Question

Alicia collected pecans from a tree outside. She is using a nutcracker to crack them open. She has to squeeze the handles 12 centimeters to crack a pecan. The part of the arms holding the nut only moves 0.3 centimeters. If Alice applies 21 Newtons of force to crack the pecan, how much force would she need WITHOUT the nutcracker.(1 point)
Responses

840 N
840 N

61 N
61 N

.525 N
.525 N

64 N

Answer 1

To find the amount of force Alicia would need to apply without the nutcracker, we can use the concept of the mechanical advantage of the nutcracker. The mechanical advantage (MA) can be calculated using the distance moved by the handles and the distance moved by the nut.

The formula for mechanical advantage is:

\[
\text{MA} = \frac{\text{Distance input}}{\text{Distance output}}
\]

In this case:
- Distance input (the distance the handles move) = 12 cm
- Distance output (the distance the nut moves) = 0.3 cm

Now we can calculate the mechanical advantage:

\[
\text{MA} = \frac{12}{0.3} = 40
\]

This means that the force applied with the nutcracker is multiplied by 40.

Now, to find the force Alicia would need to apply without the nutcracker, we can multiply the force she applies with the nutcracker by the mechanical advantage:

\[
\text{Force without nutcracker} = \text{Force with nutcracker} \times \text{MA}
\]
\[
\text{Force without nutcracker} = 21 \, \text{N} \times 40 = 840 \, \text{N}
\]

Therefore, Alicia would need **840 N** of force to crack the pecan without the nutcracker.

The correct response is **840 N**.