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GCSEPhysics: Combined ScienceAQARevision Notes1. Energy1.1 Energy Changes in a System1.1.6 KE, GPE & EPE

KE, GPE & EPE (AQA GCSE Physics: Combined Science)

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KE, GPE & EPE

  • When a mass on a vertical spring oscillates up and down, energy is transferred between stores

  • Although the total energy of the mass-spring system will remain constant, it will have changing amounts of energy in its: 
    • Elastic potential energy (EPE) store 
    • Kinetic energy (KE) store
    • Gravitational potential energy (GPE) store

Change in Spring Energy, downloadable AS & A Level Physics revision notes

Energy changes when a spring is stretched

  • At position A:
    • The spring has some energy in its elastic potential store since it is slightly compressed
    • The spring has zero energy in its kinetic store since it is stationary
    • The amount of energy in its gravitational potential store is at a maximum because the mass is at its highest point

  • At position B:
    • The spring has some energy in its elastic potential store since it is slightly stretched
    • The energy in its kinetic store is at a maximum as it passes through its resting position at its maximum speed
    • The spring has some energy in its gravitational potential store since the mass is still above its lowest point in the oscillation

  • At position C:
    • The energy in the elastic potential store of the spring is at its maximum because it is at its maximum extension
    • The spring has zero energy in its kinetic store since it is stationary
    • The energy in the gravitational potential store of the spring is at a minimum because it is at its lowest point in the oscillation

Worked example

The diagram below shows a student before and after a bungee jump. The bungee cord has an unstretched length of 30.0 m.KE GPE EPE Worked Example, downloadable AS & A Level Physics revision notes

The mass of the student is 60.0 kg. The gravitational field strength is 9.8 N / kg.

Calculate:

a) The change in gravitational potential energy of the student at 30.0 m

b) The maximum change in the gravitational potential energy of the student

c) The speed of the student after falling 30.0 m if 90% of the energy in the student's gravitational potential store is transferred to the student's kinetic store

d) The spring constant of the bungee cord if all the energy in the gravitational potential store of the student is transferred to the elastic potential store of the bungee cord

 

Part (a)

Step 1: List the known quantities

    • Mass of the student, m = 60.0 kg
    • Gravitational field strength, g = 9.8 N/kg
    • Change in height, h = 30.0 m

Step 2: Write out the equation for gravitational potential energy

E subscript P space equals space m g h

Step 3: Calculate the change in gravitational potential energy

E subscript P space equals space 60 space cross times space 9.85 space cross times space 30

E subscript P space equals space 17 space 640 space straight J

 

Part (b)

Step 1: List the known quantities

    • Mass of the student, m = 60.0 kg
    • Gravitational field strength, g = 9.8 N/kg
    • Maximum change in height, h = 75.0 m

Step 2: Calculate the maximum change in gravitational potential energy

E subscript P space m a x end subscript space equals space m g h subscript m a x end subscript

E subscript P space m a x end subscript space equals space 60 space cross times space 9.8 space cross times space 75

E subscript P space m a x end subscript space equals space 44 space 100 space straight J

 

Part (c)

Step 1: List the known quantities

    • Mass of the student, m = 60.0 kg
    • E subscript P at 30.0 m = 17 640 J
  • Step 2: Determine 90% of the E subscript P at 30.0 m 

    E subscript K space equals space 90 percent sign space of space E subscript P

  • E subscript K space equals space 0.9 space cross times space 17 space 640
  • E subscript K space equals space 15 space 876 space straight J

Step 3: Write out the equation for KE

E subscript K space equals space 1 half m v squared

Step 4: Rearrange to make speed the subject

    • Multiply both sides by 2:

 m v squared space equals space 2 space cross times space E subscript K

    • Divide both sides by m:

 v squared space equals space fraction numerator 2 space cross times space E subscript K over denominator m end fraction

    • Take the square root of both sides:

 v space equals space square root of fraction numerator 2 space cross times space E subscript K over denominator m end fraction end root

Step 5: Calculate the speed

 v space equals space square root of fraction numerator 2 space cross times space 15 space 876 over denominator 60 end fraction end root space

v space equals space 23.0 space straight m divided by straight s

 

Part (d)

Step 1: List the known quantities

    • E subscript P space m a x end subscript = 44 100 J
    • E subscript e at 75.0 m =  E subscript e space m a x end subscript 
  • Step 2: Determine the extension of the bungee cord 
  •  
  • e space equals space 75.0 space minus space 30.0
  • e space equals space 45.0 space straight m

Step 3: Write out the equation for elastic potential energy

E subscript e space equals space 1 half k e squared

 

Step 3: Rearrange to make spring constant, k, the subject

    • Multiply both sides by 2:

 k e squared space equals space 2 space cross times space E subscript e

    • Divide both sides by e squared:

 k space equals space fraction numerator 2 space cross times space E subscript e over denominator e squared end fraction

Step 4: Calculate the spring constant

 k space equals space fraction numerator 2 space cross times space 44 space 100 over denominator 45 squared end fraction

k space space equals space 43.6 space straight N divided by straight m

Examiner Tip

If a question asks you to "state" a value, you do not need to carry out a calculation: The answer will almost certainly be a number either from a previous answer or which was given somewhere in the question.

For example, if you have just calculated the gravitational potential energy of an object and are then asked to state the kinetic energy a moment later, the answers are very likely to be the same.

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    Leander

    Author: Leander

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.