Answer in units of N.

Question

If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 43 N · m, what minimum force must be exerted by the mechanic at the end of a 29 cm-long wrench to loosen the nut? Answer in units of N.

Answer 1

Torque = Force Vector X Radial Vector = which is the cross product of the two vectors

The scalar value of this formula is

Torq = F X R = F * R * sin ( Ø ) Where F = magnitude of force vector R = magnitude of radial vector

and Ø is smallest angle applied between the tails of both vectors.

When Force is applied perpindicular to radial arm achieves the max Torque and thus yield smallest amount of force to yield the same torque. Thus the wrench is at right angle to long part of the nut is greatest torque.

yields Ø = 90. since sin (90) = 1 then our formula simplifies to

Torq = F X R = F * R * sin ( 90 ) = F * R

Torq = F * R

convert 29cm to meters since we have to have matching units. Torq is in N m (Newton meter)

29cm = 0.29 m Now to set it all up

43 N m = F * 0.29m

F = 43 N m / 0.29 m = 148 N