandescent light bulb can be measured with a light probe interfaced with a computer with Logger Pro software connected to a TI-83+LabPro, using the DataMate application, as follows:

Connect the light probe to CH 1 of the LabPro unit.

Make sure that the link cord is connected between the TI-83+ calculator and the LabPro unit (link ports are on the bottom of each unit).

Turn on the calculator and connect the AC adapter for the LabPro unit to a wall outlet.

Press the <APPS> key on the calculator.

Use the arrow keys on the calculator to highlight the application called DataMate. Press <ENTER>, then press the <CLEAR> key to reset the program. At this point the LabPro automatically checks for and identifies the probes connected to it. The calculator monitors and displays readings from the probes.

Press <1.Setup>.

Move the cursor to “Mode” and press <ENTER>.

Press <3.Events With Entry>.

Place a 40-W incandescent light bulb on a table and a meterstick with the “0” end at the center of the light bulb. Position the light probe 40 cm from the center of the bulb so that it points directly to the light bulb and away from any other light but with the light bulb off.

Press <3.Zero>.

Press <1.Light>.

Press <ENTER> to zero sensor.

Turn on bulb. Press <2.Start>. You will then be asked to press <ENTER> to collect data. Press <ENTER> when the reading on the calculator screen is stable, in order to register the intensity of the light at a distance of 40 cm from the bulb.

The calculator will now prompt you to input a value. Input 0.40 <ENTER> to indicate that this reading corresponds to a bulb-to-probe distance of 0.40 m.

Reposition the light probe so that it is 50 cm from the center of the bulb. Press <ENTER> when the reading is stable, in order to register the intensity of the light at a distance of 50 cm from the bulb. When prompted to input a value, input 0.50 <ENTER> to indicate that this reading corresponds to a bulb-to-probe distance of 0.50 m.

Repeat step 15 for distances of 60 cm, 70 cm, 80 cm, 90 cm, and 100 cm, entering, respectively, values of 0.60, 0.70, 0.80, 0.90, and 1.00.

After your last measurement, press <STO->> to see a graph of the light intensities vs. distance from bulb to probe (the window for the x-axis will match the range of distance values you have input).

Press <6.Quit>. You will be told that the distances will be displayed in L1 and the light intensities in L2. This can be verified by pressing <ENTER> (to exit the DataMate application), then pressing <STAT> and selecting EDIT. The intensities are measured in units of milliwatts per square centimeter. How would you convert this to watts per square meter?

Show answer Hide answer

__________

Enter the light intensities (in watts per square meter) and the distances from the light probe to the center of the light bulb (in meters) in the following data table:

Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     
Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     

The light intensity you have measured is received in all directions from the bulb, passing through a sphere concentric with the bulb and having a radius equal to the distance from the bulb. To find the rate at which light energy is received from the bulb (in watts), multiply this intensity (in W/m2) by the area of the sphere (4πr2, where r is the distance from the center of the bulb in meters). This is the light power received from the bulb. Calculate its value for each distance from the bulb and enter it into the data table (this can be facilitated by using a spreadsheet).

To find the efficiency with which the light bulb converts electrical energy into visible light, divide the measured light power provided by the bulb by the electrical power supplied to it (40 W). (Again, this can be facilitated by using a spreadsheet.)

Question: How does the conversion efficiency depend on the distance from the light bulb to the probe?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

The First Law of Thermodynamics tells us that energy can be converted from one form to another, without changing the total amount of energy. The Second Law of Thermodynamics tells us that after conversion the forms of energy may not be as useful as they were before the conversion took place. The incandescent light bulb is a good example of this, because only some of the energy it converts from electrical energy becomes visible light energy; the rest becomes thermal energy. What percentage of the electrical energy converted by an incandescent light bulb becomes visible light energy?

__________

  • meterstick

  • 40-W incandescent light bulb, fixture, and cord

  • TI-83 graphing calculator

  • TI CBL unit

  • TI light probe

The amount of energy converted from electrical energy to visible light energy by an incandescent light bulb can be measured with a light probe interfaced with a TI-83/CBL system, using the PHYSICS program, as follows:

Connect the light probe to CH 1 of the CBL unit.

Connect the link cord between the TI-83 calculator and the CBL unit (link ports are on the bottom of each unit). Make sure that the link cord is firmly inserted into each unit (a twisting motion helps to ensure this).

Turn on the CBL unit and calculator.

Press the <PRGM> key on the calculator.

Use the arrow keys on the calculator to highlight the program called PHYSICS. Press <ENTER>. At this point the calculator screen should have “prgmPHYSICS” showing; press <ENTER> again.

When the program title screen appears, press <ENTER>, as prompted on the screen.

If it is not already highlighted, highlight 1:SET UP PROBES and press <ENTER>.

At the prompt, “ENTER NUMBER OF PROBES,” press <1> and <ENTER>.

Select <7.MORE PROBES>. (This can be done by pressing <7> or using the arrow keys to select <7.MORE PROBES> and pressing <ENTER>.) Then select <1.LIGHT>.

When prompted to select a channel, press <1> and <ENTER>.

You should now be back at the main menu screen. Select <2.COLLECT DATA>..

From the data collection menu choose <3.TRIGGER PROMPT>. The CBL/Calculator pair is now prepared to gather data.

