The Exploding Carts is a popular introductory physics activity in which a one-dimensional explosion is simulated utilizing two dynamics carts that are pushed apart by a spring-loaded plunger released from one of the carts. Traditional treatments of the Exploding Carts usually involve multiple trials where the mass of one or both of the carts is increased, producing explosions with varying post-explosion speeds (the speed at the instant contact is lost between the carts). The subsequent analysis normally entails comparing post-explosion speeds within a given trial, which leads to the concept of momentum and its conservation. Though generally not emphasized in traditional treatments of the Exploding Carts, it is also an interesting endeavor (and the focus of this paper) to compare post-explosion speeds between different trials. Specifically, the post-explosion speed of a constant mass cart in various trials can be compared to the post-explosion speed of the equal mass explosion (no additional mass added to the carts) as the mass of the other cart is changed.
References
1.
The traditional Exploding Carts is identified by PIRA 1N20.20
http://physicslearning2.colorado.edu/PIRA/, and the particular descriptions vary by department.2.
A relatively detailed treatment of explosions using carts is presented by
Francis W.
Sears
, Mechanics, Wave Motion, and Heat
(Addison-Wesley, Reading
, MA
, 1958
), Sec. 8-6, and is described as “recoil.” A similar level of presentation appears in other texts by Sears.3.
Exploding Carts is covered with a diagram and less description than Sears (Ref. 2) by
Harvey E.
White
, Modern College Physics,
2nd ed. (D. Van Nostrand Company Inc.
, Toronto
, 1953
), Sec. 16.6, and Herbert H.
Gottlieb
, “Apparatus for Teaching Physics: Conservation of momentum in an explosion
,” Phys. Teach.
8
, 90
(Feb. 1970
). This is the typical level of presentation in most texts and demonstration notes if included at all.4.
The activity is described in some detail as a laboratory exercise by
Larry
Dukerich
, Advanced Physics with Vernier - Mechanics,
1st ed. (Vernier Software & Technology
, Beaverton, OR
, 2011
), Exp. 11.5.
The Physics Classroom Site, Momentum Conservation in Explosions
, http://www.physicsclassroom.com/Class/momentum/U4L2e.cfm also describes Exploding Carts, and includes an erroneous comparison of cart speeds between different trials, although the focus is on comparison of cart speeds within individual trials. Specifically, in the first three diagrams depicting the exploding carts in the section titled “Equal and Opposite Momentum Changes,” the speed of the constant mass cart is always given as 40 cm/s. A similar error appears in the interactive animation link on this site.6.
The exploding carts activity is often employed in the Modeling Instruction approach to teaching introductory physics. This approach utilizes experiments to introduce topics and features the discovery of underlying concepts through student-centered activities, as explained by
Eric
Brewe
, “Modeling theory applied: Modeling Instruction in introductory physics
,” Am. J. Phys.
76
, 1155
–1160
(Dec. 2008
) and Malcolm
Wells
, David
Hestenes
, and Gregg
Swackhammer
, “A modeling method for high school physics instruction
,” Am. J. Phys.
63
, 606
–619
(July 1995
). Modeling Instruction is based on the application of Piagetian theory to classroom practice:
David
Hestenes
, “A modeling theory of physics instruction
,” Am. J. Phys.
55
, 440
–454
(May 1987
), John W.
Renner
and Anton E.
Lawson
, “Piagetian theory and instruction in physics
,” Phys. Teach.
11
, 165
–169
(March 1973
), and John W.
Renner
and Anton E.
Lawson
, “Promoting intellectual development through science teaching
,” Phys. Teach.
11
, 273
–276
(May 1973
).7.
The variation of explosion duration for an explosion of a spring-loaded dynamics cart with a stationary wall and the fact that force exerted and the energy stored by the spring-loaded plunger depends only on the compression of the spring and the spring constant has been previously demonstrated in a slightly different context and is not often cited in descriptions of the exploding carts.
T. A.
McMath
, “A dynamics cart demonstration: Momentum, kinetic energy, and more
,” Phys. Teach.
24
, 282
–283
(May 1986
).8.
The mass ratio of Vernier or PASCO carts is typically adjusted in experiments by adding blocks that have approximately the same mass as one cart; see The Physics Classroom site or Refs. 11–13 and 18 for more detail. The addition of two to four blocks is usually sufficient to show the intended effect described by Eq. (2) and this is the usual range utilized by the Modeling Instruction version. It is not usually practical to add more than four blocks to the carts or to add blocks with the WDSS in place on the cart.
9.
A similar experiment to Exploding Carts was presented by
Marvin
Ohriner
, “Apparatus for Teaching Physics: An explosive pendulum to show conservation of momentum
,” Phys. Teach.
4
, 190
(April 1966
), in which the heights reached by the pendula were used to compare speeds. We presently employ the suspended mass in order to alter the mass ratio over a larger range. Our analysis focuses on comparing the speeds of the constant mass cart, and we do not further consider the motion of the suspended mass.10.
The use of a smartphone acceleration sensor has been suggested for a similar purpose.
Patrik
Vogt
and Jochen
Kuhn
, “Analyzing collision processes with the smartphone acceleration sensor
,” Phys. Teach.
52
, 118
–119
(Feb. 2014
).11.
12.
PASCO Explorations in Physics Manual PS-2810A
, Impulse and Change in Momentum – Collision
, p. 247
.13.
Ref. 4, Exp. 10.
14.
Patrick
Twomey
, Colm
O’Sullivan
, John
O’Riordan
, and Stephen
Fahy
, “Collisions with springs: A useful context for the study of analytical dynamics
,” Phys. Teach.
50
, 83
–86
(Feb. 2012
) describes the details of oscillations of a spring fixed to a force probe in collisions with a cart and identifies that the collision time is , which is half the period of oscillation for a mass M attached to a spring with spring constant K. In our experiment, the cart is not fixed and the collision time is less than this prediction.15.
Stephen
Fahy
, John
O’Riordan
, Colm
O’Sullivan
, and Patrick
Twomey
, “How reflected wave fronts dynamically establish Hooke’s law in a spring
,” Eur. J. Phys.
33
, 417
–426
(March 2012
) describes reflected waves along a spring and identifies a travel time of . This may explain the additional periodic “noise” seen in our acceleration profile.16.
17.
A negative noise feature appears in all acceleration profiles, and it is likely attributable at least in part to oscillations of the spring-loaded plunger. This feature is more pronounced for lower values of k. Deploying the plunger against only the air should ideally yield no acceleration profile, but a non-zero time interval and a non-zero area for the initial positive acceleration profile are registered. The time interval is consistently Δt0 = 0.009 s for this case, and this is comparable with the calculated time interval for the low k cases of 10 and 20 g. The mass of the plunger is approximately 17 g, comparable to the low k masses.
18.
See Appendixes A and B under the “Supplemental” tab at TPT Online, https://doi.org/10.1119/1.5008341 .
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2017
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