AQA GCSE Physics

Systems and stores

A system is an object or a group of objects that you choose to look at. Energy is not a substance that flows around; it is a quantity that is stored in different ways, and when a system changes the way its energy is stored changes too. The main stores are kinetic (moving objects), gravitational potential (objects raised above the ground), elastic potential (stretched or compressed objects), thermal (the random motion of particles), chemical (fuels, food and batteries), nuclear and magnetic.

Energy moves from one store to another in four ways: by a force doing work (mechanical work), by an electric current doing work, by heating, and by waves such as light and sound. The total amount of energy is the same before and after a change; only its distribution differs.

Describing a change means naming the stores that lose energy and the stores that gain it:

• An object thrown upwards starts with energy in its kinetic store. As it rises, the kinetic store shrinks and the gravitational potential store grows, and at the top of its flight almost all the energy is in the gravitational store.
• A moving object that hits an obstacle loses kinetic energy. Some goes to the thermal store of the object and obstacle, and some is carried away as sound.
• An object accelerated by a constant force gains kinetic energy, and the force does work on it. The energy comes from whatever is driving the force, for example the chemical store of a fuel.
• A vehicle slowing down loses kinetic energy, and the brakes and tyres warm up, so the thermal store rises.
• An electric kettle bringing water to the boil transfers energy electrically from the mains to the heating element, then by heating to the thermal store of the water.

Kinetic energy

The kinetic energy of a moving object depends on its mass and, much more strongly, on its speed, because speed is squared.

$E_k$ is the kinetic energy in joules (J), $m$ is the mass in kilograms (kg) and $v$ is the speed in metres per second (m/s).

Doubling the speed of an object makes its kinetic energy four times bigger. A car travelling at 30 m/s has nine times the kinetic energy of the same car at 10 m/s.

Worked example

A cyclist and bike of total mass 80 kg travel at 6.0 m/s.

Gravitational potential energy

When an object is lifted, work is done against the pull of gravity and the energy is stored in the gravitational potential store. The amount depends on the mass, the height gained and the gravitational field strength.

$E_p$ is in joules, $m$ in kilograms, $g$ is the gravitational field strength in newtons per kilogram (N/kg) and $h$ is the height in metres. Near the Earth's surface $g$ is about 9.8 N/kg, and a question will give the value to use.

Worked example

A 2.5 kg book is lifted 1.2 m onto a shelf, with $g = 9.8$ N/kg.

If the book falls off, ignoring air resistance, that 29.4 J becomes kinetic energy by the time it reaches the floor. So $\tfrac{1}{2} m v^2 = 29.4$, which gives $v^2 = 2 \times 29.4 \div 2.5 = 23.52$ and $v = 4.85$ m/s.

Elastic potential energy

A stretched or compressed spring stores energy in its elastic potential store, provided it has not been stretched past its limit of proportionality (the point beyond which it no longer obeys $F = ke$).

$E_e$ is in joules, $k$ is the spring constant in newtons per metre (N/m) and $e$ is the extension in metres. A spring with $k = 40$ N/m stretched by 0.10 m stores $0.5 \times 40 \times 0.10^2 = 0.20$ J.

The energy is put in by the work done in stretching the spring, and it is released again as kinetic energy when the spring returns to its original length.

Investigating gravitational to kinetic transfers

A trolley or ball released from a known height on a ramp gains kinetic energy as it loses gravitational potential energy. Light gates at the bottom of the ramp measure the speed, and the height is measured with a ruler. The kinetic energy at the bottom is always a little less than the potential energy lost, because some energy is transferred to the thermal store by friction and air resistance.

Power

Power is the rate at which energy is transferred, or the rate at which work is done. It tells you how quickly a change happens rather than how big it is.

$P$ is power in watts (W), $E$ is the energy transferred in joules, $W$ is the work done in joules and $t$ is the time in seconds. One watt is a transfer of one joule per second.

Two electric motors can lift the same weight through the same height, so both transfer the same energy to the gravitational store. If one does it in 4 s and the other in 8 s, the first has twice the power.

Worked example

A motor lifts a load and transfers 900 J of energy in 12 s.