Physics · Lesson 7

Simple machines

JAMBWAECNECO

What the syllabus asks

JAMB: Simple machines: types, MA, VR, efficiency, relationship between them, applications

WAEC: Simple machines: definition, mechanical advantage, velocity ratio and efficiency; levers (three classes), pulleys (single and block and tackle), inclined plane, wheel and axle, screw jack, gears, hydraulic press; effect of friction; work input and output

NECO: Simple machines: definition, mechanical advantage, velocity ratio and efficiency; levers (three classes), pulleys (single and block and tackle), inclined plane, wheel and axle, screw jack, gears, hydraulic press; effect of friction; work input and output

What you will learn

Define machine, load, effort, MA, VR and efficiency.
Derive and use efficiency = MA/VR × 100%.
Classify levers and solve lever problems.
Find VR and efficiency of pulleys, inclined planes and wheel and axle.
Find VR of screw jacks, gears and hydraulic presses.
Explain why efficiency is less than 100% and how to improve it.

Key points

MA = load/effort; VR = effort distance/load distance; both have no units.
Efficiency = MA/VR × 100% = work output/work input × 100%.
Levers: classes 1, 2, 3 have fulcrum, load, effort in the middle; VR = effort arm/load arm.
Pulleys: VR = number of rope sections supporting the movable block.
Inclined plane: VR = l/h = 1/sin θ.
Wheel and axle R/r; screw jack 2πr/p; gears teeth driven/driver; hydraulic A/a.
Real machines: MA < VR, efficiency < 100% due to friction and moving parts.
Improve efficiency with lubrication, bearings and lighter parts.

Start here: What a machine does

A machine is any device that allows a force (the effort) applied at one point to overcome a resisting force (the load) at another point. A crowbar lifting a heavy stone, a pulley raising a bucket from a well, a ramp for loading a lorry, a car jack: all are machines.

Machines help in three ways:

Force multiplier: a small effort overcomes a large load (car jack).
Speed or distance multiplier: the load moves further or faster than the effort (bicycle gears at high speed, fishing rod).
Change of direction: pulling down to lift something up (a single fixed pulley on a flagpole).

A machine cannot give out more work than is put in. If it multiplies force, the effort must move a greater distance.

Worked example 7.1

A man uses a ramp to push a 500 N drum onto a platform 2 m high. He pushes along a 10 m ramp. Ignoring friction, find the effort needed.

Work output = 500 × 2 = 1000 J.
Ideal machine: work input = output: E × 10 = 1000.
E = 100 N.

100 N

He uses one fifth of the force, but pushes five times as far. This trade-off is at the heart of every machine.

⚠️ Common mistake: thinking a machine saves work. It reduces the force (or changes direction); the work is the same or more.

Try it yourself. What does a single fixed pulley on a flagpole mainly do?

Show solution

It changes the direction of the force (pull down to raise the flag).

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Practice questions

1. A machine has VR 8 and MA 6. Find its efficiency.

Show worked answer

6/8 × 100 = 75%.

2. A 900 N load is raised by a 300 N effort. Find MA.

Show worked answer

3. A ramp is 12 m long and 3 m high. A 400 N box needs a 125 N effort. Find VR, MA and efficiency.

Show worked answer

VR 4; MA 3.2; 80%.

4. A block and tackle has 4 pulleys and is 70% efficient. Find the effort to lift 1400 N.

Show worked answer

MA = 2.8; E = 500 N.

5. A screw jack has pitch 0.4 cm and handle 28 cm. Find VR (π = 22/7).

Show worked answer

2 × 22/7 × 28/0.4 = 440.

Key words

Machine: A device that enables work to be done more easily or conveniently.
Load: The force overcome by the machine.
Effort: The force applied to the machine.
Mechanical advantage (MA): The ratio load ÷ effort.
Velocity ratio (VR): Distance moved by effort ÷ distance moved by load in the same time.
Efficiency: Useful work output as a percentage of work input.
Fulcrum: The pivot point of a lever.
Pitch: The distance between adjacent threads of a screw.
Block and tackle: A pulley system with several pulleys in two blocks.
Ideal machine: A frictionless, weightless machine with MA = VR and 100% efficiency.
Work input: Effort × distance moved by effort.
Work output: Load × distance moved by load.

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