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
Explore, describe, and represent patterns and trends for everyday examples of physical phenomena, such as motion and forces.Ministry of Education (2007). The New Zealand Curriculum, p. 60.
🌿 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?