Questions: A wagon is pulled along level ground by exerting a force of 30 pounds on a handle that makes an angle of 30° with the horizontal. How much work is done pulling the wagon 60 feet? W ≈ □ foot-pounds (Round to the nearest whole number as needed.)

Solution Steps

The problem involves calculating the work done when a force is applied at an angle to the direction of movement. The force applied is 30 pounds, the angle with the horizontal is \(30^\circ\), and the distance moved is 60 feet.

The formula for work done when a force is applied at an angle is: \[ W = F \cdot d \cdot \cos(\theta) \] where \(W\) is the work done, \(F\) is the force applied, \(d\) is the distance moved, and \(\theta\) is the angle between the force and the direction of movement.

Substitute the given values into the formula:

• \(F = 30\) pounds
• \(d = 60\) feet
• \(\theta = 30^\circ\)

\[ W = 30 \cdot 60 \cdot \cos(30^\circ) \]

The cosine of \(30^\circ\) is \(\frac{\sqrt{3}}{2}\).

Substitute \(\cos(30^\circ) = \frac{\sqrt{3}}{2}\) into the equation: \[ W = 30 \cdot 60 \cdot \frac{\sqrt{3}}{2} \]

Calculate the work: \[ W = 30 \cdot 60 \cdot 0.8660 \approx 1558.8 \]

Round the result to the nearest whole number: \[ W \approx 1559 \]

Final Answer