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)

Question

Responses

84 N
84 N

61 N
61 N

0.525 N
0.525 N

840 N

Answer 1

To determine how much force Luisa would need without the nutcracker, we can use the concept of mechanical advantage. The mechanical advantage (MA) is defined as the ratio of the input distance to the output distance.

Given:

• Input distance (distance the handles are squeezed): 12 cm
• Output distance (distance the arms holding the walnut move): 0.3 cm
• Force applied with the nutcracker: 21 N

First, we calculate the mechanical advantage:

\[ \text{Mechanical Advantage (MA)} = \frac{\text{Input Distance}}{\text{Output Distance}} = \frac{12 \text{ cm}}{0.3 \text{ cm}} = 40 \]

This indicates that the force output (the force exerted on the walnut) is 40 times the force input (the force applied by Luisa).

Next, to find the force that Luisa would need to apply without the nutcracker, we multiply the force applied with the nutcracker by the mechanical advantage:

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

Therefore, the force Luisa would need without the nutcracker is 840 N.

The correct response is:

840 N