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?

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 force applied (in newtons),
- \( d \) is the distance moved (in meters),
- \( \theta \) is the angle between the force and the direction of motion.

Given:
- \( F = 115 \, \text{N} \)
- \( d = 1600 \, \text{m} \)
- \( \theta = 25^\circ \)

Now, we plug the values into the equation. First, calculate \( \cos(25^\circ) \).

Using a calculator:

\[
\cos(25^\circ) \approx 0.9063
\]

Now, substituting the values into the work formula:

\[
\text{Work} = 115 \, \text{N} \cdot 1600 \, \text{m} \cdot \cos(25^\circ)
\]
\[
\text{Work} = 115 \, \text{N} \cdot 1600 \, \text{m} \cdot 0.9063
\]
\[
\text{Work} \approx 115 \cdot 1600 \cdot 0.9063
\]
\[
\text{Work} \approx 115 \cdot 1450.08
\]
\[
\text{Work} \approx 166.056 \, \text{J}
\]

Now we complete the calculation:

\[
\text{Work} \approx 166,056 \, \text{J} \approx 167,000
\]

Therefore, the work done is approximately:

\[
\text{Work} \approx 166,056 \, \text{J}
\]

Thus, the final answer is:

\[
\text{Work} \approx 166,000 \, \text{J} \text{ (or 166 kJ)}
\]