There are mainly two types of energy you need to know for the exam:

• Kinetic Energy
• (Gravitational) Potential Energy

All types of energy are measured in Joules (J).

1 kilojoule (KJ) = 1000 J
1 megajoule (MJ) = 1,000,000 J

### Kinetic Energy

Bodies which are in motion have kinetic energy.

Formula for Kinetic Energy:
Kinetic Energy = ½ (mass of body) x (velocity)²
KE = ½mv² Consider the above vehicle. It has a mass of 2000 kg and it is moving at a velocity of 10 m/s.

Its KE = ½ (2000) (10)²
KE = ½ (2000) (100)
KE = 1000 (100)
KE = 100000 Joules or 100 KJ

### Potential Energy

As an object is moved above the ground, it gains gravitational potential energy.
The amount of energy it gains depends on:

• The object’s mass (m) in kilograms (kg)
• The height (h) above the ground in metres (m)
• The acceleration due to gravity (g)

The formula for gravitational potential energy:

GPE = mass x height x acceleration due to gravity
GPE = mgh

The acceleration due to gravity on Earth is 10 m/s². Other celestial objects such as the Moon or other planets have a different value for the acceleration due to gravity. In the above diagram, the ball is move 8 m above the ground. It has a mass of 500 g (0.5 kg). The value of g is 10.

GPE of ball = 0.5 x 8 x 10
GPE = 4 x 10
GPE = 40 J

### KE to GPE and GPE to KE

Let us say a ball is hanging in the air. It will have the maximum GPE possible for the height.

If the ball is cut loose, it will fall downwards due to gravity. Since it will start moving downwards, it will have start to gain some kinetic energy.
Therefore, some of the GPE will transferred to KE.

Similarly, if an object is thrown upwards, it will have some KE. When it reaches its highest possible point, all of its KE will be transferred to GPE.

For a split second, it will have no KE and maximum GPE. As soon as it starts falling, it will start to lose GPE and gain KE.

Question relating to KE and GPE are in relation to SUVAT Equations

Example:
A person throws a ball upwards with a velocity of 12 m/s.
I) Calculate the height that it will reach after 2 seconds.
II) Calculate its GPE at that height if its mass is 400 g.

Solution:
The best way to start of a question like this is to write down the information given to you and the information that you already know.

We are given:
initial velocity (u) = 12
time (t) = 2

We know:
acceleration (due to gravity) = -10
The acceleration is negative because the ball is moving upwards and the action of gravity is actually downwards.

I) We can use the equation: s = ut + ½at²
s = 12 (2) + ½ [-10 (2)²]
s = 24 + ½ [-40]
s = 24 + (-20)
s =  4 metres

II) We know:
Mass = 400 g = 0.4 kg
Height = 4 metres
Value of g = 10
GPE = 0.4 x 4 x 10 = 1.6 x 10 = 16 Joules