Wrench force calculation

We used a force of 85 N to loosen the nut when using a 20 cm long wrench. How much force do we use to loosen the nut when using a 10 cm long wrench?

Final Answer:

F₂ =  170 N

Step-by-step explanation:

$$\begin{gathered} r_1=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ {F}_1=85\text{N} \\ {r}_2=10\text{cm}\to \text{m}=10:100\text{m}=0.1\text{m} \\ {M}_1=M_2 \\ {r}_1\cdot F_1=r_2\cdot F_2 \\ {F}_2=\frac{r_1}{r_2}\cdot F_1=\frac{\frac{1}{5}}{\frac{1}{10}}\cdot 85=170\text{N} \end{gathered}$$

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