Question

A car applies a force of 36.8 Newtons for a 668-meter loop; what was the work done?
0 J
705 J
24,600 J
18.2 J
0 J
A 8.43-Newton force was applied for an unknown displacement; however, it is known that 376 joules of work was done. What is the value of the mystery displacement?
368 m
3170 m
384 m
44.6 m

Answer 1

To find the work done by the car when a force is applied to move along a distance, we can use the work formula:

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

Where:
- *Work* is measured in joules (J)
- *Force* is measured in newtons (N)
- *Distance* is measured in meters (m)
- *θ* is the angle between the force and the direction of displacement. In this case, since the force is applied in the direction of the displacement (the loop), we assume θ = 0 degrees, and thus \(\cos(0) = 1\).

For the first part:

\[
\text{Work} = 36.8 \, \text{N} \times 668 \, \text{m}
\]
\[
\text{Work} = 36.8 \times 668 \approx 24,605.4 \, \text{J}
\]

Rounding this value gives us approximately:

\[
\text{Work} \approx 24,600 \, \text{J}
\]

So the answer to the first question is **24,600 J**.

---

For the second part, using the work formula again to find the displacement (d):

\[
\text{Work} = \text{Force} \times \text{Displacement}
\]
\[
376 \, \text{J} = 8.43 \, \text{N} \times d
\]

Now, rearranging to solve for displacement (d):

\[
d = \frac{\text{Work}}{\text{Force}} = \frac{376 \, \text{J}}{8.43 \, \text{N}} \approx 44.6 \, \text{m}
\]

So the value of the mystery displacement is **44.6 m**.

In summary:
1. First question answer: **24,600 J**
2. Second question answer: **44.6 m**