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AP Physics C: Mechanics
4.4 Elastic and Inelastic Collisions
IntermediateMCQMathematicalConceptual23.1k
A horizontal straight line represents a frictionless track. On the left side of the track, a rectangle labeled Cart 1 has mass m and a horizontal arrow pointing to the right labeled v_0. On the right side of the track, an identical rectangle labeled Cart 2 has mass m with a label indicating speed 0. A dashed vertical line is drawn midway between the two carts to denote the collision line. No other labels, lines, text, or axes appear.
Two identical carts on a frictionless track before colliding.
A cart of mass \(m\) moves with speed \(v_0\) along a horizontal, frictionless track toward an identical cart of mass \(m\) initially at rest. The carts interact in four separate one-dimensional collision trials with identical initial velocities:

Trial 1 (Superelastic): A compressed internal spring mechanism triggers upon contact, releasing stored potential energy to propel the carts apart.

Trial 2 (Elastic): An ideal spring bumper acts between the carts, conserving the mechanical kinetic energy of the system.

Trial 3 (Inelastic): The carts collide, rebound, and separate, with a portion of the mechanical kinetic energy dissipated as thermal energy.

Trial 4 (Completely Inelastic): The carts stick together upon contact and continue moving as a single combined unit.

Which of the following correctly ranks the total final kinetic energy \(K_f\) of the two-cart system in each trial?

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