Place a 40-W light bulb on a table and a meterstick with the “0” end at the center of the light bulb. Position the light probe 40 cm from the center of the bulb so that it points directly to the light bulb and away from any other light. Eliminate all other ambient light in the laboratory.

Turn on bulb. Monitor the CBL and press <TRIGGER> on the CBL unit when the reading is stable. The calculator will now prompt you to input a value. Input 0.40 <ENTER> to indicate that this reading corresponds to a bulb-to-probe distance of 0.40 m.

Reposition the light probe so that it is 50 cm from the center of the bulb. From the data collection menu choose <1.MORE DATA>. Monitor the CBL and press <TRIGGER> on the CBL unit when the reading is stable. The calculator will now prompt you to input a value. Input 0.50 <ENTER> to indicate that this reading corresponds to a bulb-to-probe distance of 0.50 m.

Repeat step 15 for distances of 60 cm, 70 cm, 80 cm, 90 cm, and 100 cm, entering, respectively, values of 0.60, 0.70, 0.80, 0.90, and 1.00.

After your last measurement choose <2.STOP AND GRAPH> from the data collection menu. The calculator will display a graph of light intensity (in L2) vs. distance (in L1).

After you have finished viewing your graph, press <ENTER> and respond to the prompt “REPEAT?” If you wish to collect more data, input <2.YES>; otherwise <NO>, and <7.QUIT> from the main menu.

The intensities in L2 are measured in units of milliwatts per square centimeter. How would you convert this to watts per square meter?

Show answer Hide answer

__________

Enter the light intensities (in watts per square meter) and the distances from the light probe to the center of the light bulb (in meters) in the following data table:

Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     
Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     

The light intensity you have measured is received in all directions from the bulb, passing through a sphere concentric with the bulb and having a radius equal to the distance from the bulb. To find the rate at which light energy is received from the bulb (in watts), multiply this intensity (in W/m2) by the area of the sphere (4πr2, where r is the distance from the center of the bulb in meters). This is the light power received from the bulb. Calculate its value for each distance from the bulb and enter it into the data table (this can be facilitated by using a spreadsheet).

To find the efficiency with which the light bulb converts electrical energy into visible light, divide the light power provided by the bulb by the electrical power supplied to it (40 W). (Again, this can be facilitated by using a spreadsheet.)

Question: How does the conversion efficiency depend on the distance from the light bulb to the probe?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

The First Law of Thermodynamics tells us that energy can be converted from one form to another, without changing the total amount of energy. The Second Law of Thermodynamics tells us that after conversion the forms of energy may not be as useful as they were before the conversion took place. The incandescent light bulb is a good example of this, because only some of the energy it converts from electrical energy becomes visible light energy; the rest becomes thermal energy. What percentage of the electrical energy converted by an incandescent light bulb becomes visible light energy?

__________

  • meterstick

  • 40-W incandescent light bulb, fixture, and cord

  • computer

  • Logger Lite version 1.2 or later

  • TI light probe

  • Go! Link

The amount of energy converted from electrical energy to visible light energy by an incandescent light bulb can be measured with a light probe interfaced with a computer and running on the software program Logger Lite.

Connect the light probe to the Go! Link, and the Go! Link to the computer.

Launch Logger Lite.

Choose Data Collection from the Experiment menu.

Change the Mode to Events with Entry.

Locate the Column Name field, and enter “Distance.”

Locate the Short Name field, and enter “D.”

Locate the Units field, and enter “m.”

Click “Done” to close the dialog box.

Place a 40-W incandescent light bulb on a table and a meterstick with the “0” end at the center of the light bulb. Position the light probe 40 cm from the center of the bulb so that it points directly to the light bulb and away from any other light but with the light bulb off.

Choose Zero from the Experiment menu to zero the light sensor.

Turn on bulb. Click “Collect.” Click “Keep” when the reading on the calculator screen is stable, in order to register the intensity of the light at a distance of 40 cm from the bulb.

Logger Lite will now prompt you to enter a value for the distance. Enter “0.40” and click “OK” to indicate that this reading corresponds to a bulb-to-probe distance of 0.40 m.

Reposition the light probe so that it is 50 cm from the center of the bulb. Click “Keep” when the reading is stable, in order to register the intensity of the light at a distance of 50 cm from the bulb. Logger Lite will again prompt for a distance value. Enter “0.50” and click “OK” to indicate that this reading corresponds to a bulb-to-probe distance of 0.50 m.

Repeat step 13 for distances of 60 cm, 70 cm, 80 cm, 90 cm, and 100 cm, entering, respectively, values of 0.60, 0.70, 0.80, 0.90, and 1.00 for the distance in meters.

After your last measurement click “Stop” to see a graph of the light intensity vs. distance from bulb to probe. You may want to rescale the graph by choosing Autoscale → Autoscale from 0 from the Analyze menu.

Inspect your data table. The TI light sensor reads irradiance approximately in mW/cm2. How would you convert this to watts per square meter?

Show answer Hide answer

__________

Enter the light intensities (in watts per square meter) and the distances from the light probe to the center of the light bulb (in meters) in the following data table:

Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     
Distance from center of bulb (m) Light intensity (W/m2Area of sphere (m2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     

The light intensity you have measured is received in all directions from the bulb, passing through a sphere concentric with the bulb and having a radius equal to the distance from the bulb. To find the rate at which light energy is received from the bulb (in watts), multiply this intensity (in W/m2) by the area of the sphere (4πr2, where r is the distance from the center of the bulb in meters). This is the light power received from the bulb. Calculate its value for each distance from the bulb and enter it into the data table (this can be facilitated by using a spreadsheet).

