A resultant force
Tug of war: 300 N left, 250 N right
Resultant: 300 − 250 = 50 N to the left
Newton's laws of motion Does a moving object need a force to keep it moving?
Foundation and Higher · AQA · 45 minutes
Students see on a graph how a trolley's mass changes its acceleration, then meet Newton's three laws: balanced forces keep things still or steady, a resultant force accelerates them, and forces come in pairs on two objects. Slides, a vote on a car at a steady speed that shows who's stuck, a virtual block with friction and a push, practice and homework.
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A trolley of mass m kg is pulled by a resultant force: across is the force in newtons, up its acceleration in m/s². Move m. For a 6 N pull, what does doubling the mass do to the acceleration?
y = x/2
The idea in one minute
The resultant force is all the forces on an object added up, with their directions. When it is zero the forces are balanced and the object stays still or keeps moving at a steady velocity: Newton's first law. A moving object needs no force to keep moving, only to speed up, slow down or turn. When there is a resultant force, it accelerates: F = m a, the second law. And whenever two objects interact they push or pull on each other equally and oppositely: the third law, a pair of forces of the same type on two different objects.
The lesson takes on what most students think, that motion needs a force: the hook leaves it open, and a vote on a car at a steady speed shows who still thinks it. It builds the three laws with forces along a line, mass and weight (W = m g), friction that holds a block still until the push is too big, and pairs of forces told apart from balanced forces. In a virtual scene students push a block on a rough floor until it moves, then tilt a slope until a block slides: it stays still while friction balances the other forces and moves once there is a resultant.
By the end, students can
- find the resultant of forces along a line, and say when forces are balanced
- use Newton's first law: zero resultant, still or a steady velocity
- use F = m a to find a force, a mass or an acceleration
- tell mass (kg) from weight (N) with W = m g
- name a third-law pair: same type of force, equal, opposite, on two objects
Key words
- resultant force
- balanced forces
- Newton's first law
- Newton's second law
- Newton's third law
- inertia
- friction
- weight
Before this lesson
Builds on the lesson before, speed, velocity and acceleration (a in m/s²). Students should know a force is a push or pull in newtons, and rearrange a formula.
Taught in Speed, velocity and acceleration.
Next: Moments, levers and gears.
The lesson, step by step
45 minutes in total. The stretch is optional.
5 min 1 · Hook · students think
Heavier, slower?
Students move a trolley's mass on a graph of acceleration against resultant force.
Say“Up is how quickly the trolley speeds up; across is how hard it is pulled. Move its mass. What changes, and what stays the same?”
Ask- With no resultant force, what is the acceleration? Does that mean the trolley is still?
- For a 6 N pull, what is the acceleration when m = 2? When m = 4?
- Why does the line always go through (0, 0)?
Watch forSaying no force means the trolley must be still: keep it for the vote, it is the lesson's question.
For the teacher
Give a minute to think, then read the graph together at 6 N for two masses: doubling the mass halves the acceleration.
Leave the question open: with no resultant force there is no acceleration, but is the trolley stopped? The vote comes back to it.
Ask for a prediction before each move: m = 2 gives 3 m/s² for 6 N, m = 4 gives 1.5 m/s². Then ask what an acceleration of 0 means: it is still or moving steadily. Don't settle it yet.
Shorter: Read one mass only (−2 min).
12 min 2 · Explain · you explain
Three laws, one idea
The resultant force; the first law and balanced forces; F = m a; mass and weight; third-law pairs; friction.
Say“Every law today is about the resultant force: all the forces added up, with their directions.”
Ask- A cyclist rides at a steady 6 m/s: is her pedalling force bigger than the forces against her, or equal?
- Why does a full shopping trolley need a bigger push to get going?
- A book on a table: what pulls it down? What does it pull on in return?
Watch forA third-law pair placed on the same object.
F = m a
A 1000 kg car, resultant force 2500 N
a = F ÷ m = 2500 ÷ 1000 = 2.5 m/s²
Mass and weight
A 50 kg student on Earth, g = 9.8 N/kg
W = m g = 50 × 9.8 = 490 N
For the teacher
Resultant force: add forces along a line, those one way minus those the other. Tug of war: 300 N left and 250 N right make 50 N to the left.
