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Chapter 10: Problem 30

Computing Work A wagon is pulled horizontally by exerting a force of 20 pounds on the handle at an angle of \(30^{\circ}\) with the horizontal. How much work is done in moving the wagon 100 feet?

Short Answer

Expert verified
The work done is \(1000 \sqrt{3}\) foot-pounds.

Step by step solution

01

Identify the Formula for Work

The formula to calculate work is given by: \[ W = F \times d \times \text{cos}(\theta) \] where: - \( W \) is the work done, - \( F \) is the force applied, - \( d \) is the distance moved, - \( \theta \) is the angle between the force and the direction of movement.
02

Substitute the Given Values

Identify the values given in the problem: - Force \( F = 20 \) pounds - Distance \( d = 100 \) feet - Angle \( \theta = 30^{\theta} \) Substitute these values into the formula: \[ W = 20 \times 100 \times \text{cos}(30^{\theta}) \]
03

Compute the Cosine of the Angle

Calculate the cosine of the angle \( 30^{\theta} \): \[ \text{cos}(30^{\theta}) = \frac{\sqrt{3}}{2} \] Substitute this value into the equation: \[ W = 20 \times 100 \times \frac{\sqrt{3}}{2} \]
04

Simplify the Expression

Simplify the expression to find the work done: \[ W = 20 \times 100 \times \frac{\sqrt{3}}{2} = 2000 \times \frac{\sqrt{3}}{2} \] \[ W = 1000 \sqrt{3} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Work formula
Work in physics is a measure of energy transfer that occurs when a force is applied to move an object over a distance. The general formula to calculate work (\(W\)) is:

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Most popular questions from this chapter

The letters \(x\) and \(y\) represent rectangular coordinates. Write each equation using polar coordinates \((r, \theta) .\) $$ x^{2}+y^{2}=x $$

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