To find the efficiency with which the light bulb converts electrical energy into visible light, divide the measured light power provided by the bulb by the electrical power supplied to it (40 W). (Again, this can be facilitated by using a spreadsheet.)

Question: How does the conversion efficiency depend on the distance from the light bulb to the probe?

Show answer Hide answer

__________

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

The First Law of Thermodynamics tells us that energy can be converted from one form to another, without changing the total amount of energy. The Second Law of Thermodynamics tells us that after conversion the forms of energy may not be as useful as they were before the conversion took place. The incandescent light bulb is a good example of this, because only some of the energy it converts from electrical energy becomes visible light energy; the rest becomes thermal energy. What percentage of the electrical energy converted by an incandescent light bulb becomes visible light energy?

__________

  • meterstick

  • 40-W incandescent light bulb, fixture, and cord

  • computer

  • Logger Pro software

  • Vernier LabPro unit

  • TI light probe (if this is connected to a Vernier Go! Link unit, a LabPro unit is not required)

The amount of energy converted from electrical energy to visible light energy by an incandescent light bulb can be measured with a light probe interfaced with a computer with Logger Pro software connected to a Vernier LabPro system, or connected to a Vernier Go! Link unit, as follows:

Connect the light probe to CH 1 of the LabPro unit, and connect the AC adapter for the LabPro unit to a wall outlet. If you are using a Vernier Go! Link unit, use it to connect the light probe directly to the computer.

Open Vernier Logger Pro on the computer. Logger Pro should automatically recognize that the light probe has been connected.

Click on the icon with the graph and stopwatch (Data Collection), and select “Events with Entry.” In the Name field enter “distance.” For Short Name enter “d,” and for Units enter “cm.” Then click “Done.”

Place a 40-W incandescent light bulb on a table and a meterstick with the “0” end at the center of the light bulb. Position the light probe 40 cm from the center of the bulb so that it points directly to the light bulb and away from any other light.

You are now ready to collect data. With the light bulb on, click “Collect.” With the light probe 40 cm from the center of the bulb, click “Keep,” and enter “40” to represent the distance (40 cm) at which the measurement is made. This will register the first point in a graph of light intensity (in mW/cm2) vs. distance.

Now reposition the light probe so that it is 50 cm from the center of the bulb. Click “Keep,” in order to register the intensity of the light at a distance of 50 cm from the bulb, and enter “50” to represent the distance (50 cm) at which this measurement is made. This will register the second point in a graph of light intensity vs. distance.

Repeat step 6 for distances of 60 cm, 70 cm, 80 cm, 90 cm, and 100 cm, entering, respectively, values of “60, 70, 80, 90 and 100” to represent these distances in centimeters.

After your last measurement, you will need to add a “New Calculated Column” from the Data menu three times. The first is to calculate the area of a sphere whose radius is the distance from the light bulb to the light probe, defined by 4 times pi (selected from the parameters in Logger Pro) times the square of the distance.

The second “New Calculated Column” is to calculate the “light power,” found by multiplying the light intensity by the area of the sphere. If the light intensity is in units of mW/cm2, and the area of the sphere is in cm2, what would be the units of the “light power”? What would you need to do to convert them to watts?

Show answer Hide answer

__________

The third “New Calculated Column” is to calculate the “efficiency of conversion,” found by dividing the “light power” (converted to watts) by the 40-W electrical power supplied to the bulb. When all the additional columns are added, you should have a spreadsheet looking like the following:

Distance from center of bulb (cm) Light intensity (mW/cm2Area of sphere (cm2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     
Distance from center of bulb (cm) Light intensity (mW/cm2Area of sphere (cm2Light power (W) Efficiency of conversion 
0.40     
0.50     
0.60     
0.70     
0.80     
0.90     
1.00     

Question: How does the conversion efficiency depend on the distance from the light bulb to the probe?

Show answer Hide answer

__________

PROCESS SKILLS: Identifying conversions of energy from one form to another

OBJECTIVE: The objective of this activity is to enhance student awareness of the various forms of energy and the devices that convert energy from one form to another, within what is hoped will be an enjoyable game format.

IDEA: The First Law of Thermodynamics speaks about the conservation of energy as it is transformed from one form to another. The idea here is to provide what is intended to be an enjoyable game format for students to increase their awareness of the various forms of energy and the devices or processes that transform energy from one form to another.

“Energy Bingo” can be used for a test review at the middle school level and as an introduction to forms of energy and their conversions at the high school level. Discussion can be generated if there is disagreement on the placement of the name of a particular energy conversion device on a bingo card.

The “Energy in an Electric Circuit” game reinforces the direction of electron flow and the conversion of electrical energy to thermal energy and light at the bulb while electrons continue to flow around the circuit.

LEVEL: middle level (7, 8, 9)

DURATION: approximately 40 minutes per game

STUDENT BACKGROUND: Students need to be able to follow directions. Experience in identifying forms of energy and processes or devices that transform energy from one form to another is an asset.

