Lesson 3: Newton's Second Law — F = ma | Tōpana = Papatipu × Kōiri
Force = mass × acceleration. Students verify this experimentally using trolleys and weights, apply it to Rocket Lab's Electron rocket, and solve waka acceleration problems in an Aotearoa Pacific context.
📎 Learning Intentions
Know | Mōhio
- Newton's Second Law: Net Force = mass × acceleration (F = ma).
- That acceleration (a) is the rate of change of velocity, measured in m/s².
- That doubling the force doubles the acceleration (for fixed mass); doubling the mass halves the acceleration (for fixed force).
- That Rocket Lab, founded in New Zealand, uses these exact principles to launch satellites — a world-leading NZ science success story.
Demonstrate | Whakaatu
- Collect experimental data (force, mass, acceleration) using the trolley lab and plot a force vs. acceleration graph showing a linear relationship.
- Use F = ma to solve 5 applied problems including Rocket Lab thrust calculations and waka acceleration scenarios.
- Re-arrange F = ma to solve for mass (m = F/a) and acceleration (a = F/m).
📐 Curriculum Alignment
Identify and describe the patterns associated with physical phenomena found in simple everyday situations involving movement, forces, electricity and magnetism, light, sound, waves, and heat. For example, identify and describe energy changes and conservation of energy, simple electrical circuits, and the effect of contact and non-contact on the motion of objects.Ministry of Education (2007). The New Zealand Curriculum. Science achievement objectives, Level 5.
🌿 Whakatūwhera
Tūhoe mai, tūhoe atu — ko te kaha o ngā ringa ka ahu ake ki ruia.
"The strength of many hands lifts even the heaviest load." More paddlers on a waka = more force = greater acceleration. Newton encoded this truth into F = ma — the most important equation in classical mechanics.
🎤 Kaiako Hook (5 min)
Show the Rocket Lab Electron launch video. Ask: "Electron weighs 12.5 tonnes. How much thrust is needed just to lift off the ground — before it even accelerates? Now how much extra thrust is needed to reach orbital velocity?"
Reveal: At liftoff, thrust must exceed weight. F_net = F_thrust − F_weight = ma. The race against gravity begins.
📚 Lesson Content
Part 1: Newton's Second Law — The Equation (10 min)
🔑 F = ma
F = Net Force (Newtons, N) — the vector sum of all forces.
m = Mass (kilograms, kg) — resistance to acceleration (inertia).
a = Acceleration (metres per second squared, m/s²) — rate of velocity change.
Re-arrangements: a = F/m m = F/a
Part 2: Trolley & Weights Lab (25 min)
Equipment: Dynamics trolley, pulley, hanging masses (50 g, 100 g, 150 g, 200 g), ticker-tape timer or motion sensor, track.
Procedure:
- Set up trolley on level track with pulley at one end.
- Attach hanging mass via string over pulley — this provides a known net force F = mg (weight of hanging mass, where g = 9.8 m/s²).
- Release trolley and measure acceleration from ticker tape (spacing between dots) or motion sensor.
- Repeat with 4 different hanging masses, keeping trolley mass constant.
- Record data in table; plot Force (x-axis) vs. Acceleration (y-axis).
| Hanging mass (kg) | Force F=mg (N) | Trolley mass (kg) | Measured acceleration (m/s²) | Calculated a = F/m | % difference |
|---|---|---|---|---|---|
| 0.050 | 0.49 | ||||
| 0.100 | 0.98 | ||||
| 0.150 | 1.47 | ||||
| 0.200 | 1.96 |
Analysis: Is the relationship between F and a linear? What does the slope of the graph equal? (It should equal 1/m — the inverse of the trolley mass.)
Part 3: Rocket Lab Case Study (10 min)
Rocket Lab's Electron rocket specifications:
- Total mass at launch: 12,500 kg
- 9 Rutherford engines, each producing 24,000 N thrust
- Total thrust: 9 × 24,000 = 216,000 N
- Weight (on Earth): F_weight = mg = 12,500 × 9.8 = 122,500 N
Calculate: Net upward force = Thrust − Weight = 216,000 − 122,500 = 93,500 N
Initial acceleration: a = F_net / m = 93,500 / 12,500 = 7.48 m/s²
As the rocket burns fuel, mass decreases → the same engine force causes increasing acceleration. By staging (dropping the first stage), mass drops dramatically — acceleration surges toward orbital velocity.
Part 4: Waka Acceleration Problems (5 min guided practice)
- A 1,500 kg waka is accelerating at 0.5 m/s². What is the net force from paddlers?
- If the same waka carries 500 kg of cargo (total mass 2,000 kg) and paddlers apply the same force, what is the new acceleration?
- How many extra paddlers are needed to restore the original 0.5 m/s² acceleration with the cargo loaded? (Assume each paddler adds 75 N of thrust.)
✅ Assessment
🎟 Exit Ticket
- A 2 kg kete (basket) is pulled with a net force of 8 N. What is its acceleration?
- A car of mass 1,200 kg accelerates at 3 m/s². What net force acts on it?
- Rocket Lab wants to accelerate a 200 kg satellite at 2 m/s² in space (no gravity). What engine force is needed?
- Why does Rocket Lab's Electron accelerate faster as it burns fuel, even with the same engine thrust?