Tightened 83632

The key works like a lever, where one arm is the radius of the bolt, and the other is the length of the key. If key no. 12 (for screws with a diameter of 12 mm) and a length of 12 cm can be tightened with a maximum force of 100 N, what force does the wrench exert on the screw?

Correct answer:

F₁ =  2000 N

Step-by-step explanation:

$$\begin{gathered} F_2=100\text{N} \\ {d}_1=12\text{mm}\to \text{cm}=12:10\text{cm}=1.2\text{cm} \\ {r}_2=12\text{cm} \\ {r}_1=d_1/2=1.2/2=\frac{3}{5}=0.6\text{cm} \\ {M}_1=M_2 \\ {F}_1\cdot r_1=F_2\cdot r_2 \\ {F}_1=F_2\cdot \frac{r_2}{r_1}=100\cdot \frac{12}{0.6}=2000\text{N} \end{gathered}$$

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