ADVANCE PREPARATION: Prepare needed copies of energy conversion dominoes (ideally backed onto card stock), Energy Transformation Bingo cards, Energy in an Electric Circuit game board, cutout squares of colored poster paper, and hex nuts.

MANAGEMENT TIPS: Emphasize the need to read and follow instructions. Keep sets of energy conversion dominoes rubber banded together.

Lockable plastic bags are a good way to store sets of cutout squares of colored poster paper and hex nuts for the “Energy in an Electric Circuit” game.

RESPONSES TO SOME QUESTIONS: The energy conversion dominoes give suggestions of processes and devices that convert energy among various forms.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: The primary outcome of this activity should be an enhanced student awareness of the many forms of energy and their transformations that play an important part in our everyday lives.

POSSIBLE EXTENSIONS: An extension of “Energy Dominoes” is to have students write a paragraph to describe the system listed on a tile and its conversion of energy from one form to another. Students can also be encouraged to make up more tiles based on energy conversions in their everyday lives.

Students can practice drawing energy flow diagrams, such as those presented in Art Hobson’s Physics: Concepts and Connections (2nd ed.) (Prentice Hall, Upper Saddle River, NJ, 1999), pp. 151, 152, 177; these have also been published in Art Hobson, “Energy Flow Diagrams for Teaching Physics Concepts,” Phys. Teach.42, 113–117 (Feb. 2004).

Qualitative insight into energy transformations can also be obtained from a scheme of bar graphs described by Alan Van Heuvelen and Xueli Zou, “Multiple Representations of Work-Energy Processes,” Am. J. Phys. 69(2), 184–194 (Feb. 2001), reproduced in Appendix G of of this resource book. These authors point out the distinction between work done by external forces and changes in potential and internal (thermal) energy—only if the system under consideration is chosen to include the Earth, a spring, or both surfaces rubbing against each other are the latter appropriate.

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

One of the things that makes energy an important quantity in our lives is the many forms it can take. How many forms can you think of?

__________

  • Energy conversion dominoes

  • Energy bingo cards

  • “Energy in an Electric Circuit” game board, plus four 1/4” square cutout pieces of colored poster paper per player and hex nuts

One form of energy in our lives is energy of motion. This is known as kinetic energy. The motion can be of different things. If the motion is of a large object, the kinetic energy is said to be mechanical. If the moving objects are electrically charged, they are said to form an electric current. If the moving objects are individual molecules, there are two possibilities. If their motion is organized into waves, their kinetic energy is associated with sound. If their motion is completely disorganized, their kinetic energy is associated with what we call heat (scientists call it “thermal energy” or “internal energy”). Another form of kinetic energy is light (and other forms of electromagnetic radiation, like radio waves and microwaves).

Other forms of energy do not have the form of motion, but they can cause motion at a later time. Water at the top of a dam can spill over the dam. A battery can produce an electric current when it is connected into a circuit. Fuels can be burned to produce thermal energy. Water at the top of a dam, batteries, and fuels are all examples of potential energy.

Energy in one form, kinetic or potential, can be converted into any other form. The purpose of this activity is to give you experience in identifying energy conversions in your life and the devices that bring about these conversions. One way to see how many of these devices you can name is to fill in the energy conversion chart below. If you are not familiar with a lot of energy conversion devices, you might want to learn more about them by playing Energy Conversion Dominoes, described below. A good final check of your understanding of energy conversions and the devices that bring them about is to play “Energy Transformations Bingo.” You can also simulate the behavior of electrons in an electric circuit and their role in energy transfer in a game format with “Energy in an Electric Circuit.”

Energy Conversion Chart: Energy exists in many forms in our everyday lives, among them mechanical (energy of motion of large objects), electrical, chemical, thermal, sound, and light. Energy in any of these forms can be converted to energy in any other form. In the chart below, write the name of a device that converts energy from each form to another. Do this for as many cases as you can.

TO / FROM Mechanical Electrical Chemical Thermal Sound Light 
Mechanical       
Electrical       
Chemical       
Thermal       
Sound       
Light       
TO / FROM Mechanical Electrical Chemical Thermal Sound Light 
Mechanical       
Electrical       
Chemical       
Thermal       
Sound       
Light       

Energy Conversion Dominoes: Cut out the 24 energy conversion dominoes on the handout. Place them face down on a table. Distribute 12 of the dominoes equally among the players. That is, if there are two players, each draws six dominoes, three players will each draw four, four players will each draw three, and five or six players will each draw two. (The game is not suitable for a larger number of players.)

In “regular” dominoes, the highest “double” is played first. The energy conversion dominoes corresponding to “doubles” are those that convert a form of energy to the same form:

  • the refinery (converting one form of chemical fuel to another chemical fuel)

  • the transformer (converting electrical energy to another form of electrical energy)

  • the drive shaft (converting one form of motion to another form of motion).

Whoever has the “double” beginning with the earliest letter of the alphabet (in the order “chemical,” “electrical,” and “motion”) plays it first, and play continues counterclockwise from that point. Succeeding players complete their turn as follows: if they have a domino in their hand that can connect to exposed ends of dominoes on the board (e.g., the internal combustion engine, which uses chemical fuel, connected to the chemical fuel output of the refinery), they may play one domino from their hand per turn. If they cannot properly play a domino from their hand, they must draw from the still overturned dominoes (historically called the “graveyard”) until they draw a domino that can be properly played. The first player to play all his/her dominoes wins.

