Some ways of talking about energy are clearer and more helpful than others.

Energy stores

It is helpful to talk about energy stores. A spring, or a rubber band, can rather obviously store energy. You do work to stretch them (or to squash the spring), and you can get back pretty much the same amount of energy when they relax. These then are two of the best iconic examples for grasping what ‘potential energy’ is all about. It is energy in a mechanical store.

Many students find the term ‘potential’ confusing. They think ‘potential energy’ is somehow different from actual energy. Talking about energy stores offers a way of deferring the term ‘potential energy’ until later, for students who choose to continue studying physics.

You can similarly feel energy being stored when magnets are pushed together or pulled apart.

The example nearly all textbooks give of potential energy is perhaps the most difficult of all. It is the gravitational energy of a lifted mass. Now the energy is said to be ‘in’ the lifted object – as for a spring it is said to be ‘in’ the spring. If you have the courage, you could say that the energy is stored between the Earth and the lifted object (in the gravitational field). The trouble is of course that an external examiner might score that truthful answer as wrong because specialist understanding is not required at this level.

Another kind of energy store is a mixture of fuel and oxygen. In this case bonds between carbon and oxygen atoms can snap shut, releasing energy in a fire or explosion. It is common to talk about just the fuel – for example petrol – as the energy store, but do remember that for this chemical spring to snap shut, there must be oxygen too.

There are a limited number of energy stores:

• chemical (e.g. fuel + oxygen)
• kinetic (in a moving object)
• gravitational (due to the position of an object in a gravitational field)
• elastic (e.g. in a stretched or compressed spring)
• thermal (in a warm object)
• magnetic (in two separated magnets that are attracting, or repelling)
• electrostatic (in two separated electric charges that are attracting, or repelling)
• nuclear (released through radioactive decay, fission or fusion)

Energy carriers (or pathways) and energy transfers

It is often helpful to think of energy being carried from one place to another. For example, light carries energy from the Sun to the Earth. Light is not itself ‘energy’ – it is after all an electromagnetic wave, or a stream of photons (however you care to look at it). But energy does travel with the light. The same is true of radio waves. In a microwave oven microwaves carry energy from the microwave generator to the interior of the food. Other kinds of waves carry energy too, for example ocean waves.

Electric current in a circuit is another energy carrier. It is helpful to think about a power circuit as a way of moving energy from one place to another. The National Grid distributes energy from a number of power stations, via the wires and cables, to homes and factories.

It is often handy to think of moving matter as carrying energy, too. A strong wind delivers energy to a wind turbine. But, equally often, it is better to think of the moving mass as storing energy. A train has to be given energy to get it moving, and energy has to be taken from the train to stop it. This is what we call kinetic energy.

Energy carriers (or pathways, or transfers)

• mechanically (when a force moves through a distance)
• electrically (when a charge moves through a potential difference)
• by heating (because of a temperature difference)
• by radiation (e.g. light, microwaves)

With all of these, we are interested in the rate at which energy is being transferred and not the amount stored anywhere.

You can use flow diagram representations to strengthen the distinction between energy stores and carriers, for example:

There are some very important scientific ideas in this way of looking at things. Among them are:

• that energy tends, in most cases, to spread from a more concentrated store to more dispersed stores; and that this makes it less useful for doing anything more
• that the energy often ends up warming the environment

Visit School Science Review for two useful papers: Richard Boohan Making sense of energy and Robin Millar 'Teaching about energy: from everyday to scientific understandings':

School Science Review

In physics, there is a standard way to work out how much energy has been transferred. It is to calculate the work done.

Work is done when an applied force causes something to move in the direction of the force.

ΔE = work done = force x distance moved in the direction of the force.

Notice that no energy is shifted in the two situations below:

• when an object rests on a shelf – although the object has weight, there is no movement.
• if the force is perpendicular to the direction of movement - e.g. a satellite in orbit around the Earth.

This equation leads to the definition of the SI unit for energy, the joule: 1 joule is the work done when a 1 N force moves through a distance of 1 m.

For example, a motor or a human arm might raise kilogram masses onto different height shelves. The change in energy stored gravitationally can be calculated using the formula,

ΔE = weight x Δh =mgΔh, where Δh is the vertical distance a mass m has been raised, and g is the gravitational field strength.

