Question

Suppose a child pulls on the rope of a sled with a force of 75N and at an angle of 20° with the ground. If the sled moves 40 m along the surface of the ground, how much work was done?

Answer 1

To calculate the work done on the sled by the child, we can use the formula for work, which is given by:

\[
W = F \cdot d \cdot \cos(\theta)
\]

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

In this case:
- \( F = 75 \, \text{N} \)
- \( d = 40 \, \text{m} \)
- \( \theta = 20^\circ \)

First, we need to find \( \cos(20^\circ) \):

\[
\cos(20^\circ) \approx 0.9397
\]

Now we can substitute these values into the work formula:

\[
W = 75 \, \text{N} \cdot 40 \, \text{m} \cdot \cos(20^\circ)
\]

Calculating this:

\[
W = 75 \cdot 40 \cdot 0.9397
\]
\[
W = 3000 \cdot 0.9397
\]
\[
W \approx 2819.1 \, \text{J}
\]

Therefore, the work done by the child on the sled is approximately **2819.1 Joules**.