First law: when the resultant force is zero the forces are balanced, and the object stays still or keeps the same velocity. A cyclist at a steady 6 m/s pushes forwards exactly as hard as air resistance and friction push back. Moving needs no resultant; changing speed or direction does. (Higher) Inertia is how objects tend to stay as they are.
Second law: resultant force = mass × acceleration, F = m a, in N, kg and m/s². A bigger resultant gives a bigger acceleration; a bigger mass, a smaller one, as the hook showed. Required practical 7 measures exactly this with a trolley.
Mass and weight: mass is how much stuff, in kg, the same everywhere. Weight is the pull of gravity on it, W = m g, in N; g is 9.8 N/kg on Earth and about 1.6 N/kg on the Moon.
Third law: when two objects interact, each pushes or pulls on the other with an equal and opposite force, of the same type. The Earth pulls the book down; the book pulls the Earth up. The table's push up on the book balances the book's weight, but that is the first law, two forces on one object.
Friction: it acts against sliding. Push a heavy box gently and friction matches the push, so it stays still. Push harder than friction can hold and there is a resultant: it moves. The scenes in the practice show exactly that.
Students write F = m a and W = m g with their units: newtons, kilograms, m/s², N/kg. Both are to be learnt for AQA.
Shorter: Skip the friction slide; do mass and weight in a sentence (−4 min).
8 min 3 · Your turn · students write
Worked, then yours
Each worked example beside a twin that students solve themselves.
Say“Draw the object as a box, an arrow for each force. Find the resultant before anything else.”
Ask- Is that one force or the resultant?
Watch forUsing the driving force in F = m a without taking off the resistive forces.
A resultant
120 N forwards, 30 N and 40 N backwards
Resultant: 120 − 30 − 40 = 50 N forwards
Then theirs
500 N forwards, 200 N and 300 N backwards
A force
A 0.5 kg ball accelerates at 12 m/s²
F = m a = 0.5 × 12 = 6 N
Then theirs
A cyclist and bike, 70 kg, accelerate at 0.8 m/s²
An acceleration
A 1200 kg car: driving force 3600 N, resistance 600 N
Resultant 3000 N; a = 3000 ÷ 1200 = 2.5 m/s²
Then theirs
An 800 kg car: driving force 2600 N, resistance 1000 N
A weight
A 60 kg astronaut on Earth, 9.8 N/kg
W = 60 × 9.8 = 588 N
Then theirs
The same astronaut on the Moon, 1.6 N/kg
For the teacher
Work the first example aloud with a box and arrows. Its twin comes to 0 N: ask what the object is doing. Still, or a steady speed: the first law.
The third pair catches 2600 ÷ 800 with the resistance left in; the fourth, a mass given as 96 kg on the Moon.
Open the answers slide once most have finished their twins.
Shorter: Do the first and third pairs only (−3 min).
15 min 4 · Who's stuck? · students vote
Vote, then practise
One question shows who's stuck; then practice in levels with a virtual block, friction and a push.
Say“Choose an answer on your own. Nobody talks until everyone has chosen.”
Ask- Is the car's velocity changing? So what is the resultant force?
Watch forQuick answers from everyday feeling: ask each student what the car's velocity is doing before they defend their choice.
Show your working on paper. Forces are in newtons (N), masses in kg, accelerations in m/s². Take g = 9.8 N/kg. The scenes are virtual experiments: move only the setting the question names. The stretch is optional.
The question that shows who's stuck
- A car drives along a straight, flat road at a steady 30 m/s. What is true about the forces on it?
In your Classroom, as they answer (an example) - A13
- B9
- C3
- D2
Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.
- In a tug of war, one team pulls left with 420 N and the other pulls right with 380 N. The resultant force is ___ N to the ___.
- A 1200 kg car accelerates at 2.5 m/s². What is the resultant force on it, in newtons?
- An astronaut has a mass of 80 kg on Earth. She goes to the Moon, where g = 1.6 N/kg. What is her mass on the Moon?
- A book rests on a table. The Earth pulls the book down (its weight). Which force is the other half of this Newton's third law pair?
