Lesson 7: Work & Energy Conservation | PHY 2.4

Lesson at a Glance | He Tirohanga Whakamua

Do NowWhy carrying a heavy suitcase horizontally does zero work on the bag10 min

Work & Potential EnergyWork

W = F d

& Gravitational

E_{p} = m g h

15 min

Energy ConservationConservation of Mechanical Energy (

E_{p} \to E_{k}

)15 min

Portfolio EntryWrite Section 7: Work-Energy Theorem & Conservation Map10 min

Exit DrillCalculate velocity of a roller coaster cart at the bottom of a 20m drop5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

That Mechanical Work ( $W = F d$ ) is done only when force moves an object parallel to the direction of motion (measured in Joules).
The formulas for Gravitational Potential Energy ( $E_{p} = m g h$ ) and Kinetic Energy ( $E_{k} = \frac{1}{2} m v^{2}$ ).
How to apply Conservation of Mechanical Energy ( $E_{p, t o p} = E_{k, b o t t o m}$ ) to determine maximum velocity ( $v = \sqrt{2 g h}$ ) in ideal systems.

Students will demonstrate

By calculating impact speed of a 0.5kg ball dropped from a 15m height.
By completing Section 7 of their Level 2 Physics Mechanics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Physics Definition of Work Prompt:

"If a waiter holds a 5kg heavy tray stationary at shoulder height for 2 hours, your arms get exhausted. How much mechanical work did the waiter do on the tray?"

Unpack: Zero Joules! Work requires displacement in the direction of the force ( $W = F \times d$ ). Since displacement ( $d$ ) is zero, no mechanical work is done on the tray. (The waiter's muscle fibres do microscopic chemical work inside their arms, but the tray gains zero mechanical energy!).

Conservation of Mechanical Energy ( $E_{p} \leftrightarrow E_{k}$ ) (15 min)

1. Top of Drop ( $h = h_{m a x}$ )

All mechanical energy is stored as Gravitational Potential Energy ( $E_{p} = m g h$ ). Kinetic energy is zero ( $E_{k} = 0$ ).

2. Bottom of Drop ( $h = 0$ )

All potential energy has converted into Kinetic Energy ( $E_{k} = \frac{1}{2} m v^{2}$ ). Equating $m g h = \frac{1}{2} m v^{2}$ yields speed $v = \sqrt{2 g h}$ .

Work and Gravitational Potential Energy (15 min)

1. Work needs motion along the force

$W = F d \cos θ$ , in joules. Only the component of force along the displacement does work. Carry a suitcase horizontally and you do no work on it against gravity, because the upward force and the horizontal motion are perpendicular, however tired your arm gets.

2. Lifting stores energy

$E_{p} = m g h$ , where $h$ is measured from whatever zero level you choose. State that zero level explicitly, because only the CHANGE in $E_{p}$ is physically meaningful. Lifting a 5 kg box 1.2 m stores $5 \times 9.8 \times 1.2 = 58.8$ J.

Do this now: calculate the work done dragging a 30 kg crate 4 m with a 90 N force applied at 25° above horizontal.

Whakawhiti | Take it further — the work of hauling a waka ashore

Bringing a waka up a beach is the work–energy theorem with nothing abstracted away: some of the work raises the hull, and some is lost to friction along the way. Separating those two terms is the whole skill.

Take these values (a scenario, not a measurement): a waka of mass 800 kg is hauled 25 m up a beach that rises 1.5 m over that distance, against an average friction force of 600 N along the path.

Calculate all three: the work done against gravity, the work done against friction, and the total work required. Then rollers are placed under the hull and friction drops to 200 N — recalculate, and state what percentage of the total work has been saved.

Then the conceptual one. One of your two terms can be reduced by technique or technology and the other cannot, no matter how good the rollers are. Say which, and explain why in terms of what each term depends on. This is the distinction that separates a Merit answer from an Excellence one here.

Kaiako — mātauranga handoff. The energy analysis is ours to run. Hauling practice, the waka itself and the knowledge held about launching and landing on a particular beach belong to those who hold them. Please involve kaiako Māori and, where a waka is held locally, the people who care for it, before teaching this section.

📁 Physics Mechanics Portfolio — Section 7: Work-Energy Theorem & Conservation

Students open their Level 2 Physics Portfolio and complete Section 7:

Section 7 Requirements:

1. Energy Transformation Diagram: Draw a roller coaster track showing $E_{p}$ , $E_{k}$ , and total mechanical energy bars at peak, mid-slope, and bottom loop.

2. Conservation Calculation: Calculate initial $E_{p}$ , bottom $E_{k}$ , and maximum velocity for a 60kg skier starting from rest at the top of a 25m slope.

3. Excellence Work-Energy Theorem Analysis: 1-paragraph explanation of how friction does negative work on the skier ( $W_{f r i c t i o n} = F_{f} d$ ), converting mechanical energy into thermal energy ( $Q$ ).

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 7 equates mgh to 1/2mv^2 to prove that a skier's maximum speed depends solely on height dropped (v = sqrt(2gh) = 22.1 m s⁻¹) regardless of mass."

Teacher Planning & NCEA Alignment

NCEA Level 2 Physics Alignment (6 Credits External):

Work & Energy: Demonstrate understanding of work done ( $W = F d$ ), gravitational potential energy ( $E_{p} = m g h$ ), kinetic energy ( $E_{k} = \frac{1}{2} m v^{2}$ ), and energy conservation.
Energy Dissipation: Account for thermal energy losses due to friction.

Vocabulary: Work done ( $W = F d$ ), Gravitational Potential Energy ( $E_{p}$ ), Kinetic Energy ( $E_{k}$ ), Conservation of Energy, mechanical energy, thermal dissipation.

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 7: Work, Gravitational Potential & Kinetic Energy Conservation