how do pulleys increase ratio of rope needed for movement of an object


sorry weird phrasing, i’ll do my best to explain.

I understand how mechanical advantage works, the general idea being that by doing the same work over a different distance you can increase or decrease the force needed to move the object.

however I don’t understand how pulleys work.

If you pull a rope 1m, the other end of the rope should also move 1m, Since the rope is all one connected object.

So how is it that when you pull 1m in a pulley system, the other end of the rope will only move lets say, 0.5m. Physically what happens in a pulley system for that to work, as I just can’t visualise it.

In: Physics

Let’s say is a simple compound pulley system with just two pulleys.

When you pull your end of the rope 1m *both* of the segments of rope between the pulles shorten by .5m. So you have added 1m “outside” all the pulleys and subtracted .5 and .5 from “inside” the pulleys, so it balances out.

I’ll see if I can make a quick sketch for you.

In the ideal case where there is no slipping between pulley and rope, no friction at the hinge of pulley and no elongation in the string, etc., If you pull the string 1 meter other side will move one meter. But ideal cases don’t exist in real life scenarios..

Smarter every day did a nice episode on this: