Ngā Kaha me te Neke · Motion and Forces
Newton's Laws, velocity, acceleration, and pressure in fluids · Years 9–10
Ngā Whāinga Akoranga · Learning Intentions
- Explain Newton's Three Laws of Motion and give everyday examples of each.
- Distinguish between speed, velocity, and acceleration, and read motion graphs.
- Draw free body diagrams showing balanced and unbalanced forces on objects.
- Apply F = ma to calculate force, mass, or acceleration in practical contexts.
- Explain how pressure changes with depth in fluids and with altitude in the atmosphere.
Paearu Angitu · Success Criteria
- I can state and explain Newton's First, Second, and Third Laws in my own words.
- I can calculate velocity and acceleration from motion data or graphs.
- I can draw a free body diagram and identify whether forces are balanced or unbalanced.
- I can use F = ma to solve for force, mass, or acceleration when two values are given.
- I can explain why pressure increases with depth in water and decreases with altitude.
Hononga Marautanga · Curriculum Connections
This activity addresses the following Science curriculum statements (Draft 2025, Phase 4 — Years 9, 10):
- Motion and Forces: The action of forces on the movement of objects can be described using Newton's Laws of Motion.
- Newton's First Law: When the net force on an object is zero, the object stays at rest or moves at constant velocity; when net force is non-zero, motion changes. Objects resist changes in motion — this is inertia.
- Newton's Second Law: More force causes more acceleration on the same mass; more massive objects accelerate less for the same force. The relationship F = ma gives force in newtons.
- Newton's Third Law: Forces are always paired as action-reaction pairs; every interaction between objects involves equal and opposite forces acting on each object.
- Velocity: Velocity is the rate at which an object moves (speed in a given direction).
- Acceleration: Acceleration is the rate at which an object's velocity changes.
- Motion graphs: Motion can be represented using graphs that show changes in velocity or distance over time.
- Free body diagrams: Forces acting on a rigid body can be summarised in a free body diagram to determine net force.
- Net force: Net force is the overall force acting on an object, after all individual forces (including directions) are combined.
- Friction: Friction opposes relative motion across surfaces and through fluids (e.g. air resistance and water resistance are types of friction).
- Pressure in liquids: Pressure in liquids increases with depth due to the increasing weight of liquid above.
- Atmospheric pressure: Atmospheric pressure decreases with altitude because the weight of air above reduces as height increases.
- Upthrust: Upthrust determines whether objects float or sink.
- F = ma: The relationship between force, mass, and acceleration is given by F = ma.
- Unit: Force is measured in newtons (N).
- Historical context: Isaac Newton (1643–1727) developed the laws of motion and universal gravitation, forming the foundation of classical mechanics.
- Historical context: Blaise Pascal (1623–1662) formulated Pascal's principle of pressure and contributed to fluid mechanics and probability theory.
Wāhanga 1 · Newton's Three Laws of Motion
Isaac Newton (1643–1727) described how forces affect the motion of objects. His three laws underpin all of classical mechanics.
An object stays at rest or keeps moving at constant velocity unless a net force acts on it.
Objects resist changes in motion — this resistance is called inertia. A more massive object has more inertia.
Example: A ball rolling on a frictionless surface never slows down. A passenger lurches forward when a car brakes suddenly — their body wants to keep moving forward.
The acceleration of an object depends on the net force applied to it and its mass: F = ma
- More force → more acceleration (same mass)
- More mass → less acceleration (same force)
- Force is measured in newtons (N); 1 N = 1 kg m/s²
Example: Pushing a shopping trolley — a full trolley (more mass) accelerates more slowly than an empty one for the same push.
Every force has an equal and opposite reaction force. Forces always come in pairs.
When object A exerts a force on object B, object B exerts an equal force back on object A — in the opposite direction. Note: the forces act on different objects, so they do not cancel each other out.
Example: A rocket pushes hot gas downward (action); the gas pushes the rocket upward (reaction). A swimmer pushes the wall backward; the wall pushes the swimmer forward.
Match each scenario to the correct Newton's Law:
| Scenario | Which Law? (1st / 2nd / 3rd) | Explanation |
|---|---|---|
| A book sits still on a desk | ||
| A larger force makes a ball accelerate faster | ||
| Jumping off a skateboard makes it roll the other way | ||
| A car skids forward when the driver brakes hard |
Wāhanga 2 · Velocity and Acceleration
Speed in a stated direction. Because it has direction, velocity is a vector.
Example: 60 km/h north (not just 60 km/h)
Velocity = distance ÷ time (in a given direction)
The rate at which velocity changes over time.
Speeding up, slowing down, or changing direction = accelerating
a = change in velocity ÷ time = Δv ÷ t
Reading Motion Graphs
A distance–time graph shows how far an object has moved; the gradient = speed. A velocity–time graph shows how velocity changes; the gradient = acceleration; area under the graph = distance.
Distance–Time Graph
Draw lines to show: (a) constant speed, (b) stationary, (c) accelerating (curved line), (d) decelerating
Velocity–Time Graph
Draw lines to show: (a) constant velocity, (b) uniform acceleration, (c) uniform deceleration
Practice — Calculating velocity and acceleration:
| Scenario | Given values | Find | Answer |
|---|---|---|---|
| Tāmati runs 100 m north in 12 s | d = 100 m, t = 12 s | velocity | |
| A car speeds from 0 to 30 m/s in 6 s | Δv = 30 m/s, t = 6 s | acceleration | |
| A bird decelerates from 20 m/s to 5 m/s in 5 s | Δv = 15 m/s, t = 5 s | deceleration |
Wāhanga 3 · Free Body Diagrams and Net Force
A free body diagram (FBD) shows all forces acting on a single object as arrows. Arrow length represents force size; arrow direction shows the direction of the force. The net force is found by adding all forces (including their directions).
When all forces cancel out, net force = 0 N. The object stays at rest or moves at constant velocity (Newton's 1st Law).
Example: A book on a table — gravity pulls down (weight), the table pushes up (normal force). Both equal — balanced.
When forces do not cancel, net force is non-zero. The object accelerates in the direction of the net force (Newton's 2nd Law).
Example: A rocket — thrust force upward is greater than weight downward → net force up → accelerates upward.
Common forces to include in FBDs:
downward, W = mg
perpendicular to surface
opposes motion
direction of propulsion
along a string/rope
opposes velocity direction
Draw FBDs for each scenario and calculate net force:
Forces: engine thrust = 3000 N forward; friction = 3000 N backward
Net force = _______ Direction = _______ Accelerating? _______
Forces: thrust = 500,000 N up; weight = 450,000 N down
Net force = _______ Direction = _______ Accelerating? _______
Wāhanga 4 · Applying F = ma
Force (N) = mass (kg) × acceleration (m/s²)
acceleration = force ÷ mass
mass = force ÷ acceleration
Rearrange to find any unknown. Always check units: N = kg⋅m/s²
| Problem | Formula used | Working | Answer |
|---|---|---|---|
| A 50 kg student accelerates at 2 m/s². What is the net force? | |||
| A 600 N force acts on a 120 kg box. What is its acceleration? | |||
| A 400 N force causes an acceleration of 8 m/s². What is the object's mass? | |||
| A waka (canoe) has mass 180 kg. Paddlers apply 540 N net force forward. Find acceleration. |
Wāhanga 5 · Friction and Resistance Forces
Friction is a force that opposes the relative motion between two surfaces, or between an object and a fluid. It acts in the opposite direction to motion.
Between solid surfaces (e.g. a box being pushed across a floor)
Friction between an object and air (e.g. a cyclist, a parachute)
Friction between an object and water (e.g. a fish, a swimmer)
Effect on motion: Friction reduces velocity. Without friction, objects would keep accelerating indefinitely. Streamlined shapes (like fish or aircraft) reduce drag by minimising the cross-section facing the direction of motion.
Investigate — predicting resistance forces:
Drop three objects (a flat cardboard, a scrunched cardboard ball, a rubber ball) of similar mass from the same height. Record your predictions and observations:
| Object | Predicted order (1st to land) | Observed order | Explanation (air resistance) |
|---|---|---|---|
| Flat cardboard | |||
| Scrunched cardboard | |||
| Rubber ball |
Wāhanga 6 · Pressure in Fluids
Blaise Pascal (1623–1662) showed that pressure in a fluid is transmitted equally in all directions, and that it increases with the weight of fluid above. This principle underpins hydraulics and explains phenomena from deep-sea diving to mountain weather.
