The Law of Conservation of Energy

Step 1: Define the System Boundary: Clearly identify what objects are included in your system. This determines whether an interaction is internal (energy transformation) or external (work done on the system).

Step 2: Identify Initial and Final Stores: List all types of energy present at the start and end of the process. For example, a falling object starts with Gravitational Potential Energy ($GPE$) and ends with Kinetic Energy ($KE$) and Thermal Energy ($E_{th}$).

Step 3: Apply the Conservation Equation: Use the balance equation: $E_{initial} + W_{in} = E_{final} + W_{out}$. If the system is isolated, this simplifies to $\sum E_{initial} = \sum E_{final}$.

Step 4: Account for Dissipation: In real-world scenarios, friction and air resistance transfer energy to the thermal store of the surroundings. This 'wasted' energy must be included in the final sum to satisfy the law of conservation.

Useful Energy: This is the energy transferred to the store required for the intended purpose of the device or process. For a lightbulb, the useful energy is the light (radiation).

Wasted (Dissipated) Energy: This is energy that is transferred to non-useful stores, typically the thermal store of the surroundings. Once energy is dissipated, it becomes 'spread out' and difficult to use for further work.

Identify the 'Hidden' Store: If a question mentions 'friction' or 'air resistance,' you must account for energy being transferred to the thermal store. Never assume $100\%$ efficiency unless the problem states the system is 'ideal' or 'frictionless.'

Unit Consistency: Always ensure energy is measured in Joules (J). If given power in Watts (W) and time in seconds (s), remember that $1 \text{ J} = 1 \text{ W} \times 1 \text{ s}$.

The 'Beaker' Analogy: Think of energy stores as containers of water. Pouring water from one container to another changes the 'store' but the total volume of water remains the same unless some 'leaks' (dissipates) to the surroundings.

The 'Lost' Energy Myth: Students often say energy is 'lost' when it is actually just transferred to a non-useful store. In physics, energy is never truly lost from the universe; it is merely dissipated.

Confusing Power and Energy: Energy is the total amount of 'work' capacity ($J$), while power is the rate at which that energy is transferred ($J/s$). Conservation applies to the total Joules, not necessarily the rate.

Ignoring the Surroundings: When calculating the energy of a system, failing to include the thermal energy transferred to the air or tracks will lead to an apparent violation of the conservation law.