---
title: "A cart of mass \\(m\\) travels with speed \\(v_0\\) along a horizontal, frictionless track toward a stationary cart of mass \\(2m\\). The collision is tested under two different experimental conditions: in Setup 1, the collision is perfectly elastic, and in Setup 2, the carts latch together in a completely inelastic collision. The initial kinetic energy of the system before each collision is \\(K_0\\). Which row in the table correctly compares the magnitude of the impulse \\(J_{\\text{target}}\\) delivered to the cart of mass \\(2m\\), the total final kinetic energy \\(K_f\\) of the system in Setup 2, and the post-collision center-of-mass speed \\(v_{\\text{cm}}\\) of the system?  | Row | Impulse on Target Cart | Final Kinetic Energy in Setup 2 | Post-Collision Center-of-Mass Speed | | :— | :— | :— | :— | | A | \\(J_1 = J_2\\) | \\(K_f = \\dfrac{1}{3} K_0\\) | \\(v_{\\text{cm},1} = v_{\\text{cm},2}\\) | | B | \\(J_1 = 2J_2\\) | \\(K_f = \\dfrac{2}{3} K_0\\) | \\(v_{\\text{cm},1} = v_{\\text{cm},2}\\) | | C | \\(J_1 = 2J_2\\) | \\(K_f = \\dfrac{1}{3} K_0\\) | \\(v_{\\text{cm},1} = v_{\\text{cm},2}\\) | | D | \\(J_1 = \\dfrac{1}{2}J_2\\) | \\(K_f = \\dfrac{1}{3} K_0\\) | \\(v_{\\text{cm},1} > v_{\\text{cm},2}\\) |"
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url: "https://nerd-notes.com/ubq/120782/"
date_modified: "2026-08-23T04:43:20+00:00"
---

# A cart of mass \(m\) travels with speed \(v_0\) along a horizontal, frictionless track toward a stationary cart of mass \(2m\). The collision is tested under two different experimental conditions: in Setup 1, the collision is perfectly elastic, and in Setup 2, the carts latch together in a completely inelastic collision. The initial kinetic energy of the system before each collision is \(K_0\). Which row in the table correctly compares the magnitude of the impulse \(J_{\text{target}}\) delivered to the cart of mass \(2m\), the total final kinetic energy \(K_f\) of the system in Setup 2, and the post-collision center-of-mass speed \(v_{\text{cm}}\) of the system?

| Row | Impulse on Target Cart | Final Kinetic Energy in Setup 2 | Post-Collision Center-of-Mass Speed |
| :— | :— | :— | :— |
| A | \(J_1 = J_2\) | \(K_f = \dfrac{1}{3} K_0\) | \(v_{\text{cm},1} = v_{\text{cm},2}\) |
| B | \(J_1 = 2J_2\) | \(K_f = \dfrac{2}{3} K_0\) | \(v_{\text{cm},1} = v_{\text{cm},2}\) |
| C | \(J_1 = 2J_2\) | \(K_f = \dfrac{1}{3} K_0\) | \(v_{\text{cm},1} = v_{\text{cm},2}\) |
| D | \(J_1 = \dfrac{1}{2}J_2\) | \(K_f = \dfrac{1}{3} K_0\) | \(v_{\text{cm},1} > v_{\text{cm},2}\) |

A cart of mass \(m\) travels with speed \(v_0\) along a horizontal, frictionless track toward a stationary cart of mass \(2m\). The collision is tested under two different experimental conditions: in Setup 1, the collision is perfectly elastic, and in Setup 2, the carts latch together in a completely inelastic collision. The initial kinetic energy of the system before each collision is \(K_0\). Which row in the table correctly compares the magnitude of the impulse \(J_{\text{target}}\) delivered to the cart of mass \(2m\), the total final kinetic energy \(K_f\) of the system in Setup 2, and the post-collision center-of-mass speed \(v_{\text{cm}}\) of the system?

| Row | Impulse on Target Cart | Final Kinetic Energy in Setup 2 | Post-Collision Center-of-Mass Speed |
| :--- | :--- | :--- | :--- |
| A | \(J_1 = J_2\) | \(K_f = \dfrac{1}{3} K_0\) | \(v_{\text{cm},1} = v_{\text{cm},2}\) |
| B | \(J_1 = 2J_2\) | \(K_f = \dfrac{2}{3} K_0\) | \(v_{\text{cm},1} = v_{\text{cm},2}\) |
| C | \(J_1 = 2J_2\) | \(K_f = \dfrac{1}{3} K_0\) | \(v_{\text{cm},1} = v_{\text{cm},2}\) |
| D | \(J_1 = \dfrac{1}{2}J_2\) | \(K_f = \dfrac{1}{3} K_0\) | \(v_{\text{cm},1} > v_{\text{cm},2}\) |

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120782/*