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GPE & KE (Edexcel GCSE Physics)

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Leander Oates

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Gravitational Potential Energy

  • Energy in the gravitational store of an object is defined as:

The energy an object has due to its height in a gravitational field

  • This means:

    • If an object is lifted up, energy is transferred to its gravitational potential store 

    • If an object falls, energy will be transferred away from its gravitational potential store

gpe man, IGCSE & GCSE Physics revision notes

Energy is transferred to the gravitational potential store of the mass as it is lifted through a gravitational field

  • The change in the gravitational potential energy, ΔGPE of an object can be calculated using the equation:

increment G P E space equals space m cross times g cross times increment h

  • Where:

    • ΔGPE = change in gravitational potential energy, in joules (J)

    • m = mass, in kilograms (kg)

    • g = gravitational field strength in newtons per kilogram (N/kg)

    • Δh = change in vertical height in metres (m)

  • In Physics, Δ is the capital Greek letter 'delta' which stands for 'change in'

  • The two graphs below show how GPE changes with height for a ball being thrown up in the air and when falling down

GPE graphs, downloadable AS & A Level Physics revision notes

Graphs showing the linear relationship between GPE and height

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Kinetic Energy

  • Energy in an object's kinetic store is defined as:

The amount of energy an object has as a result of its mass and speed

  • This means that any object in motion has energy in its kinetic energy store

1-7-2-kinetic-energy-cie-igcse-23-rn

 

  • Kinetic energy can be calculated using the equation:

K E space equals space 1 half cross times m cross times v squared

  • Where:

    • KE = kinetic energy in joules (J)

    • m = mass of the object in kilograms (kg)

    • v = speed of the object in metres per second (m/s)

Energy Equivalency

  • In a perfect energy transfer, there is no wasted energy

  • Energy transfers can be assumed to be perfect if the wasted energy transfer is negligible

    • Some exam questions will state to ignore air resistance for example

    • In reality, there is no such thing as a perfect energy transfer

  • Ignoring wasted energy transfers is helpful in calculations because it allows energy values to be equated

  • Pendulums are often used as examples of perfect energy transfers

    • All of the energy in the kinetic store of the pendulum is transferred mechanically into its gravitational potential store

    • And then all of the energy in the gravitational potential store of the pendulum is transferred mechanically into its kinetic store

    • Energy is transferred back and forth between these two stores as the pendulum swings

    • Therefore, it can be said that:

K E subscript t o t a l end subscript space equals space G P E subscript t o t a l end subscript

Worked Example

The diagram shows a rollercoaster going down a track.

The rollercoaster takes the path A → B → C → D.

WE - Energy transfers question image, downloadable AS & A Level Physics revision notes

The rollercoaster begins at a height of 15 m above the ground and ends at ground level.

Breaking to stop the ride begins after it passes position D.

The mass of the rollercoaster is 100 kg.

Calculate the maximum speed of the rollercoaster at position D. Ignore any frictional effects before passing point D.

Answer:

Step 1: List the known quantities

  • Height, h = 15 m

  • Mass, m = 100 kg

  • Gravitational field strength, g = 10 N/kg

Step 2: Write out the equation for gravitational potential energy

increment G P E space equals space m space cross times space g space cross times space increment h

Step 3: Calculate the gravitational potential energy

increment G P E space equals space 100 space cross times space 10 space cross times space 15

increment G P E space equals space 15 space 000 space straight J

Step 4: Use energy equivalency to equate the gravitational potential and kinetic energy

  • Frictional effects are to be ignored therefore a perfect energy transfer can be assumed

increment G P E space equals space K E

Step 5: Write out the equation for kinetic energy

K E space equals space 1 half space cross times space m space cross times space v squared

Step 6: Rearrange to make speed the subject:

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

Step 7: Calculate the maximum possible speed of the rollercoaster at position D

  •  At position D the rollercoaster is at ground level

  • Therefore all the energy has been transferred from the gravitational potential to the kinetic store

  • The maximum possible speed is using the assumption of a perfect energy transfer

v space equals space square root of fraction numerator 2 space cross times space 15 space 000 over denominator 100 end fraction end root

v space equals space 17 space straight m divided by straight s

Examiner Tips and Tricks

When the question tells you to ignore the effects of resistance (ie wasted energy transfers) this is a clue that may need to use energy equivalency to find the missing quantity needed for your calculation.

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    Leander Oates

    Author: Leander Oates

    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.