Conservation of Energy

This lesson covers the principle of conservation of energy, energy transfer diagrams and the concept of dissipation, as required by the Edexcel GCSE Combined Science specification (1SC0). This is one of the most important ideas in all of physics.

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The Principle of Conservation of Energy

Energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed.

This means:

• The total energy in a closed system is always the same before and after any change.
• Energy is never lost — it is always transferred somewhere.
• When we say energy is "wasted", we mean it has been transferred to a store that is not useful (usually the thermal store of the surroundings).

Exam Tip: You must be able to state the conservation of energy principle in your own words. A good version is: "The total energy of an isolated system remains constant; energy is transferred between stores but the total stays the same."

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Closed Systems

A closed system is one where no energy (or matter) can enter or leave. In a closed system, the total energy is constant.

In reality, perfect closed systems are rare. However, for many calculations we treat systems as closed — for example, a ball falling in a vacuum or a perfectly insulated container.

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Energy Transfer Diagrams

Energy transfer diagrams show how energy moves between stores in a system. They help you track where the energy goes and check that the total is conserved.

Example: A Swinging Pendulum

flowchart LR
    A["GPE store\n(at highest point)"] -->|Mechanically| B["KE store\n(at lowest point)"]
    B -->|Mechanically| A
    B -->|By heating| C["Thermal store\n(surroundings)"]

• At the highest point, all the energy is in the gravitational potential store.
• At the lowest point, all the energy has been transferred to the kinetic store.
• With each swing, a small amount of energy is transferred to the thermal store of the surroundings (dissipated) due to air resistance and friction at the pivot.
• Eventually the pendulum stops — all the initial energy is now in the thermal store of the surroundings.

Example: A Ball Dropped from Height

Stage	GPE (J)	KE (J)	Thermal (J)	Total (J)
Top (at rest)	100	0	0	100
Halfway down	50	45	5	100
Just before impact	0	90	10	100
After hitting ground	0	0	100	100

Exam Tip: In a table like this, the total in each row should always be the same. If you are asked to fill in a missing value, add up the known stores and subtract from the total.

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Energy Dissipation

Dissipation means energy has been transferred to the surroundings in a way that is not useful, usually as thermal energy (heating).

Common Causes of Dissipation

Cause	Energy wasted to
Friction between moving parts	Thermal store of surfaces and surroundings
Air resistance	Thermal store of air and object
Electrical resistance	Thermal store of wires
Sound	Thermal store of surroundings (eventually)

Reducing Dissipation

Method	How it helps
Lubrication (oil, grease)	Reduces friction between moving parts
Streamlining	Reduces air resistance
Insulation	Reduces energy transfer by heating
Smoother surfaces	Reduces friction

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Applying Conservation of Energy to Calculations

Worked Example 1

A 2 kg ball is dropped from 5 m. What is its speed just before hitting the ground? (g = 10 N/kg, ignore air resistance)

1. Conservation of energy: GPE lost = KE gained
2. $mgh = \frac{1}{2}mv^2$mgh=21​mv2
3. $2 \times 10 \times 5 = \frac{1}{2} \times 2 \times v^2$2×10×5=21​×2×v2
4. $100 = v^2$100=v2
5. $v = \sqrt{100} = 10 \text{ m/s}$v=100​=10 m/s
6. Answer: v = 10 m/s

Worked Example 2

A spring with k = 50 N/m is compressed by 0.1 m and launches a 0.02 kg ball upward. What is the maximum height reached? (g = 10 N/kg, ignore air resistance)

1. EPE stored = GPE gained at maximum height
2. $\frac{1}{2}ke^2 = mgh$21​ke2=mgh
3. $\frac{1}{2} \times 50 \times 0.1^2 = 0.02 \times 10 \times h$21​×50×0.12=0.02×10×h
4. $0.25 = 0.2h$0.25=0.2h
5. $h = 1.25 \text{ m}$h=1.25 m
6. Answer: h = 1.25 m

Exam Tip: In problems that link two energy equations, set the initial energy store equal to the final energy store and solve for the unknown. This is one of the most powerful techniques at GCSE.

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Energy and Perpetual Motion

A perpetual motion machine would run forever without any external energy input. These are impossible because:

• Energy is always dissipated (friction, air resistance, etc.).
• A machine always transfers some energy to the thermal store of the surroundings.
• Eventually, all the useful energy is dissipated and the machine stops.

This is a direct consequence of the conservation of energy — you cannot get more energy out than you put in.

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Summary

• The conservation of energy principle states that energy cannot be created or destroyed — only transferred between stores.
• In a closed system, the total energy remains constant.
• Dissipation is the transfer of energy to useless stores (usually thermal).
• Friction, air resistance and electrical resistance all cause dissipation.
• Lubrication, streamlining and insulation reduce energy waste.
• Use conservation of energy to set one energy equation equal to another and solve for unknowns.
• Perpetual motion machines are impossible because energy is always dissipated.

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Extended Worked Examples

Worked Example 3 — Specific Heat Capacity Link

A 2 kg block of copper slides along a rough surface and comes to rest, dissipating 500 J to its own thermal store. Using $E = cm\Delta\theta$E=cmΔθ with c = 385 J/kg·°C for copper, calculate the temperature rise.