### How much?

So far we have introduced an energy perspective, seeing processes as shifting energy between different kinds of stores and along various pathways. Now we turn our attention to the question of how much energy is being shifted. Being able to answer this question is of great practical importance, whether in designing car engines, estimating the energy demands of a city or thinking about the insulating properties of a new material.

Calculating energy changes is not required of pupils in the 11–14 age range, although it certainly is during the next stage of schooling. We are therefore including much of the material in this episode to allow you, the teacher, to develop a broader and deeper understanding of the topic.

Thinking about lifting things is a good place to start investigating the how much?

question. For example, how much energy is shifted when you lift a stool up onto the bench at school? How does this compare with the energy shifted when you lift a book up onto a shelf?

In both cases energy is shifted from the chemical store of your muscles to the gravitational store of the stool or book in the Earth's field. Furthermore, thinking back to the ideas of episode 03, the energy is shifted along a mechanical working pathway.

### Lifting boxes

The amount of energy shifted in lifting the book or stool depends on just two things:

- The lifting force
- The height through which the object is lifted

In fact, you can calculate how much energy (in joules) is shifted by multiplying the force (in newtons) by the height (in metres).

Suppose the stool has a mass of 3 kilogram and the bench top is 1.5 metre above the floor. The energy shifted can be calculated energy = force of gravity × height (or, in symbols: *E* = *F* × *d*).

Working with this data:

energy = 30 N × 1.5 m

You can work out that the energy shifted is 45 J

Notice that here we are assuming that a 30 newton force is being used to lift the 3 kg mass. In other words, the lifting force is taken to be equal to the gravity force acting on the object. Underlying this assumption is the idea that the stool is lifted at a steady speed. Thus, once the stool is set into upwards motion, the lifting force equals the gravity force, the resultant force is zero and the stool moves at a steady speed. If this is not too clear you'll find more help in episode 02 of the SPT: Motion topic.

### Dragging boxes

There are countless situations in which energy is shifted by mechanical working. For example, if I push my car along the road, energy is shifted from the chemical store of my muscles to the kinetic store of the car through mechanical working. All such cases involve a force acting for a certain distance (I might push my car 20 metre along the road) and the energy shifted can be calculated as follows:

energy = force × distance

With units:

energy/joule = force/newton × distance/metre

and, as symbols:*E* = *F* × *d*

Here we are assuming that the force acting is constant in strength and direction throughout the movement and is along the same line as the distance moved. In general terms, the constant force exerted multiplied by the distance moved by the force (in the direction in which it is exerted) gives you the energy shifted from one store to another. Back to dragging boxes for a recap.