Calculating Mechanical Advantage of a Pulley or Lever

Hey, I'm Atlas — and today we're going to figure out how a simple machine lets you lift something heavier than you could ever lift alone. Here's the key idea: **Mechanical advantage (MA)** is the ratio of the output force (the load the machine lifts) to the input force (the effort you apply). **MA = Output Force ÷ Input Force** If MA = 3, the machine multiplies your push or pull three times. You push with 50 N and the machine pushes back with 150 N. That's a huge help! **Levers** give you MA through arm lengths. A lever pivots on a fulcrum. The distance from the fulcrum to where you push is the *effort arm*. The distance from the fulcrum to the load is the *resistance arm*. **MA (lever) = Effort Arm Length ÷ Resistance Arm Length** Example: effort arm = 120 cm, resistance arm = 30 cm → MA = 120 ÷ 30 = 4. You only need one-quarter of the load's weight to lift it! **Pulleys** give you MA by adding rope segments. In a movable pulley system, count how many rope segments support the moving block — that number is the MA. Example: 3 rope segments support the load → MA = 3. Important trade-off: a higher MA means you pull a *longer* rope or push the lever handle *farther* — but the load itself rises only a short distance. The output end moves less while the input end moves more; they trade in opposite directions. Energy is never created; you trade a longer push distance for a larger output force, and the total work stays the same. That is math, not magic.