Note that proper play of the energy conversion dominoes requires not only matching the same forms of energy but matching them in the same direction. That is, the energy output from one domino must match the energy input to the domino adjacent to it. (This is not a requirement of “regular” dominoes!) An actual device corresponding to the sequences of dominoes, which is characterized by a sequence of energy conversions, is known as a “Rube Goldberg” device. You may have seen devices like this on sale at gift shops, particularly at airports.

Energy Transformations Bingo: In playing Energy Transformations Bingo, each player receives a card looking much like the energy conversion chart above, but with only five columns and five rows, like an ordinary bingo card. Each column is headed by one of five different forms of energy, and the rows are labeled by the same five forms. Squares along the diagonal, corresponding to transformation energy into the same form, are “FREE.” Like the caller in a bingo game, someone calls out a sequence of devices or processes that transform energy. If the device or process transforms energy from a form listed in a vertical column to a form listed in a horizontal row of your card, write the name of that process or device in the appropriate square of your card. The first player to complete five squares across or five down is the winner and should call out “bingo!” No award is given for diagonals or for four corner squares.

Energy Transformations Bingo was presented by Jim Nelson at the Summer 2002 AAPT Meeting, Boise, ID, paper DE02 (AAPT Announcer, 32(2), 105 (Summer 2002)).

Energy in an Electric Circuit: Batteries provide electric potential energy to electrons. In turn the electrons flow through wires to transfer this energy to elements connected to these wires in an electric circuit. If the circuit element is a filament in a light bulb, the electric potential energy is converted to thermal energy and light. If the circuit element is a motor, the electric potential energy is converted to kinetic energy.

To simulate how electrons pass through a circuit to provide energy to light a light bulb, play the following game for two to four players, according to these rules (see sample game board on page 139):

  1. Each player begins with four electron tokens in the battery of the game board. (These can be cut-out squares of colored poster paper, with a different color for the tokens of each player.)

  2. Each player takes a turn, in a predetermined order, by throwing three dice.

  3. The number on each die enables a player to do the following:

    • Each “6” allows a player to place an energy token atop an electron token in the battery. (Hex nuts make suitable energy tokens.)

    • Each number on a die allows a player to move an energized electron token that number of spaces from the negative terminal of the battery into the wire or along the wire, subject to the following restrictions:

      1. In order for an electron to energize the light bulb, the number on a die must exactly match the number of spaces to land exactly on the light bulb space. When this happens, the energy token is removed from the electron token and placed in front of the player.

      2. An electron token can move into the positive side of the battery only if the number on a die exactly matches the number of spaces to the battery. Electron tokens returning to the positive side of the battery are placed in one of the spaces of the battery to await reenergizing by throwing a “6.”

      3. Except for spaces in the battery at the beginning of the game and the light bulb, only one electron token may occupy a space.

      4. If a token may not be moved the number of spaces shown on a die, the movement allowed by that die is forfeited.

  4. The game can end at any time. When the end of the game is called, the winner is the player with the largest number of energy tokens.

Instructions to Bingo Caller: Copy this sheet and cut out the individual squares. Place the cut-out squares in a container from which they can be randomly drawn to be called. After the name of an energytransforming device or method is called, place the square with the name of that device or method in its matching place in the grid on this sheet, so that it can be easily checked when a player calls out “Bingo!”

