Work Done and GPE

The basics of energy stores and transfers are covered in a separate post (click here to refresh your memory if necessary).

We now need to think specifically about ways in which energy can be transferred by the action of forces. For the purposes of GCSE Physics, we will restrict our thoughts to mechanical forces but the same principles also apply to other situations so it’s worth getting these concepts clear if you are thinking about studying Physics in more depth after you have completed the GCSE course.

Energy is transferred when a force is moved through a certain distance (in the direction of the force). This type of energy transfer is known as “work done” and is calculated using the following equation;

work done (J) = force (N) x distance (m)

This can be tested in an abstract question, such as; calculate the energy transferred when a force of 50 N is moved through a distance of 12 m. The answer is 600 J.

It can also be tested in a more descriptive question, such as; calculate the energy that is required to slide a cupboard a distance of 2.6 m along a floor when the force required to move the cupboard is 375 N. The answer is 975 J.

But there is much more to this equation than that!

For one thing; this equation contains within it the equation for Gravitational Potential Energy, which you should recall is;

change in GPE (J) = mass (kg) x gravitational field strength (N/kg) x change in height (h)

(The “change in” is important because it enables us to set the starting point wherever we wish. You might also recall that we can write “change in” using scientific shorthand by replacing it with the delta symbol.)

You should also know that objects have weight when they are affected by a gravitational field, and that weight is calculated as follows;

weight (N) = mass (kg) x gravitational field strength (N/kg)

We can then substitute weight into the equation for GPE;

change in GPE (J) = weight (N) x change in height (m)

Weight is a force and height is a distance in a particular direction (up or down). So the equation for GPE is actually a specific case of the general equation for work done!

As we will see later in the course, a similar analysis can also be done for the energy that is stored in a stretched spring.

More immediately, you will see that the equation for work done also explains why levers are gears are so important in machinery.