Physics · Lesson 6

Work, energy and power

JAMBWAECNECO

What the syllabus asks

JAMB: Work, energy and power; simple machines; conservation of energy

WAEC: Work, energy and power: concept of work (W = Fd cos θ), forms of energy, kinetic and potential energy, conservation of mechanical energy, power, efficiency; simple machines (levers, pulleys, inclined plane, screw, wheel and axle): mechanical advantage, velocity ratio and efficiency; energy sources and the kilowatt-hour

NECO: Work, energy and power: concept of work (W = Fd cos θ), forms of energy, kinetic and potential energy, conservation of mechanical energy, power, efficiency; simple machines (levers, pulleys, inclined plane, screw, wheel and axle): mechanical advantage, velocity ratio and efficiency; energy sources and the kilowatt-hour

What you will learn

Define work and calculate it, including forces at an angle.
Describe forms of energy and energy conversions.
Calculate kinetic and potential energy.
Apply conservation of mechanical energy.
Define and calculate power and efficiency.
Calculate MA, VR and efficiency of simple machines.
Calculate electrical energy in kWh and its cost.

Key points

Work W = Fd cos θ, measured in joules; no movement or perpendicular motion means no work.
The area under a force–distance graph equals work done.
Energy is the capacity to do work; it is conserved and changes form.
KE = ½mv² (doubling speed quadruples KE); PE = mgh; spring energy = ½ke².
Free fall: mgh = ½mv², v = √(2gh), independent of mass.
Net work done = change in kinetic energy.
Power P = W/t = Fv, in watts.
Efficiency = useful output ÷ input × 100%, always below 100%.
Machines: MA = L/E, VR = dₑ/dₗ, η = MA/VR; pulleys VR = supporting strands; ramp VR = length/height.
1 kWh = 3.6 × 10⁶ J; cost = kWh × tariff.

Start here: What is work in physics?

In everyday language, reading for an exam is "hard work". In physics, work has a precise meaning: a force must move something.

Work is done when a force moves its point of application in the direction of the force.
W = F × d, where F is the force (N) and d the distance moved in the direction of the force (m).
Unit: the joule (J). 1 J = 1 N × 1 m.

If a farmer pushes a wheelbarrow with a force of 50 N for 4 m, the work done is 50 × 4 = 200 J. But if a security man stands holding a heavy bag for an hour without moving, he does no work on the bag in physics, even though he feels tired, because the bag does not move.

Three conditions for no work

No force acts.
The object does not move (d = 0).
The motion is perpendicular to the force. A woman carrying a basin of water on her head while walking on level ground does no work on it against gravity: the force (upward) is at 90° to the motion (horizontal).

Worked example 6.1

A student lifts a 20 kg bag of rice onto a lorry 1.5 m high. Find the work done against gravity. (g = 10 m/s²)

Force needed = weight = mg = 20 × 10 = 200 N.
W = 200 × 1.5 = 300 J.

300 J

Worked example 6.2

How much work is done when a force of 25 N pushes a box 80 cm?

Convert: 80 cm = 0.8 m.
W = 25 × 0.8 = 20 J.

20 J

⚠️ Common mistake: using mass instead of weight. Work against gravity uses the force mg, in newtons, not kilograms.

Try it yourself. A man pushes against a wall with 400 N for 2 minutes. How much work does he do on the wall?

Show solution

Zero: the wall does not move.

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Practice questions

1. A force of 40 N moves a crate 7 m along its line of action. Find the work done.

Show worked answer

280 J.

2. Find the KE of a 0.15 kg ball moving at 40 m/s.

Show worked answer

½ × 0.15 × 1600 = 120 J.

3. A 3 kg mass falls from 12 m. Find its speed just before impact.

Show worked answer

√240 ≈ 15.5 m/s.

4. An engine does 90 kJ of work in 1.5 minutes. Find its power.

Show worked answer

90,000/90 = 1,000 W.

5. A machine of VR 8 lifts 2,000 N with an effort of 400 N. Find its efficiency.

Show worked answer

MA = 5; 62.5%.

Key words

Work: Product of force and distance moved in the direction of the force.
Joule (J): Work done when a force of 1 N moves through 1 m.
Energy: The capacity to do work.
Kinetic energy: Energy a body has because of its motion.
Potential energy: Energy a body has because of its position or state.
Conservation of energy: Energy cannot be created or destroyed, only changed from one form to another.
Power: Rate of doing work or transferring energy.
Watt (W): One joule per second.
Efficiency: Useful energy (or work) output ÷ energy input, × 100%.
Machine: A device that makes work easier by changing the size or direction of a force.
Mechanical advantage (MA): Load ÷ effort.
Velocity ratio (VR): Distance moved by effort ÷ distance moved by load.

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