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.