---
title: "Two blocks of mass \\(M\\) and \\(2M\\) are connected by a light string and placed on a horizontal, frictionless surface. A time-dependent horizontal force \\(F(t)\\) is applied to the block of mass \\(M\\) in a direction away from the other block. The magnitude of the force increases linearly from \\(0\\) at \\(t = 0\\) to a maximum value \\(F_0\\) at \\(t = T/2\\), and then decreases linearly back to \\(0\\) at \\(t = T\\). The system is initially at rest. \\n\\nWhat is the magnitude of the impulse delivered to the block of mass \\(2M\\) by the string during the time interval from \\(t = 0\\) to \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/110261/"
date_modified: "2026-04-01T02:42:06+00:00"
---

# Two blocks of mass \(M\) and \(2M\) are connected by a light string and placed on a horizontal, frictionless surface. A time-dependent horizontal force \(F(t)\) is applied to the block of mass \(M\) in a direction away from the other block. The magnitude of the force increases linearly from \(0\) at \(t = 0\) to a maximum value \(F_0\) at \(t = T/2\), and then decreases linearly back to \(0\) at \(t = T\). The system is initially at rest. \n\nWhat is the magnitude of the impulse delivered to the block of mass \(2M\) by the string during the time interval from \(t = 0\) to \(t = T\)?

Two blocks of mass \(M\) and \(2M\) are connected by a light string and placed on a horizontal, frictionless surface. A time-dependent horizontal force \(F(t)\) is applied to the block of mass \(M\) in a direction away from the other block. The magnitude of the force increases linearly from \(0\) at \(t = 0\) to a maximum value \(F_0\) at \(t = T/2\), and then decreases linearly back to \(0\) at \(t = T\). The system is initially at rest. \n\nWhat is the magnitude of the impulse delivered to the block of mass \(2M\) by the string during the time interval from \(t = 0\) to \(t = T\)?

![A horizontal surface with two rectangular blocks. The left block is labeled 2M and the right block is labeled M. A thin line representing a string connects the centers of the two blocks. A large arrow points to the right from the block labeled M and is labeled F(t).](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775011326-wFBcwg.jpg)

![A plot of Force F vs Time t. The vertical axis is labeled Force F and the horizontal axis is labeled Time t. A line starts at the origin (0,0), increases with a constant positive slope to a peak at coordinates (T/2, F_0), and then decreases with a constant negative slope to the point (T, 0) on the horizontal axis.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-2-1775011326-CqCDVv.jpg)

- **A.** \( \dfrac{F_0 T}{6} \)
- **B.** \( \dfrac{F_0 T}{3} \)
- **C.** \( \dfrac{F_0 T}{2} \)
- **D.** \( \dfrac{2 F_0 T}{3} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110261/*