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?

Question

Responses

61 N

84 N

840 N

0.525 N

Answer 1

To determine the force Luisa would need to crack the walnut without using the nutcracker, we can use the principle of leverage and the concept of mechanical advantage.

The mechanical advantage (MA) of the nutcracker can be calculated as the ratio of the distance the handles move to the distance the cracking part moves:

\[ MA = \frac{\text{Distance handled moves}}{\text{Distance cracking moves}} = \frac{12 \text{ cm}}{0.3 \text{ cm}} \]

Calculating the mechanical advantage:

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

Now, we know that the force applied multiplied by the mechanical advantage equals the force exerted on the walnut:

\[ \text{Force exerted on walnut} = \text{Force applied} \times MA \]

Given that Luisa applies a force of 21 Newtons:

\[ \text{Force exerted on walnut} = 21 \text{ N} \times 40 = 840 \text{ N} \]

Therefore, without the nutcracker, Luisa would need 840 Newtons of force to crack a walnut.

So the correct response is:

840 N