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Modeling the Mousetrap Car
2.The car shown in Fig. 1, and used in this paper for analysis, is a “hybrid car,” one designed to optimize use of the potential energy from both a mousetrap power plant and gravity, via a starting position atop a half-meter high ramp. Cars of this type are typically designed with higher mass rear wheel systems than are flat run cars. For the purposes of the model and data presented here, the car was run on a flat surface (i.e., mousetrap-only energy source mode). Extending the presently described model to include a ramp is straightforward, but it would have unnecessarily complicated the initial introduction to the essential modeling concepts and made for a lengthy write-up.
3.Some designs forego adding an arm and simply attach the string to the business end of the mousetrap spring.
4.Peter Levan, “Setting a mousetrap,” Phys. Teach. 28, 32–33 (Jan. 1988).
5.Measuring the torque at three angles and applying a quadratic equation fit gives a modest improvement (typically less than 5%), performance trending and the overall modeling strategy remaining unchanged.
6.Decreasing the step size from 0.1 m to .01 m typically gives less than 1% improvement.
7.Effects due to the shifting mass of the arm are not included here. Also, for most front wheel system designs, the rotational kinetic energy and energy loss due to friction will be a small fraction of that of the rear wheel system, which is typically much more massive and the dominant source of kinetic friction energy loss due to tension from the spring. For those cases where the front wheel system has a large moment of inertia, extension of the model to include the front wheel system is straightforward and can be an interesting exercise for a student.
8.Absolute accuracy of the models performance prediction is generally of less importance than is the relative correctness of the trending of the performance predictions with respect to the various design variable inputs. Hence, for the sake of simplicity, modeling with just one of the two drag terms (first or second order) and the kinetic friction term will likely suffice. (Mousetrap cars typically operate with speeds in the range 0–3 m/s. Determination of their Reynolds numbers and assessing the regimes and respective contributions to the drag is an unresolved issue at the present time.)
9.For helpful discussions of similar rotational systems, and for those wishing to derive Eq. (16) and (17), see: Carl E. Mungan, “Acceleration of a pulled spool,” Phys. Teach. 39, 481–485 (Nov. 2001), and
9.Carl E. Mungan, “A primer on work-energy relationships for introductory physics,” Phys. Teach. 43, 10–16 (Jan. 2005).
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Many high school and introductory college physics courses make use of mousetrap car projects and competitions as a way of providing an engaging hands-on learning experience incorporating Newton's laws, conversion of potential to kinetic energy, dissipative forces, and rotational mechanics. Presented here is a simple analytical and finite element spreadsheet model for a typical mousetrap car, as shown in Fig. 1. It is hoped that the model will provide students with a tool for designing or modifying the designs of their cars, provide instructors with a means to insure students close the loop between physical principles and an understanding of their car's speed and distance performance, and, third, stimulate in students at an early stage an appreciation for the merits of computer modeling as an aid in understanding and tackling otherwise analytically intractable problems so common in today's professional world.
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