---
title: "A block of known mass \\(M\\) rests on a rough horizontal table. It is attached to a lightweight, inextensible string that passes over an ideal pulley at the edge of the table. A mass hanger of negligible mass is attached to the other end of the string. The student is provided with a set of varying known masses \\(m\\) that can be added to the mass hanger, a ruler, and a stopwatch. The student is tasked with designing experiments to determine both the coefficient of static friction \\(\\mu_s\\) and the coefficient of kinetic friction \\(\\mu_k\\) between the block and the table."
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url: "https://nerd-notes.com/ubq/112328/"
date_modified: "2026-04-23T01:45:03+00:00"
---

# A block of known mass \(M\) rests on a rough horizontal table. It is attached to a lightweight, inextensible string that passes over an ideal pulley at the edge of the table. A mass hanger of negligible mass is attached to the other end of the string. The student is provided with a set of varying known masses \(m\) that can be added to the mass hanger, a ruler, and a stopwatch. The student is tasked with designing experiments to determine both the coefficient of static friction \(\mu_s\) and the coefficient of kinetic friction \(\mu_k\) between the block and the table.

A block of known mass \(M\) rests on a rough horizontal table. It is attached to a lightweight, inextensible string that passes over an ideal pulley at the edge of the table. A mass hanger of negligible mass is attached to the other end of the string. The student is provided with a set of varying known masses \(m\) that can be added to the mass hanger, a ruler, and a stopwatch. The student is tasked with designing experiments to determine both the coefficient of static friction \(\mu_s\) and the coefficient of kinetic friction \(\mu_k\) between the block and the table.

![A horizontal table with a rectangular block labeled M resting on it. A string connects to the right side of the block, extends horizontally to a small circular pulley mounted at the right edge of the table, and goes downward. A small hanger labeled m is suspended from the vertical portion of the string.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1776908703-Of6GHx.jpg)

**Part a)** The student first attempts to determine the coefficient of static friction, \(\mu_s\). The student proposes adding a mass \(m\) large enough to cause the block to accelerate, releasing the system from rest, and using the stopwatch and ruler to measure the time \(t\) it takes the block to travel a horizontal distance \(d\). **Explain** why this procedure is incorrect for determining the coefficient of static friction. *(1 points)*

**Part b)** **Describe** a valid experimental procedure the student could use to determine \(\mu_s\) using the provided equipment. Detail the steps taken and what observations or measurements will be made. *(2 points)*

**Part c)** The student now wishes to determine the coefficient of kinetic friction, \(\mu_k\). **Describe** an experimental procedure to collect the necessary data to determine \(\mu_k\) using the ruler and stopwatch. Include any steps taken to reduce experimental uncertainty. *(2 points)*

**Part d)** The student plans to plot a linear graph of the data collected in Part (c) to determine \(\mu_k\). *(4 points)*

**Part e)** In a new experiment, a spring bumper of known spring constant \(k\) is secured to the table. The block is released from rest and travels a distance \(D\) before making contact with the uncompressed spring. The block compresses the spring a maximum distance \(x\) before momentarily coming to rest. Assume the hanging mass \(m\) does not reach the floor during this motion. **Derive** an expression for \(\mu_k\) using work and energy principles. Express your answer in terms of \(M\), \(m\), \(k\), \(D\), \(x\), and fundamental constants. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112328/*