---
title: "Block A of mass \\(m_A\\) is placed on a rough inclined plane that makes an angle \\(\\theta\\) with the horizontal. The coefficient of kinetic friction between Block A and the plane is \\(\\mu_k\\). Block A is connected to Block B of mass \\(m_B\\) by a lightweight string that passes over a pulley.  The pulley is a uniform solid disk of mass \\(M\\) and radius \\(R\\), and its rotational inertia is \\(I = \\dfrac{1}{2} M R^2\\). The pulley rotates on a frictionless axle.   The system is released from rest. Assume that \\(m_B\\) is sufficiently large that Block B accelerates downward and Block A accelerates up the incline. The string does not slip on the pulley."
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/111192/"
date_modified: "2026-04-10T06:07:41+00:00"
---

# Block A of mass \(m_A\) is placed on a rough inclined plane that makes an angle \(\theta\) with the horizontal. The coefficient of kinetic friction between Block A and the plane is \(\mu_k\). Block A is connected to Block B of mass \(m_B\) by a lightweight string that passes over a pulley.

The pulley is a uniform solid disk of mass \(M\) and radius \(R\), and its rotational inertia is \(I = \dfrac{1}{2} M R^2\). The pulley rotates on a frictionless axle. 

The system is released from rest. Assume that \(m_B\) is sufficiently large that Block B accelerates downward and Block A accelerates up the incline. The string does not slip on the pulley.

Block A of mass \(m_A\) is placed on a rough inclined plane that makes an angle \(\theta\) with the horizontal. The coefficient of kinetic friction between Block A and the plane is \(\mu_k\). Block A is connected to Block B of mass \(m_B\) by a lightweight string that passes over a pulley.

The pulley is a uniform solid disk of mass \(M\) and radius \(R\), and its rotational inertia is \(I = \dfrac{1}{2} M R^2\). The pulley rotates on a frictionless axle. 

The system is released from rest. Assume that \(m_B\) is sufficiently large that Block B accelerates downward and Block A accelerates up the incline. The string does not slip on the pulley.

![A wedge forming an inclined plane at angle theta on the left. Block A is on the incline. A string attached to Block A goes up parallel to the incline, passes over a solid disk pulley at the top vertex of the wedge, and hangs vertically down. Block B is attached to the vertical part of the string. The pulley has radius R and mass M. The coefficient of friction mu_k is indicated on the incline.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1775801261-B6v2HS.jpg)

**Part a)** The system accelerates after being released. *(4 points)*

**Part b)** **Derive** an expression for the magnitude of the acceleration of Block B. Express your answer in terms of \(m_A\), \(m_B\), \(M\), \(\theta\), \(\mu_k\), and fundamental constants. *(4 points)*

**Part c)** **Indicate** how the magnitude of the tension \(T_A\) in the string pulling on Block A compares to the magnitude of the tension \(T_B\) in the string pulling on Block B while the system is accelerating. - [ ] \(T_A > T_B\) - [ ] \(T_A < T_B\) - [ ] \(T_A = T_B\) **Justify** your answer using physical principles. *(2 points)*

**Part d)** After Block B has fallen a distance \(D\), the blocks are moving with speed \(v\). At this instant, the string breaks. **Derive** an expression for the distance \(d\) that Block A travels up the incline *after* the string breaks before coming to a momentary halt. Express your answer in terms of \(v\), \(\theta\), \(\mu_k\), and fundamental constants. *(3 points)*

**Part e)** Immediately after the string breaks, **indicate** the magnitude of the angular acceleration of the pulley. - [ ] It is greater than it was before the string broke. - [ ] It is less than it was before the string broke, but greater than zero. - [ ] It is zero. **Justify** your answer. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111192/*