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.

1.6 × 104 J
3.5 × 104 J
5.8 × 104 J
9.0 × 104 J

1 answer

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

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

where:

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

In this case:

  • \( F = 2000 , \text{N} \)
  • \( d = 30 , \text{m} \)
  • \( \theta = 15^\circ \)

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

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

Now we can substitute the values into the work formula:

\[ W = 2000 , \text{N} \cdot 30 , \text{m} \cdot \cos(15^\circ) \] \[ W \approx 2000 \cdot 30 \cdot 0.9659 \] \[ W \approx 60000 \cdot 0.9659 \] \[ W \approx 57954 , \text{J} \]

Rounding to two significant figures gives us:

\[ W \approx 5.8 \times 10^4 , \text{J} \]

So, the amount of work Carlos did is \( \boxed{5.8 \times 10^4 , \text{J}} \).