Question

If the torque required to loosen a nut on a wheel has a magnitude of 40.0 N·m and the force exerted by a mechanic is 133 N, how far from the nut must the mechanic apply the force?

Answer 1

Answer:

The displacemnent of the nut will be 0.3 m.

Explanation:

As we know the torque ($\large{\overrightarrow{\tau}}$) is given by

$\large{\overrightarrow{\tau} = \overrightarrow{r} \times \overrightarrow{F}}$

where $\large{\overrightarrow{r}}$ is the displacement and $\large{\overrightarrow{F}}$ is the applied force.

Given, $\large{|\overrightarrow{\tau}|} = 40 N-m$ and $\large{|\overrightarrow{F}|} = 133 N$

So the magnitude of the displacement of the nut is given by

$\large{r} = \dfrac{\tau}{F} = \dfrac{40}{133} = 0.3 m$