---
title: "Three rectangular blocks of mass \\(m\\), \\(2m\\), and \\(3m\\) are stacked vertically on a frictionless horizontal table, with the block of mass \\(m\\) on top, the block of mass \\(2m\\) in the middle, and the block of mass \\(3m\\) at the bottom. The coefficient of static friction between any two contacting block surfaces is \\(\\mu_s\\), and the blocks do not tip. In three separate trials, a horizontal pulling force of magnitude \\(F_1\\), \\(F_2\\), or \\(F_3\\) is applied to the block of mass \\(m\\), \\(2m\\), or \\(3m\\), respectively. Which of the following correctly ranks the maximum magnitudes of \\(F_1\\), \\(F_2\\), and \\(F_3\\) for which the entire three-block stack accelerates together without slipping at any interface?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124151/"
date_modified: "2026-09-28T13:30:46+00:00"
---

# Three rectangular blocks of mass \(m\), \(2m\), and \(3m\) are stacked vertically on a frictionless horizontal table, with the block of mass \(m\) on top, the block of mass \(2m\) in the middle, and the block of mass \(3m\) at the bottom. The coefficient of static friction between any two contacting block surfaces is \(\mu_s\), and the blocks do not tip. In three separate trials, a horizontal pulling force of magnitude \(F_1\), \(F_2\), or \(F_3\) is applied to the block of mass \(m\), \(2m\), or \(3m\), respectively. Which of the following correctly ranks the maximum magnitudes of \(F_1\), \(F_2\), and \(F_3\) for which the entire three-block stack accelerates together without slipping at any interface?

Three rectangular blocks of mass \(m\), \(2m\), and \(3m\) are stacked vertically on a frictionless horizontal table, with the block of mass \(m\) on top, the block of mass \(2m\) in the middle, and the block of mass \(3m\) at the bottom. The coefficient of static friction between any two contacting block surfaces is \(\mu_s\), and the blocks do not tip. In three separate trials, a horizontal pulling force of magnitude \(F_1\), \(F_2\), or \(F_3\) is applied to the block of mass \(m\), \(2m\), or \(3m\), respectively. Which of the following correctly ranks the maximum magnitudes of \(F_1\), \(F_2\), and \(F_3\) for which the entire three-block stack accelerates together without slipping at any interface?

![A side-view diagram shows three rectangular blocks stacked on a horizontal ground line. The bottom block is the widest and has mass label \(3m\) centered inside it. Directly atop it rests a second rectangular block of medium width with mass label \(2m\) centered inside it. Directly atop that rests a third rectangular block of narrow width with mass label \(m\) centered inside it. The horizontal ground beneath the bottom block is drawn as a smooth solid horizontal line. No force arrows are drawn. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602246-nXIVsL.jpg)

- **A.** \(F_3 = F_2 > F_1\)
- **B.** \(F_3 > F_2 > F_1\)
- **C.** \(F_2 > F_3 > F_1\)
- **D.** \(F_1 > F_2 > F_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124151/*