If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 33 N · m, what minimum force must be exerted by the mechanic at the end of a 30 cm-long wrench to loosen the nut?

The minimum force that must be exerted by the mechanic at the end of a 30 cm-long wrench to loosen the nut is 110N

Explanation:

Torque = Fd sin θ

For a torque, the minimum force must be applied perpendicular to the lever arm, so that θ = 90° and sin θ = sin 90° = 1

Torque = 33 N. m

F = Force applied = ?

d = 30 cm = 0.3 m

F = Torque/d = 33/0.3 = 110 N

110 N.

Explanation:

Torque = F * (d sin θ)

Where,

F = force applied

d = distance perpendicular to the force applied.

Minimum force applied is at 90° to the force. Therefore,

Torque = F * (d sin 90°)

33 = F * (0.3 * 1)

= 33/0.3

= 110 N.