This physics grades 9-10 lesson on work and power notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on work and power and check yourself with the quiz.
Quick answer: Work is the energy that a force transfers when it moves an object, so you find it from W = F × d and measure it in joules. Power is how fast a system transfers energy, so P = E ÷ t, and you measure it in watts. kinetic energy is KE = ½ m v² and gravitational potential energy is GPE = m g h.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: HS-PS3-1
Work and power notes: the key ideas
What is work done in physics?
In physics, work is not tiredness. A force does work when it moves an object, so the amount of work equals the energy that the force transfers. For example, pushing a heavy cart a long way transfers a lot of energy. However, pushing a wall that does not move transfers none.
Work done is the energy that a force transfers when it moves an object through a distance in the direction of the force. You measure it in joules (J). Therefore one joule is the work that a force of 1 N does when it moves an object 1 m.
W = F × d
W = work done in joules (J), F = force in newtons (N), d = distance moved in the direction of the force in metres (m).
Chiamaka in Lagos pulls a crate with a steady force of 150 N for 12 m along a level path.
W = F × d = 150 × 12 = 1800 J.
If the force is not steady, plot a graph of force against distance. The work is the area under the graph, as the next figure shows for a stretched spring.
How do you calculate power?
Two people can do the same work in different times, so the one who is quicker has more power.
Power is the rate of doing work or transferring energy. Its unit is the watt (W): 1 W = 1 J/s. Also, a kilowatt is 1000 W.
P = W ÷ t = E ÷ t
P = power in watts (W), W or E = work done or energy transferred in joules (J), t = time in seconds (s).
Aarav in Pune lifts a 20 kg sack of rice onto a shelf 1.5 m high in 3.0 s. use g = 9.8 N/kg.
weight = 20 × 9.8 = 196 N; W = F × d = 196 × 1.5 = 294 J.
P = W ÷ t = 294 ÷ 3.0 = 98 W.
| Device or activity | Typical power |
|---|---|
| Phone charger | 5 W |
| Walking up stairs (a student) | about 200 W |
| Kettle | 2000 W (2 kW) |
| Car engine at cruising speed | about 20 000 W (20 kW) |
What are kinetic and gravitational potential energy?
Work changes the energy of an object, so two stores matter most in mechanics: the energy of motion and the energy of height.
KE = ½ × m × v² and GPE = m × g × h
KE = kinetic energy (J), m = mass (kg), v = speed (m/s), GPE = gravitational potential energy (J), g = 9.8 N/kg, h = height gained (m).
A motorbike and rider have a mass of 150 kg and travel at 20 m/s.
KE = ½ × 150 × 20² = ½ × 150 × 400 = 30 000 J (30 kJ).
For example, students double the speed and expect double the energy. Because you square v, doubling the speed makes the kinetic energy four times bigger. Also, forgetting to square v, or squaring ½ × m too, are the other classic slips.
How are work and energy linked?
Work done on an object equals the energy that the object receives. For example, a braking force does work against the motion, and that work removes the kinetic energy. When air resistance is small, a falling object converts potential energy into kinetic energy and the total stays constant.
A car of mass 1000 kg moves at 15 m/s and stops with a constant braking force of 5000 N.
Firstly, KE = ½ × 1000 × 15² = 112 500 J. Work by brakes = F × d = KE, so d = 112 500 ÷ 5000 = 22.5 m.
Convert to SI units before you calculate: grams to kilograms, minutes to seconds, kilojoules to joules, and km/h to m/s by dividing by 3.6. Also, write the units next to every number.
- Work: W = F × d, in joules, with d in the direction of the force.
- Power: P = W ÷ t = E ÷ t; 1 W = 1 J/s and 1 kW = 1000 W.
- Kinetic energy: KE = ½ m v²; doubling the speed makes it 4 times larger.
- Gravitational potential energy: GPE = m g h, with g = 9.8 N/kg.
- The area under a force-distance graph equals the work done.
Work done, power and mechanical energy: frequently asked questions
What is the difference between work and power?
Work is the energy that a force transfers, and you measure it in joules. Power is how fast the force does that work, and you measure it in watts, so P = W ÷ t.
Why does carrying a bag along a level path do no work on the bag?
The upward force from your hands is at right angles to the horizontal motion. However, work needs a force in the direction of movement, so the work on the bag by that force is zero.
Why is kinetic energy proportional to speed squared?
The work needed to speed something up depends on both the force and the distance, and both grow with speed. This gives KE = ½ m v², so double the speed means four times the energy.
How many watts are in a kilowatt?
There are 1000 watts in one kilowatt. For example, a 2 kW kettle transfers 2000 J every second.
Is the unit of work the same as the unit of energy?
Yes. Both use joules, because work is a way of transferring energy. In addition, one joule equals one newton metre.
