Question

The tune-up specifications of a car call for the spark plugs to be tightened to a torque of 50 N·m . You plan to tighten the plugs by pulling on the end of a 30-cm-long wrench. Because of the cramped space under the hood, you'll need to pull at an angle of 130° with respect to the wrench shaft.
with what force must you pull ??

Answer 1

$\! \! \! \! \! \! \! \! \! r = 30$cm $ = 0.3$m$\\ \tau = 50$Nm$\\ \theta = 130\degree$

$\! \! \! \! \! \! \! \! \! $Torque, $\vec{\tau} = \vec{r}\times \vec{F}\\\\ \tau = rF\sin \theta \\\\ F = \frac{\tau}{r\sin\theta} = \frac{50}{0.3\times \sin130\degree} = 217.57$N$$