---
title: "A block of mass \\(m_1\\) is placed on a rough plane inclined at an angle \\(\\theta\\) above the horizontal. The block is connected by a light, ideal string that passes over a frictionless, massless pulley to a second block of mass \\(m_2\\) that hangs vertically. The coefficient of kinetic friction between block 1 and the incline is \\(\\mu_k\\). The blocks are released from rest such that block 2 descends and block 1 moves up the incline. Which of the following is a correct expression for the magnitude of the acceleration \\(a\\) of the blocks?"
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url: "https://nerd-notes.com/ubq/114617/"
date_modified: "2026-07-03T04:46:29+00:00"
---

# A block of mass \(m_1\) is placed on a rough plane inclined at an angle \(\theta\) above the horizontal. The block is connected by a light, ideal string that passes over a frictionless, massless pulley to a second block of mass \(m_2\) that hangs vertically. The coefficient of kinetic friction between block 1 and the incline is \(\mu_k\). The blocks are released from rest such that block 2 descends and block 1 moves up the incline. Which of the following is a correct expression for the magnitude of the acceleration \(a\) of the blocks?

A block of mass \(m_1\) is placed on a rough plane inclined at an angle \(\theta\) above the horizontal. The block is connected by a light, ideal string that passes over a frictionless, massless pulley to a second block of mass \(m_2\) that hangs vertically. The coefficient of kinetic friction between block 1 and the incline is \(\mu_k\). The blocks are released from rest such that block 2 descends and block 1 moves up the incline. Which of the following is a correct expression for the magnitude of the acceleration \(a\) of the blocks?

![A block labeled m1 sits on a ramp inclined at angle theta. A string attached to m1 goes up the ramp, over a pulley at the top corner, and down to a hanging block labeled m2. Arrows indicate m2 moving down and m1 moving up the ramp.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1783053989-rinL4F.jpg)

- **A.** \(a = \dfrac{g(m_2 - m_1(\sin\theta + \mu_k \cos\theta))}{m_1 + m_2}\)
- **B.** \(a = \dfrac{g(m_2 - m_1(\sin\theta - \mu_k \cos\theta))}{m_1 + m_2}\)
- **C.** \(a = \dfrac{g(m_2 - m_1(\cos\theta + \mu_k \sin\theta))}{m_1 + m_2}\)
- **D.** \(a = \dfrac{g(m_2 - m_1(\sin\theta + \mu_k \cos\theta))}{m_1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114617/*