Question

If the torque required to loosen a nut holding a wheel on a car is 89 n · m, what force must be exerted at the end of a 0.25 m lug wrench to loosen the nut when the angle between the force and the wrench is 52◦ ? answer in units of n.

Answer 1

The torque is defined as:

`\tau = F d \sin \theta`
where
F is the force applied
d is the distance of the arm

`\theta` is the angle between the direction of the force and the arm

In this problem, the torque required must be
`\tau=89 Nm`, the length of the arm (the lug wrench) is
`d=0.25 m` and the angle between the force and the wrench is
`\theta=52^(\circ)`, therefore we can find the magnitude of the force by re-arranging the previous equation and by plugging these data into it:

`F= (\tau)/(d \sin \theta)= (89 Nm)/((0.25 m)(\sin 52^(\circ)))=451.8 N`