How fast? Power and efficiency

From the powerlifter to the data centre: the same work can cost very different power

Physics · 2A · 12/10/2026
Something does not add up

Two lifters, one barbell

  • Same barbell: mass 80 kg, so weight 800 N
  • Same lift: from the floor up by 0.75 m
  • Lifter A, a powerlifter, does it in 0.6 s
  • Lifter B, a gym-goer, does it in 3.0 s, with effort
Take g = 10 N/kg, as in the coursebook.

Raise your hand: who wins?

Who is stronger?
  • A (fast)
  • B (slow)
  • same
Who gives the bar more energy?
  • A (fast)
  • B (slow)
  • same
Who is more powerful?
  • A (fast)
  • B (slow)
  • same

Same lift, different time

time elapsed0.00 s
Force on the bar: 800 N
Height gained: 0.75 m

A crane: same load, same height

time to lift50 s
Load weight 5.0 kN, lifted by 20 m
Numbers from the coursebook crane example (5.0 kN, 20 m): W = F × d = 100 kJ.

Power: how fast energy is transferred

Definition
Power is the work done, or the energy transferred, in each second.
P=\frac{W}{t}=\frac{\Delta E}{t}
Ppower, in watts (W) · 1 W = 1 J/s W,\ \Delta Ework done, or energy transferred, in joules (J) ttime taken, in seconds (s)
Multiples: kilowatt 1 kW = 1000 W · megawatt 1 MW = 1 000 000 W
Exercise 1 · try it on paper

Climbing stairs

A student of mass 50 kg climbs a staircase of vertical height 3.0 m. Take g = 10 N/kg.

  1. Calculate the work done against gravity.
  2. The climb takes 4.0 s. Calculate the power.
  3. The same climb takes 12 s. Calculate the power. What has changed, and what has not?
  4. A motor of power 2.0 kW runs for 15 s. How much energy does it transfer? If all of it lifts a 150 kg load, how high does the load rise?
Next question

A 60 W incandescent bulb

Every second it takes 60 J of electrical energy.

Only 6 J come out as light (10 %).

Where do the other 54 J go?

Typical incandescent lamp: about 90 % of the input energy is wasted as heat.

Efficiency

Definition
Efficiency is the fraction of the energy supplied that is transferred usefully.
\text{efficiency}=\frac{\text{useful energy out}}{\text{total energy in}}=\frac{\text{useful power out}}{\text{total power in}}
\text{efficiency}\ (\%)=\frac{\text{useful energy out}}{\text{total energy in}}\times100
  • Energy is conserved: useful + wasted = total in, so the efficiency is never above 100 %
  • The wasted energy is usually transferred as thermal energy to the surroundings
Coursebook P2.02, energy efficiency.

Same light, less energy

efficiency of the lamp10 %
Useful output fixed at 6.0 W of light. LEDs use at least 75 % less energy than incandescent lighting (U.S. Department of Energy).
Exercise 2 · try it on paper

Motors and lamps

  1. A motor takes 800 J of electrical energy and lifts a 20 kg load by 2.0 m (g = 10 N/kg). Calculate the useful energy output.
  2. Calculate the efficiency of the motor, as a percentage.
  3. Where does the rest of the energy go?
  4. A lamp takes 12 W and emits 3.0 W of light. Calculate its efficiency and the power wasted.
  5. A second motor is 80 % efficient. It must deliver 400 J of useful energy. How much energy must it take in?
A phone, a charger, a claim

"50 % in 20 minutes"

  • iPhone 17: battery about 3692 mAh, that is 14.3 Wh
  • Apple: with a 40 W adapter, 50 % in 20 minutes
  • Energy for 50 %: 7.15 Wh = 25 740 J (1 Wh = 3600 J)
  • Average power: 25 740 J / 1200 s = 21.5 W. Not 40 W. Why?
Sources: Apple, iPhone 17 fast-charge claim; battery capacity as reported by specification sites (approximate).

How long to reach 50 %?

adapter power20 W
Ideal case: all the adapter power goes into the battery, at constant power. Real charging is slower than this at high power.
Exercise 3 · try it on paper

Charging a phone

The battery of an iPhone 17 stores 14.3 Wh. (1 Wh = 3600 J)

  1. Calculate the energy stored in the battery, in joules.
  2. An old 5 W charger delivers its full power to the empty battery. How long to fill it? Give hours and minutes.
  3. Repeat for a 20 W charger.
  4. The 20 W charger takes 25 W from the socket. Calculate its efficiency and the power wasted as thermal energy.

