Early in 2016, a friend's daughter asked her to explain the difference between energy and force. Mum duly turned to me for help and I recognised a good question. After congratulating her daughter for having the insight to ask a good question, I gave my best shot at an answer a school pupil (that I guess is about 13) might understand, starting with some comments on what Mum had managed as her initial attempts at answering. (I ended by pointing out that asking questions is what science is all about.) As this was well received, I chose to publish it here, adapted from plain text e-mail to HTML, for the sake of anyone else who might find it instructive.

# Distinguish Energy From Force

The short answer is that a force does work when it acts through a distance; and doing work spends energy. So they're closely related: force is a way to transfer energy (among other things).

you need energy to apply force, I think…

Nope. If a wheel spins on well-oiled bearings, in a vacuum so there's no air resistance, it'll keep doing this indefinitely; no energy is being used; but the spokes exert an inward force on the rim to keep it from flying away, without using any energy. As long as a force acts perpendicular to the direction in which relevant things are moving, it does no work – but it still transfers momentum.

Energy and force can't be the same thing, because force has a direction

hmm … well, kinda, mostly … but think about pressure, which doesn't have a direction, but … well, it isn't force, it actually (kinda) is energy, but it exerts a force … and then there's momentum which is a lot like energy and does have a direction, so … perhaps best not to get into this line of thinking too much !

Energy is an abstract concept

Any kid can see that.

It's also a very accurate answer, none the less: energy emerges as a quantity that our models of the universe predict shall be conserved and we've been able to check that it is, provided we allow that lots of differnt forms of energy are all counted. So the question is tricky.

Energy is a conceptual amalgam of several things, that arises from the book-keeping of physics and expresses stuff that other physically self-evident things do. Force is one of those actual physical things.

A force always has the effect of trying to make something move. It may be countered by an equal and opposite force, leading to no actual acceleration; or the thing it makes accelerate may be moving sideways to the force, so that it doesn't change speed (it changes the direction of its velocity, instead) as when the rim of a wheel spins.

Energy comes in many forms:

• heat is a form of energy; it's actually motion energy of molecules or atoms of the hot material, bouncing around a lot on a tiny scale; all the other forms of energy have a tendency to end up turning into heat; and intense heat has a tendency to spread itself out so as to become dull heat;
• an object in motion has energy associated with its motion – when the vase hits the floor, it spends its motion energy on breaking; when I use the brakes of my bike to slow down, my motion energy turns into heat in the brakes;
• an object high up has energy that it can release by falling; when I ride my bike down-hill, I start high up and get lower, releasing height energy to make me go fast down-hill; I have to work hard to go up-hill, storing height energy as I climb;
• when we squash or stretch a spring, we store mechanical energy in it, that make it exert a force that resists our stretching or squashing; if we let that force act, it'll return the energy we put in;
• when we charge a battery, we re-arrange its internal chemistry into a form that stores energy; when we let the battery power a circuit, that chemistry drives a current that does work in the circuit, delivering the energy we stored in it while charging;
• when fuel burns it releases energy; wood burning on the fire produces heat; a car burns fuel in a very controlled way (many many little explosions every second) to push the parts of the engine around, that in turn push the car along; our bodies burn sugars to make energy that powers our brains and muscles (our brains produce lots of heat as a result).

The list could go on for ever; but I've tried to stick with examples with which a school pupil might actually have some familiarity.

These are all different expressions of energy; energy in each of these forms can be converted to energy in the other forms – and usually at least some of the converted energy ends up as heat, regardless of which other form of energy you were trying to convert to.

Force is always the same, transfering momentum from one thing to another, which is what tends to make each accelerate. It can be mediated by many different processes – gravity, magnetism, electricity, springs (actually electrical forces, embodied in the structure of the matter of the spring), air pressure differences (driving wind) and so on – but it's always one thing pushing or pulling on another.

## Foot-note: Energy, momentum, pressure and stress

… and momentum is a whole fun thing of its own, a lot like energy of the motion with which it's associated, but still different from energy. In fact, in relativistic physics, energy, momentum and pressure/stress are all different aspects (along with mass) of the same one thing, that causes space-time to curve; so momentum isn't all that different from energy. It's just a spatial aspect of the same thing whose time aspect is energy.

Written by Eddy.