To find out how much force the gardeners use to lift the tree with the lever, we can use the concept of mechanical advantage.
The mechanical advantage (MA) of a lever is given by the ratio of the distances from the fulcrum (pivot point) to the points where the forces are applied. The formula for mechanical advantage is:
\[ \text{MA} = \frac{\text{Distance from fulcrum to effort}}{\text{Distance from fulcrum to load}} \]
In this scenario, the distance the lever is pressed down (effort distance) is 2 meters, and the distance the potted tree is lifted (load distance) is 0.45 meters (which is 45 centimeters).
Now we can calculate the mechanical advantage:
\[ \text{MA} = \frac{2 , \text{meters}}{0.45 , \text{meters}} = \frac{2}{0.45} \approx 4.44 \]
Now, we can relate the input force (effort) and the output force (load) using the mechanical advantage:
\[ \text{Force} (effort) = \frac{\text{Force} (load)}{\text{MA}} \]
Given that the force needed to lift the tree (load) is 960 N, we can now find the required effort:
\[ \text{Force} (effort) = \frac{960 , \text{N}}{4.44} \approx 216 , \text{N} \]
Thus, the amount of force they use to lift the tree with the lever is approximately 216 N.
The correct response is:
216 N