 Chemical Electrical Gravitational Potential Internal “Heat” Kinetic Light “Radiation” Nuclear Sound Spring Potential 
Chemical FREE Electrolysis  Endothermic reaction  Photosynthesis Ionizing radiation   
Electrical Battery FREE Hydroelectric plant Gas turbine Electrical generator Solar cell Nuclear power plant Microphone  
Gravitational Potential R°Cket Electric powered r°Cket FREE R°Cket Throw a ball up     
Internal “Heat” Battery-operated heater Toaster Watermelon falls, hits ground FREE Bullet hits wall Microwave oven    
Kinetic Internal combustion engine Electric motor Downward free fall Steam engine FREE Radiometer Nuclear submarine Vibrating eardrum Wind-up toy car 
Light “Radiation” Firefly Light bulb  Glowing object  FREE Cerenkov radiation   
Nuclear       FREE   
Sound Firecracker Speaker Watermelon falls, hits ground  Tuning fork Radio  FREE  
Spring Potential     Car hits spring bumper    FREE 
 Chemical Electrical Gravitational Potential Internal “Heat” Kinetic Light “Radiation” Nuclear Sound Spring Potential 
Chemical FREE Electrolysis  Endothermic reaction  Photosynthesis Ionizing radiation   
Electrical Battery FREE Hydroelectric plant Gas turbine Electrical generator Solar cell Nuclear power plant Microphone  
Gravitational Potential R°Cket Electric powered r°Cket FREE R°Cket Throw a ball up     
Internal “Heat” Battery-operated heater Toaster Watermelon falls, hits ground FREE Bullet hits wall Microwave oven    
Kinetic Internal combustion engine Electric motor Downward free fall Steam engine FREE Radiometer Nuclear submarine Vibrating eardrum Wind-up toy car 
Light “Radiation” Firefly Light bulb  Glowing object  FREE Cerenkov radiation   
Nuclear       FREE   
Sound Firecracker Speaker Watermelon falls, hits ground  Tuning fork Radio  FREE  
Spring Potential     Car hits spring bumper    FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #1 Chemical Electrical Gravitational Potential Internal “Heat” Nuclear 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Nuclear     FREE 
Energy Bingo Card #1 Chemical Electrical Gravitational Potential Internal “Heat” Nuclear 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Nuclear     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #2 Electrical Gravitational Potential Internal “Heat” Kinetic Light “Radiation” 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
LIght “Radiation”     FREE 
Energy Bingo Card #2 Electrical Gravitational Potential Internal “Heat” Kinetic Light “Radiation” 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
LIght “Radiation”     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #3 Gravitational Potential Internal “Heat” Kinetic Chemical Sound 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Sound     FREE 
Energy Bingo Card #3 Gravitational Potential Internal “Heat” Kinetic Chemical Sound 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Sound     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #4 Internal “Heat” Kinetic Chemical Electrical Spring Potential 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Spring Potential     FREE 
Energy Bingo Card #4 Internal “Heat” Kinetic Chemical Electrical Spring Potential 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Spring Potential     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #5 Chemical Electrical Gravitational Potential Internal “Heat” Sound 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Sound     FREE 
Energy Bingo Card #5 Chemical Electrical Gravitational Potential Internal “Heat” Sound 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Sound     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #6 Electrical Gravitational Potential Internal “Heat” Kinetic Nuclear 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
Nuclear     FREE 
Energy Bingo Card #6 Electrical Gravitational Potential Internal “Heat” Kinetic Nuclear 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
Nuclear     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #7 Gravitational Potential Internal “Heat” Kinetic Chemical Spring Potential 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Spring Potential     FREE 
Energy Bingo Card #7 Gravitational Potential Internal “Heat” Kinetic Chemical Spring Potential 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Spring Potential     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #8 Internal “Heat” Kinetic Chemical Electrical Light “Radiation” 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Light “Radiation”     FREE 
Energy Bingo Card #8 Internal “Heat” Kinetic Chemical Electrical Light “Radiation” 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Light “Radiation”     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #9 Chemical Electrical Gravitational Potential Internal “Heat” Spring Potential 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Spring Potential     FREE 
Energy Bingo Card #9 Chemical Electrical Gravitational Potential Internal “Heat” Spring Potential 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Spring Potential     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #10 Electrical Gravitational Potential Internal “Heat” Kinetic Sound 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
Sound     FREE 
Energy Bingo Card #10 Electrical Gravitational Potential Internal “Heat” Kinetic Sound 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
Sound     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #11 Gravitational Potential Internal “Heat” Kinetic Chemical Light “Radiation” 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Light “Radiation”     FREE 
Energy Bingo Card #11 Gravitational Potential Internal “Heat” Kinetic Chemical Light “Radiation” 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Light “Radiation”     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #12 Internal “Heat” Kinetic Chemical Electrical Nuclear 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Nuclear     FREE 
Energy Bingo Card #12 Internal “Heat” Kinetic Chemical Electrical Nuclear 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Nuclear     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #13 Chemical Electrical Gravitational Potential Internal “Heat” Light “Radiation” 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Light “Radiation”     FREE 
Energy Bingo Card #13 Chemical Electrical Gravitational Potential Internal “Heat” Light “Radiation” 
Chemical FREE     
Electrical  FREE    
Gravitational Potential   FREE   
Internal “Heat”    FREE  
Light “Radiation”     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #14 Electrical Gravitational Potential Internal “Heat” Kinetic Spring Potential 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
Spring Potential     FREE 
Energy Bingo Card #14 Electrical Gravitational Potential Internal “Heat” Kinetic Spring Potential 
Electrical FREE     
Gravitational Potential  FREE    
Internal “Heat”   FREE   
Kinetic    FREE  
Spring Potential     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #15 Gravitational Potential Internal “Heat" Kinetic Chemical Nuclear 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Nuclear     FREE 
Energy Bingo Card #15 Gravitational Potential Internal “Heat" Kinetic Chemical Nuclear 
Gravitational Potential FREE     
Internal “Heat”  FREE    
Kinetic   FREE   
Chemical    FREE  
Nuclear     FREE 

On the Energy Transformations Bingo card below, fill in boxes with the name of devices or processes that convert from a form of energy listed in a vertical column to a form of energy listed in a horizontal row. The first person to complete five squares across or five squares down is the winner. No credit is given for diagonals or for four corner squares.

Energy Bingo Card #16 Internal “Heat” Kinetic Chemical Electrical Sound 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Sound     FREE 
Energy Bingo Card #16 Internal “Heat” Kinetic Chemical Electrical Sound 
Internal “Heat” FREE     
Kinetic  FREE    
Chemical   FREE   
Electrical    FREE  
Sound     FREE 

PROCESS SKILLS: Observe, Calculate, Test

OBJECTIVE: The objective of this activity is to demonstrate the fundamental role played by energy in nuclear and atomic systems, where quantum mechanical considerations must be used.

