---
title: "A cart of mass \\(m_1\\) moves to the right with initial speed \\(v_0\\) along a frictionless horizontal track toward a second cart of mass \\(m_2\\), which is initially at rest. Attached to the left bumper of the second cart is an ideal, massless spring with force constant \\(k\\). During the collision, the carts interact solely through the spring. In terms of the given quantities, what is the maximum compression of the spring during the interaction?"
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url: "https://nerd-notes.com/ubq/120731/"
date_modified: "2026-08-23T04:42:53+00:00"
---

# A cart of mass \(m_1\) moves to the right with initial speed \(v_0\) along a frictionless horizontal track toward a second cart of mass \(m_2\), which is initially at rest. Attached to the left bumper of the second cart is an ideal, massless spring with force constant \(k\). During the collision, the carts interact solely through the spring. In terms of the given quantities, what is the maximum compression of the spring during the interaction?

A cart of mass \(m_1\) moves to the right with initial speed \(v_0\) along a frictionless horizontal track toward a second cart of mass \(m_2\), which is initially at rest. Attached to the left bumper of the second cart is an ideal, massless spring with force constant \(k\). During the collision, the carts interact solely through the spring. In terms of the given quantities, what is the maximum compression of the spring during the interaction?

![A horizontal straight line at the bottom represents a track. On the left sits a rectangular box labeled \(m_1\) with a horizontal arrow pointing to the right above it labeled \(v_0\). To the right sits a second rectangular box labeled \(m_2\). Attached to the left vertical face of box \(m_2\) is a horizontal coil spring extending toward \(m_1\), labeled \(k\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460173-tAN1yu.jpg)

- **A.** \(v_0 \sqrt{\dfrac{m_1 m_2}{k(m_1 + m_2)}}\)
- **B.** \(v_0 \sqrt{\dfrac{m_1^2}{k(m_1 + m_2)}}\)
- **C.** \(v_0 \sqrt{\dfrac{m_1}{k}}\)
- **D.** \(v_0 \sqrt{\dfrac{m_2}{k}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120731/*