Lesson 9: Power & Energy Efficiency | PHY 2.4

Lesson at a Glance | He Tirohanga Whakamua

Do NowWork vs Power: Walking vs sprinting up 4 flights of stairs10 min

Portfolio EntryWrite Section 9: Power & Energy Dissipation Analysis10 min

Exit CalculationCalculate engine power required for a car maintaining

25 {ms}^{- 1}

against 600N drag5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

That Power ( $P = \frac{W}{t}$ ) measures the rate of energy transformation in Watts ( $W = {J s}^{- 1}$ ).
How to calculate power at constant velocity: $P = F v$ (derived from $P = \frac{F d}{t}$ ).
How to perform Percentage Efficiency calculations ( $Efficiency = \frac{Useful Energy Output}{Total Energy Input} \times 100 %$ ) and account for thermal friction dissipation.

Students will demonstrate

By calculating electric motor power output and thermal efficiency for a 500kg elevator lifting 10m in 8s.
By completing Section 9 of their Level 2 Physics Mechanics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Work vs Power Prompt:

"If a 70kg athlete slowly walks up 5 metres of stairs in 20 seconds, and then sprints up the exact same 5 metres in 4 seconds, how does their mechanical work and power output compare?"

Unpack: The mechanical work done is identical ( $W = m g h = 70 \times 9.8 \times 5 = 3430 J$ ). But sprinting in 4 seconds requires 5 times more Power: $P_{w a l k} = \frac{3430}{20} = 171.5 W$ , whereas $P_{s p r i n t} = \frac{3430}{4} = 857.5 W$ !

Power & Energy Efficiency Equations (30 min)

1. Rate of Work ( $P = \frac{W}{t} = F v$ )

$P$ : Power ( $W$ or ${J s}^{- 1}$ )
$F$ : Thrust force overcoming resistive drag ( $N$ )
$v$ : Constant velocity ( ${m s}^{- 1}$ ).

2. Energy Efficiency ( $η$ )

$η = \frac{E_{u s e f u l}}{E_{i n p u t}} \times 100 % = \frac{P_{o u t}}{P_{i n}} \times 100 %$ . Energy lost to thermal friction $Q = E_{i n p u t} - E_{u s e f u l}$ .

Whakawhiti | Take it further — the question kaitiakitanga asks of an efficiency figure

Efficiency is the ratio of useful output to total input, and engineering choices are routinely justified by it. Kaitiakitanga asks a second question of the same choice, and it is not a softer one.

Take these values (a scenario, not a measurement): a crew of six each sustain 150 W of mechanical output over a two-hour crossing, and 25% of that becomes useful forward motion of the hull.

Calculate: the total work done by the crew, the useful energy delivered to the hull, and the average power lost. Express the loss as a percentage and say where, physically, you would expect it to have gone.

Then the harder question, and answer it in full sentences. An efficiency figure captures energy in and energy out. Name two real costs of a transport choice that this figure does not capture, and say who bears each of them. Then state whether you think an engineering decision should be made on efficiency alone — and defend it.

Kaiako — mātauranga handoff. The physics of efficiency is ours to run. Kaitiakitanga is not a values-add-on to an engineering calculation; it is a framework held by whānau, hapū and iwi with obligations attached. Please involve kaiako Māori before teaching this section, and be careful that the lesson does not reduce kaitiakitanga to "thinking about the environment".

📁 Physics Mechanics Portfolio — Section 9: Power & Energy Dissipation Analysis

Students open their Level 2 Physics Portfolio and complete Section 9:

Section 9 Requirements:

1. Energy Flow Diagram (Sankey): Draw a scaled Sankey diagram for an electric winch motor (1000J electrical input $\to$ 750J $E_{p}$ gained $\to$ 250J heat dissipation).

2. Highway Power Calculation: Calculate engine thrust power required for a car maintaining $28 {ms}^{- 1}$ (100 km/h) against 450N of air resistance ( $P = F v$ ).

3. Excellence Hydroelectric Efficiency Rationale: 1-paragraph explanation of energy losses in a hydro dam ( $E_{p}$ water $\to$ $E_{k}$ turbine $\to$ Electrical energy $η \approx 90 %$ ).

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 9 uses P = Fv to calculate 12.6 kW engine power for highway driving and calculates 75% winch motor efficiency."

Teacher Planning & NCEA Alignment

NCEA Level 2 Physics Alignment (6 Credits External):

Power & Efficiency: Demonstrate understanding of power ( $P = \frac{W}{t} = F v$ ), energy dissipation, and efficiency.
Energy Transfers: Quantify useful vs wasted thermal energy in mechanical systems.

Vocabulary: Power ( $P$ ), Watt ( $W$ ), constant velocity ( $P = F v$ ), energy efficiency ( $η$ ), thermal dissipation, Sankey diagram.

Same concept, shorter route: the Guided Viewing & Problem Practice version of this unit covers it in Work, Energy and Power Transformations. That route is a compact viewing-and-practice sequence; this one builds the concept over ten sections with a formative portfolio.

Lesson 9: Power & Energy Efficiency in Physical Systems