🎯 WALT & Key Information

WALT (We Are Learning To): Analyze and calculate kinetic and potential energy, applying the law of conservation of energy to complex scenarios.

Success Criteria — I can:

✅ Use the formula Ep = mgh to calculate gravitational potential energy

✅ Use the formula Ek = ½mv² to calculate kinetic energy

✅ Apply conservation of energy principles to solve multi-step problems

📐 Formulae & Constants (use these throughout):

Gravitational Potential Energy:   Ep = mgh   |   Kinetic Energy:   Ek = ½mv²

where: m = mass (kg), g = 9.81 m/s², h = height (m), v = speed (m/s)

Law of Conservation of Energy: Energy cannot be created or destroyed — it only changes form. Total energy at the top = Total energy at the bottom (ignoring friction).

🌱 Part 1: Scaffolded Questions (Tautoko — Support)

Kia ora! Work through these questions step by step. The formula and hints are provided to help you. Ka pai for giving it a go!

Step 1 — Write the formula:   Ep = mgh

Step 2 — Substitute values:   

Step 3 — Calculate:   

Answer: The gravitational potential energy is 

Mark Scheme Hint: Show all calculations for full marks.

Step 1 — Write the formula:   Ek = ½mv²

Step 2 — Substitute values:   Ek = 

Step 3 — Calculate:   Ek = 

Answer: The kinetic energy is 

Mark Scheme Hint: Include units in your final answer.

🚗 Car A: mass = 1000 kg, speed = 10 m/s    |    🚙 Car B: mass = 500 kg, speed = 20 m/s

Step 1 — Calculate Ek for Car A: 

Step 2 — Calculate Ek for Car B: 

Answer: 

Show your working:

Mark Scheme Hint: Justify your answer with calculations.

📐 Part 2: Core Questions (Matua — Main Level)

Whakarongo mai! Read each problem carefully, show all working, and include units in your answers.

(a) Calculate the student's gravitational potential energy at the top of the board.

Ep = mgh = 

Answer: 

(b) The student dives off and reaches the water. Using conservation of energy, what is their kinetic energy just before they hit the water? (Assume no energy is lost to friction or air resistance.)

Ek =

Answer: 

(c) Calculate the student's speed just before they hit the water.

Using Ek = ½mv², we rearrange to find v: v =

Answer: The speed just before hitting the water is 

Mark Scheme Hint: Show all calculations and reasoning.

(a) Calculate the ball's gravitational potential energy at its highest point.

Ep = mgh = 

Answer: The gravitational potential energy at the highest point is 

(b) What was the ball's kinetic energy just as it left the thrower's hand? Explain your reasoning.

Since energy is conserved, the kinetic energy when thrown equals the potential energy at the highest point: Ek = 

Answer: The kinetic energy just as it left the hand is 

Mark Scheme Hint: Use energy conservation principles in your explanation.

(a) Calculate the car's kinetic energy.

Ek = 

Answer: The kinetic energy is

(b) The car brakes and comes to a complete stop. What happens to the kinetic energy? Where does it go?

The kinetic energy is transformed into thermal energy due to friction in the brakes and the road.

Answer: 

Mark Scheme Hint: Discuss energy transformation in your answer.

🚀 Part 3: Extension Questions (Whakawhanake — Deeper Thinking)

Tino pai mō tō mahi! These questions will challenge your thinking. Apply what you know and justify your answers.

(a) Calculate the biker's gravitational potential energy at the top of the hill.

Ep =

Answer: The gravitational potential energy at the top is 

(b) Calculate the biker's kinetic energy at the bottom of the hill.

Ek = 

Answer: The kinetic energy at the bottom is 

(c) Is energy conserved in this situation? Use your calculations to explain why or why not. What might account for any difference?

Mark Scheme Hint: Compare energies and discuss any discrepancies.

(a) Calculate the speed of the car at point B (ground level). Assume no energy losses.

At point A, Ep =
At point B, all potential energy converts to kinetic energy: Ek =

Answer: The speed at point B is 

(b) Using conservation of energy, calculate the speed of the car at point C (18 m high). Hint: At point C, the car has both Ep and Ek. Total energy = Ep at A.

At point C, Ep = mgh =
Total energy =               
 so Ek at C =
 Thus, v =

Answer: The speed at point C is 

(c) In real life, would the car actually reach point C? Explain your thinking using scientific language.

In reality, the car would not reach point C due to energy losses from friction and air resistance, which are not accounted for in this ideal scenario.

Answer: 

Mark Scheme Hint: Discuss real-world factors affecting energy conservation.

🌿 Whakaaro Hōhonu (Deep Thinking): How does the law of conservation of energy connect to sustainability and energy use in Aotearoa New Zealand? Write 2–3 sentences below.

🔑 Answer Key

Ep = mgh = 2 kg × 9.81 m/s² × 3 m = 58.86 J

Ek = ½mv² = ½ × 0.5 kg × (6 m/s)² = 9 J

Car A: Ek = 50000 J; Car B: Ek = 100000 J. Car B has more kinetic energy due to higher speed.

Ep = mgh = 60 kg × 9.81 m/s² × 5 m = 2943 J

Ek = 2943 J

v = √(2Ek/m) = √(2 × 2943 J / 60 kg) = 11.0 m/s

Ep = mgh = 0.2 kg × 9.81 m/s² × 8 m = 15.696 J

Ek = 15.696 J

Ek = ½mv² = ½ × 1500 kg × (20 m/s)² = 300000 J

The kinetic energy is transformed into thermal energy due to friction.

Ep = mgh = 70 kg × 9.81 m/s² × 40 m = 27468 J

Ek = 20160 J

Energy is not conserved; potential energy at the top is greater than kinetic energy at the bottom due to losses.

v = 61.23 m/s

v = 15.38 m/s

The car would not reach point C due to energy losses from friction and air resistance.