Question

Suppose a 115 N force is applied to a lawnmower handle at an angle of 25° with the ground and the lawnmower moves along the surface of the ground. If the lawnmower moves 1,600 m, how much work was done?

Group of answer choices

255,400 J

34,677 J

25,433 J

166,761 J

Answer 1

To calculate the work done when a force is applied at an angle, we can use the formula:

\[
\text{Work} = F \cdot d \cdot \cos(\theta)
\]

Where:
- \( F \) is the applied force,
- \( d \) is the distance moved in the direction of the force,
- \( \theta \) is the angle between the force and the direction of movement.

Given:
- \( F = 115 \, N \)
- \( d = 1,600 \, m \)
- \( \theta = 25^\circ \)

First, we need to calculate \( \cos(25^\circ) \):

\[
\cos(25^\circ) \approx 0.9063 \quad (\text{using a calculator})
\]

Now, plug in the values into the work formula:

\[
\text{Work} = 115 \, N \times 1,600 \, m \times \cos(25^\circ)
\]
\[
\text{Work} = 115 \, N \times 1,600 \, m \times 0.9063
\]
\[
\text{Work} \approx 115 \times 1,600 \times 0.9063
\]
\[
\text{Work} \approx 166,761.12 \, J
\]

Rounding it to the nearest whole number:

\[
\text{Work} \approx 166,761 \, J
\]

Thus, the work done is approximately **166,761 J**.

The correct answer from the given choices is **166,761 J**.