Conservation of Energy, Stores and Transfers
Energy Stores
Energy cannot be created or destroyed — it can only be transferred between energy stores. The key stores to know are: kinetic, thermal (heat), chemical, elastic potential, gravitational potential (GPE), electrostatic, magnetic, and nuclear. Each store holds energy until a transfer pathway moves it elsewhere.
Kinetic energy is the energy stored in a moving object. It is calculated using:
$$E_k = \frac{1}{2} m v^2$$
Where \(E_k\) is kinetic energy in joules (J), \(m\) is mass in kilograms (kg), and \(v\) is speed in m/s. Notice that doubling the speed quadruples the kinetic energy (because of \(v^2\)).
Eight energy stores: kinetic, thermal, chemical, elastic potential, gravitational potential, electrostatic, magnetic, nuclear. Key equation: \(E_k = \tfrac{1}{2}mv^2\). Doubling speed quadruples \(E_k\); doubling mass only doubles it. This explains why faster vehicles are much harder to stop.
Gravitational Potential Energy
Gravitational potential energy (GPE) is calculated using:
$$E_p = m g h$$
Where \(E_p\) is GPE in joules, \(m\) is mass in kg, \(g\) is gravitational field strength (10 N/kg near Earth’s surface), and \(h\) is height in metres. GPE increases when an object is raised and decreases when it falls.
Elastic potential energy is stored in stretched or compressed elastic objects (springs, rubber bands):
$$E_e = \frac{1}{2} k e^2$$
Where \(E_e\) is elastic potential energy in J, \(k\) is the spring constant in N/m, and \(e\) is the extension (or compression) in metres. This equation only applies below the limit of proportionality — beyond this, the spring deforms permanently and the equation no longer holds.
Energy Transfer Pathways
Energy moves between stores via four transfer pathways: by mechanical work (a force moving an object), by electrical work (a current doing work), by heating (thermal conduction, convection, or radiation), and by radiation (electromagnetic or sound waves). The pathway is not the same as the store — heating is a pathway; thermal energy is a store.
A useful example: when a ball is thrown upwards, energy transfers from the kinetic store (moving ball) to the gravitational potential store (raised ball). At the peak, the ball is momentarily still — kinetic store is empty, GPE store is at its maximum. As the ball falls, the transfer reverses.
A 3 kg ball is dropped from a height of 5 m. Assuming all GPE converts to kinetic energy (no air resistance), calculate the speed just before it hits the ground.
Step 1: \(E_p = mgh = 3 \times 10 \times 5 = 150\) J
Step 2: Set \(E_k = E_p\): \(\tfrac{1}{2}mv^2 = 150\)
Step 3: \(v^2 = \frac{2 \times 150}{3} = 100\); so \(v = 10\) m/s
The Law of Conservation of Energy
The law of conservation of energy states that the total energy in a closed system always remains constant. Energy is never lost — it is transferred usefully, or it is dissipated (spread out to the thermal store of the surroundings). In a real system, some energy is always dissipated as thermal energy.
Conservation of energy: total energy in a closed system is constant. In a real motor, input electrical energy = useful kinetic energy output + thermal energy dissipated. Energy is not ‘lost’ — it is spread out as low-grade heat in the surroundings.
Mechanical Work Done
When a force moves an object through a distance, energy is transferred as mechanical work:
$$W = F s$$
Where \(W\) is work done in joules, \(F\) is force in newtons, and \(s\) is the distance moved along the direction of the force in metres. 1 joule = 1 newton–metre. If you push a wall and it doesn’t move, no work is done — even if you exert a large force.
Efficiency
Efficiency measures how well a device converts input energy to useful output energy:
$$\text{efficiency} = \frac{\text{useful output energy}}{\text{total input energy}}$$
Efficiency can be expressed as a decimal (e.g. 0.75) or a percentage (75%). No real device is 100% efficient because some energy is always dissipated as thermal energy. Efficiency can also be calculated using power: efficiency = useful output power / total input power.
An electric motor receives 600 J of electrical energy and transfers 450 J as useful kinetic energy. Calculate its efficiency as a percentage.
Efficiency = 450 / 600 = 0.75 = 75%
The remaining 150 J (25%) is dissipated as thermal energy in the motor’s windings. Efficiency could be improved by reducing friction in the bearings or using better insulating materials.
Power
Power is the rate of energy transfer or the rate of doing work:
$$P = \frac{E}{t} = \frac{W}{t}$$
Where \(P\) is power in watts (W), \(E\) is energy in joules, \(W\) is work done in joules, and \(t\) is time in seconds. One watt equals one joule per second. A 100 W light bulb transfers 100 J of energy every second. For a force moving an object at constant speed, power can also be written as \(P = Fv\), where \(v\) is speed in m/s — useful when calculating engine power output.
This core practical uses water, not a metal block. Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Water in an insulated container is heated electrically with a known power supply, and the temperature is measured at regular time intervals. The energy supplied is calculated as \(E = P \times t\), and specific heat capacity is found from \(Q = mc\Delta T\) rearranged to \(c = Q / (m \Delta T)\). The same core practical also asks you to plot a temperature–time graph while ice melts. Insulating the container reduces the systematic error from heat lost to the room. This practical belongs to the particle model topic, so it is examined on the second paper.