---
title: "An experiment is conducted to determine the coefficient of kinetic friction \\(\\mu_k\\) between a block of known mass \\(M\\) and a horizontal surface. A force sensor pulls the block at an angle \\(\\theta\\) above the horizontal, as shown in the diagram. In each trial, the angle \\(\\theta\\) is set to a different value, and the magnitude of the pulling force \\(F\\) is adjusted so that the block moves across the surface at a constant velocity. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph that can be used to determine \\(\\mu_k\\), and what is the physical meaning of the vertical intercept of the best-fit line?"
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url: "https://nerd-notes.com/ubq/120601/"
date_modified: "2026-08-23T04:41:54+00:00"
---

# An experiment is conducted to determine the coefficient of kinetic friction \(\mu_k\) between a block of known mass \(M\) and a horizontal surface. A force sensor pulls the block at an angle \(\theta\) above the horizontal, as shown in the diagram. In each trial, the angle \(\theta\) is set to a different value, and the magnitude of the pulling force \(F\) is adjusted so that the block moves across the surface at a constant velocity. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph that can be used to determine \(\mu_k\), and what is the physical meaning of the vertical intercept of the best-fit line?

An experiment is conducted to determine the coefficient of kinetic friction \(\mu_k\) between a block of known mass \(M\) and a horizontal surface. A force sensor pulls the block at an angle \(\theta\) above the horizontal, as shown in the diagram. In each trial, the angle \(\theta\) is set to a different value, and the magnitude of the pulling force \(F\) is adjusted so that the block moves across the surface at a constant velocity. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph that can be used to determine \(\mu_k\), and what is the physical meaning of the vertical intercept of the best-fit line?

![A rectangular block labeled \(M\) rests on a flat horizontal line representing a tabletop. A straight arrow representing the pulling force \(\vec{F}\) originates from the center of the right edge of the block, extending upward and to the right at an acute angle \(\theta\) relative to the horizontal. A horizontal dashed line extends to the right from the base of the arrow \(\vec{F}\), and a curved arc labeled \(\theta\) denotes the angle between the dashed line and the arrow. A separate horizontal arrow above the block points toward the right and is labeled \(\vec{v}\) to indicate motion at constant velocity. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460113-nmEhuM.jpg)

- **A.** Vertical axis: \(F\); Horizontal axis: \(\cos\theta\); Vertical intercept: \(\mu_k M g\)
- **B.** Vertical axis: \(F\cos\theta\); Horizontal axis: \(\sin\theta\); Vertical intercept: \(M g\)
- **C.** Vertical axis: \(F\sin\theta\); Horizontal axis: \(F\cos\theta\); Vertical intercept: \(\mu_k M g\)
- **D.** Vertical axis: \(F\cos\theta\); Horizontal axis: \(F\sin\theta\); Vertical intercept: \(\mu_k M g\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120601/*