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.
1.6 × 10⁴ j
3.5 × 10⁴ j
5.8 × 10⁴ j
0.0 × 10⁴ j

Explanation:

Step1: Recall the work formula

The formula for work done by a force at an angle is $W = Fd\cos\theta$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between the force and the displacement.

Step2: Identify the given values

We have $F = 2000\text{ N}$, $d = 30\text{ m}$, and $\theta = 15^{\circ}$.

Step3: Calculate $\cos(15^{\circ})$

$\cos(15^{\circ})\approx0.9659$.

Step4: Substitute values into the formula

$W=(2000\text{ N})(30\text{ m})\cos(15^{\circ})=(2000\times30\times0.9659)\text{ J}$.
First, calculate $2000\times30 = 60000$. Then, $60000\times0.9659 = 57954\text{ J}$.

Step5: Round to two significant figures

$57954\text{ J}\approx5.8\times 10^{4}\text{ J}$.

Answer:

$5.8 \times 10^{4}\text{ J}$