Kinetic Energy
There are many different forms of energy including, but not limited to, heat energy, light energy, chemical energy and nuclear energy. In this course we deal with a type of energy called mechanical energy which exists in two forms, kinetic energy (KE) and gravitational potential energy (GPE).
Kinetic Energy (KE)
What is kinetic energy?
 Kinetic Energy is the energy formed by an object’s movement.
 Kinetic energy is a scalar quantity, it can not be negative
 The work done by a resultant force that acts to move an object in a particular direction will be equal to the change in kinetic energy of the object
How is kinetic energy calculated?
 A particle can only have kinetic energy when it is moving
 If a particle with mass, m kg is moving with speed v m s^{1 }then its kinetic energy can be calculated using the formula

 If the particle is moving in two dimensions with the velocity vector v then kinetic energy can be calculated in two ways
 Using the formula on each component individually and finding the sum of the KE in each component
 Finding the magnitude of the velocity to get the speed and then using the formula for KE
 If the particle is moving in two dimensions with the velocity vector v then kinetic energy can be calculated in two ways
 Kinetic energy is measured in joules (J)
 1 Kilojoule = 1000 joules (1 kJ = 1000 J)
How do we derive the formula for the change in kinetic energy?
 The work done by the resultant force is equal to the change in kinetic energy
 This is the final kinetic energy minus the initial kinetic energy
 The formula for the change in kinetic energy is
where u is the initial velocity and v is the final velocity

 This is often written as
 Newton’s Second Law () and the 'suvat' equation can be used to derive the formula for the change in kinetic energy
Worked Example
A jogger increases her speed from 2 m s^{1} to 3 m s^{1} and her change in kinetic energy is 150 J, find the mass of the jogger.
Exam Tip
 Always double check the units are in kg for mass and m s^{1 }for velocity before carrying out any calculations.
 Be careful not to make the mistake of using the difference between the velocities with the equation, remember it should be the difference between the squares of the speeds.
 Make sure you are familiar with the method for the derivation of the formula for the change in kinetic energy.
Gravitational Potential Energy
What is potential energy?
 Potential energy is the energy stored in a stationary object
 Gravitational potential energy (GPE) is the energy a particle possesses when it is at a fixed height and gravity is acting on it
 There are other types of potential energy but in this module only GPE is dealt with and so sometimes GPE is referred to as potential energy (PE)
 GPE will change as the vertical height of an object changes
 The work done against gravity on a particle as it moves upwards is equal to its increase in GPE
 The work done by gravity on a particle as it moves downwards is equal to its decrease in GPE
How is gravitational potential energy calculated?
 Gravitational potential energy is equal to the product of the force of the weight of an object and its vertical height, h , above a fixed point

 If the object is sitting on the ground or the point chosen as the fixed base level, the object will have no gravitational potential energy
 As the object moves upwards, its GPE will increase
 As the object moves downwards again, its GPE will decrease
 When mass is measured in kg, acceleration due to gravity is measured in m s^{2} and height is in metres, m, gravitational potential energy is measured in joules (J)
 1 kilojoule = 1000 joules (1 kJ = 1000 J)
Worked Example
A ball of mass 400 grams is thrown vertically upwards from a height of 1 metre above the ground. It reaches a maximum height of 4 metres before falling to the ground again. Stating clearly whether is represents a gain or a loss, write down the change in the gravitational potential energy of the ball
Exam Tip
 Always double check the units are in kg for mass and m for height before carrying out any calculations.
 Remember that it is the vertical height that must be used within the calculations for GPE, if you are given the slant height you must use trigonometry to find the vertical height first.