Energy and the human body

However, there is more than this to working out how much energy has been transferred. When you lift bricks your body also gets warmer, due to the energy from digested food. It does not look as if there is any “force x distance” here. But the energy that is transferred by heating to make it warmer can be calculated in this way, and can be measured in the same unit, joules. (See food packets, labelling portions in kJ.)

Human beings are only about 25% efficient for doing mechanical jobs. For every 1,000 joules of energy which are transferred from fuel stored in muscles, only 250 joules are transferred to raising a load or doing some other kind of job. 750 joules are stored thermally (the body warms up). Thermodynamics shows that muscles could be more than 70% efficient in transferring their energy to do useful jobs, but only if the action was conducted infinitely slowly. So when estimating the useful energy transferred from energy stored in food to muscles in order to climb the stairs, for an eight hour day, then the answer needs to be multiplied by four to find the demand on food.

When a 1kg mass is raised by a height of 1 metre, then 10 J of energy is now stored gravitationally . This can be obtained from four grains of sugar, a mini-snack. One grain of sugar is for doing work to raise the load, and three grains are for heating the room. If you raise 1 kg through a height of 1 m every second requiring 1 mini-snack per second then this is about 10 grams of sugar per hour. Not enough to allow you to eat a cream-cake or a bar of chocolate without putting on weight (i.e. mass)!

Transferring energy electrically

Energy transferred electrically is calculated using the equation ΔE = IVt , where I is the current, V is the potential difference and t is time.

Heating with friction

In frictional rubbing, a force moves over a surface, but just makes it hot. You measure the rise in temperature of the material, and how much of it is warmed up. Then, next time something gets warmer, you know what amount of “force x distance” or work would have been needed if the warming up had been done in this way.

Sooner or later you’ll need to tell a story about what “getting hotter” means, in energy terms. It just means that the invisible atoms or molecules are moving about faster. Energy is stored kinetically by a large number of molecules. And it isn’t easy to claim it back again, because they have shared it out randomly amongst a huge number of particles.

There are plenty of practical examples of friction making something hotter. Car (or bicycle) brakes are a case where we want to transfer the energy of a moving car stored kinetically as speedily as possible. Exercise bicycles let students feel how what seems a large amount of mechanical work done produces only what seems like a modest heating effect.

A key teaching point is not to let ‘friction’ become a kind of excuse for things not working properly. It’s the way that the work done by forces ‘gets inside’ matter.

Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.

Energy transferred = work done = force x distance moved in the direction of the force

When energy is transferred from energy stored chemically in muscles to energy in a raised load, or to energy stored elastically in a stretched spring, the energy transferred is a measure of how much work has been done.

Energy transferred = mgΔh

This second equation is illustrated by raising kilograms onto different height shelves. You can show that the equation is a good summary of what happens. It takes account of the mass, the height raised and whether the kilogram is raised on the Earth or the Moon.

The useful thing which you get from fuels by burning them is a transfer of energy, so that a load can be raised, or an object accelerated.

However, not all the energy available does a useful job. If you lift a lot of bricks, you can get too hot. As well as transferring energy to the raised bricks, some of the energy in your muscles warms you up. The transfer of energy is not 100% efficient and not all the energy transferred is represented by mgh. Nor do you know how much total energy is stored gravitationally. You can only calculate energy that is transferred.

Concepts develop with steam engines

Humans first domesticated animals to do useful work and later found other ways of exploiting energy from natural sources, such as falling water and wind. But the abstract idea of an ‘engine’ really developed with steam engines.

By the 1820s the concept of ‘work’ as mechanical effect had been introduced into discussions about what are now called power technologies. Early on, a major use of steam engines was pumping water out of mines. Manufacturers such as Boulton & Watt persuaded mine owners in Cornwall to buy a steam engine in place of their pit ponies, by comparing the amount of work each could do.

Watt went even further, developing the concept of rate of working, or power, with his steam engines described in ‘horsepower’. Steam engines enabled the output of many Cornish mines to quadruple.

An analogy to use when teaching about energy transfers

Consider two bank accounts. If I transfer a £1 cheque from my account to yours then my account goes down by £1 and yours will go up by £1. But a cheque is not cash of any kind. It is an instruction to my bank to pay out £1 into your account. We have to pay the banks for doing the job for us and so although my account falls by £1 yours may only gain 95p because you have to pay bank charges. It is also impossible in this transaction to know how much is stored in each account.

