1.1 Energy stores and transfers — Learn

Prerequisites: multiplying and dividing numbers; using a formula by substitution; the units kilogram, metre, second, joule and watt.

By the end of this section you can: name the energy stores; describe how energy moves between them; and calculate the energy in the kinetic, gravitational potential, elastic potential and thermal stores, plus the power of an energy transfer.

1. Systems and energy stores

A system is an object, or a group of objects, that we choose to study. A falling ball is a system. So is a kettle and the water inside it.

Energy is stored in a system in several ways. Each way is called an energy store. These are the stores you need to know.

Store	What it is
Kinetic	The energy of a moving object.
Gravitational potential	The energy an object has because of its height above the ground.
Elastic potential	The energy stored in a stretched or squashed spring.
Thermal	The energy of the particles in a warm object.
Chemical	The energy stored in food, fuel and batteries.
Nuclear	The energy stored inside the nucleus of an atom.
Magnetic	The energy stored between magnets.
Electrostatic	The energy stored between electric charges.

Energy is transferred from one store to another. It is never created and it is never destroyed. This is the principle of conservation of energy. You will use it in Section 1.2.

2. How energy is transferred

There are three transfers you need to describe:

by heating, from a hotter object to a cooler one;
by work done by forces, when a force moves an object;
by work done when a current flows, in an electric circuit.

A transfer is not a store. When a battery lights a lamp, chemical energy is transferred electrically to the thermal store of the lamp and its surroundings.

3. Describing a change in a system

To describe a change, name the store that changes, then say what it changes into. Here are the examples the specification asks for.

An object projected upwards. Chemical energy in the muscles is transferred to the kinetic store. As it rises, the kinetic store empties and the gravitational potential store fills.
A moving object hitting an obstacle. The kinetic store empties. Energy is transferred to the thermal store of the object and the obstacle.
An object accelerated by a constant force. Energy is transferred by the force to the kinetic store, which fills.
A vehicle slowing down. The kinetic store empties. Brakes transfer the energy to the thermal store of the brakes and the air.
Bringing water to a boil in an electric kettle. Energy is transferred electrically to the thermal store of the water and the kettle.

4. Gravitational potential energy

The energy in the gravitational potential store of an object raised above the ground is

E_p = m g h

where $m$ is the mass in kilograms, $g$ is the gravitational field strength in newtons per kilogram, and $h$ is the height in metres. On the Earth, $g$ is about $9.8\,\text{N/kg}$ .

Worked example 1. A pupil of mass 65 kg climbs 4.0 m up a rope. Take $g = 9.8\,\text{N/kg}$ . Calculate the energy gained by the gravitational potential store.

\begin{aligned} E_p &= m g h \\ &= 65 \times 9.8 \times 4.0 \\ &= 2548\,\text{J} \\ &= 2500\,\text{J} \quad (2\ \text{significant figures}) \end{aligned}

5. Kinetic energy

The energy in the kinetic store of a moving object is

E_k = \tfrac{1}{2} m v^2

where $m$ is the mass in kilograms and $v$ is the speed in metres per second. The speed is squared.

Worked example 2. A car of mass 1200 kg travels at 15 m/s. Calculate the energy in its kinetic store.

\begin{aligned} E_k &= \tfrac{1}{2} m v^2 \\ &= 0.5 \times 1200 \times 15^2 \\ &= 0.5 \times 1200 \times 225 \\ &= 135000\,\text{J} \\ &= 1.4 \times 10^5\,\text{J} \quad (2\ \text{significant figures}) \end{aligned}

Watch out. The speed is squared, so a car at 30 m/s has four times the kinetic energy of the same car at 15 m/s, not twice. Check the mass first: 500 g is 0.5 kg, not 500 kg. Re-check by asking whether the answer is bigger or smaller than the object's mass suggests.

6. Elastic potential energy

The energy stored in a stretched spring is

E_e = \tfrac{1}{2} k e^2

where $k$ is the spring constant in newtons per metre and $e$ is the extension in metres. This equation holds while the spring is not stretched past its limit of proportionality, the point beyond which the stretch is no longer proportional to the force.

