The big idea: MA = load ÷ effort — a ratio of FORCES, with no units.
On a lever it is also the effort arm ÷ the load arm. On gears it comes from the tooth counts, and on a pulley or belt from the diameters. Same idea, four places to read it from.
One lever, stepped through: the ratio, the distance it costs, and the case where MA below 1 is wanted.
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| Mechanism | How to find MA | Worked example |
|---|---|---|
| Lever | Effort arm ÷ load arm, both measured from the fulcrum | Effort 600 mm out, load 40 mm out: MA = 600 ÷ 40 = 15 |
| Gear pair | Teeth on the driven gear ÷ teeth on the driver — the torque is multiplied by that ratio | 12-tooth driver into a 48-tooth gear: MA = 48 ÷ 12 = 4 |
| Pulley or belt drive | Driven diameter ÷ driver diameter | 40 mm driver, 160 mm driven: MA = 160 ÷ 40 = 4 |
| Pulley block (lifting) | The number of rope sections supporting the moving block | Four rope falls under the block: MA = 4, and the rope is pulled four metres to lift one |
Always driven over driver: Teeth on the driven gear divided by teeth on the driver. Diameter of the driven pulley divided by the driver.
Taking it the other way up is the single commonest arithmetic error in this topic, and it turns a slow strong output into a fast weak one.
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| MA value | What it means | A product that wants it |
|---|---|---|
| Above 1 | More force at the load than the effort applied, and less movement | Bolt cutters, a car jack, a nutcracker, a crowbar, a garlic press |
| Exactly 1 | The same force in a different place or direction, and nothing else | A pulley redirecting a rope, a bicycle brake cable, a bell crank with equal arms |
| Below 1 | Less force at the load and MORE movement and speed | Tweezers, a fishing rod, a broom, a garden spade, the human forearm |
MA is geometry; efficiency is friction: The MA a drawing predicts is the ideal one. The MA a product delivers is always lower, because friction takes a share.
Keep the two ideas apart: the ratio comes from the dimensions, and the shortfall comes from the bearings, the teeth and the pivots.
How this is tested — calculating mechanical advantage in gear, pulley, belt and lever systems. It comes up two ways:
Paper 1 — multiple choice
- Calculate MA from a load and an effort.
- Calculate MA from two tooth counts or two diameters.
Paper 2 — analysing a product
- Calculate the MA of a named product and say what it buys.
- Explain why a product was given an MA above or below 1.
The trap: Taking the ratio the wrong way up. Driven over driver, every time — and load over effort, not effort over load.
A pair of bolt cutters has 450 mm handles pivoting 30 mm from the jaw, feeding a second linkage of ratio 6. Apply MA to find the force at the jaws from a 250 N hand force, and state what it costs the user.
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