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Chapter 6: Problem 56

A wagon is pulled along level ground by exerting a force of 25 pounds on a handle that makes an angle of \(38^{\circ}\) 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 100 feet is approximately 1976 foot-pounds.

Step by step solution

01

Identify the components of the force

Since the force is exerted at an angle to the direction of motion, we need to find the horizontal component of the force. This can be found using the cosine of the angle which is the adjacent component in a right triangle. So, the force in the direction of the wagon's movement (\( F_x \)) is \( F \cos(\theta) \), where \( F = 25 \) pounds is the total force and \( \theta = 38^{\circ} \) is the angle.
02

Calculate the force in the direction of the movement

Substitute the given force and angle into the equation for \( F_x \) to get \( F_x = 25 \cos(38^{\circ}) \). When we calculate this we get approximately \( F_x = 19.76 \) pounds.
03

Calculating the Work Done

Now that we have the force in the direction of the motion, we can calculate the work done. The formula for work done is \( Work = force \times distance \) or \( W = F_x \times d \), where \( d = 100 \) feet is the distance travelled by the wagon. Substituting these numerical values will aid in calculating the work done.
04

Calculate the final value

Now it's time to substitute our values into the work equation to get \( W = 19.76 \times 100 \). This gives us the work done, in foot-pounds, as 1976 foot-pounds.

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