Levers and simple machines for QCE Engineering Unit 4

Syllabus dot point

“Analyse the three classes of lever using the principle of moments, and identify how simple machines such as levers, pulleys, wheel-and-axle and inclined planes provide mechanical advantage”

QCEEngineeringUnit 4: Machines and mechanisms6 min readUpdated 29 May 2026

Quick answer

A lever balances when the moment of the effort equals the moment of the load about the fulcrum: $F_e \times d_e = F_l \times d_l$ . Levers come in three classes set by the order of the fulcrum (F), load (L) and effort (E) along the bar. Class 1 has the fulcrum in the middle (a seesaw, pliers); class 2 has the load in the middle (a wheelbarrow, nutcracker) and always gives mechanical advantage; class 3 has the effort in the middle (tweezers, the human forearm) and always gives a force less than the load but more movement. The other simple machines (the pulley, the wheel-and-axle, the inclined plane, the wedge and the screw) all multiply force in exchange for moving through a greater distance, conserving work.

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What this dot point is asking
The answer
Exam-style questions

What this dot point is asking

QCAA wants you to analyse levers using the principle of moments and to recognise the family of simple machines that all do the same fundamental job: change the size or direction of a force. You need to classify the three lever types by where the effort, load and fulcrum sit, and explain how each simple machine trades force against distance. This underpins the mechanical-advantage calculations that follow.

The answer

The principle of moments in a lever

A lever is a rigid bar that turns about a pivot, the fulcrum. It balances when the turning effect of the effort equals the turning effect of the load:

F_e \times d_e = F_l \times d_l

where $F_e$ is the effort applied at distance $d_e$ from the fulcrum and $F_l$ is the load at distance $d_l$ . Rearranging shows that a long effort arm lets a small effort lift a large load, which is the source of a lever's mechanical advantage.

The three classes of lever

The class depends on the order of the fulcrum (F), load (L) and effort (E) along the bar:

Class 1: fulcrum in the middle, effort and load on opposite sides (a seesaw, a crowbar, scissors). Mechanical advantage can be greater or less than one depending on the arm lengths, and the effort and load move in opposite directions.
Class 2: load in the middle, between the fulcrum and the effort (a wheelbarrow, a nutcracker, a bottle opener). The effort arm is always longer than the load arm, so this class always gives a mechanical advantage greater than one.
Class 3: effort in the middle, between the fulcrum and the load (tweezers, tongs, the human forearm). The effort arm is always shorter, so the effort is always larger than the load, but the load moves further and faster, which is useful for speed and range of movement.

The other simple machines

Every simple machine changes a force at the cost of distance, leaving the work done the same (ignoring friction):

Pulley: a fixed pulley changes direction only; a movable or block-and-tackle system multiplies force by the number of supporting rope sections.
Wheel and axle: effort applied at the large wheel radius produces a larger force at the small axle radius, like a steering wheel or a winch.
Inclined plane: raising a load along a slope needs less force than lifting it vertically, in proportion to the slope length over the height.
Wedge and screw: these are inclined planes in disguise; an axe wedge and a screw thread both convert a smaller applied force over a long distance into a large force over a short one.

Effort to lift a load with a class 2 lever

Find the effort for a wheelbarrow

A wheelbarrow is a class 2 lever. The wheel axle is the fulcrum. A $400\,\text{N}$ load sits $0.40\,\text{m}$ from the axle, and the person lifts the handles $1.2\,\text{m}$ from the axle. Find the effort needed and the mechanical advantage.

Apply the principle of moments about the fulcrum (the axle):

F_e \times d_e = F_l \times d_l

F_e \times 1.2 = 400 \times 0.40

F_e = \frac{160}{1.2} = 133\,\text{N}

So a lift of only $133\,\text{N}$ balances a $400\,\text{N}$ load.

Mechanical advantage:

\text{MA} = \frac{F_l}{F_e} = \frac{400}{133} = 3.0

The wheelbarrow multiplies the effort threefold, which equals the ratio of the arm lengths $1.2/0.40 = 3.0$ , confirming the result. The trade-off is that the handles move three times as far as the load.

Why this matters for machines and mechanisms

Levers and the other simple machines are the building blocks of every mechanism. A complex machine is a combination of these elements, and its overall force multiplication is found by analysing each in turn. Recognising the lever class in a design tells you immediately whether you are gaining force (class 2), gaining speed and range (class 3) or simply changing direction. This feeds straight into the mechanical advantage, velocity ratio and efficiency calculations of Unit 4.

Common errors

Mislabelling the lever class: The class is fixed by which of fulcrum, load and effort lies in the middle, not by whether there is mechanical advantage.
Expecting a class 3 lever to multiply force: Class 3 always needs more effort than the load; its benefit is increased movement and speed of the load, not force.
Using the wrong arm length: The moment uses the perpendicular distance from the fulcrum to the line of the force, which for an angled bar is not the bar length itself.
Thinking a machine creates energy: A simple machine trades force for distance; the work out cannot exceed the work in. Multiplying force always costs extra movement.

Exam-style questions

Questions in the style of QCAA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.

Practice4 marks

Explain the purpose of a crowbar using the concepts of mechanical advantage and velocity ratio. Include a sketch to support your response.

Show worked answer →

A crowbar is a class-1 lever (fulcrum between effort and load). Four marks: one for an appropriate sketch and three for the explanation.

Sketch: a crowbar resting on a fulcrum, with the load (F_L) on the short arm and the effort (F_E) applied at the far end of the long arm [1 mark].

Purpose: the crowbar provides a mechanical advantage that reduces (amplifies) the effort force needed to move a load, by pivoting about the fulcrum [1 mark].

Mechanical advantage: MA = F_L / F_E. Placing the fulcrum close to the load makes the effort arm much longer than the load arm, so the leverage is large and the effort needed is small [1 mark for wording that links a longer effort arm to reduced effort].

Velocity ratio: VR = d_E / d_L, the distance moved by the effort divided by the distance moved by the load. The long effort arm sweeps a much greater distance than the load rises, which is the cost of the force multiplication [1 mark].

Practice5 marks

An effort of 120 N is applied at the end of the lever arm of a screw jack for 180 seconds to raise an object 150 mm. The screw has a pitch of 12 mm and the lever arm is 300 mm. a) Calculate the work done on the lever arm. b) Calculate the power input.

Show worked answer →

A screw jack is a simple machine: one full turn of the lever raises the load by one pitch. Five marks total (four for part a, one for part b).

Part a (work done on the lever arm):

Number of turns to raise the load = lift / pitch = 150 / 12 = 12.5 rotations [1 mark].
The effort moves in a circle of radius equal to the lever arm, r = 300 mm = 0.3 m (convert mm to m) [1 mark].
Distance moved by the effort = turns x circumference = 12.5 x 2 x pi x 0.3 = 23.56 m [1 mark].
Work done = F x d = 120 x 23.56 = 2827.2 J [1 mark].

Part b (power input): P = W / t = 2827.2 / 180 = 15.7 W [1 mark].

The large effort distance (23.56 m) for a 150 mm lift is the velocity ratio at work: the screw jack multiplies force heavily, so the effort must travel a long way.

Practise this

Sources & how we know this

Engineering General senior syllabus 2025 — QCAA