---
title: "A small block of mass \\(m\\) is released from rest at Point A, which is at a height \\(H\\) on a frictionless, curved track. The block slides down the track and transitions smoothly onto a horizontal surface. The horizontal surface is frictionless except for a rough patch of length \\(L\\) between position \\(x = 0\\) (Point B) and \\(x = L\\) (Point D), where the coefficient of kinetic friction between the block and the surface is \\(\\mu_k\\). At \\(x = L\\), the block immediately contacts one end of an uncompressed, ideal spring of spring constant \\(k\\). The other end of the spring is attached to a fixed wall. The block compresses the spring to a maximum distance \\(D\\), coming to rest momentarily at position \\(x = L + D\\) (Point E)."
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url: "https://nerd-notes.com/ubq/109187/"
date_modified: "2026-04-01T09:02:07+00:00"
---

# A small block of mass \(m\) is released from rest at Point A, which is at a height \(H\) on a frictionless, curved track. The block slides down the track and transitions smoothly onto a horizontal surface. The horizontal surface is frictionless except for a rough patch of length \(L\) between position \(x = 0\) (Point B) and \(x = L\) (Point D), where the coefficient of kinetic friction between the block and the surface is \(\mu_k\). At \(x = L\), the block immediately contacts one end of an uncompressed, ideal spring of spring constant \(k\). The other end of the spring is attached to a fixed wall. The block compresses the spring to a maximum distance \(D\), coming to rest momentarily at position \(x = L + D\) (Point E).

A small block of mass \(m\) is released from rest at Point A, which is at a height \(H\) on a frictionless, curved track. The block slides down the track and transitions smoothly onto a horizontal surface. The horizontal surface is frictionless except for a rough patch of length \(L\) between position \(x = 0\) (Point B) and \(x = L\) (Point D), where the coefficient of kinetic friction between the block and the surface is \(\mu_k\). At \(x = L\), the block immediately contacts one end of an uncompressed, ideal spring of spring constant \(k\). The other end of the spring is attached to a fixed wall. The block compresses the spring to a maximum distance \(D\), coming to rest momentarily at position \(x = L + D\) (Point E).

![A 2D physical setup showing a curved track on the left that starts at height H (labeled Point A) and slopes down to a flat horizontal surface. A small rectangular block of mass m is at Point A. The flat surface begins at a vertical dashed line labeled 'x = 0 (Point B)'. Between x = 0 and another dashed line at 'x = L (Point D)', the surface is shaded with cross-hatching to indicate friction, labeled '\(\mu_k\)'. To the right of x = L, the surface is smooth again. At x = L, an uncompressed horizontal spring of constant k is attached to a vertical wall on the far right. A final dashed line to the right of x = L is labeled 'x = L + D (Point E)'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774067975-WRqDsY.jpg)

**Part a)** The system to be analyzed is defined as the block, the spring, and Earth. The energy of the system at Point A is purely gravitational potential energy, \(PE_g\). **Shade** the provided bar charts to qualitatively represent the kinetic energy \(KE\), gravitational potential energy \(PE_g\), and spring potential energy \(PE_s\) of the system at Point B, Point D, and Point E. If a quantity is zero, **write** a "0" below the corresponding bar. *(3 points)*

**Part b)** **Sketch** a solid line on the axes below to represent the kinetic energy \(KE\) of the block as a function of its position \(x\) from \(x = 0\) to \(x = L + D\). *(3 points)*

**Part c)** The original block is removed and replaced by a new block of mass \(2m\). The new block is released from rest from the same initial height \(H\) at Point A. All surface properties and the spring remain identical. **Indicate** whether the new maximum compression of the spring will be greater than, less than, or equal to \(D\sqrt{2}\). - [ ] Greater than \(D\sqrt{2}\) - [ ] Less than \(D\sqrt{2}\) - [ ] Equal to \(D\sqrt{2}\) **Justify** your answer using physical principles. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109187/*