Luisa uses a nutcracker to crack walnuts. She has to squeeze the handles 12 centimeters to crack a walnut. The part of the arms holding the walnut only move 0.3 centimeters. If Luisa applies 21 Newtons of force to crack the walnut, how much force would she need without the nutcracker?(1 point) Responses
A. 61 N
B. 0.525 N
C. 840 N
D. 84 N
To solve this problem, we can use the concept of mechanical advantage. The mechanical advantage of a machine is defined as the ratio of the output force to the input force.
In this case, the output force is the force applied to crack the walnut, which is 21 N. The input force is the force that needs to be applied without the nutcracker.
To find the mechanical advantage, we can use the formula:
Mechanical Advantage = Output Force / Input Force
Given that the mechanical advantage is equal to the distance moved by the handles divided by the distance moved by the arms holding the walnut, we can write:
Mechanical Advantage = (Distance moved by handles) / (Distance moved by arms holding the walnut)
Plugging in the given values, we have:
Mechanical Advantage = 12 cm / 0.3 cm = 40
Now we can rearrange the formula to solve for the input force:
Input Force = Output Force / Mechanical Advantage
Input Force = 21 N / 40
Input Force = 0.525 N
Therefore, the answer is B. 0.525 N.