The big idea: Every lever has a fulcrum, an effort and a load, and the class is whichever of the three sits in the middle — F, L, E for first, second and third.
The arithmetic is one equation: effort × effort arm = load × load arm, with both arms measured from the fulcrum.
The same beam three times, with the fulcrum, load and effort moved.
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Four steps, on any lever
Find the fulcrum
The point the beam turns about — a hinge, a rivet, an axle, or the edge it rocks on. It is usually the easiest of the three to spot.
Measure both arms from it
Effort arm to where the hand actually grips, not to the end of the tool. Load arm to where the load actually acts.
Apply the moment equation
Effort × effort arm = load × load arm. Rearrange for whichever quantity the question asks for.
Sense-check the answer
A longer effort arm must give a smaller effort. If the effort came out larger than the load on a first- or second-class lever, the arms went in the wrong way round.
A worked pair: A wheelbarrow carries 800 N with the load 0.4 m from the axle and the handles 1.2 m from it.
Effort × 1.2 = 800 × 0.4, so effort = 320 ÷ 1.2 = 267 N. The MA is 800 ÷ 267 = 3, which is also 1.2 ÷ 0.4 — the two routes agree, which is the check.
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| Requirement | Class | Why |
|---|---|---|
| Multiply force, with the load between the hands and the pivot | Second class | The effort arm is always longer, so the MA is always above 1 — a wheelbarrow, a nutcracker, a bottle opener |
| Multiply force AND reverse the movement | First class | Effort and load on opposite sides of the fulcrum — scissors, pliers, a crowbar, a claw hammer |
| Multiply movement, speed or reach | Third class | The effort is between the fulcrum and the load, so force is divided and movement multiplied — tweezers, a fishing rod, a broom |
| A hand force in an awkward place | Any class, plus a linkage | Each bar of a linkage is itself a lever, so a linkage is a way of putting a lever where a lever will not fit |
The arms set the ergonomics too: A large MA needs a long effort arm, and a long effort arm needs a long, sweeping hand movement.
So the ratio is bounded by the user, not by the mechanism: bolt cutters whose handles had to open beyond an arm's reach would be useless whatever their MA said.
How this is tested — analysing load, effort and fulcrum, and calculating them. It comes up two ways:
Paper 1 — multiple choice
- Identify the class of a lever from a drawing.
- Calculate an effort or a load from the arm lengths.
Paper 2 — analysing a product
- Calculate the effort needed in a named product.
- Analyse a lever system and recommend a change.
The trap: Measuring the effort arm to the end of the tool rather than to where the hand actually grips. Moving your grip changes the arm, and therefore the answer.
A wheelbarrow carries 900 N with the load 0.35 m from the axle and the handles 1.05 m from it. Apply the moment equation to find the effort and the MA, then recommend one change and calculate its effect.
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