---
title: "A block of mass \\(M\\) slides along a horizontal surface with a constant coefficient of kinetic friction \\(\\mu_k\\). At position \\(x = 0\\), the block has speed \\(v_0\\) and makes contact with the free end of an uncompressed horizontal ideal spring of spring constant \\(k\\), whose other end is fixed to a wall. The block moves in the positive \\(x\\)-direction until it momentarily comes to rest at maximum compression \\(x = x_{\\text{max}}\\). Which of the following correctly compares the elastic potential energy \\(U_s\\) stored in the spring at \\(x = x_{\\text{max}}\\) to the block’s initial kinetic energy \\(K_0 = \\dfrac{1}{2}M v_0^2\\) at \\(x = 0\\), and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/120673/"
date_modified: "2026-08-23T04:42:37+00:00"
---

# A block of mass \(M\) slides along a horizontal surface with a constant coefficient of kinetic friction \(\mu_k\). At position \(x = 0\), the block has speed \(v_0\) and makes contact with the free end of an uncompressed horizontal ideal spring of spring constant \(k\), whose other end is fixed to a wall. The block moves in the positive \(x\)-direction until it momentarily comes to rest at maximum compression \(x = x_{\text{max}}\). Which of the following correctly compares the elastic potential energy \(U_s\) stored in the spring at \(x = x_{\text{max}}\) to the block’s initial kinetic energy \(K_0 = \dfrac{1}{2}M v_0^2\) at \(x = 0\), and provides the correct justification?

A block of mass \(M\) slides along a horizontal surface with a constant coefficient of kinetic friction \(\mu_k\). At position \(x = 0\), the block has speed \(v_0\) and makes contact with the free end of an uncompressed horizontal ideal spring of spring constant \(k\), whose other end is fixed to a wall. The block moves in the positive \(x\)-direction until it momentarily comes to rest at maximum compression \(x = x_{\text{max}}\). Which of the following correctly compares the elastic potential energy \(U_s\) stored in the spring at \(x = x_{\text{max}}\) to the block's initial kinetic energy \(K_0 = \dfrac{1}{2}M v_0^2\) at \(x = 0\), and provides the correct justification?

![A side-view diagram of a horizontal track with a rough surface texture indicated by short hash marks below the baseline. On the left, a rectangular block of mass \(M\) moves to the right with a horizontal velocity vector arrow labeled \(v_0\) extending from its center. At position \(x = 0\), the unattached left end of a horizontal helical spring is depicted. The right end of the spring is attached to a rigid vertical wall labeled with hatched backing lines. A horizontal position axis below the track shows a tick mark labeled \(x = 0\) at the spring's uncompressed end and a tick mark labeled \(x_{\text{max}}\) further to the right. The coefficient of kinetic friction between the block and track is labeled \(\mu_k\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460156-VpC7JQ.jpg)

- **A.** \(U_s < K_0\), because the nonconservative force of kinetic friction does negative work on the block, converting a portion of the mechanical energy into thermal energy.
- **B.** \(U_s = K_0\), because the spring force is conservative, so all of the initial kinetic energy is converted into elastic potential energy when the block momentarily stops.
- **C.** \(U_s < K_0\), because the conservative spring force does negative work that removes total mechanical energy from the block-spring system.
- **D.** \(U_s > K_0\), because the force exerted by the spring and the kinetic friction force both do positive work on the block as it slows down.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120673/*