Understand the principle of the conservation of energy and apply it to complex examples involving multiple stages, including the interpretation of Sankey diagrams.
Energy can change form but the total energy of an isolated system stays constant.
Mathematically:
\$E{\text{total}} = E{\text{kinetic}} + E{\text{potential}} + E{\text{thermal}} + \dots\$
Think of energy like a bank account: you can deposit (store) or withdraw (use) energy, but the total balance remains the same unless you add or remove money.
When a system goes through several stages, track the energy at each stage.
Example: A roller‑coaster cart starts at height h and ends at the bottom with speed v. Assume 10 % of the initial potential energy is lost to friction.
| Stage | Energy | Expression |
|---|---|---|
| Initial | Potential | \$mgh\$ |
| After 10 % loss | Remaining Potential | \$0.9\,mgh\$ |
| Final | Kinetic | \$0.5\,mv^2\$ |
Energy conservation gives: \$0.9\,mgh = 0.5\,mv^2 \;\;\Rightarrow\;\; v = \sqrt{1.8\,gh}\$
A Sankey diagram shows the flow of energy between stages. The width of each arrow is proportional to the amount of energy.
Key points:
Example: A power plant diagram might show 100 kW of electrical output, 30 kW lost as heat, and 70 kW used for mechanical work. The diagram would have arrows of widths 100, 30, and 70 respectively.
🔍 Read the question carefully – identify all energy forms and stages.
📐 Draw a diagram (including Sankey if requested) to visualise energy flows.
✏️ Show all steps – teachers look for the energy balance equation.
⚖️ Check units – energy in joules (J), power in watts (W).
🧠 Use analogies in your answer if they help explain the process.
⏱️ Time management – allocate 5 min for setting up the problem, 10 min for calculations, 5 min for checking.
Good luck, and remember: energy never disappears, it just changes form! 🚀