Asked in PhysicsMechanicsStaticsPulleys
What does a fixed pulley change?
December 13, 2010 2:06PM
In a simple case of lifting a weight using a pulley, there are two ways to do it and two different results.
First, attach a pulley to the ceiling, and a rope to the weight which is on the floor. Run the rope through the pulley. Now we simply pull down on the rope and the weight is lifted up.
In the second case, we attach one end of the rope to the ceiling, the pulley to the weight, and pass the unattached end of the rope through the pulley. Now we have to pull the rope up, and the weight is lifted.
Now let's look at each job and what happens.
In the first case, pull the rope tight without lifting and hold the rope at the top, next to the pulley. If you now pull the rope all the way down to the floor, the weight goes all the way up to the ceiling. Note also that the tension in the rope is equal to the weight being lifted and that there is only one tensioned rope pulling the weight upwards. Passing over the pulley changes the direction of the tension in the rope but doesn't change it's pulling power. Pulling that rope from ceiling to floor is exactly the same as lifting the weight from floor to ceiling.
In the second case, tighten the rope before lifting and hold the rope where it exits the pulley on the weight. Now pull and your hand moves from there to the ceiling - about the same distance (but the other way) as you moved your hand in the other case. However, notice now that the weight is only half way to the ceiling. It is hanging on a loop of rope, one side going to the hook and the other going to your hand. This suggests that the weight is shared by these two parts of the rope and therefore the tension in each piece only needs to be half the weight. Your hand is holding half the weight. The ceiling hook is still holding the other half.
To finish the job, you will have to keep pulling more rope - all the rope which is still there from hook to weight pulley and back to your hand. That's the floor to ceiling distance. In the second case, you pull twice as much rope to finish the job.
And because it takes twice as long, it only needs half the force at any stage.