---
title: "A crate of mass \\(m\\) is pulled a distance \\(d\\) along a flat, horizontal surface by a constant force of magnitude \\(F\\) directed at an angle \\(\\theta\\) above the horizontal, where \\(0 < \\theta < 90^\\circ\\). The crate moves purely horizontally to the right. Which of the following correctly identifies the work done on the crate by the applied force \\(W_F\\), the gravitational force \\(W_g\\), and the normal force \\(W_N\\) during this displacement?"
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url: "https://nerd-notes.com/ubq/120699/"
date_modified: "2026-08-23T04:42:44+00:00"
---

# A crate of mass \(m\) is pulled a distance \(d\) along a flat, horizontal surface by a constant force of magnitude \(F\) directed at an angle \(\theta\) above the horizontal, where \(0 < \theta < 90^\circ\). The crate moves purely horizontally to the right. Which of the following correctly identifies the work done on the crate by the applied force \(W_F\), the gravitational force \(W_g\), and the normal force \(W_N\) during this displacement?

A crate of mass \(m\) is pulled a distance \(d\) along a flat, horizontal surface by a constant force of magnitude \(F\) directed at an angle \(\theta\) above the horizontal, where \(0 < \theta < 90^\circ\). The crate moves purely horizontally to the right. Which of the following correctly identifies the work done on the crate by the applied force \(W_F\), the gravitational force \(W_g\), and the normal force \(W_N\) during this displacement?

![A rectangular crate labeled m rests on a horizontal ground line. A horizontal displacement vector arrow labeled d points to the right. A solid arrow labeled F extends from the upper-right corner of the crate directed upward and to the right at an angle labeled \theta above the horizontal. A downward vertical arrow labeled F_g extends from the center of the crate, and an upward vertical arrow labeled F_N extends from the bottom of the crate. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460164-2oTHqZ.jpg)

- **A.** \(W_F = F d\) , \(W_g = -m g d\) , \(W_N = 0\)
- **B.** \(W_F = F d \cos\theta\) , \(W_g = 0\) , \(W_N = 0\)
- **C.** \(W_F = F d \cos\theta\) , \(W_g = -m g d\) , \(W_N = (m g - F \sin\theta)d\)
- **D.** \(W_F = F d \sin\theta\) , \(W_g = 0\) , \(W_N = 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120699/*