Measuring energy transfers

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.