Question

Luisa collected pecans from a tree outside. She is using a nutcracker to crack them open. She has to squeeze the handles 10 centimeters to crack a pecan. The part of the arms holding the nut only moves 0.2 centimeters. If Luisa applies 21 Newtons of force to crack the pecan, how much force would she need
WITHOUT the nutcracker? (1 point)

840 N

42 N

210 N

1050 N

Answer 1

To find the force that Luisa would need without the nutcracker, we can use the concept of mechanical advantage, which is the ratio of the input distance to the output distance.

In this scenario:
- Input distance (distance that Luisa squeezes the handles) = 10 cm
- Output distance (distance that the nut moves) = 0.2 cm
- Input force (force exerted by Luisa) = 21 N

Mechanic advantage (MA) can be calculated as follows:

\[
MA = \frac{\text{Input distance}}{\text{Output distance}} = \frac{10 \text{ cm}}{0.2 \text{ cm}} = 50
\]

Now, the output force (force needed without the nutcracker) can be calculated using the relationship between input and output forces and the mechanical advantage:

\[
\text{Output force} = \text{Input force} \times MA
\]

So,

\[
\text{Output force} = 21 \text{ N} \times 50 = 1050 \text{ N}
\]

Therefore, the force Luisa would need without the nutcracker is **1050 N**.