---
title: "A block of mass \\(m_B\\) rests on a rough horizontal table with a coefficient of kinetic friction \\(\\mu_k\\). It is connected by a light string that passes over an ideal pulley at the right edge of the table to a hanging sphere of mass \\(m_S\\), as shown in Figure 1. The mass of the block is greater than the mass of the sphere (\\(m_B > m_S\\)). The system is released from rest, and the block accelerates toward the right edge of the table."
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url: "https://nerd-notes.com/ubq/110332/"
date_modified: "2026-04-02T07:11:15+00:00"
---

# A block of mass \(m_B\) rests on a rough horizontal table with a coefficient of kinetic friction \(\mu_k\). It is connected by a light string that passes over an ideal pulley at the right edge of the table to a hanging sphere of mass \(m_S\), as shown in Figure 1. The mass of the block is greater than the mass of the sphere (\(m_B > m_S\)). The system is released from rest, and the block accelerates toward the right edge of the table.

A block of mass \(m_B\) rests on a rough horizontal table with a coefficient of kinetic friction \(\mu_k\). It is connected by a light string that passes over an ideal pulley at the right edge of the table to a hanging sphere of mass \(m_S\), as shown in Figure 1. The mass of the block is greater than the mass of the sphere (\(m_B > m_S\)). The system is released from rest, and the block accelerates toward the right edge of the table.

![A line drawing of a physics apparatus. A horizontal table extends from the left side of the image, ending at a right edge. On top of the table rests a rectangular block labeled 'm_B'. A string connects to the right side of the block, extends horizontally to the right, and passes over a circular pulley mounted exactly at the top right edge of the table. The string then hangs vertically downward. Attached to the bottom of the vertical string is a solid sphere labeled 'm_S'. The top surface of the table has small hatch marks indicating a rough, frictional surface. The vertical height from the floor to the top of the table is indicated by a dashed line and labeled 'H'. The initial horizontal distance between the front edge of the block and the pulley is marked with a bracket and labeled 'D'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775043428-zA5aWh.jpg)

**Part a)** **Draw** and **label** the forces (not components) that act on the block and the sphere while the system is accelerating. Each force must be represented by a distinct arrow starting on, and pointing away from, the appropriate dot. *(2 points)*

**Part b)** **Derive** an expression for the magnitude of the acceleration \(a\) of the block while it is sliding on the table. Express your answer in terms of \(m_B\), \(m_S\), \(\mu_k\), and fundamental constants. *(3 points)*

**Part c)** A student observes the motion and claims, "If we swap the positions of the two objects—placing the sphere on the table and hanging the block—the acceleration of the system will be greater. This is because the downward pull on the system will be larger and the friction resisting the motion will be smaller." *(4 points)*

**Part d)** In the original configuration (block on the table, sphere hanging), the block starts a distance \(D\) from the pulley. Just as the block reaches the edge of the table (and before the sphere hits the ground), the string breaks. The table has height \(H\) above the floor. **Derive** an expression for the horizontal distance \(x\) from the edge of the table to the point where the block lands on the floor. Express your answer in terms of \(m_B\), \(m_S\), \(\mu_k\), \(D\), \(H\), and fundamental constants. *(4 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110332/*