Calculating KE & GPE

By the end of your GCSE Physics course you will be able to calculate four different types of energy; kinetic, gravitational, electrical and strain. At this stage, however, we will limit ourselves to the first two.

Kinetic energy (KE) is the energy that is stored by moving objects. We are only interested in objects that are moving linearly, which will normally mean forwards, upwards or downwards. It can be calculated using the equation;

KE = 1/2 x m x v²

• KE is kinetic energy, measured in joules (J)
• m is mass, measured in kilograms (kg)
• v is velocity, measured in m/s (m/s)

Note that the value for the velocity MUST be squared in this equation.

Gravitational potential energy (GPE) is the energy that is stored by objects in a gravitational field. GPE is only meaningful when objects are able to change their height above a position of relative stability. For example, a book resting securely on a table can be considered to have zero GPE because it cannot change its vertical position. But as soon as the book is slid off the table it will start to fall – and as it falls it will transfer GPE.

Because of this “relativeness” we calculate GPE as a change in energy that is dependent on the change in height. We use the symbol delta (Δ) to indicate “change in”, as shown in the equation below;

ΔGPE = m x g x Δh

• ΔGPE is the change in gravitational potential energy, measured in joules (J)
• m is mass, measured in kilograms (kg)
• g is the gravitational field strength, measured in newtons per kilogram (N/kg)
• Δh is the change in height, measured in metres (m)

The value of g is usually taken to be 10 N/kg on the surface of the Earth. The true value is more like 9.8 N/kg but rounding to 10 N/kg represents only a very small error (2%) so is acceptable for the GCSE Physics course. (Incidentally, the value of g on the surface of our moon is much less, at around 1.6 N/kg.)

The energy of a thrown ball

There is an important interchange between KE and GPE when a ball is thrown upwards. The ball is thrown with a certain initial velocity and slows down as it rises into the air, so its kinetic energy starts with a maximum value then decreases. At the same time, as the ball rises it has further to fall back down so its gravitational potential energy increases.

At the top of the throw, the ball is stationary for a moment and therefore has zero kinetic energy. It is also at its highest point, so it has maximum gravitational potential energy.

As the ball starts to fall back down it gains speed. It is therefore losing gravitational potential energy and gaining kinetic energy. In an ideal situation, where there is no air resistance, the total energy, given by the sum of the ball’s gravitational potential energy and its kinetic energy, is always constant.

The ball’s maximum gravitational energy will be equal to the ball’s maximum kinetic energy but these two events will occur at different times and in different places; one at the top of the throw and the other at the bottom. And at every point in the ball’s movement, the sum of its GPE and KE will always be equal to the same value (provided that we are ignoring the effects of air resistance, which will normally be the case).

This is an example of the Law of the Conservation of Energy, which states that energy can never be created or destroyed: it can only ever be transferred from one type of energy to another.

To check that you understand these ideas I have created a worksheet that contains practice questions and a recall exercise concerning velocity-time graphs. To download the worksheet, click here.