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

64 N
64 N

.525 N

Answer 1

To find out how much force Alicia would need to crack the pecan without the nutcracker, we can use the principle of mechanical advantage provided by the nutcracker.

The mechanical advantage (MA) can be calculated as the ratio of the input distance to the output distance:

\[ \text{MA} = \frac{\text{Input distance}}{\text{Output distance}} \]

In this case:

- Input distance (distance Alicia squeezes the handles of the nutcracker) = 12 cm
- Output distance (distance the part holding the nut moves) = 0.3 cm

Now, calculate the mechanical advantage:

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

Now that we have the mechanical advantage, we can find the force required without the nutcracker by multiplying the force applied with the mechanical advantage:

\[ \text{Force without nutcracker} = \text{Force with nutcracker} \times \text{MA} \]

Given that the force with the nutcracker is 21 N:

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

So, Alicia would need **840 N** of force to crack the pecan without the nutcracker. Hence, the answer is:

**840 N**