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=(T)/(dsin\theta) \\ F=\frac{22\text{ N.m}}{0.30\text{ m}* sin(60)} \\ F=\frac{22\text{ N.m}}{0.30*(√(3))/(2)} \\ F=157.8\text{ N} \end{gathered}`

Thus, the magnitude of the force is 157.8 N.