From power to the bill

Energy used
E=P\times t
power in watts × time in seconds gives joules
  • The electricity meter counts in a bigger unit: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
  • Wholesale energy price in Italy, September 2026 (PUN): 0.2075 € per kWh
  • Your bill is higher: it also includes transport, taxes and the supplier's margin
Source: GME, PUN Index, September 2026 monthly average (energy only). The kWh is shown here only to read a bill.
Exercise 4 · try it on paper

Lamps in the classroom

A classroom has 12 incandescent lamps of 60 W. They are replaced by 12 LED lamps of 15 W giving the same light. The lamps are on 6.0 h each day, for 200 days a year.

  1. Calculate the power saved by the change.
  2. Calculate the energy saved in one day, in joules and then in kWh.
  3. Using 0.2075 € per kWh, calculate the money saved in one year.

Data centres: power on a city scale

One square = the average power of the Bologna area (600 MW). 79 squares in total.
  • World data centres, 2024: 415 TWh of electricity
  • As average power: 47 GW (47 × 10⁹ W)
  • Bologna metropolitan area: 5251.7 GWh a year, 600 MW on average
  • Nearly all of it ends as thermal energy: it must be cooled
Sources: IEA, Energy and AI (2024 value); Terna via Città metropolitana di Bologna (2023 consumption). Different years: order of magnitude.
Exercise 5 · try it on paper

One data centre and one city

A data centre uses 100 MW continuously. The Bologna area uses 5251.7 GWh in a year (1 GWh = 3.6 × 10¹² J; 1 year = 3.15 × 10⁷ s).

  1. Calculate the energy used by the data centre in one day, in joules.
  2. Convert the yearly energy of Bologna to joules and calculate its average power.
  3. How many such data centres would use as much power as Bologna?

Back to the lifters

Who is stronger?
Who gives the bar more energy?
Who is more powerful?
  • Same force on the bar, same energy given to it: 600 J
  • Different time, so different power: A 1000 W, B 200 W

In summary

  • P=W/t=\Delta E/t: power is the energy transferred per second, in watts
  • Same work does not mean same power: the time decides
  • Efficiency = useful output / total input: the rest is wasted, mostly as thermal energy
  • E=P\,t: energy used, from a lamp to a data centre
  • Next lesson, Monday 19/10: Lab 2, lifting and measuring power and efficiency
For Monday 19/10

Homework

  • Read coursebook chapter P2: P2.02 (efficiency) and P2.05 (power)
  • Do questions P2.07, P2.10, P2.12
  • Do questions P2.34, P2.35, P2.36, P2.37
  • Do Practice Questions 8 and 9 at the end of the chapter
Write the full working: formula, substitution, result with unit.
Your own task · due Friday 30/10

Make an infographic: energy resources

  • Individual work. Use coursebook P2.03, pages 563 to 568
  • One page, A4 or A3, on paper or digital
  • Goal: someone who has never read the chapter understands it in two minutes
  • The structure is on the next slide

Structure of the infographic

  1. Headline: title and one sentence with your message
  2. Two zones: renewable and non-renewable (use the key words)
  3. One card per resource, at least 7 of: coal, oil, natural gas, nuclear, solar, wind, hydroelectric, geothermal, biofuels, waves, tides
  4. Comparison strip on the book's criteria: renewability, cost, availability, reliability, scale, environmental impact
  5. Sources and your name
Each card has the same 4 lines
  • Name + a small drawing
  • Energy chain: store → … → electricity
  • Renewable? yes or no, and why
  • One advantage, one disadvantage
Same layout for every card: clarity comes from repetition. Use few words, symbols, arrows.

Example of the format (layout only)

Where does our electricity come from?Same job, different energy stores and impacts.RENEWABLENON-RENEWABLEWINDChain: wind (kinetic) → turbine →generator → electricityRenewable: yes. Wind keeps blowing.+ no fuel, no CO₂ while running− output depends on the weathercard 2: same four linescard 3: same four linesCOALChain: coal (chemical) → boiler →steam → turbine → generator →electricityRenewable: no. Millions of years to form.+ steady output on demand− releases CO₂ when burnedcard 2: same four linescard 3: same four lines… at least 7 cards in total, same layoutComparison (the book's criteria)WINDCOALrenewabilityyesnorunning costlowfuel neededavailabilitywindy sitesneeds supplyreliabilityvariessteadyscalemany turbinesone big stationenvironmental impactlow CO₂high CO₂Sources: coursebook P2.03, pp. 563–568; …Name: ____________________
  • One page: A4 or A3, portrait or landscape
  • Headline, then two zones
  • Every card has the same four lines
  • Comparison strip on the book's criteria
  • Sources and name at the bottom
  • This sample shows 2 cards: you complete at least 7, with your own words and drawings