Revision NotesExam QuestionsPast Papers
A LevelFurther MathsEdexcelFurther Mechanics 1Revision NotesWork, Energy & PowerWork, Energy & PowerKinetic & Potential Energy

Kinetic & Potential Energy (Edexcel A Level Further Maths): Revision Note

Exam code: 9FM0

Amber

Author

Amber

Last updated

Kinetic Energy

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

K E space equals space 1 half m v squared

  • 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)

  • 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

 1 half m v squared space minus 1 half m u squared

where u is the initial velocity and  v  is the final velocity

  • This is often written as 1 half straight m left parenthesis straight v squared space minus straight u squared right parenthesis

  • Newton’s Second Law (F space equals space m a) and the suvat equation v squared space equals space u squared space plus space 2 a s can be used to show why this is equivalent to the work done

algebraically demonstrating a link between f=ma, work done, and change in kinetic energy

Examiner Tips and Tricks

  • 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

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.

3-1-2-m2-energy-ke-worked-example-diagram-1

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 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

G P E space equals space m g h

    • 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)

Examiner Tips and Tricks

  • 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 distance up a slope for example, you must use trigonometry to find the vertical height first.

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. Stating clearly whether is represents a gain or a loss, write down the change in the gravitational potential energy of the ball 

(i) between the instant it is thrown and the instant it reaches its maximum height,

(ii) between the instant it is thrown and the instant it hits the ground.

 

3-1-2-m2-energy-gpe-worked-example-diagram-2-fixed

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself

    Did this page help you?

    Previous:Work DoneNext:Work-Energy Principle
    Amber

    Author: Amber

    Expertise: Maths Content Creator

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.