Here are your physics notes on Power and Collisions, presented in a simple and friendly way! 😊“`html
⚡ Power: The Rate of Doing Work
Power tells us how fast work is done or energy is transferred. Think of climbing stairs: It’s not just how many stairs you climb, but how quickly you climb them! 🏃
🔧 Key Definitions
- Average Power (\(P_{av}\)): Work done divided by total time taken. \[P_{av} = \frac{W}{t}\]
- Instantaneous Power (\(P\)): Power at a specific moment (as time interval → 0). \[P = \frac{dW}{dt} \tag{5.20}\]
- Power with Force & Velocity: If force \(F\) acts on an object moving at velocity \(v\): \[P = F \cdot v \tag{5.21}\]
🔢 Units & Fun Facts
- SI Unit: Watt (W), where 1 W = 1 J/s ⚡
- Horsepower (hp): 1 hp = 746 W (used for cars 🚗, bikes 🏍️)
- Kilowatt-hour (kWh): Energy unit! Example: A 100 W bulb 💡 running for 10 hours uses: \[100 \, \text{W} \times 10 \, \text{h} = 1 \, \text{kWh} = 3.6 \times 10^6 \, \text{J}\]
📚 Example: Elevator Power Calculation
An elevator (max load 1800 kg) moves up at 2 m/s. Friction opposes with 4000 N. Minimum motor power required?
- Total downward force = weight + friction \[F = mg + F_r = (1800 \times 10) + 4000 = 22000 \, \text{N}\]
- Power = Force × Velocity \[P = F \cdot v = 22000 \times 2 = 44000 \, \text{W}\]
- In horsepower: \[P = \frac{44000}{746} \approx 59 \, \text{hp}\]
💥 Collisions: Bounce, Crash, Conserve!
When objects collide (like billiard balls 🎱 or marbles), we study their motion using conservation laws.
🌟 Key Ideas
- We focus on momentum conservation and energy conservation during collisions.
- Typical setup: Mass \(m_1\) moves at initial speed \(v_{i1}\), hits stationary mass \(m_2\) (Fig. 5.10).
- After collision, masses fly off in different directions. We can relate:
- Masses (\(m_1\), \(m_2\))
- Velocities (before & after)
- Angles of motion
Note: “No loss of generality” if we assume \(m_2\) starts at rest – this simplifies problems!
🎯 NEET High-Yield Concepts
- Power formula \(P = F \cdot v\) (e.g., elevators, vehicles).
- Unit conversions: Watts (W) ↔ Horsepower (hp) ↔ kWh ↔ Joules (J).
- Collision setup: Conservation laws for momentum/energy when masses collide.
- Force balance: Calculating net force (like in elevator example: \(mg + F_r\)).
