Force Multiplication and Simple Machines
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device, or machine system. The device fundamentally trades off distance for force to achieve the desired output.
Simple machines like levers, pulleys, inclined planes, and gears do not create energy—that would violate the laws of thermodynamics. Instead, they allow you to apply a smaller force over a longer distance to move a heavier load over a shorter distance. The ratio of the output force (the load being moved) to the input force (the effort you apply) is the mechanical advantage.
Ideal vs. Actual Mechanical Advantage
There are two ways to measure this:
- Ideal Mechanical Advantage (IMA): Calculated based solely on the physical dimensions of the machine (e.g., the length of a lever arm or the number of ropes on a pulley). It assumes a perfect world with zero friction.
- Actual Mechanical Advantage (AMA): Calculated by measuring the actual forces. Because friction always exists in the real world, AMA is always strictly less than IMA.
The Formula
Example Calculation
Suppose you are using a hydraulic jack to lift a truck that weighs $20,000 , ext{N}$. If you only need to apply $400 , ext{N}$ of force to the handle of the jack:
- Divide Output by Input: $20,000 / 400 = 50$.
The mechanical advantage is $50$. This means the jack multiplies your effort force 50 times. However, because energy is conserved, you will have to pump the handle 50 times further than the truck is lifted.