We have developed the means to measure position rapidly and precisely as a function of time in the general physics laboratory. These measurements are of sufficient quality that velocities and accelerations can be calculated from the position data using numerical derivatives. The precision of the measurements is such that any disagreement between theoretical expectations and experimental measurements is less than a few percent. Measurements of the system under study can be made as rapidly as every 200 μs, which is faster than the typical time scales over which the system changes. Measuring rapidly also allows one to investigate additional phenomena not previously accessible and to see features of the physics previously unobserved. The measurement system is based on commercially available sensors, computer hardware, and computer software (LABVIEW™). Many general physics laboratories based on this system have been developed but only an investigation of Newton’s second law will be described here.
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22.
The quadrature linear LED sensors (HEDS-9200-R00) can be obtained from US Digital, www.usdigital.com, 360.260.2468.
23.
The 200 lines/in. mylar strips (24 by 1/2 in., LIN-200-24) can be obtained from US Digital, www.usdigital.com, 360.260.2468.
24.
LABVIEW™ is available from National Instruments Corporation, www.natinst.com, 512.794.0100.
25.
The distributor’s website (www.usdigital.com/knowledge/body_glossary.shtml) and the National Instrument Website (www.ni.com/sensors/quad.html) contain brief descriptions of the quadrature technique for position measurements.
26.
The high-speed counter/timer board, model 6602, was produced by National Instruments Corporation, www.natinst.com.
27.
ORIGIN, data analysis and graphing software, is available from OriginLab™ Corporation, www.OriginLab.com.
28.
In fact the potential energy stored in the bumpers can be determined, albeit with some difficulty, and energy conservation can be shown. Assuming a linear response for the bumpers (because the compression is not large in these collisions) a spring constant can be determined by measuring the position of the carts with the computer as various forces are applied to push the carts together. The data of the collision itself can be used to determine the amount of compression. This compression can be determined by examining the arbitrary measured distances between the two carts. If there were no compression, this difference of the two positions would always be constant during the contact period. It is not and this allows one to determine the size of the compression.
29.
The 1000 strips/turn rotary codewheels (HEDS-6100-B06) are available from Newark Electronics, www.newark.com. The quadrature rotary LED sensors (HEDS-9000-B00) can be obtained from US Digital, www.usdigital.com.
30.
The Sub-Cub-D is manufactured by Red Lion Controls and is available from Digikey Electronics, 701 Brooks Ave. South, P.O. Box 667, Thief River Falls, MN 56701-0677.
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© 2002 American Association of Physics Teachers.
2002
American Association of Physics Teachers
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