Question

Assume the magnitude of all of the forces is the same. Which force will result result in the maximum torque exerted on the door? Which force will result in the least amount of torque exerted on the door?

Answer 1

The torque generated by a force F that is applied making an anlge θ with the line that connects the point where F is applied to the axis of rotation, is:

`\tau=rF\sin\theta`

Where r is the distance from the axis of rotation to the point where F is applied.

Since the sine of the angle θ is maximum when θ=90º and minimum when θ=0º, then, the force that exerts the greatest torque is force B, since it is applied perpendicular to the door. The least amount of torque is exerted by force A, since it is parallel to the door.

Therefore, the force that results in the maximum torque exerted on the door is force B.

The force that results in the least amount of torque exerted on the door is force A.