Energy

Energy stores and transfer pathways

A system can have energy in kinetic, potential (gravitational, chemical or elastic), nuclear and internal stores. Energy moves between stores through a pathway; it is not itself “stored as heating” or “stored as electricity”.

Example: as a falling ball speeds up, the gravitational potential energy of the ball–Earth system decreases while the ball’s kinetic store increases. Air resistance does work and increases the internal energy of the ball and air. Heating specifically names transfer caused by a temperature difference.

Complete the account before checking: a battery torch lights a dark room. The lamp gets warm and its light is absorbed by the walls. Choose a boundary that lets you account for the battery's decrease, then name the starting store, the pathway to the lamp and the pathway from the lamp to the walls. Where does the absorbed energy go?

Conservation of energy

Energy cannot be created or destroyed. It can be transferred from one store to another, and the total energy of a system remains constant when no energy enters or leaves it.

If an appliance receives 500 J and produces 120 J of useful light, the remaining 380 J has not disappeared. It is transferred to other stores, mainly as thermal energy in the lamp and surroundings.

Kinetic and gravitational potential energy

Speed is squared. Doubling speed makes kinetic energy four times as large when mass is unchanged. Near Earth's surface, gravitational potential energy is proportional to mass and vertical height change.

Choose a reference level where gravitational potential energy is zero. With approximately constant g near Earth, ΔE_p = mg(h_final − h_initial). A rise increases this energy; a fall decreases it. Changing the chosen zero changes both heights equally, so the energy change is unchanged. Use vertical height, not the distance along a slope.

Compare before calculating: at the same speed, doubling mass doubles kinetic energy. At the same mass, tripling speed multiplies kinetic energy by nine. Doubling both mass and speed multiplies it by eight, because both factors contribute.

A reliable conservation method

1. Choose the system and the start and end points.
2. Identify the stores that decrease and increase.
3. Include energy crossing the boundary. For a system with no transfer across it, write “total energy before = total energy after”, including increases in internal energy.
4. Substitute SI units, solve, and check that the answer fits the physical situation.

Try a descent with dissipation

A 2.0 kg trolley starts from rest 5.0 m above the bottom of a track. Use the bottom as the gravitational reference, take g = 10 N/kg, and include the trolley, Earth, track and nearby air in the system. During the descent their internal energy increases by 36 J. Neglect all other changes and transfers across the boundary.

Write the energy account before substituting. Find the final kinetic energy and speed. Explain the first error in a solution that sets ½mv² = mgh.

Work done by a force

W = Fs

Work done is the energy transferred when a force moves an object through a distance in the direction of that force. Use force F in newtons and distance s in metres; the work done W is in joules.

Power: how quickly energy is transferred

P = Et

Power is measured in watts (W), where 1 W = 1 J/s. A 60 W device transfers 60 J every second. More powerful does not necessarily mean it transfers more energy overall; time also matters.

Compare two lifts: motor A does 600 J of work in 10 s; motor B does the same work in 30 s. Which transfers more energy, and which has greater average power?

Common calculation mistakes

Using mass in grams

Convert to kilograms before using the energy equations.

Forgetting that speed is squared

Evaluate v² before multiplying by ½m.

Treating dissipated energy as destroyed

Include energy transferred to thermal stores and sound.

Using path length for h

Use the vertical height change in mgh.

Worked example: a falling object

A 2.0 kg object falls 5.0 m from rest. Ignore air resistance and useg = 10 N/kg. Find its speed just before it reaches the ground.

1. Loss of gravitational potential energy = mgh = 2.0 × 10 × 5.0 = 100 J.
2. By conservation, kinetic energy gained = 100 J.
3. ½mv² = 100, so ½ × 2.0 × v² = 100.
4. v = 10 m/s.

Connect stores, equations, work and power

Independent self-check

1. A 4.0 kg load is raised vertically by 3.0 m. Use g = 10 N/kg. Find the increase in gravitational potential energy.

   Answer

   E_p = 4.0 × 10 × 3.0 = 120 J.

2. A machine does 2,400 J of work in 8.0 s. Calculate its power.

   Answer

   P = 2,400/8.0 = 300 W.

3. A cyclist doubles speed without changing total mass. By what factor does kinetic energy change?

   Answer

   It becomes four times as large because kinetic energy is proportional to v².

4. A falling object loses 90 J from its gravitational store but gains only 72 J in its kinetic store. Account for the difference.

   Answer

   The remaining 18 J is accounted for by increases in internal energy of the object and air and by sound. Air resistance does work; heating specifically means transfer caused by a temperature difference. Total energy is still conserved.

Try this next: close every answer, change one number or condition, and solve the question again from the governing principle.

Check the whole Energy topic

Take the Energy topic check to find what to practise next: stores and pathways, kinetic or gravitational energy, work, power, conservation or energy transferred to the surroundings.

The questions match the course shown at the top of this page. The check routes focused practice and does not award mastery on its own.