Question

Carlos uses a rope to pull his car 30 m to a parking lot because it ran out of gas. If Carlos exerts 2,000 N of force to pull the rope, and the rope is at an angle of 15° to the road, how much work did he do? Round your answer to two significant figures.

Answer 1

To calculate the work done by Carlos while pulling the car, we can use the work formula:

\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]

where:
- \(\text{Work}\) is the work done (in joules),
- \(\text{Force}\) is the force applied (in newtons),
- \(\text{Distance}\) is the distance over which the force is applied (in meters),
- \(\theta\) is the angle between the force and the direction of movement (in degrees).

Given:
- \(\text{Force} = 2000 \, \text{N}\)
- \(\text{Distance} = 30 \, \text{m}\)
- \(\theta = 15^\circ\)

First, we need to calculate \(\cos(15^\circ)\):

\[
\cos(15^\circ) \approx 0.9659
\]

Now we can plug the values into the work formula:

\[
\text{Work} = 2000 \, \text{N} \times 30 \, \text{m} \times \cos(15^\circ)
\]

\[
\text{Work} = 2000 \, \text{N} \times 30 \, \text{m} \times 0.9659
\]

Calculating this gives:

\[
\text{Work} \approx 2000 \times 30 \times 0.9659 = 57954 \, \text{J}
\]

Rounding this to two significant figures:

\[
\text{Work} \approx 58000 \, \text{J}
\]

Thus, the work done by Carlos is approximately **58,000 J**.