---
title: "Block A of mass \\(m\\) and block B of mass \\(2m\\) are on a horizontal, frictionless surface. Block A moves to the right with speed \\(4v_0\\), and block B moves to the left with speed \\(v_0\\), as shown. A light spring is attached to the front of block B. The blocks collide, compressing the spring until the blocks reach a common velocity at the moment of maximum compression.  Let \\(J\\) be the magnitude of the impulse delivered to block A from the start of the collision until the moment of maximum compression, and let \\(P_{sys}\\) be the magnitude of the total momentum of the two-block system. What is the ratio \\(J/P_{sys}\\)?"
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url: "https://nerd-notes.com/ubq/109342/"
date_modified: "2026-03-21T23:31:07+00:00"
---

# Block A of mass \(m\) and block B of mass \(2m\) are on a horizontal, frictionless surface. Block A moves to the right with speed \(4v_0\), and block B moves to the left with speed \(v_0\), as shown. A light spring is attached to the front of block B. The blocks collide, compressing the spring until the blocks reach a common velocity at the moment of maximum compression.

Let \(J\) be the magnitude of the impulse delivered to block A from the start of the collision until the moment of maximum compression, and let \(P_{sys}\) be the magnitude of the total momentum of the two-block system. What is the ratio \(J/P_{sys}\)?

Block A of mass \(m\) and block B of mass \(2m\) are on a horizontal, frictionless surface. Block A moves to the right with speed \(4v_0\), and block B moves to the left with speed \(v_0\), as shown. A light spring is attached to the front of block B. The blocks collide, compressing the spring until the blocks reach a common velocity at the moment of maximum compression.

Let \(J\) be the magnitude of the impulse delivered to block A from the start of the collision until the moment of maximum compression, and let \(P_{sys}\) be the magnitude of the total momentum of the two-block system. What is the ratio \(J/P_{sys}\)?

![A horizontal surface with two blocks, labeled A and B. Block A on the left has mass m and a vector arrow labeled 4v_0 pointing to the right. Block B on the right has mass 2m and a vector arrow labeled v_0 pointing to the left. A light, uncompressed spring is attached to the left face of block B.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774135867-jvRpa3.jpg)

- **A.** \(1/3\)
- **B.** \(2/3\)
- **C.** \(3/2\)
- **D.** \(5/3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109342/*