---
title: "A motorized winch is used to lift a crate of mass \\(M\\) vertically. In the first phase of the motion, the winch accelerates the crate upward from rest with a constant acceleration \\(a = g\\), where \\(g\\) is the acceleration due to gravity. At the instant the crate reaches a speed \\(v\\), the winch immediately adjusts its output so that the crate continues to move upward at that constant speed \\(v\\). Let \\(P_1\\) be the instantaneous power delivered by the winch to the crate at the moment it reaches speed \\(v\\) while still accelerating. Let \\(P_2\\) be the power delivered by the winch while the crate is moving at the constant speed \\(v\\).   What is the ratio \\(\\dfrac{P_1}{P_2}\\)?"
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url: "https://nerd-notes.com/ubq/109313/"
date_modified: "2026-03-21T23:23:50+00:00"
---

# A motorized winch is used to lift a crate of mass \(M\) vertically. In the first phase of the motion, the winch accelerates the crate upward from rest with a constant acceleration \(a = g\), where \(g\) is the acceleration due to gravity. At the instant the crate reaches a speed \(v\), the winch immediately adjusts its output so that the crate continues to move upward at that constant speed \(v\). Let \(P_1\) be the instantaneous power delivered by the winch to the crate at the moment it reaches speed \(v\) while still accelerating. Let \(P_2\) be the power delivered by the winch while the crate is moving at the constant speed \(v\). 

What is the ratio \(\dfrac{P_1}{P_2}\)?

A motorized winch is used to lift a crate of mass \(M\) vertically. In the first phase of the motion, the winch accelerates the crate upward from rest with a constant acceleration \(a = g\), where \(g\) is the acceleration due to gravity. At the instant the crate reaches a speed \(v\), the winch immediately adjusts its output so that the crate continues to move upward at that constant speed \(v\). Let \(P_1\) be the instantaneous power delivered by the winch to the crate at the moment it reaches speed \(v\) while still accelerating. Let \(P_2\) be the power delivered by the winch while the crate is moving at the constant speed \(v\). 

What is the ratio \(\dfrac{P_1}{P_2}\)?

![A vertical setup showing a motorized winch at the top of a frame. A single cable extends downward from the winch and is attached to the top of a square crate labeled with mass M. A vertical arrow pointing upward next to the crate is labeled with velocity vector v. The background is a simple laboratory or warehouse setting.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774135430-ricPDt.jpg)

- **A.** \(1/2\)
- **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/109313/*