Calculating changes in energy

Changes in energy occur when a force brings about a change to an object's speed, height or shape.

Our task in this section is to calculate exactly how much energy an object has in its kinetic or gravitational potential or elastic potential stores when a force causes such a change to an object.

Calculating Kinetic Energy

When a force causes an object to move, we say that it has gained kinetic energy. The size of its kinetic energy store can be calculated very easily using the equation:

(You should already know from your KS3 work that the quantity Energy is always measured using the unit joules which has the unit symbol, capital J.)

Let's do an example of a calculation using this equation:

Before we move on, let's do one more example:

So, as we would expect, a boy of small mass, 21 Kg, moving at only 21m/s has far less energy in his kinetic store than a car of mass 1450 Kg moving at 20 m/s.

Nevertheless, if the came to a hill, we would notice that as it began to climb the hill, its speed would decrease as the amount of energy in its kinetic store decreased!
Where would the "lost kinetic energy" be going?
It would be moving to a Gravitational Potential Energy store, and this is what we are going to discuss next!

Calculating Gravitational Potential Energy

Whenever a force causes an object to gain height, the energy in its gravitational potential store increases. To caclculate the amount by which it increases, we use the equation:

So, returning to our car example; as the car climbs the hill, its gravitational potential store of energy increases, so its kinetic store must decrease. That is why it gets slower and slower as it climbs higher and higher!

Now before you all starting shouting that I am wrong and that cars don't slow down when they climb up hills as I suggest - the reason you don't usually see them slow down is that you don't notice that the driver is pressing a little harder on the accelerator pedal when the car comes to a hill which means that more fuel and so more energy from the chemical store is used to keep the kinetic store constant! So, in most modern cars you don't notice it slowing down when it is going up a hill but you also don't notice that more fuel is used up and that isn't a good thing!

OK, let's do an example calculation for gravitational potential energy:

Calculating elastic potential energy

When a force causes an object to be stretched or to be compressed from its original length, the object gains elastic potential energy.

To caclculate the amount by which it increases, we use the equation:

All "stretchable" or "compressible" objects have a spring constant.

This is a value that tells us about how strechable or compressible the object is.

If the value is large then the object does not stretch or compress easily, meaning you need a large force to extend it (increase its length) or compress it (decrease its length) by a certain amount, hence its unit, newtons per metre.

A typical spring constant for an object is 100 N/m meaning that you need to apply 100N to extend the object's length or decrease its length by one metre.

OK, let's do an example calculation for elastic potential energy:

NB. Where does the energy come from in order for this amount of elastic potential energy to be stored in the spring?

It must come from the chemical store within the man pulling the spring, so his chemical store will have decreased by 11.88 J.

The next section, 4.1.1.3 Energy changes in systems is really a continuation of this section but it is specifically about the energy changes in a system when its temperature changes.