---
title: "A motorized crate of mass \\(M\\) is moved up a loading ramp at a constant speed \\(v\\). The ramp is inclined at an angle \\(\\theta\\) above the horizontal, and friction between the crate and the ramp is negligible. In a second trial, the same crate is moved up the same ramp at a constant speed \\(2v\\). What is the ratio \\(\\dfrac{P_2}{P_1}\\) of the average power delivered by the motor in the second trial to the average power delivered in the first trial?"
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url: "https://nerd-notes.com/ubq/112716/"
date_modified: "2026-04-30T21:06:55+00:00"
---

# A motorized crate of mass \(M\) is moved up a loading ramp at a constant speed \(v\). The ramp is inclined at an angle \(\theta\) above the horizontal, and friction between the crate and the ramp is negligible. In a second trial, the same crate is moved up the same ramp at a constant speed \(2v\). What is the ratio \(\dfrac{P_2}{P_1}\) of the average power delivered by the motor in the second trial to the average power delivered in the first trial?

A motorized crate of mass \(M\) is moved up a loading ramp at a constant speed \(v\). The ramp is inclined at an angle \(\theta\) above the horizontal, and friction between the crate and the ramp is negligible. In a second trial, the same crate is moved up the same ramp at a constant speed \(2v\). What is the ratio \(\dfrac{P_2}{P_1}\) of the average power delivered by the motor in the second trial to the average power delivered in the first trial?

![A side view of a crate of mass M on a ramp inclined at an angle theta. A small arrow labeled v points up parallel to the ramp surface. A motor at the top of the ramp is connected to the crate by a cable, pulling it upward.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777583215-VLn36E.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(1\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112716/*