Power and efficiency - Physics 1 AP Study Notes

Power is defined as the rate of doing work or the rate of energy transfer. In Cambridge terms, power measures how quickly energy is transferred or work is done. The SI unit is the watt (W), where 1 watt equals 1 joule per second.

Key Equations:

P = W/t (Power = Work done ÷ Time taken)

P = E/t (Power = Energy transferred ÷ Time taken)

P = Fv (Power = Force × velocity, when force acts in the direction of motion)

This third equation derives from P = W/t = (Fs)/t = F(s/t) = Fv, connecting power to mechanics.

Efficiency measures how effectively a device converts input energy into useful output energy. It's expressed as a percentage or decimal (never greater than 1 or 100%). The Cambridge definition: efficiency is the ratio of useful energy output to total energy input.

Key Equations:

Efficiency = (Useful energy output / Total energy input) × 100%

Efficiency = (Useful power output / Total power input) × 100%

Important Note: No real device is 100% efficient due to energy dissipation as heat, sound, or other non-useful forms. This follows the principle of conservation of energy—energy cannot be created or destroyed, only transformed.

Mnemonic for Power: Power Works Tirelessly (P = W/t)

Mnemonic for Efficiency: Useful Over Total Input = UOTI ("you owe tea eye"—useful output ÷ total input)

Power in Everyday Life:

Consider two students climbing identical staircases (same height). Student A takes 10 seconds; Student B takes 20 seconds. Both do the same work against gravity (W = mgh), but Student A has twice the power because they complete the task in half the time. This illustrates that power isn't about the total work—it's about the rate of energy transfer.

Analogy: Think of power as the "speed" of energy transfer. A 100W light bulb transfers 100J of energy every second, while a 60W bulb transfers only 60J/s. Both can light a room, but one does it more quickly and brightly.

Real-World Power Applications:

• Car engines: A 150 kW engine can accelerate faster than a 75 kW engine because it transfers energy to kinetic energy more rapidly
• Electric kettles: A 3000W kettle boils water in 2 minutes; a 1500W kettle takes 4 minutes (same energy, different power)
• Solar panels: Rated power (e.g., 250W) indicates energy generation rate under standard conditions

Efficiency in Action:

Traditional incandescent bulbs are only ~5% efficient—most input electrical energy converts to heat, not light. LED bulbs achieve ~80% efficiency, producing the same light output with far less electrical energy input.

Sankey diagrams visually represent energy transfers: arrow width shows energy quantity. For a petrol car (~25% efficient), a thick arrow enters (chemical energy), splits into smaller arrows: useful kinetic energy (25%) and wasted thermal/sound energy (75%).

Key Insight: High efficiency doesn't mean high power. A cyclist might be 25% efficient, an electric motor 90% efficient, but the motor has far greater power output.