Question

Gardeners would need to use 960 Newtons of force to lift a potted tree 45 centimeters onto a deck. Instead, they set up a lever. If they press the lever down 2 meters, how much force do they use to lift the tree?(1 point)
Responses

21,600 N
21,600 N

216 N
216 N

432 N
432 N

1,920 N

Answer 1

To solve this problem, we can use the principle of levers, specifically the relationship between the forces and distances from the fulcrum.

The formula relating the input force (F1), output force (F2), the distance from the fulcrum for the input force (d1), and the distance from the fulcrum for the output force (d2) is given by:

\[ F1 \cdot d1 = F2 \cdot d2 \]

In this case:
- \( F2 = 960 \, \text{N} \) (force required to lift the tree)
- \( d2 = 0.45 \, \text{m} \) (distance the tree is lifted)
- \( d1 = 2 \, \text{m} \) (distance the lever is pressed down)

Rearranging the formula to find \( F1 \):

\[ F1 = \frac{F2 \cdot d2}{d1} \]

Substituting the known values:

\[ F1 = \frac{960 \, \text{N} \cdot 0.45 \, \text{m}}{2 \, \text{m}} \]

Calculating this:

\[ F1 = \frac{432 \, \text{N} \cdot \text{m}}{2} = 216 \, \text{N} \]

Thus, the force used to lift the tree with the lever is **216 N**.

So, the correct response is:

**216 N**.