---
title: "Block 1 of mass \\(m_1\\), Block 2 of mass \\(m_2\\), and Block 3 of mass \\(m_3\\) are connected by strings of negligible mass that pass over ideal pulleys, as shown in Figure 1. Block 2 rests on a horizontal table where the coefficient of kinetic friction between Block 2 and the table is \\(\\mu_k\\). The system is released from rest, and the mass of Block 1 is large enough that it accelerates downward."
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url: "https://nerd-notes.com/ubq/110589/"
date_modified: "2026-04-08T04:08:26+00:00"
---

# Block 1 of mass \(m_1\), Block 2 of mass \(m_2\), and Block 3 of mass \(m_3\) are connected by strings of negligible mass that pass over ideal pulleys, as shown in Figure 1. Block 2 rests on a horizontal table where the coefficient of kinetic friction between Block 2 and the table is \(\mu_k\). The system is released from rest, and the mass of Block 1 is large enough that it accelerates downward.

Block 1 of mass \(m_1\), Block 2 of mass \(m_2\), and Block 3 of mass \(m_3\) are connected by strings of negligible mass that pass over ideal pulleys, as shown in Figure 1. Block 2 rests on a horizontal table where the coefficient of kinetic friction between Block 2 and the table is \(\mu_k\). The system is released from rest, and the mass of Block 1 is large enough that it accelerates downward.

![A rectangular horizontal table. Block 2, labeled 'm2', sits flat on the middle of the table. A string is attached to the left side of Block 2, runs horizontally to the left, passes over a pulley located at the left edge of the table, and hangs straight down, attaching to Block 1, labeled 'm1'. A second string is attached to the right side of Block 2, runs horizontally to the right, passes over a pulley at the right edge of the table, and hangs straight down, attaching to Block 3, labeled 'm3'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775539283-Ci5fqh.jpg)

**Part a)** The dots below represent the three blocks. On each dot, **draw** and **label** the forces (not components) that are exerted on the block. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. *(3 points)*

**Part b)** **Derive** an expression for the magnitude of the acceleration of Block 2 while it moves to the left. Express your answer in terms of \(m_1\), \(m_2\), \(m_3\), \(\mu_k\), and fundamental constants, as appropriate. *(3 points)*

**Part c)** Consider a limiting case where the mass of Block 1 is extremely large (\(m_1 \gg m_2 + m_3\)). *(3 points)*

**Part d)** Return to the original scenario where all blocks have comparable finite masses. While the system is accelerating, the string connecting Block 2 and Block 3 is suddenly cut. **Indicate** whether the tension in the string connecting Block 1 and Block 2 increases, decreases, or stays the same immediately after the string is cut. - [ ] Increases - [ ] Decreases - [ ] Stays the same **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/110589/*