Energy and the Principle of Conservation of Energy

1. Definition

A. Energy

Energy is a conserved quantity that can be stored in systems and transferred between them. When energy is transferred mechanically by a force, work is done.

• SI unit: joule (J)
• Scalar quantity: energy has magnitude only

2. Key Ideas

• Energy is stored in energy stores (e.g. kinetic, gravitational potential, chemical, elastic, nuclear, internal).
• Energy is transferred between stores/objects:
  • mechanically (by a force acting over a distance)
  • electrically (by an electric current)
  • by heating (due to a temperature difference)
  • by waves (electromagnetic and mechanical)
• Conservation of energy: total energy is constant; energy is transferred between stores but is not created or destroyed.
• Core equations (O Level):
  • Eₖ = 1/2mv² (J)
  • Eₚ = mgh (J, near Earth’s surface)
• In problems with friction/air resistance:
  energy at start = energy at end + energy dissipated (usually to internal energy and sound).

Scroll diagram horizontally to read all labels.

3. Detailed Explanations

A. Principle of conservation of energy

The principle of conservation of energy states that energy cannot be created or destroyed.

• Total energy stays constant (if you include all the stores and transfers).
• Energy can be transferred from one object to another and from one store to another.
  • Example: a television transfers energy electrically, then outputs energy by waves (light and sound) and by heating to the surroundings.

B. Energy stores vs energy transfers (O Level)

When you describe energy changes, it helps to separate:

• Energy stores (e.g. kinetic, gravitational potential, chemical, elastic, nuclear, internal)
• Energy transfers (how energy moves between objects/stores)

Common energy transfer pathways:

• Mechanically (a force doing work): see Work
• Electrically (an electric current): see Electric Current
• By heating (due to a temperature difference): see Internal Energy
• By waves (mechanical and electromagnetic): e.g. Sound, What Is Light?

C. Core equations (O Level)

Kinetic energy:

Eₖ = 1/2mv²

Gravitational potential energy (near Earth’s surface):

Eₚ = mgh

where m is mass (kg), v is speed (m s⁻¹), g is gravitational field strength (N kg⁻¹ or m s⁻²), and h is height (m).

D. How to set up conservation of energy questions

1. State the initial and final energy stores.
2. Add an energy dissipated term if there is friction/air resistance.
3. Write the equation in one line:

Energy at start = Energy at end + Energy dissipated

E. Example: gravitational potential energy ↔ kinetic energy

If an object is at height h above a reference level (often the ground), it has gravitational potential energy Eₚ = mgh.

When it falls, energy is transferred from the gravitational potential store to the kinetic store (if air resistance is small).

Scroll diagram horizontally to read all labels.

If air resistance is not negligible, some energy is transferred to the internal energy stores of the object and surroundings, with a small transfer by sound. The final kinetic energy is therefore smaller.

4. Common Mistakes

• Mixing up energy stores and energy transfers (e.g. “heat energy” is not a store; “heating” is a transfer).
• Forgetting to include energy dissipated when friction/air resistance is mentioned.
• Using h as the distance along a slope (for GPE, h is the vertical height change).
• Using mass in grams instead of kilograms.
• Using g = 10 without checking what the question states.

5. Exam Tips

• For “describe the energy changes”, write:
  • initial store → transfer pathway → final store (and add “dissipated as internal energy/sound” if needed).
• For calculations, start with a one-line conservation equation, then substitute values with units.
• If the object is at rest (e.g. at maximum height), Eₖ = 0.
• Always state your reference level for gravitational potential energy.

6. Worked Examples

Example 1: Kinetic energyCore

Find the kinetic energy of a 3.0 kg object moving at 4.0 m s⁻¹.

Show Answer

Eₖ = 1/2mv²; = 1/2(3.0)(4.0²); = 24 J

Example 2: Gravitational potential energyCore

A 2.5 kg book is lifted vertically by 1.2 m. Take g = 10 N kg⁻¹. Find the gain in gravitational potential energy.

Show Answer

Δ Eₚ = mgh; = (2.5)(10)(1.2); = 30 J

Example 3: Conservation of energy with no air resistanceCore

A ball is dropped from rest from 5.0 m above the ground. Take g = 10 N kg⁻¹. Find its speed just before it hits the ground (ignore air resistance).

Show Answer

Decrease in GPE = increase in KE: mgh = 1/2mv²

Mass cancels: gh = 1/2v² Rightarrow v = sqrt2gh = sqrt2(10)(5.0) = 10 m s⁻¹

Example 4: Describing energy transfersCore

A car brakes to a stop on a level road. Describe the energy changes.

Show Answer

The car’s kinetic energy store decreases. Energy is transferred to the surroundings by heating due to friction in the brakes/tyres/road and by sound.

Example 5: Height from gravitational potential energyCore

A 0.60 kg ball has gravitational potential energy of 18 J relative to the ground. Take g = 10 N kg⁻¹. Find its height above the ground.

Show Answer

Using Eₚ = mgh: h = Eₚ/mg = 18/(0.60)(10) = 3.0 m

More practice

For more exam-style calculations (including energy losses), go to Energy Calculations.

7. Mind Stretchers

Mind stretcher 1: Maximum height from an initial speedExtension

A ball is thrown vertically upwards at 12 m s⁻¹. Take g = 10 N kg⁻¹. Find the maximum height reached (ignore air resistance).

Show Answer

At maximum height, Eₖ = 0, so initial KE = gain in GPE: 1/2mv² = mgh

Mass cancels: h = v²/2g = 12²/2(10) = 7.2 m

Mind stretcher 2: Energy dissipated by air resistanceExtension

A 0.50 kg ball is dropped from 10 m. Air resistance transfers 8.0 J from the ball–Earth system to the internal energy stores of the air and ball. Take g = 10 N kg⁻¹. Find its speed just before it hits the ground.

Show Answer

Initial GPE: Eₚ = mgh = (0.50)(10)(10) = 50 J

Final KE: Eₖ = 50 - 8.0 = 42 J

42 = 1/2(0.50)v²; v² = 168; v = 13.0 m s⁻¹

8. Practice, Quiz and Next Step

Close your notes and use Energy and the Principle of Conservation of Energy in the supplied context below. This requires a constructed explanation or working, not recognition of an option.

Fresh context: A battery-powered toy car accelerates, then slows after the motor is switched off.

1. Retrieve: define energy stores, transfers and conservation in your own words, including units, sign or conditions where relevant.
2. Represent: Draw an energy-store and transfer-pathway diagram for both stages, including dissipated transfer.
3. Apply: Use conservation to explain the changes without saying energy is used up or lost.

Check the response before looking back

• The chosen system and transfer pathway are stated before applying conservation.
• Energy and power are not used interchangeably, and all quantities use compatible units.
• The numerical result is checked against the physical situation and any efficiency limit.

If one check fails, name that exact gap, revisit the matching explanation or worked example, and redo the task with different values or a different situation. Then use theO-Level topic checks orpractice browser for an independent re-test.