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74 * EST A “gravity force car” is powered by the force exerted by Earth on an object of mass M. The object is tied to a rope that is turning the axle of the rear wheels, as shown in Figure P7.74 The mass of the car (excluding the hanging object) is m. As the car accelerates, the object descends a distance h. (a) Ignoring air resistance and friction in the pulley and wheels, derive an expression for the final speed of the car. (b) Based on your answer to part (a), what would you suggest to the designers of such a car if the goal is to achieve the greatest final speed? (c) Estimate the maximum final speed of a tabletop version of a gravity force car (think of reasonable values for the variables in the equation that you derived).1
1 This problem was inspired by Gordon Aubrecht, who sadly passed away in 2016.
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