Evaluate an energy transfer rate and a power constraint

1. Orient: Evaluate an energy transfer rate and a power constraint

Average power is energy transferred or converted divided by elapsed time. A joule per second is a watt, W. Two devices can perform the same work but require different power if they take different times. Energy and power therefore need different units and answer different design questions.

2. Explain and derive

For a force with component along instantaneous velocity, power is P=Fv cosθ. It follows by dividing a short-interval work FΔs cosθ by its duration. A perpendicular force has zero instantaneous power in that ideal model even when its magnitude is large. For variable power, total work is the signed area under a power–time graph.

An ideal constant-speed lift of mass m through height h requires useful work mgh and useful power mgh/t=mgv. Efficiency η compares useful output energy with input energy over the stated boundary, giving required input power Puseful/η in this steady model. The remainder is other energy output, not vanished energy.

A schedule can demand more power than a device can supply. The model compares required input power with an assigned 250 W limit and rejects excessive schedules; it does not claim the load still follows that motion. Actual acceleration, torque, force, temperature and duty-cycle limits need additional checks beyond average power. Startup and stopping are omitted here.

3. Work an example

For a 10 kg load lifted 3 m in 2 s using g=10 m/s², useful energy is 300 J and useful power 150 W. At 80% efficiency, input power is 187.5 W and input energy 375 J, leaving 75 J in other outputs. The same height in 1 s would require 375 W input, exceeding the assigned 250 W limit.

4. Predict and investigate

Predict first: If the lift duration doubles while height stays fixed, which changes: useful energy, required useful power, input energy or required input power?

Compare the same height over 1,2 and 4 s. Reconstruct useful and input energies separately from powers, then locate a schedule that fails the 250 W screen. Explain why satisfying this screen alone is not a validated real lifting design. Use the lesson controls and retain the settings with your evidence.

5. Transfer and explain

Try a new practice case

A lift needs 160 W useful power at 80% efficiency. Find required input power.

Your numerical result (W) Check number

Reveal worked check (practice, not mastery)

This extra practice is not saved and does not award mastery. Record your first answer, explanation and whether you revealed help in the lesson notebook. Use the lesson’s saved question separately.

6. Reflect and retain evidence

A motor’s power–time graph is 200 W for 2 s and 100 W for 3 s. Compute energy by area and compare it with multiplying peak power by the full duration.

Retain a first attempt, signed ledger, units, system boundary, assumptions and a changed-case prediction. Public worked checks are practice, not independent mastery evidence. Synthetic outputs are not physical measurements.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 3 topic mapping: 3.5; 3.4. Checked 30 October 2026; this is a content cross-reference, not AP authorization.