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AP Physics 1 — Algebra-Based
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Lesson 9 of 194 hours

Power, Efficiency, and Energy Transfer

Start with the lesson question, connect the representations, and test the model with evidence.

powerefficiencyworkenergy transferforce velocitythermal energy

Learning objectives

  • Define a system and represent its energy stores and transfers.
  • Relate external work to changes in a system's energy.
  • Compare energy and force-and-motion solution paths and justify the more useful model.
Lesson flowHook, model, explanationShow guidance

Inspect the opening phenomenon

Predict what changes, then name the evidence.

Apply in the lab

Name the evidence before reading the answer.

Read only what helps

Then use the lab and recall check.

More when needed

Transcript and resources stay available below.

Course progress

AP Physics 1 — Algebra-Based · Work, Energy, and Power · Lesson 9

Power, Efficiency, and Energy Transfer

In progress

Decision challenge

Observe the phenomenon. Then connect the representations.

Use the opening example to make a prediction, identify evidence, and explain which model supports it.

Same Stairs, Different Power | AP Physics 1

Predict whether two identical stair climbs completed in different times require the same average power.

Calculate gravitational energy and compare average power for five-second and ten-second climbs.

Before

Predict whether two identical stair climbs completed in different times require the same average power.

During

Pause after the 2352-joule energy change appears and calculate the five-second average power.

After

Explain why greater power does not necessarily mean greater total energy transfer.

Reference drawerTranscript, source notes, scripts, and package status stay tucked away until you need them.7 files

Lesson reading

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4 hr

Video script

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Transcript fallback

available

courses/ap-physics-1/modules/03-work-energy-and-power/lessons/02-power-efficiency-and-energy-transfer/video-transcript.md

Mechanical Power on a Stairway

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1 hr 10 min

Mastery check

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7 questions / 15 min

Book section:courses/ap-physics-1/modules/03-work-energy-and-power/lessons/02-power-efficiency-and-energy-transfer/book-section.md
Transcript for accessibility and fallback

# Accessible transcript: Same Stairs, Different Power Same stairs, same energy—but not the same power. A sixty-kilogram student climbs four meters. Gravitational energy gained is m g h: two thousand three hundred fifty-two joules. Do it in five seconds. Average mechanical power is energy divided by time: about four hundred seventy watts. Take ten seconds and the energy is unchanged, but power is half as large. Quick check: does greater power always mean more total energy? Pause. No. Total energy also depends on how long power is delivered. Learn work and energy free at EduQuest AI. ## Visual description Two identical climbs show the same gravitational-energy bar but different timers. Dividing by five and ten seconds produces different power bars. A final prompt separates rate from total energy.

Reading lab

Core explanation

Connect the lesson's words, diagrams, graphs, evidence, and equations.

Driving question

How quickly is energy transferred, and where does the transferred energy go?

Before learning: same stairs, different time

Two students of equal mass climb the same stairs. They gain the same gravitational potential energy, but one takes half as long. Compare their work and power before calculating.

Hook: same energy, twice the power

Power measures transfer rate, not total energy:

Pavg=ΔEΔt=WΔt.P_{avg}=\frac{\Delta E}{\Delta t}=\frac{W}{\Delta t}.

One watt is one joule per second. Completing the same energy transfer in half the time requires twice the average power.

Equal energy transfers completed over different time intervals

Work and power

For a constant force acting through displacement,

W=Fdcos⁡θ.W=Fd\cos\theta.

Instantaneous mechanical power is

P=F⃗⋅v⃗=Fvcos⁡θ.P=\vec F\cdot\vec v=Fv\cos\theta.

Only the force component parallel to velocity transfers mechanical energy at that instant.

Worked example: stair climb

A 60.0 kg60.0\text{ kg} student rises 4.0 m4.0\text{ m} in 5.0 s5.0\text{ s} at roughly constant speed:

ΔUg=mgh=(60.0)(9.8)(4.0)=2352 J,\Delta U_g=mgh=(60.0)(9.8)(4.0)=2352\text{ J}, Pavg=23525.0=470 W.P_{avg}=\frac{2352}{5.0}=470\text{ W}.

This is mechanical output power associated with gravitational energy change, not total metabolic input power.

Power from force and velocity

A motor pulls a cart with 120 N120\text{ N} parallel to its 3.0 m/s3.0\text{ m/s} velocity:

P=(120)(3.0)=360 W.P=(120)(3.0)=360\text{ W}.

If the force is 60∘60^\circ from velocity, power is 180 W180\text{ W}. A perpendicular force can change direction while doing zero instantaneous work.

Force decomposed into parallel and perpendicular components relative to velocity

Efficiency is an energy ratio

Efficiency is

η=Euseful,outEtotal,in=Puseful,outPtotal,in\eta=\frac{E_{useful,out}}{E_{total,in}}=\frac{P_{useful,out}}{P_{total,in}}

for consistent intervals and steady operation. Report it as a decimal or percentage. It cannot exceed 100% for a complete, correctly defined passive/energy-converting system account.

