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Physics HL · Chapter 3: Work, Energy and Power

3.5 Power, Efficiency, and Energy-Transfer Diagrams

Quantify rate of transfer and evaluate useful output using efficiency and transfer diagrams.

Estimated time: 20 minutes

Power as a Rate

Power measures how quickly work is done or energy is transferred. Two systems can transfer the same total energy but feel very different if one does so over a much shorter time. That is why power is central in engine design, electrical devices, and athletic performance.

P=ΔEΔt=WtP = \frac{\Delta E}{\Delta t} = \frac{W}{t}

For constant speed with a resisting force, useful mechanical power can be estimated with P = Fv.

P=FvP = Fv

Instantaneous power from a force equals force component along motion multiplied by speed.

Efficiency and Useful Output

Efficiency compares desired output to total input. It can be written using energies or powers over the same process. Values are below 100% because some transfer almost always spreads into less-useful pathways such as heating, sound, or vibration.

efficiency=useful output energyinput energy=useful powerinput power\text{efficiency} = \frac{\text{useful output energy}}{\text{input energy}} = \frac{\text{useful power}}{\text{input power}}

Multiply by 100 to express efficiency as a percentage.

Sankey-Style Energy Accounting

Energy-transfer diagrams help communicate where input energy ends up. A wider output branch represents a larger share of transferred energy. This visual accounting is especially useful in engineering decisions, because it makes dominant loss channels obvious and guides where optimization effort should go.

Test Yourself

A motor takes in 900 J and delivers 630 J of useful lifting energy. Enter the efficiency as a percentage.

Hint: Efficiency = (useful output / input) × 100.

Chapter 3 Key Takeaways

  • Work is directional transfer: positive, negative, or zero depending on force-displacement alignment.
  • Net work equals change in kinetic energy.
  • Potential energies provide endpoint bookkeeping for conservative interactions.
  • Mechanical energy can drop while total energy remains conserved once dissipation is included.
  • Power and efficiency evaluate transfer rate and usefulness, not just totals.