If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 31.0 N·m, what minimum force must be exerted by the mechanic at the end of a 34.0 cm lug wrench to accomplish the task?
To determine the minimum force that must be exerted by the mechanic at the end of the lug wrench, we can use the equation:
Torque = Force × Distance
Given:
Torque (τ) = 31.0 N·m
Distance (d) = 34.0 cm = 0.34 m
Rearranging the equation, we have:
Force = Torque / Distance
Let's substitute the given values into the equation:
Force = 31.0 N·m / 0.34 m
Simplifying the equation will give us the minimum force:
Force ≈ 91.18 N
Therefore, the minimum force that must be exerted by the mechanic at the end of the lug wrench is approximately 91.18 Newtons.