---
title: "A block of mass \\(M\\) is initially at rest at the bottom of a rough ramp inclined at an angle \\(\\theta\\) above the horizontal. A constant force of magnitude \\(F\\) is applied to the block in a direction parallel to the ramp, pulling it upward. The coefficient of kinetic friction between the block and the ramp is \\(\\mu_k\\). After the block has traveled a distance \\(D\\) along the ramp, what is the speed of the block?"
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url: "https://nerd-notes.com/ubq/109172/"
date_modified: "2026-03-20T10:54:12+00:00"
---

# A block of mass \(M\) is initially at rest at the bottom of a rough ramp inclined at an angle \(\theta\) above the horizontal. A constant force of magnitude \(F\) is applied to the block in a direction parallel to the ramp, pulling it upward. The coefficient of kinetic friction between the block and the ramp is \(\mu_k\). After the block has traveled a distance \(D\) along the ramp, what is the speed of the block?

A block of mass \(M\) is initially at rest at the bottom of a rough ramp inclined at an angle \(\theta\) above the horizontal. A constant force of magnitude \(F\) is applied to the block in a direction parallel to the ramp, pulling it upward. The coefficient of kinetic friction between the block and the ramp is \(\mu_k\). After the block has traveled a distance \(D\) along the ramp, what is the speed of the block?

![A block of mass M on a ramp inclined at angle theta. A force vector F points up the ramp. The distance traveled is labeled D. A dashed line represents the horizontal base.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774004052-AOXGwC.jpg)

- **A.** \(\sqrt{\dfrac{2D}{M}(F - Mg(\sin\theta + \mu_k\cos\theta))}\)
- **B.** \(\sqrt{\dfrac{2D}{M}(F - Mg(\cos\theta + \mu_k\sin\theta))}\)
- **C.** \(\sqrt{\dfrac{2D}{M}(F - Mg\sin\theta)}\)
- **D.** \(\sqrt{\dfrac{2D}{M}(F + Mg(\sin\theta - \mu_k\cos\theta))}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109172/*