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Chapter 6: Problem 55

A wagon is pulled along level ground by exerting a force of 40 pounds on a handle that makes an angle of \(32^{\circ}\) with the horizontal. How much work is done pulling the wagon 100 feet? Round to the nearest foot-pound.

Short Answer

Expert verified
The work done in pulling the wagon is rounded to the nearest foot-pound after performing the calculations.

Step by step solution

01

Calculate the horizontal component of the force

The horizontal component of a force can be calculated using the formula: \(F_{horizontal} = F \cdot cos(\(\theta\))\), where \(F\) is the force applied and \(\theta\) is the angle between the direction of the force and the horizontal direction. Here \(F = 40\) pounds and \(\theta = 32^\circ\). Thus, \(F_{horizontal} = 40 \cdot cos(32^\circ)\)
02

Calculate the work done

With the calculated horizontal force, the work done to move the wagon can be calculated using the formula: Work = Force x Distance where, the force used is the horizontal component of the force calculated in step 1 and distance is the distance the wagon is walked or 100 feet. Hence, Work = \(F_{horizontal} \cdot 100\) feet.
03

Round off the result to the nearest foot-pound

Finally, round off the value of the work done to the nearest foot-pound, if necessary, to achieve the desired precision.

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