To find the force applied using a simple machine, we can use the work formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
In this case, we know the work done is 216 Joules and the distance is increased from 3 meters (the input distance) to 27 meters (the output distance). However, we will use the input distance to find the force applied since that's where the effort is applied.
Given that:
- Work = 216 J
- Distance = 3 m (input distance)
We can rearrange the formula to solve for force:
\[ \text{Force} = \frac{\text{Work}}{\text{Distance}} \]
Now, substituting the known values:
\[ \text{Force} = \frac{216 \text{ Joules}}{3 \text{ meters}} = 72 \text{ N} \]
Thus, the applied force is 72 N.