Conservation of Energy
Explore the fundamental law that energy can never be created or destroyed — only transformed from one form to another — and calculate efficiency in real-world systems.
The Law of Conservation of Energy
"Energy cannot be created or destroyed; it can only be transformed from one form to another. The total amount of energy in a closed system remains constant."
This is one of the most important laws in all of science. It means that whenever energy seems to “disappear” from a system, it has actually been converted into another form — most commonly heat (thermal energy) due to friction or resistance.
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Kinetic Energy
Energy of motion
KE = ½mv²
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Gravitational PE
Energy due to height
GPE = mgh
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Thermal Energy
Energy from heat
(often from friction)
Energy Transformations
Energy constantly changes from one form to another. A Sankey diagram shows how energy is distributed after a transformation, with the width of arrows proportional to the amount of energy.
Rollercoaster: GPE ↔ KE
At the top: maximum GPE, minimum KE. At the bottom: minimum GPE, maximum KE. Total mechanical energy is conserved (ignoring friction).
Common Energy Transformation Examples
Efficiency
No real-world device is 100% efficient because some energy is always “wasted” (usually as heat or sound). Efficiency tells us what fraction of the input energy is converted into useful output energy:
Efficiency = (Useful output energy ÷ Total input energy) × 100%
LED light globe
Input: 10 J electrical
Useful output: 9 J light
Wasted: 1 J heat
Efficiency: 90%
Incandescent globe
Input: 100 J electrical
Useful output: 10 J light
Wasted: 90 J heat
Efficiency: 10%
Key Energy Formulae
Kinetic Energy
KE = ½mv²
m = mass (kg), v = velocity (m/s), KE in joules (J)
Gravitational Potential Energy
GPE = mgh
m = mass (kg), g = 9.8 m/s² (on Earth), h = height (m), GPE in joules (J)
Key Vocabulary
| Term | Definition |
|---|---|
| Conservation of energy | The law stating that the total energy in a closed system is constant; energy cannot be created or destroyed. |
| Kinetic energy | The energy an object possesses because of its motion (KE = ½mv²). |
| Gravitational potential energy | The energy stored in an object due to its position above a reference point (GPE = mgh). |
| Efficiency | The ratio of useful output energy to total input energy, expressed as a percentage. |
Worked Examples
Calculating kinetic energy of a cyclist.
Given: A cyclist and bike have a combined mass of 80 kg and are moving at 10 m/s.
Step 1: KE = ½ × m × v²
Step 2: KE = 0.5 × 80 × 10² = 0.5 × 80 × 100
Answer: KE = 4 000 J (4 kJ)
Using conservation of energy to find speed at the bottom of a ramp.
Given: A 5 kg ball rolls from rest at the top of a 2 m high ramp. Ignore friction. g = 9.8 m/s².
Step 1: At the top, all energy is GPE: GPE = mgh = 5 × 9.8 × 2 = 98 J
Step 2: At the bottom, all GPE converts to KE: KE = 98 J
Step 3: ½mv² = 98 → v² = (2 × 98) ÷ 5 = 39.2 → v = √39.2
Answer: v ≈ 6.26 m/s
Calculating efficiency of a motor.
Given: An electric motor uses 500 J of electrical energy to lift a load, giving it 350 J of gravitational potential energy. The remaining energy is lost as heat.
Step 1: Efficiency = (Useful output ÷ Total input) × 100%
Step 2: Efficiency = (350 ÷ 500) × 100%
Answer: Efficiency = 70%. The other 30% (150 J) is wasted as thermal energy.
Knowledge Check
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Key Concepts Summary
- •Energy cannot be created or destroyed — only converted between forms (law of conservation of energy).
- •KE = ½mv² (kinetic energy); GPE = mgh (gravitational potential energy).
- •In a closed system without friction, total mechanical energy (KE + GPE) is conserved.
- •Efficiency = (useful output ÷ total input) × 100%; always less than 100% in real systems due to heat losses.
- •Sankey diagrams visually show energy inputs, useful outputs, and wasted energy.