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Work, Energy and Power
Learn the basic ideas, important formulas, units, worked examples and common mistakes in this essential physics topic.
Introduction
Everyday activities such as lifting a bag, pushing a box, running, and operating a machine involve work, energy or power. In physics, these words have precise meanings.
Work is a way of transferring energy. Energy is the ability to do work. Power describes how quickly work is done or energy is transferred. Understanding the connection between them helps us explain motion, machines and many practical systems.
1. What Is Work?
Work is done when a force causes an object to move through a displacement. The force must have a component in the direction of the displacement.
For a constant force acting in the same direction as the displacement:
More generally, if the force makes an angle θ with the displacement:
The SI unit of work is the joule (J). One joule is equal to one newton-metre:
Positive, negative and zero work
Positive work
Work is positive when the force has a component in the same direction as the displacement. For example, a push that speeds up a trolley does positive work.
Negative work
Work is negative when the force has a component opposite to the displacement. Friction usually does negative work on a sliding object.
Zero work
Work is zero when there is no displacement, or when the force is perpendicular to the displacement. For example, the upward force on a book carried horizontally can do zero work on the book in the idealized model.
Net work
Net work is the total work done by all forces acting on an object. It determines the change in the object’s kinetic energy.
Work done by a pushing force
A student pushes a box with a constant horizontal force of 30 N through a distance of 5 m in the same direction as the force. Find the work done.
- Use the formula: W = Fd.
- Substitute the values: W = 30 × 5.
- Calculate: W = 150 J.
Answer: The force does 150 J of work.
2. What Is Energy?
Energy is the capacity of a system to do work or cause change. Energy can be transferred from one object to another and can change from one form to another.
Work and energy have the same SI unit, the joule (J), because doing work transfers energy.
Kinetic energy
Kinetic energy is the energy an object has because of its motion.
Because speed is squared, increasing an object’s speed can greatly increase its kinetic energy.
Kinetic energy of a moving ball
A ball has a mass of 2 kg and moves at 3 m/s. Find its kinetic energy.
- Formula: KE = ½mv2.
- Substitute: KE = ½ × 2 × 32.
- Square the speed: 32 = 9.
- Calculate: KE = 1 × 9 = 9 J.
Answer: The ball has 9 J of kinetic energy.
Gravitational potential energy
Gravitational potential energy is stored energy due to an object’s position in a gravitational field. Near Earth’s surface:
For many school calculations near Earth’s surface, use g ≈ 9.8 m/s2. The reference level for height can be chosen conveniently, but it should be used consistently.
Gravitational potential energy
A 4 kg object is lifted to a height of 2 m. Using g = 9.8 m/s2, find its gravitational potential energy relative to the ground.
- Formula: GPE = mgh.
- Substitute: GPE = 4 × 9.8 × 2.
- Calculate: GPE = 78.4 J.
Answer: The object gains 78.4 J of gravitational potential energy.
Elastic potential energy
An elastic object such as a spring stores energy when it is stretched or compressed. For an ideal spring:
This formula applies when the spring follows the ideal elastic model and the deformation remains within its elastic limit.
3. The Work–Energy Theorem
The work–energy theorem states that the net work done on an object equals the change in its kinetic energy.
For an object of constant mass:
If net work is positive, kinetic energy increases. If net work is negative, kinetic energy decreases. If net work is zero, the object’s kinetic energy remains unchanged.
4. Conservation of Energy
Energy cannot be created or destroyed. It can be transferred between objects or transformed from one form into another. In an isolated system, the total energy remains constant.
For a system in which mechanical energy is conserved:
For example, as an object falls, its gravitational potential energy decreases while its kinetic energy increases. If air resistance and other energy transfers are ignored, the total mechanical energy stays constant.
When friction or air resistance acts, some mechanical energy is transferred into internal energy, often associated with heating. Total energy is still conserved, but mechanical energy alone may not be.
5. What Is Power?
Power is the rate at which work is done or energy is transferred. It tells us how quickly a task is completed, not how much total work is necessarily done.
The SI unit of power is the watt (W):
A larger power means that work is done or energy is transferred more quickly. If the same amount of work is done in less time, the power is greater.
For a constant force acting in the direction of motion, power can also be written as:
Calculating average power
A machine transfers 600 J of energy in 10 s. Find its average power.
- Formula: P = W/t.
- Substitute: P = 600/10.
- Calculate: P = 60 W.
Answer: The machine has an average power of 60 W.
6. Efficiency
Real machines do not transfer all input energy into the desired output. Some energy may be transferred to the surroundings as heat, sound or unwanted motion.
Efficiency has no unit. For a real machine, it is normally less than 100%.
7. Important Formulas at a Glance
| Quantity | Formula | SI unit |
|---|---|---|
| Work | W = Fd cos θ | joule (J) |
| Kinetic energy | KE = ½mv2 | joule (J) |
| Gravitational potential energy | GPE = mgh | joule (J) |
| Elastic potential energy | Ee = ½kx2 | joule (J) |
| Work–energy theorem | Wnet = ΔKE | joule (J) |
| Power | P = W/t | watt (W) |
| Power at constant speed | P = Fv | watt (W) |
| Efficiency | useful output ÷ total input | no unit |
8. Common Mistakes and Misconceptions
- Confusing force with work: A force does not always do work. There must also be displacement with a force component along that displacement.
- Forgetting the angle: Use W = Fd cos θ when the force and displacement are not in the same direction.
- Using distance instead of displacement without checking: The direction of the force matters in work calculations.
- Forgetting to square speed: In KE = ½mv2, square the speed before multiplying.
- Mixing units: Convert mass to kilograms, distance to metres, time to seconds and speed to metres per second when using SI formulas.
- Thinking power is the same as energy: Energy is the amount transferred; power is how quickly it is transferred.
- Assuming mechanical energy is always conserved: Friction and air resistance can transfer mechanical energy into other forms.
- Ignoring signs: Positive work can increase kinetic energy, while negative work can reduce it.
9. How to Solve Work, Energy and Power Problems
- Read the problem carefully and identify what is given and what must be found.
- Choose a system and decide which energy transfers or forces are important.
- Write the appropriate formula before inserting numbers.
- Convert quantities to SI units where necessary.
- Substitute values with their units and calculate carefully.
- Check the answer for a sensible size and correct unit.
Quick Recap
- Work is done when a force causes displacement: W = Fd cos θ.
- The SI unit of work and energy is the joule (J).
- Kinetic energy is energy of motion: KE = ½mv2.
- Gravitational potential energy depends on height: GPE = mgh.
- The net work done equals the change in kinetic energy: Wnet = ΔKE.
- Energy is transferred or transformed, but the total energy of an isolated system is conserved.
- Power is the rate of doing work: P = W/t.
- The SI unit of power is the watt (W), where 1 W = 1 J/s.