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.