IDEA: When it comes to describing the behavior of electrons in atoms or of neutrons and protons in a nucleus, quantum mechanics must be used, and here energy has a primary role: the purpose of Schrödinger’s equation in quantum mechanics is to calculate the possible energy levels of atomic and nuclear systems due to excitation of one or more of their individual particles. This activity focuses on energy levels in atoms, and most particularly on the simplest atom of all: an atom of hydrogen. Although these energy levels were first determined in 1913 by Niels Bohr in a special theory that turned out to apply to only hydrogen atoms, the Schrödinger equation in quantum mechanics calculates the same values and is the basis for calculating energy levels for all other atoms as well.

LEVEL: high school (10, 11, and 12)

DURATION: approximately 40 minutes (20 minutes to observe spectra, 20 minutes to perform calculations).

STUDENT BACKGROUND: Students need to be able to perform calculations with scientific notation.

ADVANCE PREPARATION: Cut strips of red paper or cardboard 1.20 cm long, strips of bluegreen paper or cardboard 1.65 cm long, and strips of violet paper or cardboard 1.85 cm long. Make copies of student handouts.

MANAGEMENT TIPS: Elicit student response to the Reflective Question before proceeding on to the activity.

Sets of the three colored paper or cardboard strips can be conveniently organized into lockable sandwich bags for both storage and distribution to students. Make sure to warn students about the safety precautions that must be taken with high-voltage power supplies—they should not touch anything in the apparatus used to excite the atoms in the hydrogen gas tube.

Spectroscopes or spectrometers, which employ diffraction gratings, can be used instead of the simpler gratings if they are available, but students will need to be instructed on how to use them.

RESPONSES TO SOME QUESTIONS: If students are not familiar with the quantum theory, their responses to the Reflective Question can vary considerably. The point of question 2 in this activity is to teach students that, according to the quantum theory,

  • atomic and nuclear systems can exist in only certain energy levels and

  • light (or other electromagnetic radiation) is absorbed or emitted in quanta called photons.

The energy of these photons is given by the product of Planck’s constant h (6.626 × 10-34 J.s) and frequency f. A photon of energy E = hf can be emitted or absorbed by an atom or nucleus when there are two energy levels in the atom or nucleus differing by the amount of energy in the quantum.

The energies of the first five electron energy levels in Bohr’s theory of the hydrogen atom and the photon energies for the three visible lines of the hydrogen spectrum, their frequencies, and their wavelengths are calculated as follows:

level number Energy (eV) Energy (J)   
-13.60 -2.176E-18   
-3.40 -5.440E-19   
-1.51 -2.418E-19   
-0.85 -1.360E-19   
-0.54 -8.704E-20   
     
initial level final level Photon energy (J) Frequency (Hz) Wavelength (nm) 
4.570E-19 6.896E+14 434.7 
4.080E-19 6.158E+14 486.9 
3.022E-19 4.561E+14 657.3 
level number Energy (eV) Energy (J)   
-13.60 -2.176E-18   
-3.40 -5.440E-19   
-1.51 -2.418E-19   
-0.85 -1.360E-19   
-0.54 -8.704E-20   
     
initial level final level Photon energy (J) Frequency (Hz) Wavelength (nm) 
4.570E-19 6.896E+14 434.7 
4.080E-19 6.158E+14 486.9 
3.022E-19 4.561E+14 657.3 

Thus the red strip of paper fits between levels E3 and E2, the blue-green strip between E4 and E2, and the violet strip between E5 and E2. Transitions between higher energy levels and E1 correspond to higher energies and frequencies than those of visible light. These transitions are marked by the emission and absorption of ultraviolet radiation. Transitions between levels above E2 correspond to lower energies and frequencies than visible light; they are marked by the emission and absorption of infrared radiation.

POINTS TO EMPHASIZE IN SUMMARY DISCUSSION: After students have become comfortable with the notion of energy levels as a way to describe atoms might be a good opportunity to mention that similar considerations also apply to nuclei of atoms. However, in contrast to the electron volt (eV) unit of energy used to describe energy levels in atoms, the unit used to describe excited energy levels of nuclei is a million times as large—the megaelectron volt (MeV). When an excited nucleus makes a transition to the lowest energy level (otherwise known as the ground state), the photon given off is a gamma ray. Because the energies of excited nuclei are typically millions of times as great as the energies of excited atoms, the energy of a gamma ray is typically millions of times as great as that of a photon of visible light. This reflects the fact that particles are bound in nuclei by the strong nuclear force, which is much stronger than the electromagnetic force binding electrons in atoms. The energy of gamma rays is too great for them to be used in laboratory experiments without proper shielding. Gamma rays are used in radiation therapy to treat some forms of cancer, but indis-criminate exposure to them can cause cancer.

POSSIBLE EXTENSIONS: Students can be invited to view the visible spectra of such other elements as helium, neon, mercury, and sodium. However, the energy level diagrams for these atoms are more complicated than that for the hydrogen atom. Furthermore, because of “selection rules” that restrict changes in angular momentum between the initial and final states of a transition, not every possible transition will appear as an actual line in the spectrum.

You can also show students energy level diagrams for specific nuclei and determine possible energies of gamma rays that can be emitted from these nuclei in their excited states. Here, too, “selection rules” that restrict changes in angular momentum between the initial and final states of a transition are at work.

Name(s): __________ Date: __________ Period: __________

Reflective Question: Write a response in your journal to the question in the box below. Discuss your response with others in your group. Can you arrive at a consensus in your discussion? Be prepared to report to your class the result of your group’s discussion.

