To find out how much force Luisa would need to crack a walnut without the nutcracker, we can use the principle of mechanical advantage, which is a concept in physics that relates to the force applied and the movements resulting from that force.
The mechanical advantage (MA) can be calculated as the ratio of the distance the input moves to the distance the output moves:
\[ MA = \frac{d_{input}}{d_{output}} \]
Where:
- \(d_{input}\) is the distance the handles are squeezed (12 cm)
- \(d_{output}\) is the distance the arms holding the walnut move (0.3 cm)
Calculating the mechanical advantage:
\[ MA = \frac{12 , \text{cm}}{0.3 , \text{cm}} = 40 \]
Next, we can find the output force required without the nutcracker by multiplying the input force by the mechanical advantage:
\[ F_{output} = F_{input} \times MA \]
Given the input force \(F_{input} = 21 , \text{N}\):
\[ F_{output} = 21 , \text{N} \times 40 = 840 , \text{N} \]
Therefore, the force Luisa would need to crack a walnut without the nutcracker is 840 N.