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10.2Energy and Its Conservation

Kinetic and Gravitational Potential Energy — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 4 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Recall and use Ek = ½mv2.Kinetic energy = ½ × mass × speed2: Ek = ½mv2 (J, kg, m/s).Change in gravitational potential energy = mass × gravitational field strength × change in height: ΔEp = mgΔh (J, kg, N/kg, m).Weight = mass × gravitational field strengthW = mg (N, kg, N/kg).g on…

  • Rearranged
  • Work–energy theorem
  • Elastic energy in a spring (extension)
  • Weight and mass are different
  • To find speed from kinetic energy, rearrange
  • A 1200 kg car travels at 25 m/s. Calculate its kinetic energy

Section 1 of 7Kinetic and Gravitational Potential Energy

Essential knowledge
10.2 Kinetic and Gravitational Potential… concept map: Weight = mass × gravitational, Rearranged, Work–energy theorem, Elastic energy in a spring (e, The work–energy theorem
Visual guide to the key ideas explained in this lesson.
Any moving object has energy in its kinetic store. The amount depends on mass and on the square of speed, so speed has the bigger effect: a car at 30 m/s has four times the kinetic energy it had at 15 m/s. This is why stopping distances rise sharply with speed.
Kinetic energy is a scalar and cannot be negative; direction of motion does not matter, only speed.
When an object is lifted, work is done against its weight. The work done equals weight × vertical height = mgΔh, and this energy goes into the gravitational potential store.
Only the vertical height change counts. A skier who descends 50 m vertically loses the same GPE whether the slope is steep or gentle.
GPE is measured from a reference level that you choose, usually the ground or the lowest point in the problem. Below the reference level GPE is negative, but the change in GPE is the same whatever reference level is chosen.
The equation ΔEp = mgΔh assumes g is constant, which is true close to the Earth's surface. For satellites far from Earth a different expression is needed (beyond this course).
The work–energy theorem
The work–energy theorem the net (resultant) force on an object multiplied by the distance moved equals the change in kinetic energy. A resultant forward force increases KE; a resultant backward force (braking) decreases KE.
A stretched or compressed spring stores elastic potential energy. For a spring that obeys Hooke's law (F = kx) the stored energy equals the area under the force–extension graph, ½Fx = ½kx2.
Weight and mass are different
Weight and mass are different mass (kg) is the same everywhere, weight (N) depends on the local gravitational field strength. The same object therefore gains less GPE when lifted 1 m on the Moon than on Earth.
To find speed from kinetic energy, rearrange
To find speed from kinetic energy, rearrange v = √(2Ek/m). Always take the square root as the final step.

Section 2 of 7Process & sequence

1
Write down the known quantities with units; convert grams to kg and km/h to m/s (÷ 3.6).
2
Choose the correct equation: Ek = ½mv2 for motion, ΔEp = mgΔh for height changes.
3
Square the speed first (and only the speed) before multiplying by ½m.
4
Substitute values, keeping g = 9.8 N/kg unless told otherwise.
5
Rearrange if needed: v = √(2Ek/m) and Δh = ΔEp/(mg).
6
Give the answer to 2–3 significant figures with the unit J (or m, m/s).

Calculating speed from kinetic energywrite these steps in this order; each step is a marking point.

1
Write Ek = ½mv2.
2
Multiply the kinetic energy by 2.
3
Divide by the mass in kg to get v2.
4
Take the square root to find v.
5
State the answer in m/s to sensible significant figures.

Section 3 of 7Compare

Comparing kinetic and gravitational potential energy
FeatureKinetic energyGravitational potential energy
Depends onMass and speedMass, g and height change
EquationEk = ½mv2ΔEp = mgΔh
Doubling speed/heightKE ×4 (speed is squared)GPE ×2
Zero whenObject is at restObject is at the chosen reference level
Can be negative?NoYes, below the reference level

Section 4 of 7Worked examples

Worked examples
A 1200 kg car travels at 25 m/s. Calculate its kinetic energy.
  • Ek = ½mv2 = 0.5 × 1200 kg × (25 m/s)2 = 0.5 × 1200 × 625 = 375 000 J = 3.8 × 105 J (2 s.f.).
    What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
A 55 kg student climbs stairs of vertical height 4.0 m. Calculate the gain in gravitational potential energy (g = 9.8 N/kg).
  • ΔEp = mgΔh = 55 kg × 9.8 N/kg × 4.0 m = 2156 J ≈ 2.2 × 103 J.
    What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
A 0.15 kg ball has 30 J of kinetic energy. Find its speed.
A 0.15 kg ball has 30 J of kinetic energy. Find its speed.
  • v = √(2Ek/m) = √(2 × 30 J ÷ 0.15 kg) = √400 = 20 m/s.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Kinetic energy (KE, Ek) · Gravitational potential energy (GPE, Ep) · Mass (m) · Speed (v) · Gravitational field strength (g) · Weight (W) · Change in height (Δh) · Reference level · Elastic potential energy · Mechanical energy · Work–energy theorem · Terminal velocity
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
KE = ½mvKE = ½mv2 (speed squared).
2
GPE = mg × distance along the slopeΔEp = mgΔh using vertical height.
3
weight is measured in kgweight is a force measured in newtons; mass is in kg.
4
doubling speed doubles KEdoubling speed quadruples KE.
5
Don't square the ½m term — Write: square only the speed, then multiply by ½m.

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