Pulleys explained: how to count the ropes and find the effort

Pulley questions show up in the EIAT's mechanical comprehension section and on most other mechanical aptitude tests. They are especially relevant to elevator work, where ropes and sheaves do the lifting. One counting rule answers almost all of them.

A single fixed pulley

A pulley fixed to a ceiling, with the rope running over it to the load, only changes the direction of the force. You pull down to lift the load up, which is more convenient, but you pull with a force equal to the load. Its mechanical advantage is 1.

A single movable pulley

If the pulley is attached to the load and moves up with it, the load hangs from two sections of rope — one on each side of the pulley. Each section carries half the weight, so you need only half the force. Its mechanical advantage is 2.

The catch: to lift the load one foot, both sections must shorten by a foot, so you pull two feet of rope.

The counting rule

For any arrangement of pulleys:

mechanical advantage = the number of rope sections supporting the moving load

Count the sections of rope that run up from the moving pulley block (or from the load itself). The rope you pull on counts only if it comes up out of the moving block; if it runs down from a fixed pulley to your hand, it does not.

• 4 supporting sections: a 200 lb load needs about 200 ÷ 4 = 50 lb of effort.
• To raise it 1 ft, you pull 4 ft of rope.

Block and tackle

A block and tackle is a set of pulleys in two blocks — one fixed, one attached to the load — with a single rope threaded between them many times. It is just the counting rule applied to more sections of rope. More sections means less effort and more rope to pull.

You never get something for nothing

Every pulley arrangement trades force for distance. The work you do — force times distance — is the same either way (ignoring friction). Halving the force doubles the rope you have to pull. Test questions often offer an answer that sounds like free energy; it is always wrong.

Real pulleys also lose some effort to friction, so the actual force is a little more than the ideal figure. Unless a question says otherwise, treat pulleys as frictionless.

The common traps

• Counting the pulleys instead of the ropes. Count rope sections holding up the moving load, not wheels.
• Counting a fixed pulley's rope. A section running from a fixed pulley down to your hand does not support the load.
• Forgetting the distance cost. Less force always means pulling more rope.

Practice

Our mechanical practice includes block-and-tackle diagrams and stepped-pulley questions with the rope sections drawn clearly enough to count.