Energy, work and power: kinetic and potential energy, conservation, work done, power
Energy, Work & Power – Mechanics (M1)
1. Kinetic Energy (KE)
💨 Kinetic energy is the energy an object has because of its motion. The faster it moves, the more KE it has.
Formula: $$K = \frac{1}{2} m v^2$$
- m = mass (kg)
- v = speed (m/s)
⚽ Example: A soccer ball kicked at 20 m/s has KE = ½ × 0.45 kg × (20 m/s)² ≈ 90 J.
2. Potential Energy (PE)
🏔️ Potential energy is stored energy due to position or configuration.
2.1 Gravitational PE
When an object is lifted to a height h above the ground.
Formula: $$U_g = m g h$$
- g ≈ 9.81 m/s² (gravity)
🏀 Example: A basketball (0.6 kg) held 2 m above the floor has U_g = 0.6 × 9.81 × 2 ≈ 11.8 J.
2.2 Elastic PE (Spring)
When a spring is compressed or stretched by x meters.
Formula: $$U_s = \frac{1}{2} k x^2$$
- k = spring constant (N/m)
🔧 Example: A spring with k = 200 N/m compressed 0.05 m stores U_s = ½ × 200 × (0.05)² = 0.25 J.
3. Conservation of Energy
🔄 Energy can change form but the total energy in an isolated system stays constant.
$$E_{\text{total}} = K + U_g + U_s = \text{constant}$$
🏰 Example: A roller‑coaster car at the top of a hill has only PE. At the bottom, PE is converted to KE.
4. Work Done (W)
🛠️ Work is the transfer of energy when a force moves an object.
Formula: $$W = F d \cos\theta$$
- F = applied force (N)
- d = displacement (m)
- θ = angle between force and displacement
⚡ Example: Pushing a box 5 m with a horizontal force of 20 N (θ = 0°) does W = 20 × 5 × cos 0° = 100 J.
5. Power (P)
⚡ Power is the rate of doing work or transferring energy.
Formula: $$P = \frac{W}{t} = F v \cos\theta$$
- t = time (s)
- v = speed (m/s)
🚗 Example: A car that does 200 J of work in 4 s has power P = 200/4 = 50 W.
6. Summary Table
| Quantity | Formula | Units |
|---|---|---|
| Kinetic Energy | $$K = \frac{1}{2} m v^2$$ | J (joule) |
| Gravitational PE | $$U_g = m g h$$ | J |
| Elastic PE | $$U_s = \frac{1}{2} k x^2$$ | J |
| Work | $$W = F d \cos\theta$$ | J |
| Power | $$P = \frac{W}{t} = F v \cos\theta$$ | W (watt) |
7. Quick Practice Questions
- Calculate the KE of a 2 kg car moving at 10 m/s.
- A 5 kg crate is lifted 3 m. What is its gravitational PE?
- If a force of 30 N pushes a box 4 m in 2 s, what is the power output?
?? Good luck! Remember: Energy is everywhere – it’s just hidden in motion or position. Keep practicing the formulas and you’ll master these concepts in no time! 🚀
Revision
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