recall and apply the principle of conservation of energy

What is Energy Conservation?

⚡️ The principle that the total energy of an isolated system remains constant over time, even though it can change form. Think of it like a closed bank account: you can transfer money between checking and savings, but the total amount stays the same. In physics, energy can shift between kinetic, potential, thermal, chemical, etc., but the sum is unchanged (ignoring external work or heat transfer).

Key Equation

For a closed system: $$E_{\text{total}} = K + U + E_{\text{other}} = \text{constant}$$

Where $K$ = kinetic energy, $U$ = potential energy, and $E_{\text{other}}$ = any other forms (thermal, chemical, etc.).

Common Examples

• 🔋 A pendulum swings: kinetic ↔︎ potential ↔︎ kinetic.
• 🚗 A car braking: kinetic → thermal (heat).
• 🧪 A chemical reaction in a battery: chemical → electrical → thermal.

Applying the Principle

When analysing a problem, follow these steps:

1. Identify the system and confirm it is closed (no external work or heat).
2. Write down the initial energy components.
3. Write down the final energy components.
4. Set the totals equal and solve for the unknown.

Example: A 2 kg block slides down a 5 m frictionless incline. Find its speed at the bottom.

Solution:

Initial: $K_i = 0$, $U_i = mgh = 2 \times 9.8 \times 5 = 98$ J. Final: $K_f = \frac{1}{2}mv^2$, $U_f = 0$. Conservation: $98 = \frac{1}{2} \times 2 \times v^2 \Rightarrow v = \sqrt{98} \approx 9.9$ m s⁻¹.

Exam Tips

📚 Remember:

• Always state whether the system is closed.
• Check units – energy is in joules (J).
• Use $g = 9.8$ m s⁻² unless otherwise specified.
• Show all steps; partial credit is awarded for correct reasoning.

⚠️ Avoid mixing up kinetic and potential energy signs – kinetic is always positive, potential can be negative depending on the chosen reference point.

Quick Review Quiz

Which of the following is NOT a form of energy that can be conserved in a closed system?

1. Electrical
2. Mechanical
3. Gravitational potential
4. Radiation (photons)

Answer: None – all can be conserved.