National 5PhysicsSQARevision NotesDynamicsEnergyConservation of Energy Calculations

Conservation of Energy Calculations (SQA National 5 Physics): Revision Note

Exam code: X857 75

Katie M

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on

Conservation of energy calculations

  • In many situations, energy is transferred between the GPE and KE stores

    • GPE is gravitational potential energy

    • KE is kinetic energy

  • Whenever mechanical work is done (when a force acts over a distance), energy is transferred mechanically 

    • This is a consequence of conservation of energy

  • The amount of energy transferred (in joules) is equal to the work done (in joules or newton-metres)

energy transferred (J) = work done (J or N m)

GPE and KE calculations

  • 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 kinetic energy of the pendulum is transferred mechanically into gravitational potential energy

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

    • Energy is converted back and forth between these forms of energy 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.

The breaking which stops the ride begins after it passes position D.

The mass of the rollercoaster is 105 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 = 105 kg

  • Gravitational field strength, g = 9.8 N/kg

Step 2: Write out the appropriate relationship

E subscript p space equals space m g increment h

Step 3: Substitute in the known values to calculate the Ep

E subscript p space equals space 105 space cross times space 9.8 space cross times space 15

E subscript p space equals space 15 space 435 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

E subscript p space equals space E subscript k

Step 5: Write out the appropriate relationship

E subscript k equals space 1 half space m 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 E subscript k 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 converted from gravitational potential to kinetic energy E_p

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

v space equals space square root of fraction numerator 2 space cross times space 15 space 435 over denominator 105 end fraction end root

v space equals space 17.146 space straight m space straight s to the power of negative 1 end exponent

Step 8: Round to an appropriate number of significant figures

  • The least precise input value is 2 s.f.

  • Therefore, the final answer can only be given to the same precision

v space equals space 17 space straight m space straight s to the power of negative 1 end exponent space open parentheses 2 space straight s. straight f. close parentheses

Examiner Tips and Tricks

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

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    Author
    Reviewer
    Katie M

    Author: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

    Caroline Carroll

    Reviewer: Caroline Carroll

    Expertise: Physics & Chemistry Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.