This note covers the forms of energy, how energy is transferred and conserved, the equations for kinetic and gravitational potential energy, work and power, efficiency, and the main energy resources used to generate electricity. Energy is the central idea that links almost every other topic in physics.
Key ideas
Forms of energy
Energy is measured in joules (J). It is stored in different ways:
- Kinetic: energy of a moving object.
- Gravitational potential: energy stored because of height in a gravitational field.
- Elastic (strain): energy stored in a stretched or compressed object such as a spring.
- Chemical: stored in fuels, food and batteries.
- Thermal (internal): energy of the random motion of particles.
- Electrical, light, sound, nuclear: other forms met elsewhere in the course.
Conservation of energy
Energy cannot be created or destroyed. It can only be transferred from one store to another, or from one place to another. The total energy before an event equals the total energy afterwards. When you describe an energy transfer, say where the energy starts and where it ends up. For example, a battery-powered torch transfers chemical energy to electrical energy, and then to light and thermal energy.
Much of the energy ends up as thermal energy that spreads out into the surroundings. This energy is dissipated (wasted). It is not destroyed, but it is not useful any more.
Kinetic and gravitational potential energy
Kinetic energy depends on mass and on the square of the speed. Doubling the speed makes the kinetic energy four times larger. Gravitational potential energy depends on mass, field strength and height. When an object falls with negligible air resistance, gravitational potential energy is transferred to kinetic energy, and the total stays constant.
Work
Work done is the energy transferred when a force moves an object. It equals the force multiplied by the distance moved in the direction of the force. One joule is the work done by a force of 1 N moving an object 1 m. Lifting a box, pushing a trolley and stretching a spring all involve work. Work done against friction becomes thermal energy.
Power and efficiency
Power is the rate of transferring energy, or of doing work. It is measured in watts (W). 1 W is 1 J every second. A more powerful machine transfers the same energy in a shorter time.
Efficiency compares the useful output with the total input. No machine is 100% efficient, because some energy is always dissipated. Efficiency = useful energy output ÷ total energy input (× 100% for a percentage). The same ratio can be written with power.
Energy resources
- Non-renewable: coal, oil and natural gas (fossil fuels) and nuclear fuel (uranium). These will run out. Fossil fuels release carbon dioxide when burned.
- Renewable: solar, wind, hydroelectric, tidal, geothermal and biofuels. These are naturally replaced. Their output may depend on the weather or the time of day, and some need large areas of land or sea.
Nearly all the energy we use comes ultimately from the Sun. The Sun produces energy by nuclear fusion, in which hydrogen nuclei combine to form helium. Fossil fuels, wind, biofuels and hydroelectric energy all trace back to the Sun. Nuclear fuel, geothermal and tidal energy do not depend on it directly.
In a power station, a fuel or other source heats water to make steam (or wind or flowing water is used directly) to turn a turbine, which turns a generator that produces electrical energy.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Conservation of energy | Energy is never created or destroyed, only transferred. |
| KE = ½ m v2 | Kinetic energy (J); m in kg, v in m/s. |
| GPE = m g h | Change in gravitational potential energy (J); g = 9.8 N/kg, h = height change (m). |
| W = F × d | Work done (J) = force (N) × distance moved in the direction of the force (m). |
| P = W ÷ t = E ÷ t | Power (W) = work done or energy transferred (J) ÷ time (s). |
| Efficiency = useful output ÷ total input | Multiply by 100 for a percentage; use energy or power. |
Worked examples
Example 1 A car of mass 1500 kg is travelling at 20 m/s. Find its kinetic energy.
Step 1: KE = ½ × m × v2.
Step 2: KE = ½ × 1500 × 202 = ½ × 1500 × 400 = 300 000 J.
Answer: 300 000 J (300 kJ).
Example 2 A ball is dropped from a height of 12 m. Ignoring air resistance, find its speed just before it hits the ground (g = 9.8 N/kg).
Step 1: all the gravitational potential energy becomes kinetic energy: m g h = ½ m v2.
Step 2: the mass m cancels: g h = ½ v2, so v2 = 2 g h.
Step 3: v2 = 2 × 9.8 × 12 = 235.2.
Step 4: v = √235.2 = 15.3 m/s.
Answer: 15.3 m/s.
Example 3 A crane lifts a 400 kg load through 25 m in 50 s. The motor takes in electrical energy at a rate of 3000 W. Find the useful work done, the useful power output and the efficiency (g = 9.8 N/kg).
Step 1: the force needed equals the weight = 400 × 9.8 = 3920 N.
Step 2: work done = F × d = 3920 × 25 = 98 000 J.
Step 3: useful power = work ÷ time = 98 000 ÷ 50 = 1960 W.
Step 4: efficiency = 1960 ÷ 3000 = 0.653, which is 65.3%.
Answer: 98 000 J, 1960 W and 65.3% efficient.
Common errors
- Saying energy is "used up" or "lost". It is transferred, and some is dissipated as thermal energy.
- Forgetting to square the speed in ½ m v2.
- Using the length of a slope instead of the vertical height in m g h.
- Confusing energy (J) with power (W). Power is energy per second.
- Writing an efficiency above 100%, or putting the input over the output.
Exam tip: In an energy-transfer question, name the store of energy at the start, the store at the end, and say what happens to the energy that is wasted. Write the equation, substitute, and give a unit.
Check yourself
- Find the kinetic energy of a 0.50 kg ball moving at 6.0 m/s.
Answer
KE = ½ × 0.50 × 6.02 = 0.25 × 36 = 9.0 J. - A 60 kg climber goes up 30 m. How much gravitational potential energy is gained (g = 9.8 N/kg)?
Answer
GPE = 60 × 9.8 × 30 = 17 640 J, about 17 600 J. - A motor does 4800 J of work in 12 s. What is its power?
Answer
P = 4800 ÷ 12 = 400 W. - A device takes in 500 J and gives out 350 J of useful energy. Find its efficiency.
Answer
Efficiency = 350 ÷ 500 = 0.70, which is 70%.