Pressure increases with depth — the greater the depth, the more liquid above, the greater its weight pressing down.
- A diver at 10 m depth experiences greater pressure than at 5 m.
- Dams are built thicker at the base because pressure is greatest there.
- Water squirts further from holes lower in a container.
Pressure decreases with altitude — the higher you go, the less air above, so less weight pressing down.
- At sea level: ~101,300 Pa (1 atmosphere).
- On Aoraki / Mt Cook (3,724 m): pressure much lower → thinner air.
- Breathing becomes harder at high altitude — less oxygen per breath.
Every object in a fluid experiences an upward force called upthrust (or buoyancy). This is because pressure below the object is greater than pressure above it, creating a net upward force.
- Float: if upthrust ≥ weight (object is less dense than the fluid)
- Sink: if upthrust < weight (object is denser than the fluid)
A waka (canoe) floats because its overall density (including air inside) is less than water. Steel ships float for the same reason — hollow shape displaces a large volume of water.
Application questions:
- A diver descends from 5 m to 20 m depth. What happens to the pressure they experience? Why?
- Why does a climber ascending Aoraki / Mt Cook need to breathe more frequently near the summit?
- A rubber duck floats in a bath. A steel coin sinks. Using upthrust and weight, explain the difference.
- Why are submarines able to both dive and surface? What must they change to control their depth?
Tūhono Aotearoa · New Zealand Connections
The double-hulled waka hourua used by Māori and Pacific ancestors to navigate Te Moana-nui-a-Kiwa applies all three of Newton's Laws: paddles push water back (3rd Law), the waka accelerates (2nd Law), and maintains velocity once paddling stops on calm water (1st Law).
At Aoraki's summit (3,724 m), atmospheric pressure is roughly 65% of sea level. Climbers must acclimatise as the thinner air means lower oxygen pressure per breath. This directly illustrates the relationship between altitude and pressure reduction.
In the tradition of Māui fishing up Te Ika-a-Māui (the North Island), consider the forces: tension in the line (upward on the fish), weight of the fish (downward), and water resistance. When tension exceeds the net downward forces, the fish accelerates upward.
New Zealand engineers like those at McLaren Automotive apply Newton's Laws and fluid dynamics to design racing cars. Streamlining minimises air resistance; downforce (generated by wings) presses tyres into the road, increasing friction to allow faster cornering.
Whakaaro Hōhonu · Deeper Thinking
- Explain why wearing a seatbelt in a car relates to Newton's First Law. What would happen to an unbelted passenger in a sudden stop?
- A 70 kg person stands on bathroom scales in an elevator. The scales read 630 N when stationary. What happens to the reading when the elevator: (a) accelerates upward, (b) decelerates to stop, (c) moves at constant speed? Explain using Newton's Laws.
- Design an experiment to measure the effect of surface area on air resistance. State your independent variable, dependent variable, and three control variables.
- Extension: Research how Newton's Laws apply to spacecraft in orbit. Why does the International Space Station not fall to Earth even though gravity is pulling it down? (Hint: it is constantly falling, but also moving sideways.)
Kuputaka · Key Vocabulary
Kaiako Planning Snapshot
Resources already provided. What to print: this handout (2 pages). All activities are self-contained — no additional photocopying required.
Classroom use: Works as a starter, formative check, or paired investigation. Linked next step: Te Wānanga for a differentiated lesson plan, or save to My Kete.
NZ pedagogy basis: Aligned to Te Mātaiaho (Draft 2025) and Tātaiako cultural competencies. Suitable for all NZ kura and schools.
Mō ngā kaiako — For teachers and ākonga:
Inclusion: ESOL / ELL ākonga — bilingual headings and visual supports built in. UDL / neurodiverse learners — chunked sections, multiple representation formats. ADHD-friendly: short, scaffolded tasks with clear structure.
Differentiation: Entry-level tasks use supported sentence frames; on-level tasks are open-ended; extension tasks require abstract reasoning. Scaffold down with word banks; stretch by removing structured supports.