---
title: "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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url: "https://nerd-notes.com/ubq/120725/"
date_modified: "2026-08-23T04:42:51+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460171-Dpo2MA.jpg)

- **A.** \(K_4 > K_3 > K_2 > K_1\)
- **B.** \(K_1 = K_2 > K_3 > K_4\)
- **C.** \(K_2 > K_1 > K_3 > K_4\)
- **D.** \(K_1 > K_2 > K_3 > K_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120725/*