---
title: "Block A of mass \\(m_A\\) rests on top of Block B of mass \\(m_B\\). Block B is more massive than Block A (\\(m_B > m_A\\)). The two-block system sits on a horizontal, frictionless surface. The coefficient of static friction between Block A and Block B is \\(\\mu_s\\), and the coefficient of kinetic friction is \\(\\mu_k\\). A horizontal force of magnitude \\(F_P\\) is applied to Block B to the right, as shown in the figure. Initially, \\(F_P\\) is small enough that Block A and Block B accelerate together without slipping."
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url: "https://nerd-notes.com/ubq/109227/"
date_modified: "2026-04-01T08:25:15+00:00"
---

# Block A of mass \(m_A\) rests on top of Block B of mass \(m_B\). Block B is more massive than Block A (\(m_B > m_A\)). The two-block system sits on a horizontal, frictionless surface. The coefficient of static friction between Block A and Block B is \(\mu_s\), and the coefficient of kinetic friction is \(\mu_k\). A horizontal force of magnitude \(F_P\) is applied to Block B to the right, as shown in the figure. Initially, \(F_P\) is small enough that Block A and Block B accelerate together without slipping.

Block A of mass \(m_A\) rests on top of Block B of mass \(m_B\). Block B is more massive than Block A (\(m_B > m_A\)). The two-block system sits on a horizontal, frictionless surface. The coefficient of static friction between Block A and Block B is \(\mu_s\), and the coefficient of kinetic friction is \(\mu_k\). A horizontal force of magnitude \(F_P\) is applied to Block B to the right, as shown in the figure. Initially, \(F_P\) is small enough that Block A and Block B accelerate together without slipping.

![A horizontal line representing a frictionless surface. A large rectangular block labeled 'Block B' is resting on the surface. A smaller rectangular block labeled 'Block A' is resting on top of Block B. A horizontal arrow pointing to the right starts from the right edge of Block B and is labeled '\(F_P\)'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774091726-feB8nO.jpg)

**Part a)** **Draw** and **label** the forces (not components) that act on Block A and Block B while they are accelerating together to the right. Draw each force as a distinct arrow starting on, and pointing away from, the dot representing the corresponding block. *(3 points)*

**Part b)** **Derive** an expression for the maximum applied force \(F_{MAX}\) that can be applied to Block B such that Block A does not slip relative to Block B. Express your answer in terms of \(m_A\), \(m_B\), \(\mu_s\), \(\mu_k\), and fundamental constants, as appropriate. *(3 points)*

**Part c)** The applied force \(F_P\) is now slowly increased from zero to a value much greater than \(F_{MAX}\). On the axes below, **sketch** a graph of the magnitude of the acceleration of Block A and the magnitude of the acceleration of Block B as a function of \(F_P\). Clearly **label** the two lines as "A" and "B". *(3 points)*

**Part d)** Suppose the experiment is repeated, but this time the horizontal force \(F_P\) is applied to Block A instead of Block B. **Indicate** whether the new maximum force that can be applied before slipping occurs is greater than, less than, or equal to the \(F_{MAX}\) derived in part (b). - [ ] Greater than \(F_{MAX}\) - [ ] Less than \(F_{MAX}\) - [ ] Equal to \(F_{MAX}\) **Justify** your reasoning 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/109227/*