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1.1.6Energy

KE, GPE and EPE — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions

5 min read 6 parts Lesson 7 of 19

📚 AQA GCSE Combined Science Trilogy 8464 - Physics Hub / Topical Revision
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Part 1 of 4Three equations

StoreEquationSymbols and units
KineticEk = ½ × m × v2m in kg, v in m/s, E in J
Gravitational potentialEp = m × g × hg = 9.8 N/kg (field strength), h in m
Elastic potentialEe = ½ × k × e2k in N/m, e in m

Part 2 of 4A mass oscillating on a vertical spring

Total energy stays constant
Top of the motion
  • Top of the motion The mass is momentarily at rest: kinetic store is zero and gravitational potential store is at a maximum.
Middle (rest position)
  • Middle (rest position) The mass moves fastest, so the kinetic store is at a maximum.
Bottom of the motion
  • Bottom of the motion The mass is again at rest, gravitational potential store is at a minimum and the elastic potential store is at its maximum because the spring is most stretched.
Overall
  • Overall Energy shuffles between the three stores.
    • In a real system some is dissipated by heating, so the oscillations die away.

Part 3 of 4Worked example: bungee jump

1
A 50 kg jumper falls 20 m before the cord goes taut. Gravitational potential energy lost: Ep = 50 × 9.8 × 20 = 9800 J.
2
If all of this becomes kinetic energy: ½ × 50 × v2 = 9800, so v2 = 392 and v ≈ 19.8 m/s.
3
The jumper falls a total of 50 m at the lowest point, so the maximum loss of gravitational potential energy is 50 × 9.8 × 50 = 24 500 J.
4
At the lowest point the jumper is momentarily still, so all of this is in the cord. The extension is 50 − 20 = 30 m, so k = 2E ÷ e2 = 49 000 ÷ 900 ≈ 54 N/m.

Part 4 of 4Problem-solving advice

Find the right points
  • Find the right points Pick the two instants being compared and say which stores hold the energy at each.
Rearranging
  • Rearranging To find speed, use v = √(2Ek ÷ m). To find spring constant, use k = 2Ee ÷ e2.
State questions
  • State questions If asked to 'state' a value, it is usually a result you have already calculated, so no new calculation is needed.

Key terms

TermMeaning
Kinetic energyEnergy of a moving object, Ek = ½mv2.
Gravitational potential energyEnergy stored by an object raised in a gravitational field, Ep = mgh.
Gravitational field strengthThe force per unit mass in a gravitational field; 9.8 N/kg near Earth's surface.
Conservation of energyEnergy cannot be created or destroyed, only transferred between stores.
OscillationRepeated back-and-forth movement about a rest position.

Avoid these mistakes

1
Forgetting to square the speed in the kinetic energy equation.
2
Using total length of the cord instead of the extension in the elastic energy equation.
3
Assuming that kinetic energy is greatest at the lowest point of a spring oscillation. It is greatest at the rest position.
4
Forgetting to take a square root when rearranging for speed.

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