Energy

1. Overview

Energy is a fundamental concept in physics, describing the "capacity to do work." In any process, energy is never created or destroyed; instead, it shifts between different stores through various transfer pathways. Understanding how energy changes form allows us to calculate the behavior of everything from falling objects to national power grids.

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Key Definitions

• Energy: The capacity of a system to do work, measured in Joules (J).
• System: An object or a group of objects being studied.
• Conservation of Energy: A fundamental law stating that the total energy of a closed system remains constant.
• Work Done: The amount of energy transferred by a force or an electrical current.

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Core Content

Energy Stores

Energy is held by objects in different "stores." You must be able to identify these:

• Kinetic: Energy of a moving object.
• Gravitational Potential (GPE): Energy stored by an object due to its position in a gravitational field (height).
• Chemical: Energy stored in bonds (e.g., food, fuel, batteries).
• Elastic (Strain): Energy stored when an object is stretched or compressed.
• Nuclear: Energy stored in the nucleus of an atom.
• Electrostatic: Energy stored when like charges are pushed together or unlike charges are pulled apart.
• Internal (Thermal): The total kinetic and potential energy of the particles within an object (experienced as temperature).

Energy Transfers

Energy moves between stores via four main pathways:

1. Mechanical Work: A force moving an object through a distance.
2. Electrical Work: Charges moving due to a potential difference (current).
3. Heating: Due to a temperature difference.
4. Waves: Energy transferred by electromagnetic radiation (light), sound, or water waves.

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The Principle of Conservation of Energy

Energy cannot be created or destroyed. In any event: Total Energy Input = Total Energy Output

Worked Example (Simple Flow): An electric fan transfers 100J of electrical energy. 80J is transferred to the kinetic store of the air, and 20J is transferred to the thermal store of the motor.

• Conservation Check: 80J + 20J = 100J.

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Extended Content (Extended Only)

Kinetic Energy ($E_k$)

The energy of a moving object depends on its mass and the square of its speed.

• Equation: $E_k = \frac{1}{2}mv^2$

Change in Gravitational Potential Energy ($\Delta E_p$)

When an object is raised or lowered, its GPE changes.

• Equation: $\Delta E_p = mg\Delta h$

Worked Example (Complex Transfer): A 2 kg block is dropped from a height of 5m. Calculate its speed just before it hits the floor (assume no air resistance, $g = 9.8 m/s^2$).

1. Calculate GPE at the top: $\Delta E_p = 2 \times 9.8 \times 5 = 98J$.
2. Apply Conservation of Energy: $GPE_{lost} = KE_{gained}$.
3. Set up KE equation: $98 = \frac{1}{2} \times 2 \times v^2$.
4. Solve for $v$: $98 = v^2 \rightarrow v = \sqrt{98} \approx 9.9 m/s$.

Sankey Diagrams

Sankey diagrams show energy efficiency. The width of the arrows represents the amount of energy.

• The horizontal arrow usually represents "useful" energy.
• The downward arrow represents "wasted" (dissipated) energy.

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Key Equations

Equation	Symbols	Units
$E_k = \frac{1}{2}mv^2$	$m$ = mass, $v$ = speed	$m$ (kg), $v$ (m/s), $E_k$ (J)
$\Delta E_p = mg\Delta h$	$m$ = mass, $g$ = gravitational field strength, $\Delta h$ = change in height	$m$ (kg), $g$ (N/kg), $\Delta h$ (m), $E_p$ (J)

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Common Mistakes to Avoid

• ❌ Wrong: Assuming the energy link between a turbine and a generator in a power station is "electrical."
• ✅ Right: The turbine-to-generator link is a physical, rotating axle; therefore, the energy is transferred mechanically.
• ❌ Wrong: Forgetting to square the velocity ($v$) when calculating Kinetic Energy.
• ✅ Right: Always calculate $v^2$ first before multiplying by $\frac{1}{2}m$.
• ❌ Wrong: Thinking total energy decreases as an object falls.
• ✅ Right: Only the GPE decreases; the total energy remains constant as it converts into Kinetic Energy.
• ❌ Wrong: Forgetting to include $g$ (gravitational field strength) in GPE calculations.
• ✅ Right: Always multiply mass by $g$ ($9.8$ or $10 N/kg$ as per paper instructions) and height.

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Exam Tips

1. Trace the Source: Remember that for hydroelectric, wind, and fossil fuels, the Sun is the original source of energy (driving the water cycle, weather patterns, and photosynthesis).
2. Units Matter: Always convert mass into kilograms (kg) and height into meters (m) before using the $E_k$ or $E_p$ formulas.
3. Sankey Width: When drawing or interpreting Sankey diagrams, use a ruler. If 1cm width equals 10J, then a 50J input must be exactly 5cm wide.