Answered: A cord is used to lower vertically a…

Name: A cord is used to lower vertically a block of mass M a distance dat a
Uploaded: 2024-03-20T06:57:25.000Z
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Description: A cord is used to lower vertically a block of mass M a distance dat a constant downward acceleration of g/4. Find the work done by the cord on the block.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A cord is used to lower vertically a block of mass M a distance dat a constant downward acceleration of g/4. Find the work done by the cord on the block.

Expert Solution

Step 1

Given:

The mass of the block is M.
The distance is d.
The downward acceleration is $a = \frac{g}{4}$ .

The following is the free body diagram of the block.

The expression of net force is given by,

$\begin{array}{rcl} F_{n} & = & M g - F \\ M a & = & M g - F \\ F & = & M (g - a) \end{array}$

Substitute the values in the above expression.

$F = M (g - \frac{g}{4}) F = \frac{3 M g}{4}$

The expression of work done is given by,

$W = F d \cos θ$

Here, $θ$ is the angle between force exerted on the block and its displacement whose value is 180 degree.

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