Newton's second law: the net force on an object equals its mass times its acceleration, F = ma. Double the net force and the acceleration doubles; double the mass and the acceleration halves.
Push an empty shopping trolley and it shoots off. Push a full one just as hard and it barely gets going. Same push, different result: by exactly how much?
You know a net force makes things accelerate. This lesson finds the exact rule.
Engage: Commit to a prediction before you test anything. A wrong guess is fine: it shows you what to look for.
Explore: Try it on the board and compare what happens with your prediction.
Explain: Use the particle model to explain what you saw.
Practise: A few on your own, to check you have it.
Elaborate: Use the same idea in a new context.
Evaluate: Look back at your first ideas and what changed.
WidthMore contexts, same idea.
Make your prediction first. Help opens once you've locked it in.
EngageCommit to a prediction before you test anything. A wrong guess is fine: it shows you what to look for.
Engage: double the mass
ExploreTry it on the board and compare what happens with your prediction.
Explore: hit a target acceleration
Change the Push until the acceleration reading is 2 m/s². (You can press Play to see it, but the reading shows before you play.)
What did you have to do to the push?
Try it yourselfYour edits are saved in this browser.
Give the 4 kg trolley an acceleration of 2 m/s².
Use the board. This ticks when you get there.
Now double the mass to 8 kg and get the same acceleration, 2 m/s².
Use the board. This ticks when you get there.
ExplainUse the particle model to explain what you saw.
Explain: F = ma
In your book: explain what happens to the acceleration when you double the force, and when you double the mass, using F = ma.
What net force gives a 1200 kg car an acceleration of 3 m/s², in N?
A net force of 50 N acts on a 10 kg box. Its acceleration, in m/s²?
A net force of 600 N gives a sprinter an acceleration of 10 m/s². Her mass, in kg?
Match each quantity to its unit.
Force (F)
Mass (m)
Acceleration (a)
Velocity (v)
PractiseA few on your own, to check you have it.
Proportions
What happens to the acceleration?
The net force doubles, same mass
The mass doubles, same net force
Both force and mass double2F ÷ 2m = F ÷ m.
The net force halves, same mass
A trolley accelerates at 6 m/s². The net force is tripled and the mass stays the same. New acceleration, in m/s²?
Elaborate TypicalUse the same idea in a new context.
Elaborate: stopping a car
A 1500 kg car brakes from 20 m/s to rest in 4 s. What is the size of its deceleration, in m/s²?
What braking force does that need, in N?
Elaborate WiderUse the same idea in a new context.
Elaborate: is it really a straight line?
EvaluateLook back at your first ideas and what changed.
Evaluate: look back
Write one sentence: "At first I thought… Now I think… because…"
Revision summary
Newton's second law:F = ma. F is the net force (N), m the mass (kg), a the acceleration (m/s²).
Rearranged: a = F ÷ m and m = F ÷ a.
Double the net force, double the acceleration. Double the mass, half the acceleration.
The acceleration points the same way as the net force.
For teachers
Students apply F = ma to find force, mass or acceleration with units, use the net force, and explain how changing force or mass changes acceleration (AC9S10U05, node 4, a hinge node). About 30 minutes.
I can use F = ma to find force, mass or acceleration, with correct units.
I can explain that F in F = ma is the net force.
I can explain what doubling the force or the mass does to the acceleration.
Before class
A concept tutorial for introducing or revising the idea; it does not replace a trolley and hanging-mass practical. Set the width with ?width=minimum, typical (default) or wider.
The hinge risks are using the applied force instead of the net force, and dropping units or direction. The net-force question in Explain targets the first.
Board notes: the acceleration reading (under the board) is the net force divided by the mass, and shows before Play, so students can tune the push without running it. No friction on this board.
Running the lesson
Engage: put the four predictions on the board; come back after Explore.
Explore: ask what push hit target 1 (8 N) and target 2 (16 N). Write F, m, a in a table.
Explain: students should say the rearrangement aloud for each number check.
In your own words: the doubling paragraph is the evidence of the qualitative relationship.
The hard part (on purpose)
Using the net force, not the push, in F = ma. When a student uses the push, ask whether anything is pushing back.
When students get stuck
A student uses the push instead of the net force. Ask: Is anything pushing back? Fix: Subtract opposing forces first: F in F = ma is the net force.
A student confuses mass and weight in F = ma. Ask: Which is in kilograms? Fix: Mass (kg) goes in F = ma. Weight is a force (N).
A student thinks doubling mass halves the force needed. Ask: For the same acceleration, what did you need for 8 kg compared with 4 kg? Fix: Twice the force. Same force on double the mass gives half the acceleration.
Stretch and support
Stretch: Rockets lose mass as they burn fuel. With the same thrust, what happens to their acceleration during the launch?
Support: Give the formula triangle (F at the top, m and a below) with one worked example of each rearrangement.
Where it leads
Next: Newton's third law (node 5), then free body diagrams with several forces (node 6) and quantitative problems (node 7).
In class: a trolley pulled by hanging masses (move masses from the trolley to the hanger to keep total mass constant), with light gates or a motion sensor.
What each step is for
Engage: double the mass: Students' guesses about the mass-acceleration relationship (no effect, half, a little less) surface before the board makes it exact.
Explore: hit a target acceleration: Tuning the push to hit a target acceleration for a given mass makes students find F = ma by doing it.
Explain: F = ma: Stating the law with units and the word net, then solving for each variable, gives the procedural fluency the later multi-force nodes need.
proportions: Reasoning with proportions, not just substitution, shows students understand the relationship rather than the formula.
Elaborate: stopping a car: Braking applies F = ma to a real stopping problem, the context named in the curriculum.
Elaborate: is it really a straight line?: Predicting the shape of an F–a graph before seeing data prepares students to assess linearity in a trolley practical.
Now you can
Use F = ma to find force, mass or acceleration, with correct units.
Explain that F in F = ma is the net force.
Explain what doubling the force or the mass does to the acceleration.