Question

Alice 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?

Answer 1

To crack the pecan without the nutcracker, Alice would need to apply a force of 840 newtons.

Step-by-step explanation:

To calculate the force needed without the nutcracker, we can use the principle of mechanical advantage. The mechanical advantage of a simple machine is the ratio of the output force to the input force. In this case, the output force is the force applied to crack the pecan (21 newtons), and the input force is the force needed without the nutcracker. We can calculate the mechanical advantage using the formula:

Mechanical Advantage (MA) = Output Force / Input Force

Given that the handles of the nutcracker move 12 centimeters while the part holding the nut moves 0.3 centimeters, the mechanical advantage can be calculated as:

MA = 0.3 cm / 12 cm = 0.025

Now, we can use the mechanical advantage formula to solve for the input force:

MA = Output Force / Input Force, where Input Force = Output Force / MA

Input Force = 21 N / 0.025 = 840 N

Therefore, Alice would need to apply a force of 840 newtons without the nutcracker to crack the pecan.