Question

A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 22 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench.

Answer 1

Given,

The magnitude of the torque is

$T=22\text{ N.m}$

The angle is

$\theta=60\text{ }$

The distance d is

$d=0.30\text{ m}$

Solution:

The torque is calculated by the formula,

$T=dFsin\theta$

Calculate the magnitude of the force.

$\begin{gathered} F=\frac{T}{dsin\theta} \\ F=\frac{22\text{ N.m}}{0.30\text{ m}\times sin(60)} \\ F=\frac{22\text{ N.m}}{0.30\times\frac{\sqrt{3}}{2}} \\ F=157.8\text{ N} \end{gathered}$

Thus, the magnitude of the force is 157.8 N.