The only way we can directly observe the behavior of atoms is by the spectrum of light and other forms of electromagnetic radiation they emit or absorb. What determines the spectrum of light and other forms of electromagnetic radiation emitted by the atom of a given element? Why, for example, do hydrogen atoms give off different colors of light than helium atoms do?

__________

  • hydrogen gas spectrum tube

  • high-voltage power supply designed to light spectrum tubes

  • diffraction gratings

  • red paper or cardboard strips 1.20 cm long; blue-green strips 1.65 cm long; violet strips 1.85 cm long

One way to observe the spectrum of light and other forms of electromagnetic radiation emitted by atoms of a given element is to observe the spectrum of light given off when those atoms are excited by a high-voltage electric power supply, an effect that occurs to produce the familiar red color of neon signs.

In this activity you will look at a “hydrogen sign”—a tube of hydrogen gas connected to a high-voltage power supply. When this power supply is turned on, electrons in some hydrogen atoms are excited to higher energy levels, because these electrons absorb energy from the collisions with electrons from the power supply. When the electrons return to lower energy levels, they give off light. Look at this light through a device called a diffraction grating, which enables you to see all the colors that comprise the spectrum of the light. What colors do you see in the spectrum of light given off by hydrogen gas?

Show answer Hide answer

__________

When you observed the spectrum of light given off by hydrogen gas, you should have seen a violet line, a blue-green line, and a red line. In 1913 Niels Bohr found that he could explain this spectrum by hypothesizing that the electron in the hydrogen atom is allowed to have only certain amounts of energy, and calculating these amounts of energy became the centerpiece of Schrödinger’s equation in quantum mechanics a little more than a decade later. An electron in a higher energy level gives off light when it goes to a lower energy level, and the amount of energy in the light is the difference in these energy levels. The color of light is determined by its frequency; and the greater the energy in the light, the greater the frequency.

The energy of the red light in the hydrogen spectrum is represented by a strip of red paper or cardboard 1.20 cm long. The energy of the blue-green light in the hydrogen spectrum is represented by a strip of blue-green paper or cardboard 1.65 cm long, and the energy of the violet light in the hydrogen spectrum is represented by a strip of violet paper or cardboard 1.85 cm long. Find out where the strips of colored paper or cardboard representing these three colors of light fit vertically between horizontal lines representing two energy levels in the diagram of electron energy levels in Bohr’s theory of the hydrogen atom below.

a.

Between which higher and lower energy level does the red strip fit? This transition between these energy levels causes hydrogen atoms to give off red light.

Show answer Hide answer

__________

b.

Between which higher and lower energy levels do the blue-green and violet strips fit?

Show answer Hide answer

__________

c.

What kind of pattern do you see in the transitions corresponding to the lines of visible light in the hydrogen spectrum?

Show answer Hide answer

__________

E5 __________

E4 __________

E3 __________

E2 __________

E1 __________

According to the quantum theory, light and—indeed—all forms of electromagnetic radiation are described in terms of quanta, and the frequency and energy of the quanta are related by Planck’s constant h (6.626 × 10-34 J.s). In the above exercise, a one-centimeter height on the energy diagram represented the energy of 1.545 electron volts (an electron volt is the amount of energy a one-volt battery gives to each electron.) Since the electric charge on an electron is 1.6 × 10-19 coulombs, an electron volt equals 1 volt × 1.6 × 10-19 coulombs = 1.6 × 10-19 joules. Calculate the values for energy levels in a hydrogen atom (in joules) by measuring the vertical distance from the top line to each energy level in centimeters, then multiplying by the scale factor of 1.545. (Keep only two decimal places in your result.) (Note that referring to the energy levels as “below the line” means that their values (relative to the “line”) are regarded to be negative; this also signifies that the electrons in these energy levels are bound to the nucleus of the atom rather than free to roam about.)

Show answer Hide answer

__________

From your knowledge of the energy level transitions that lead to each of the visible lines of the hydrogen spectrum (in question 2), what is the energy of the light quanta (also called “photons”) emitted by excited hydrogen atoms?

Show answer Hide answer

__________

Using the equation E = hf, which relates the energy of a photon to its frequency via Planck’s constant (h = 6.626 × 10-34 J.s), calculate the frequency of the visible lines of the hydrogen spectrum.

Show answer Hide answer

__________

Calculate the wavelength corresponding to each of these frequencies. (The speed of light, c, is 2.998 × 108 m/s. λ = c /f.) How do your values compare with the measured values of these frequencies: 434.2 nm (violet), 486.3 nm (blue-green), 656.5 nm (red)?

Show answer Hide answer

__________

Following the procedures in questions 4–6, calculate the energy, frequency, and wavelength for photons of the three smallest energies that result when electrons drop to energy level E1.”

Show answer Hide answer

__________

Why don’t you see the photons described in question 7?

Show answer Hide answer

__________

The activity in step 2 was presented by Jill Marshall of Utah State University at the Summer 1998 AAPT Meeting, Lincoln, NE, paper CF1 (AAPT Announcer, 28(2), 92 (July 1998)). Jay Pasachoff has achieved the same effect with physical activity in “The Bohr Staircase,” Phys. Teach. 42, 38-39 (Jan. 2004).

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