Lifting with Pulleys
A pulley is a simple machine made of a wheel on an axle or shaft that is designed to support movement and change of direction of a taut cable or belt.
When multiple pulleys are strung together into a block and tackle system, they can provide a tremendous mechanical advantage. The ideal mechanical advantage (IMA) of a pulley system is generally equal to the number of rope sections directly supporting the movable load. For example, if 4 ropes pull up on the load, the force you need to pull the rope is exactly $1/4$ of the total load weight.
Types of Pulleys
- Fixed Pulley: The axle is fixed in place. It has an IMA of 1. It doesn't reduce the effort force but allows you to pull down (using your body weight) to lift a load up.
- Movable Pulley: The axle is free to move in space. It has an IMA of 2, effectively cutting the required effort force in half.
- Block and Tackle: A combination of fixed and movable pulleys. Adding more pulleys increases the IMA proportionately.
The Formula
Example Calculation
Suppose you are lifting an engine block that weighs $2000 , ext{N}$. You are using a block and tackle system with 4 supporting rope sections.
- Identify Mechanical Advantage: $MA = 4$.
- Calculate Effort: $2000 / 4 = 500 , ext{N}$.
You only need to pull with $500 , ext{N}$ of force to lift the $2000 , ext{N}$ engine. However, to conserve energy, you will have to pull 4 meters of rope for every 1 meter the engine rises.