NDA Physics · Work, Energy and Power

Simple Machines — Levers and Mechanical Advantage

A simple machine multiplies force or changes its direction. The lever is the NDA favourite: classified into three orders by where the fulcrum, load, and effort sit — and the second-class lever (fulcrum at one end, load in the middle) is the recurring question.

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Why this matters

A small but reliable scorer — 2 PYQs (2023, 2024), both on lever classification. The whole subtopic comes down to one recall fact: the three orders of levers and where the fulcrum, load, and effort lie in each. Memorise the second-class lever and its examples and these are guaranteed marks.

Concept 1 of 2: The lever and mechanical advantage

A lever is a rigid bar that turns about a fixed point (the fulcrum). Push down on one side and the other side pushes up — and by placing the fulcrum cleverly you can lift a big load with a small effort. How much the lever multiplies your effort is its mechanical advantage.

Definition

A lever is a rigid rod free to rotate about a fixed pivot, the fulcrum, with a load to be moved and an effort applied. Its mechanical advantage is $MA = \dfrac{\text{load}}{\text{effort}} = \dfrac{\text{effort arm}}{\text{load arm}}$ — the ratio of the distances from the fulcrum. A long effort arm and a short load arm give a large mechanical advantage (a small effort lifts a big load).

Mechanical advantage of a lever

MA = \dfrac{\text{load}}{\text{effort}} = \dfrac{\text{effort arm}}{\text{load arm}}

MAmechanical advantage (no units)
$\text{effort arm}$ distance from fulcrum to effort (m)
$\text{load arm}$ distance from fulcrum to load (m)

Worked example

On a lever, the effort arm is 90 cm and the load arm is 30 cm. Find the mechanical advantage, and the effort needed to lift a 60 N load.

Practice this conceptself-check · 4 quick reps

Mechanical advantage multiplies FORCE, not work

A lever lets a small effort move a big load, but it does not create energy: you move the effort end through a larger distance. The work in roughly equals the work out — only the force is multiplied.

Concept 2 of 2: The three orders of levers

Levers come in three classes, set apart by which of the three points — fulcrum, load, effort — sits in the MIDDLE. The NDA test is almost always about the second-class lever, where the LOAD is in the middle (think wheelbarrow or bottle opener).

Definition

Levers are classified by the position of the fulcrum (F), load (L), and effort (E) along the bar:

First class: fulcrum in the MIDDLE (E – F – L) — e.g. a seesaw, scissors, crowbar.
Second class: load in the MIDDLE (F – L – E) — e.g. a wheelbarrow, bottle opener, nutcracker; always $MA > 1$ .
Third class: effort in the MIDDLE (F – E – L) — e.g. forceps, tongs, the human forearm; always $MA < 1$ .

Order	What is in the middle	Examples
First class	Fulcrum in the middle (E–F–L)	seesaw, scissors, crowbar, beam balance
Second class	Load in the middle (F–L–E)	wheelbarrow, bottle opener, nutcracker The bank's favourite. Second class = load in the middle; example = bottle opener / wheelbarrow.
Third class	Effort in the middle (F–E–L)	forceps, tongs, fishing rod, human forearm

Tell them apart by what sits in the middle: fulcrum (1st), load (2nd), effort (3rd). Second-class levers always have mechanical advantage greater than 1.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Sep 2024 · Q71Moderate

Example 2 · Work, Energy and Power · Simple Machines

Which one of the following sketches correctly describes a lever of second class ? (a) Load at one end, fulcrum in middle, effort at other (b) Effort at one end, fulcrum in middle, load at other (c) Fulcrum at one end, load in middle, effort at other end (d) Fulcrum at one end, effort in middle, load at other end

Second class = LOAD in the middle (not fulcrum)

Tell the orders apart by the MIDDLE element: fulcrum (first), load (second), effort (third). A second-class lever has the load between the fulcrum and the effort — a bottle opener or wheelbarrow, not a seesaw.

Drill 1 more on the three orders of levers

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

The lever and mechanical advantage
Mechanical advantage of a lever
$MA = \dfrac{\text{load}}{\text{effort}} = \dfrac{\text{effort arm}}{\text{load arm}}$

Reference tables (1)

The three orders of levers3 rows

Order	What is in the middle	Examples
First class	Fulcrum in the middle (E–F–L)	seesaw, scissors, crowbar, beam balance
Second class	Load in the middle (F–L–E)	wheelbarrow, bottle opener, nutcracker The bank's favourite. Second class = load in the middle; example = bottle opener / wheelbarrow.
Third class	Effort in the middle (F–E–L)	forceps, tongs, fishing rod, human forearm

Tell them apart by what sits in the middle: fulcrum (1st), load (2nd), effort (3rd). Second-class levers always have mechanical advantage greater than 1.

Watch out for (2)

Mechanical advantage multiplies FORCE, not work
→ The lever and mechanical advantage
Second class = LOAD in the middle (not fulcrum)
→ The three orders of levers

Test yourself on Work, Energy and Power

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