Pushing this analogy to its limits helps to show that whilst you can store real cash in the bank (the energy stored, for example, in a fuel + oxygen mixture), the cheque which passes between accounts is something different. The cheque is a means of transferring the cash value (the work done for example when a brick is raised). Work is energy being transferred.

As the son of a Manchester brewer, privately tutored for several years by the chemist John Dalton, James Joule took an early interest in all the technical equipment associated with brewing. In 1840, at the age of 22, he experimentally discovered that the heat generated in a coil of wire is proportional to the square of the current through it. This effect is now called ‘Joule heating’.

In the following decade, Joule sought to unify electrical, chemical and thermal phenomena by conducting dozens of different experiments to demonstrate their inter-convertibility and quantitative equivalence. He gave particular attention to the conversion of heat into mechanical work, regarding this as fundamental to the theory of steam engines.

Churning fluids

Joules’ best-known experiment involved a paddle wheel which rotated so that it churned water in a large cylinder. The wheel itself was driven by falling weights so that he could determine the work done. The same experiment was repeated using whale oil and then mercury. Joule worked meticulously, constantly improving the accurately of his results. He took great care to minimise heat losses to the surroundings and introduced appropriate correction factors.

With the help of scientific instrument-maker John Dancer, Joule was also able to use very sensitive thermometers. Some contemporaries doubted the claim that he could measure temperatures to within 1/200 of a degree Fahrenheit.

Honeymoon

Famously, Joule packed thermometers for his honeymoon in the Swiss Alps, so that he could compare the temperatures of water at the top and bottom of a waterfall near Chamonix. In fact this particular experiment failed, because the water produced too much spray at the bottom of its fall.

SI unit of energy

In recognition of Joules’ importance in demonstrating energy conservation, the SI unit of energy is named after him.

Energy is conserved. What does this really mean, and why is it true?

Water in a reservoir is more or less conserved. So the amount of water can always be calculated from the amount that was there some time ago, plus the amount that has come in, minus the amount that has gone out (you may have to take account of evaporation as well as water drawn off).

Another way of saying the same thing is that water can’t be made or destroyed. For there to be more, it has to come in; for there to be less it has to go out.

Energy is similar. If you take any volume of space, then the total energy inside that volume at a given time is always the amount that was there earlier, plus the total amount that has come in through the surface, minus the total amount that has gone out through the surface.

Another way of saying the same thing is that energy can’t be made or destroyed. For there to be more, it must have come from somewhere; for there to be less it must have gone somewhere else. This also means that energy is a calculable quantity. The practical teaching implication here is that it is important to do sums about energy changes – how much in, how much out – and not just to talk generally about it.

The conservation laws, such as the conservation of energy, give physics its backbone. They are not really statements of knowledge but they contain implicit assumptions and definitions. They are however tied to the natural world, and they contain experimental knowledge.

The emergence of energy physics

By the early 19th century, steam engines were widely used. Both physicist and engineers sought to understand them by developing a ‘theory of steam engines’. Through the 1840s, as part of this process, several key people developed the concept of energy and its conservation : Mayer, Joule, Helmholtz and Thomson.

Julius Mayer, a German physicist, was the first person to state the law of the conservation of energy, in an 1842 scientific paper. Mayer experimentally determined the mechanical equivalent of heat from the heat evolved in the compression of a gas (without appreciating that heat could be explained in terms of kinetic theory).

In 1847 another German physicist, Hermann von Helmholtz, formulated the same principle in a book titled On the Conservation of Force. By contrast with Mayer, Helmholtz did view heat as matter in motion. The idea of conservation arose from his interest in animal (body) heat. He may not have known about Mayer’s prior work.

Between 1839 and 1850 the English brewer James Joule conducted a remarkable series of experiments, seeking to unify electrical, chemical and thermal phenomena by demonstrating their inter-convertibility and their quantitative equivalence. His numerical results and conclusion were published in the Philosophical Transactions of the Royal Society with the title On the mechanical equivalent of heat.

William Thomson (later Lord Kelvin) took the next step, considering the problem of irreversible thermal processes, until that time simply a contradiction between Carnot and Joule. Carnot, in his 1824 theory of heat engines, had argued that heat could be lost; more recently Joule argued that energy was convertible from one form to another but could be destroyed. In Thomson’s 1851 scientific paper The Dynamical Equivalent of Heat, he contended that energy was "lost to man irrecoverably; but not lost in the material world". Thomson was thus the first person to understand that all energy changes involve energy dissipation.

