Question

The cylindrical head bolts on a car are to be tightened with a torque of 62.0 N⋅m. If a mechanic uses a wrench of length 20 cm, what perpendicular force must he exert on the end of the wrench to tighten a bolt correctly?

Answer 1

Question #75151, Physics / Mechanics | Relativity

The cylindrical head bolts on a car are to be tightened with a torque of 62.0 N·m. If a mechanic uses a wrench of length 20 cm, what perpendicular force must be exerted on the end of the wrench to tighten a bolt correctly?

Need to calculate:

**F - ?**

$$\boldsymbol{r} = 20 \, \text{cm} = 0.20 \, \text{m}$$ $$\boldsymbol{M} = 62.0 \, \text{N} \cdot \text{m}$$

Solution:

$$\boldsymbol{M} = \boldsymbol{F} \cdot \boldsymbol{r} \rightarrow \boldsymbol{F} = \frac{\boldsymbol{M}}{\boldsymbol{r}}, \quad \boldsymbol{F} = \frac{\boldsymbol{N} \cdot \boldsymbol{m}}{\boldsymbol{m}} = \boldsymbol{N}, \quad \boldsymbol{F} = \frac{62.0}{0.20} = 310.$$

Answer: $F = 310 \, \text{N}$

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