You work for a cable TV sports network, which is interested in developing a new form of "extreme bowling". One feature of the game will be the masses of the(rolling) bowling balls and (stationary) bowling pins will vary greatly over the course of a match. Another feature is that they will bounce off each other when a ball runs into a pin. Your boss speculates that the energy efficiency of the collisions is useful information, and that it will change with the speed of the ball and the relative masses of the balls and pins. In order to save the most spectacular collisions until the final frames, your boss asks you to determine the energy efficiencies and energy dissipation over a range of ball masses and pin masses. Is your boss correct?
You decide to test your prediction with three different cart collisions: one in which the moving cart is more massive, one in which the stationary cart is more massive, and one in which the moving and stationary carts are equally massive. As a control, you assume that the total mass of the colliding objects remains constant. For your model you use the most efficient bumper you can think of, a magnetic bumper.
Prediction: Consider the three cases described in the problem, with the same total mass of the carts for each case (m(A)+m(B)=constant). Rank the collisions from most efficient to least efficient. (Make an educated guess and explain your reasoning.)