---
title: "A block of mass \\(m\\) rests on top of a slab of mass \\(M\\), where \\(M > m\\), which is positioned on a frictionless horizontal floor. The coefficients of static and kinetic friction between the block and the slab are \\(\\mu_s\\) and \\(\\mu_k\\), respectively. A horizontal pulling force of magnitude \\(F_{\\text{bottom}}\\) applied to the slab produces the maximum acceleration the system can achieve without the block slipping relative to the slab, whereas a horizontal pulling force of magnitude \\(F_{\\text{top}}\\) applied to the block produces the maximum acceleration achievable without slip. Which of the following expressions represents the difference \\(\\Delta F = F_{\\text{bottom}} – F_{\\text{top}}\\) in terms of the given quantities and fundamental constants?"
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url: "https://nerd-notes.com/ubq/124089/"
date_modified: "2026-09-28T13:30:23+00:00"
---

# A block of mass \(m\) rests on top of a slab of mass \(M\), where \(M > m\), which is positioned on a frictionless horizontal floor. The coefficients of static and kinetic friction between the block and the slab are \(\mu_s\) and \(\mu_k\), respectively. A horizontal pulling force of magnitude \(F_{\text{bottom}}\) applied to the slab produces the maximum acceleration the system can achieve without the block slipping relative to the slab, whereas a horizontal pulling force of magnitude \(F_{\text{top}}\) applied to the block produces the maximum acceleration achievable without slip. Which of the following expressions represents the difference \(\Delta F = F_{\text{bottom}} – F_{\text{top}}\) in terms of the given quantities and fundamental constants?

A block of mass \(m\) rests on top of a slab of mass \(M\), where \(M > m\), which is positioned on a frictionless horizontal floor. The coefficients of static and kinetic friction between the block and the slab are \(\mu_s\) and \(\mu_k\), respectively. A horizontal pulling force of magnitude \(F_{\text{bottom}}\) applied to the slab produces the maximum acceleration the system can achieve without the block slipping relative to the slab, whereas a horizontal pulling force of magnitude \(F_{\text{top}}\) applied to the block produces the maximum acceleration achievable without slip. Which of the following expressions represents the difference \(\Delta F = F_{\text{bottom}} - F_{\text{top}}\) in terms of the given quantities and fundamental constants?

![A two-dimensional schematic side view of two stacked rectangular blocks on a horizontal floor. A flat horizontal ground line extends across the lower portion with diagonal hatch marks below it. Directly on top of this line rests a wide rectangular slab labeled with a centered capital letter \(M\). Centered on the flat upper surface of this slab rests a smaller rectangular block labeled with a centered lowercase letter \(m\). A horizontal bracket at the interface between the two blocks points to the text label \(\mu_s, \mu_k\). A small text annotation beneath the lower boundary of the slab reads frictionless floor. No arrows, forces, motion lines, coordinate systems, or other text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602222-cn2fui.jpg)

- **A.** \(\dfrac{\mu_s (M^2 - m^2)g}{M}\)
- **B.** \(\mu_s M g\)
- **C.** \(\dfrac{\mu_s (M^2 - m^2)g}{m}\)
- **D.** \(\dfrac{\mu_k (M^2 - m^2)g}{M}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124089/*