Energy stores and transfers, the conservation of energy, kinetic energy and gravitational potential energy, and the equations for calculating them.

What this dot point is asking

CCEA Double Award wants you to name energy stores and transfers, state the conservation of energy, and use the equations for kinetic energy and gravitational potential energy. The two energy calculations are common, so the equations and the squaring step must be secure.

Energy stores and transfers

For example, a moving car has energy in its kinetic store; braking transfers it to the thermal store of the brakes by heating.

Conservation of energy

So in any change you can track energy from the stores it starts in to the stores it ends in, and the total stays constant.

Kinetic and gravitational potential energy

When an object falls, gravitational potential energy is transferred to kinetic energy, so (ignoring air resistance) $E_p$ lost equals $E_k$ gained.

Energy transfer diagrams

A useful way to show conservation of energy is a Sankey diagram, where the width of an arrow represents the amount of energy. The total energy entering equals the total leaving: the useful output is shown by an arrow continuing forward, and the wasted (dissipated) energy is shown by arrows branching off, usually as heat. The wider the wasted-energy arrows, the less efficient the device. This is the visual form of the rule that energy is never destroyed, only transferred to useful and wasted stores.

Examples in context

Example 1. A roller coaster

At the top of the first hill the car has maximum gravitational potential energy; as it drops, this transfers to kinetic energy, so it is fastest at the bottom. Because some energy is dissipated by friction and air resistance, each later hill must be lower than the one before.

Example 2. A pendulum

A swinging pendulum transfers energy back and forth between gravitational potential (at the top of each swing) and kinetic (at the bottom), with a little dissipated as heat each swing, which is why the swing gradually dies away.

Example 3. A bouncing ball

A dropped ball converts gravitational potential energy to kinetic energy as it falls, then to elastic (strain) energy as it squashes on the floor, and back to kinetic and gravitational potential as it bounces up. It never quite reaches its starting height because some energy is transferred to heat and sound, so the bounce height falls each time.

Try this

Q1. State the principle of conservation of energy. [1 mark]

• Cue. Energy cannot be created or destroyed, only transferred or stored.

Q2. Calculate the kinetic energy of a $2.0\ \text{kg}$ ball moving at $4.0\ \text{m/s}$. [2 marks]

• Cue. $E_k = \tfrac{1}{2} \times 2.0 \times 4.0^2 = 16\ \text{J}$.

Q3. A $5.0\ \text{kg}$ box is lifted $2.0\ \text{m}$. Find the gain in gravitational potential energy ($g = 10\ \text{N/kg}$). [2 marks]

• Cue. $E_p = m g h = 5.0 \times 10 \times 2.0 = 100\ \text{J}$.