Question

Sarah uses an inclined plant to load a chest into her truck. If she does 84 Joules of work, and the inclined plane is 3 meters long, how much force does she expend?(1 point)
Responses

81 N
81 N

28 N
28 N

252 N
252 N

87 N

Answer 1

To find the force exerted by Sarah while loading the chest using the inclined plane, we can use the formula for work:

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

In this scenario, where the force is applied parallel to the distance along the incline (which we can assume means \(\cos(\theta) = 1\)), the formula simplifies to:

\[
\text{Work} = \text{Force} \times \text{Distance}
\]

Given:
- Work = 84 Joules
- Distance (length of the inclined plane) = 3 meters

We can rearrange the formula to solve for force:

\[
\text{Force} = \frac{\text{Work}}{\text{Distance}}
\]

Substituting the known values:

\[
\text{Force} = \frac{84 \text{ Joules}}{3 \text{ meters}} = 28 \text{ N}
\]

Thus, the force Sarah expends is **28 N**.