Kinetic & Potential Energy (Edexcel A Level Further Maths: Further Mechanics 1)

There are many different forms of energy including, but not limited to, heat energy, light energy, chemical energy and nuclear energy. Two forms of energy which are of particular interest in mechanics are kinetic energy (KE) and potential energy (or gravitational potential energy, GPE). Elastic potential energy is also considered when dealing with springs and strings.

What is kinetic energy?

• A particle has kinetic energy when it is moving
• Kinetic energy is a scalar quantity, it cannot 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
• Kinetic energy is measured in joules (J)
  • 1 Kilojoule = 1000 joules (1 kJ = 1000 J)

How can we link the work done to a 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 show why this is equivalent to the work done

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 such as elastic potential energy, however it is usually gravitational potential energy which is being referred to by "potential energy"
• 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 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)