From energy to thermodynamics

In the second half of the 19th century Thomson and other scientists (including Clausius, Rankine, Maxwell and, later, Boltzmann) continued to develop these ideas. Kinetic theory and the science of thermodynamics gradually became established, with energy conservation as its First law and energy dissipation as its Second law.

A discussion by Jon Ogborn, emeritus professor of science education at the Institute of Education, London.

An intrinsic problem of teaching about energy at secondary level is that school science is obliged to try to run before it can walk. School biology and chemistry need to use the idea of energy before its physical meaning or its measurement in terms of force multiplied by displacement can be taught.

Teachers want and need to talk about the role energy plays in changes, but the idea that energy is conserved (first law of thermodynamics) is simply not enough to do the job. What they need are some ideas from the second law of thermodynamics.

It is no real surprise that the world is richer and more complicated than science textbooks make it appear. And it is no surprise that it takes a lot of skill, knowledge and creativity to find good ways to explain things simply to young people.

In the resource downloadable below, I offer a rough guide to the fundamental physics, using these subtitles:

• What is energy?
• Energy is conserved
• Energy amongst the molecules
• Free energy
• Is energy needed for a change to happen?

and concluding with

• Is there a better way to teach energy?

Multiflash photography creates successive images at regular time intervals on a single frame.

Method 1: Using a digital camera in multiflash mode

You can transfer the image produced direct to a computer.

Method 2: Using a video camera

Play back the video frame by frame and place a transparent acetate sheet over the TV screen to record object positions.

Method 3: Using a camera and motor-driven disc stroboscope

You need a camera that will focus on images for objects as near as 1 metre away. The camera will need a B setting, which holds the shutter open, for continuous exposure. Use a large aperture setting, such as f3.5. Digital cameras provide an immediate image for analysis. With some cameras it may be necessary to cover the photocell to keep the shutter open.

Set up the stroboscope in front of the camera so that slits in the disc allow light from the object to reach the camera lens at regular intervals as the disc rotates.

Lens to disc distance could be as little as 1 cm. The slotted disc should be motor-driven, using a synchronous motor, so that the time intervals between exposures are constant.

You can vary the frequency of ‘exposure’ by covering unwanted slits with black tape. Do this symmetrically. For example, a disc with 2 slits open running at 300 rpm gives 10 exposures per second.

The narrower the slit, the sharper but dimmer the image. Strongly illuminating the objects, or using a light source as the moving object, allows a narrower slit to be used.

Illuminate the object as brightly as possible, but the matt black background as little as possible. A slide projector is a good light source for this purpose.

Method 4: Using a xenon stroboscope

This provides sharper pictures than with a disc stroboscope, provided that you have a good blackout. General guidance is as for Method 3. Direct the light from the stroboscope along the pathway of the object.

In multiflash photography, avoid flash frequencies in the range 15-20 Hz, and avoid red flickering light. Some people can feel unwell as a result of the flicker. Rarely, some people have photosensitive epilepsy.

General hints for success

You need to arrange partial blackout. See guidance note

Classroom management in semi-darkness

Use a white or silver object, such as a large, highly polished steel ball or a golf ball, against a dark background. Alternatively, use a moving source of light such as a lamp fixed to a cell, with suitable electrical connections. In this case, place cushioning on the floor to prevent breakage.

Use the viewfinder to check that the object is in focus throughout its motion, and that a sufficient range of its motion is within the camera’s field of view.

Place a measured grid in the background to allow measurement. A black card with strips of white insulating tape at, say, 10 cm spacing provides strong contrast and allows the illuminated moving object to stand out.

As an alternative to the grid, you can use a metre rule. Its scale will not usually be visible on the final image, but you can project a photograph onto a screen. Move the projector until the metre rule in the image is the same size as a metre rule held alongside the screen. You can then make measurements directly from the screen.

Use a tripod and/or a system of clamps and stands to hold the equipment. Make sure that any system is as rigid and stable as possible.

Teamwork matters, especially in Method 3. One person could control the camera, another the stroboscope system as necessary, and a third the object to be photographed.

• Switch on lamp and darken room.
• Check camera focus, f 3.5, B setting.
• Check field of view to ensure that whole experiment will be recorded.
• Line up stroboscope.
• Count down 3-2-1-0. Open shutter just before experiment starts and close it as experiment ends.