Why is less force required to open a door when we apply a force at a greater distance from the hinge?

Question

I know that the magnitude of a torque increases with the distance from the axis of rotation. What is the reason of that : how can a force exert a greater torque when the force is applied at a greater distance from the axis of rotation?

Answer 1

The short answer is in the definition of "torque"--namely a rotational forcing function where the magnitude is the linear force applied times the length of a lever arm.

(My definition---look up a more official definition in Wikipedia)

The best way to relate to this is perhaps by looking at a lever or a see-saw. The mechanical advantage of a lever is the ratio of the distances from the fulcrum to the points at which force is applied or measured. Consider a crowbar that is used to lift a heavy object. If the object is 1" from the fulcrum, and the opposite end of the crowbar is 30" from the fulcrum, then the "mechanical advantage" is 30. When we push on the end away from the object--with a force of 100 pounds--the force applied to the object is 3,000 pounds.

At either end, the torque is 3,000 inch-pounds