PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum
Problem
Two identical low-friction carts, X and Y, each of mass m, rest in contact at the center of a straight, horizontal track. A third cart Z of the same mass m is initially at rest 1.0\,m to the right of cart Y. A student gives cart X a push toward the right so that it begins moving with speed v0 and then collides successively with carts Y and Z. The collision between X and Y is perfectly inelastic; carts X and Y stick together. The subsequent collision between the (X+Y) pair and cart Z is perfectly elastic. Neglect external forces along the track.
(a) Without doing detailed calculations, describe qualitatively how the total momentum of the system is distributed among the carts after each collision.
(b) Explain whether the kinetic energy of the system decreases, increases, or remains the same during (i) the first collision and (ii) the second collision. Support your answers with physical reasoning based on the type of collision.
(c) Suppose the student repeats the experiment with a larger initial speed v0. Describe how, if at all, the fraction of the initial kinetic energy transferred to cart Z after all collisions compares with the previous trial. Justify your reasoning qualitatively.