Worked example 3. A spring with spring constant 250 N/m is stretched by 0.080 m. Calculate the energy in the elastic potential store.

\begin{aligned} E_e &= \tfrac{1}{2} k e^2 \\ &= 0.5 \times 250 \times 0.080^2 \\ &= 0.5 \times 250 \times 0.0064 \\ &= 0.8\,\text{J} \\ &= 0.80\,\text{J} \quad (2\ \text{significant figures}) \end{aligned}

7. Energy transferred by heating

When a substance is heated, its thermal store fills. The energy transferred is

\Delta E = m c \Delta\theta

where $m$ is the mass in kilograms, $c$ is the specific heat capacity and $\Delta\theta$ is the temperature change in degrees Celsius.

The specific heat capacity of a substance is the energy needed to raise the temperature of one kilogram of it by one degree Celsius. For water, $c = 4200\,\text{J/kg°C}$ . A large value means the substance takes a lot of energy to warm up.

Worked example 4. A 2.0 kg block of aluminium is heated from 18 °C to 68 °C. The specific heat capacity of aluminium is 900 J/kg°C. Calculate the energy transferred to the block.

\begin{aligned} \Delta E &= m c \Delta\theta \\ &= 2.0 \times 900 \times (68 - 18) \\ &= 2.0 \times 900 \times 50 \\ &= 90000\,\text{J} \\ &= 9.0 \times 10^4\,\text{J} \quad (2\ \text{significant figures}) \end{aligned}

8. Power

Power is the rate at which energy is transferred. It is measured in watts, where one watt is one joule per second.

P = \frac{E}{t}

where $E$ is the energy transferred in joules and $t$ is the time in seconds.

Worked example 5. A heater transfers 90000 J in 45 s. Calculate its power.

\begin{aligned} P &= \frac{E}{t} \\ &= \frac{90000}{45} \\ &= 2000\,\text{W} \\ &= 2.0\,\text{kW} \end{aligned}

A powerful appliance transfers the same energy in less time. A 2500 W kettle boils the water faster than a 2000 W kettle, and both change the same thermal store.

Worked example 6. A 2500 W kettle is switched on for 3.0 minutes. Calculate the energy transferred to the water.

\begin{aligned} t &= 3.0 \times 60 = 180\,\text{s} \\ E &= P t \\ &= 2500 \times 180 \\ &= 450000\,\text{J} \\ &= 4.5 \times 10^5\,\text{J} \end{aligned}

This is how a current transfers energy: the power of the appliance tells you the energy transferred each second. The same idea gives the energy used by any appliance on the mains.

9. Energy transferred by work

Work is another way to transfer energy. When a force moves an object along the line of the force, the work done is

W = F s

where $F$ is the force in newtons and $s$ is the distance moved in metres. The energy transferred equals the work done, so one newton-metre is one joule.

Worked example 7. A force of 120 N moves a trolley 15 m along the line of the force. Calculate the work done.

\begin{aligned} W &= F s \\ &= 120 \times 15 \\ &= 1800\,\text{J} \end{aligned}

Try it: energy on a drop

A ball is held above the ground and then let go. Its gravitational potential store empties and its kinetic store fills. The figure lets you change the mass and the height.

Predict first. Do not move the sliders yet. Write down your answers.

If you double the mass, what happens to the energy at the bottom?
If you double the height, what happens to the energy at the bottom?
If you double the height, what happens to the speed at the bottom?

Test. Set the mass to 2.0 kg and the height to 1.0 m. Read the energy and the speed. Now set the height to 2.0 m and read them again. Then change the mass and watch the energy.

Explain. Why does doubling the height double the energy but not double the speed? Write your answer in two or three sentences. Use the equation $E_p = m g h$ and the idea that the kinetic store ends up with the same energy.

10. Progress check

Return to the chapter problem. The stream brings 30 kg of water to the wheel each second, and the water falls 12 m. Without a calculator, decide whether the water gives up more or less than 3 kJ each second. Then work it out.

You should now be able to

name the eight energy stores and describe a transfer between them;
describe the energy changes in the common situations from Section 3;
calculate gravitational potential energy, kinetic energy and elastic potential energy;
calculate the energy transferred by heating, using specific heat capacity;
calculate power, and the work done by a force;
report an answer to the number of significant figures the data support.