AQA GCSE Physics: Energy Changes in a System — Revision Notes

Condensed for the final weeks. For the full explanation, use the Energy Changes in a System study guide.

What a “system” is

A system is an object or group of objects. When a system changes, energy is stored differently before and after the change — the total amount is conserved, but which store holds it changes.

Situations you must be able to describe (know all five): an object projected upwards, a moving object hitting an obstacle, an object accelerated by a constant force, a vehicle slowing down, and heating water in a kettle. In each, name the store(s) involved before and after.

The specification lists three routes by which a system can change (for which you must be able to calculate the associated energy): heating, work done by a force, or work done when a current flows. Many questions in this sub-topic ask you to identify which of these caused the change, but most are calculations rather than classifications.

The three core equations

kinetic energy              Ek = 1/2 m v^2
elastic potential energy    Ee = 1/2 k e^2     (within the limit of proportionality)
gravitational potential     Ep = m g h

Kinetic energy depends on v², not v. Doubling speed quadruples Ek — this single fact drives most of the harder exam questions in this sub-topic, including any question about braking distance or collision severity. (Stopping distance itself does not simply quadruple: it is thinking distance, which is proportional to speed, plus braking distance, which is proportional to speed squared, so only the braking-distance part quadruples.)

Elastic potential energy only applies within the limit of proportionality — beyond that point, force is no longer proportional to extension, and the equation no longer holds. This is a separate condition from the elastic limit, beyond which the spring is permanently (inelastically) deformed; the elastic limit lies at or beyond the limit of proportionality. Examiners test this by asking you to state the condition, not just apply the formula.

g.p.e. uses height gained, not total height. If an object falls partway, use the change in height, not the starting height above the ground.

Specific heat capacity

change in thermal energy   delta-E = m c delta-theta

Specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1°C. A substance with a high specific heat capacity needs a lot of energy for a small temperature rise — water’s is unusually high, which is why it is used in heating systems and takes so long to heat up to its boiling point.

Required practical activity 1 determines the specific heat capacity of one or more materials. The method links the decrease of one energy store (electrical work done, usually via a heater) to the resulting rise in temperature and the thermal energy gained. Know that some energy is always dissipated to the surroundings during the experiment, which is a source of systematic error the practical write-up should mention.

Power

power = energy transferred / time        P = E/t
power = work done / time                 P = W/t

Power is a rate, measured in watts. 1 joule transferred per second = 1 watt. Two devices doing the same job at different speeds have different power outputs even though they transfer the same total energy — the faster one is more powerful. This is the standard way examiners test whether you understand “rate” versus “total amount”.

Worked example

A ball of mass 0.20 kg is thrown vertically upward at 8.0 m/s (g = 9.8 N/kg).

Kinetic energy at launch: Ek = ½ × 0.20 × 8.0² = 6.4 J

At maximum height (ignoring air resistance), all Ek has become Ep: mgh = 6.4, so h = 6.4 ÷ (0.20 × 9.8) = 3.27 m

Distinguishing this sub-topic from Conservation and Dissipation

It is easy to blur 4.1.1 (this sub-topic) with 4.1.2 Conservation and Dissipation of Energy — they sit next to each other and share the idea of energy stores. The distinction is by subject matter, not by whether a question calculates or explains: 4.1.1 covers the energy associated with a system — kinetic, elastic potential and gravitational potential energy, thermal energy from heating, and power — using the equations above; 4.1.2 covers the dissipation of energy, ways of reducing unwanted energy transfers (lubrication, insulation), and calculating the efficiency of a transfer. Note that 4.1.2 has calculations of its own (efficiency), so a question is not automatically 4.1.1 just because it asks for a calculation.

Exam traps

• Forgetting the ½ in Ek and Ee — both are commonly written without it.
• Squaring the wrong quantity in Ee = ½ke² — it is the extension that is squared, not the spring constant.
• Using total height instead of height gained in Ep = mgh.
• Mixing up mass (kg) and weight (N) when substituting into g.p.e.
• Confusing power (a rate) with energy itself — always check whether the question specifies a time.
• Substituting a temperature into the specific-heat-capacity equation where a temperature change is required.

Self-test

1. State the three routes by which a system’s energy can change.
2. Write the three energy-store equations from this sub-topic.
3. What happens to Ek when speed doubles?
4. Define specific heat capacity.
5. What does Required practical activity 1 measure, and by what method?
6. State both forms of the power equation.

Answers: 1. Heating, work done by a force, work done when a current flows. 2. Ek = ½mv², Ee = ½ke², Ep = mgh. 3. It quadruples, because Ek depends on v². 4. The energy needed to raise the temperature of 1 kg of a substance by 1°C. 5. The specific heat capacity of a material, by linking the decrease of one energy store (typically electrical work done via a heater) to the resulting temperature rise and thermal energy gained. 6. P = E/t and P = W/t.

Related resources

Energy Changes in a System study guide | Energy Changes in a System practice questions | Conservation and Dissipation of Energy revision notes