Re: How do pulleys work?

Hi Kat.

A pulley is a one of the many ways of gaining mechanical advantage. Mechanical advantage is basically a multiplation of applied force. For example, we can lift a 100 pound weight by applying only 50 pounds of force. A single pulley can multiply applied force by a factor of two. Multiple pulleys used in combination are often called a block and tackle, and can achieve even higher mechanical advantage. Archimedes (3rd century BC) is reported to have used compound pulleys to pull a ship onto dry land. The idea is not new, but pulleys are still used to this day to gain mechanical advantage.

To understand how a pulley achieves mechanical advantage, all we need is a piece of string about a foot long. Take the string and hold one end in your left hand and the other in your right. If you bring the ends together and let the string dangle freely, you will notice that the length of the dangling loop is one-half of the entire length, or six inches for our string. If you take your right hand and raise it above your left by two inches, you will notice that the bottom of the loop only rises one inch. Given that bit of experimental data and knowing that energy is conserved, we can show that the force applied to the bottom of the loop is twice the force applied by your right hand. Mechanical energy is equal to force times distance, so we can write this equation:

F_e x d_e = F_l x d_l

Where:

We know from our experiment that d_l is half of d_e, if we plug that into our above equation, we find:

F_l = 2 x F_e

The pulley is placed in the bottom of the loop and a weight can be applied to its shaft. Notice that we apply force on only one end of the string, the other end is fixed. In the real world, the fixed end is usually attached to a rigid object, like the boom of a crane.

Next time you have a chance to visit a construction site, look carefully at the crane, you will see multiple pulleys at work. This way, the crane doesn't have to pull as hard. The tradeoff is that it will have to pull longer, but that's OK because electric motors are good at that. Loaders and backhoes also use mechanical advantage, in the form of hydraulic cylinders. They use a fluid instead of a string, but the principles of mechanical advantage still apply. In all of these cases, energy is conserved.