Energy-flow diagram splitting input into useful and thermal outputs

Energy is not “lost”; it becomes less useful for the chosen purpose, often transferred to thermal energy, sound, deformation, or fluid motion.

Worked efficiency example

A lift receives 8000 J8000\text{ J} electrical energy and increases a load's gravitational potential energy by 6000 J6000\text{ J}:

η=60008000=0.750=75.0%.\eta=\frac{6000}{8000}=0.750=75.0\%.

The remaining 2000 J2000\text{ J} is transferred to other stores/surroundings.

System boundary matters

Efficiency depends on chosen input, useful goal, boundary, and interval. For a battery-powered motor, decide whether input means electrical energy delivered to the motor or chemical energy decrease of the battery. Both can be valid but answer different questions.

Power versus energy graphs

Since

P=dEdt,P=\frac{dE}{dt},

slope of an energy-time graph is power. Signed area under a power-time graph is energy transferred:

ΔE=∫P dt.\Delta E=\int P\,dt.

A device can briefly exceed its long-duration rated power; model interval and thermal limits matter.

During learning: accounting audit

  1. Define system, useful goal, input channel, and interval.
  2. Distinguish energy from energy/time.
  3. Use F⃗⋅v⃗\vec F\cdot\vec v only for the relevant force and instant.
  4. Make input equal useful output plus other transfers within uncertainty.
  5. Check that numerator and denominator use matching intervals and energy categories.

Misconception clinic

“Power and energy are interchangeable.” Power is energy transfer per time.

“A powerful device always uses more energy.” Total energy also depends on operating time.

“Inefficient energy disappears.” It transfers into other forms or surroundings.

“Efficiency can exceed 100% if output power is measured at a different time.” Mismatched intervals create an invalid comparison.

“Any force produces power FvFv.” Use the dot product and relevant force.

After learning: retrieval and transfer

  1. Two machines do equal work; one takes three times longer. Compare power.
  2. When is P=FvP=Fv valid without a cosine factor?
  3. What does area under a power-time graph represent?
  4. Why must system boundary be stated for efficiency?
  5. Where might non-useful energy go in a motor-lift system?

AP-style evidence routine

  1. Define system, interval, and useful output.
  2. Draw an energy-flow account.
  3. Choose work/time, energy slope, power area, or force-dot-velocity representation.
  4. Solve symbolically and keep energy/power units distinct.
  5. Check conservation, efficiency bounds, uncertainty, and limiting cases.

Key takeaway

Energy accounting says how much transfers; power says how fast. Efficiency evaluates how much input serves a stated purpose without implying that the remainder disappears.

Further learning and alignment

Practice labMechanical Power on a StairwayOpen this when you are ready to apply the model, collect evidence, and check your explanation.1 hr 10 min

Lab: Mechanical Power on a Stairway

Objective

How does measured stair-climbing mechanical power depend on climb time while gravitational energy change remains approximately fixed?

Safety

Teacher supervision and participant consent are required. Use a dry, clear stairway with handrail, no running, no racing, one participant at a time, comfortable self-selected pace, appropriate mobility accommodations, and immediate stop for discomfort. Never pressure participation; provide a cart-lift or supplied-data alternative.

Materials

  • measured vertical stair height;
  • balance or participant-approved mass value;
  • stopwatch/video timing;
  • handrail and spotter;
  • alternative dataset or safe tabletop lift.

Steps

  1. Measure vertical height and uncertainty.
  2. Record mass with consent and appropriate privacy.
  3. Predict gravitational energy change.
  4. Climb at a comfortable walking pace while timed.
  5. Repeat up to three times only if comfortable, with rest.
  6. Optional: compare two comfortable paces, never a race.
  7. Preserve raw times and notes.
  8. Calculate mghmgh and mgh/tmgh/t.

Expected Result

For the same person and height, gravitational energy change remains similar while shorter safe climb time corresponds to greater mechanical output power.

Analysis

  • Include height, mass, and time uncertainty.
  • Compare power across trials and participants only with consent and without ranking ability.
  • Distinguish mechanical output from metabolic input.
  • Discuss timing reaction, varying center-of-mass height, pace variation, and handrail use.

Reflection Questions

  1. Why is gravitational energy similar across paces?
  2. Why is this not metabolic efficiency?
  3. Which uncertainty dominates power?
  4. What system boundary did you use?

Claim-evidence-reasoning conclusion

Claim how time affected measured mechanical power. Cite energy, times, powers, and uncertainty, then state model limitations.

Accessibility

Offer a tabletop motor/cart lift, simulation, or shared dataset as equivalent evidence. Roles include safety, measurement, timing, analysis, uncertainty, and narration. No physical stair use is required.

Extension Challenge

Use a safe small motor lifting a known load to estimate useful mechanical output power and, if electrical input data are safely available, efficiency.