State the principle of conservation of energy, describe energy stores and transfers, and apply the equations for work, kinetic and potential energy, power and efficiency

What this dot point is asking

SEAB wants you to state the principle of conservation of energy, to describe how energy is stored and transferred between stores, and to apply the simple equations for work done, kinetic energy, gravitational potential energy, power and efficiency. The calculations are short; the marks come from picking the right equation, keeping units consistent, and understanding that energy is never created or destroyed.

The answer

Conservation of energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one store to another or one form to another. The total amount of energy stays the same. The unit of energy is the joule ($\text{J}$).

Energy stores and transfers

Common energy stores include kinetic (movement), gravitational potential (height), chemical (fuel and food), elastic (stretched or compressed), thermal (internal), and electrical. Energy is transferred between stores by doing work, by heating, or electrically. For example, a falling ball transfers gravitational potential energy to kinetic energy.

Work done

Work is done when a force moves its point of application through a distance in the direction of the force:

Work done equals the energy transferred, both measured in joules.

Kinetic and potential energy

The kinetic energy of a moving object and the gravitational potential energy of a raised object are:

where $m$ is mass, $v$ is speed, $g$ is the gravitational field strength and $h$ is the height raised.

Power and efficiency

Power is the rate of transferring energy (or doing work):

measured in watts ($\text{W}$), where $1\ \text{W} = 1\ \text{J/s}$. Efficiency compares useful output to total input:

No real machine is 100% efficient, because some energy is always transferred to less useful forms such as heat.

Examples in context

Example 1. A roller coaster. At the top of the first hill the car has maximum gravitational potential energy. As it descends, that store transfers to kinetic energy so the car speeds up, then back to potential as it climbs the next hill. Friction gradually transfers some energy to heat, so each hill is lower than the last.

Example 2. An efficient kettle. A kettle puts most of its electrical energy into heating the water (useful), but some heats the casing and escapes as steam. Comparing the energy that warms the water with the electrical energy supplied gives an efficiency a little below 100%.

Try this

Q1. State the principle of conservation of energy. [2 marks]

• Cue. Energy cannot be created or destroyed; it can only be transferred from one store or form to another, and the total stays constant.

Q2. A $3.0\ \text{kg}$ object moves at $4.0\ \text{m/s}$. Calculate its kinetic energy. [2 marks]

• Cue. $E_k = \tfrac{1}{2}mv^2 = \tfrac{1}{2} \times 3.0 \times 4.0^2 = \tfrac{1}{2} \times 3.0 \times 16 = 24\ \text{J}$.

Q3. Explain why a machine can never be 100% efficient. [2 marks]

• Cue. Some energy is always transferred to less useful forms, mainly heat to the surroundings through friction, so the useful output is always less than the total input.