- A 5 kg block rests on a rough floor. Someone pushes it with 10 N and it doesn't move. What is the friction force on it, in newtons?
- Virtual experiment. The same 5 kg block on the rough floor (the scene's slope at 0°: "up the slope" is the way you push). Push it from 0, 1 N at a time, until it just starts to move. Watch the friction arrow F as you push, and note what it reads once the block moves.They change an interactive scene (inclined plane) until it does it.
- Once the block in the scene slides, friction on it is 9.8 N. What push makes the 5 kg block accelerate at 2 m/s²? Find the resultant force it needs first with F = m a. Give the push in newtons.
- Virtual experiment. No push now, and a 2 kg block on a slope. Tilt it from 10°, a degree at a time, until the block just starts to slide down. Watch friction F grow as you tilt. Then try a different mass: does the angle change?They change an interactive scene (inclined plane) until it does it.
- In the tilting scene, a block of the same material but twice the mass is put on the slope. At what angle does it start to slide? (You can try it there: the mass moves.)
- A 900 kg car has a driving force of 2400 N. Air resistance and friction add up to 600 N. What is its acceleration, in m/s²?
- Stretch (Higher): the same resultant force of 6 N gives trolley A an acceleration of 3 m/s² and trolley B 2 m/s². A's inertial mass is ___ kg and B's is ___ kg, so trolley ___ has more inertia.
Support · For the scenes: in the first, the floor is the scene's slope at 0°, so "up the slope" means the way you push. Leave the μ settings: they say how rough the surfaces are. Move only what the question lets you, a little at a time, and watch the line under the picture (still or moving) and the friction arrow F.
For the teacher
Everyone chooses before anyone explains. Ask for one reason for each answer, then ask: is the car's velocity changing?
Questions 1–4 build the ideas (resultant, F = m a, mass, pairs); 5–9 use the virtual block: still while friction holds, moving when there is a resultant; 10 is exam-style. The stretch is inertial mass (Higher).
Students show their working on paper or the board; the quiz keeps their final answers.
If the vote splits, slide a book across a desk: it slows and stops. Ask what force slowed it, then what would happen with no friction at all. The scenes are a virtual experiment, a model of a block with friction, not a substitute for required practical 7 with a real trolley. The working a scene shows after checking is A-level (μ, cos θ): GCSE students need only the forces in the picture.
Shorter: After the vote, questions 1–6 only (−6 min).
Longer: The stretch, then: why is it harder to stop a full trolley than an empty one? (+10 min).
5 min 5 · Exit · students show
A car and a rocket
An acceleration from a resultant force and one third-law pair show who has the two laws.
Say“Find the resultant first, then the acceleration. Then the pair: which two objects?”
Watch forDividing the driving force, not the resultant, by the mass.
Show your working on paper for the first question.
- A 1500 kg car has a driving force of 4000 N, and 1000 N of air resistance and friction act against it. What is its acceleration, in m/s²?
- A rocket's engine pushes hot gas backwards. Which force is the Newton's third law pair of the engine's push on the gas?
For the teacher
Students draw the car as a box with its two forces before calculating.
For the rocket, ask them to name the two objects in each force before choosing.
The answers show who finds the resultant before F = m a, and who puts a pair on two objects. Start the next lesson with whoever chose the rocket's weight. Set the homework.
Longer: The same car at a steady 25 m/s: what is its driving force? (+5 min).
One to one: for every situation ask the student to name each force on the object, who exerts it and which way it points, before any numbers. For each pair they name, ask: on which object does each force act?
Homework: Newton's laws of motion
Draw each object as a box with an arrow for every force. Find the resultant before using F = m a. Take g = 9.8 N/kg on Earth. Give units.
- A boat's engine pushes it forwards with 800 N. Water resistance is 650 N and the wind 50 N, both backwards. Find the resultant force.
- A 0.15 kg ball is hit and accelerates at 40 m/s². Find the resultant force on it.
- A 2000 kg van has a resultant force of 5000 N on it. Find its acceleration.
- A rover has a mass of 65 kg. Find its weight on Earth, and on Mars, where g = 3.7 N/kg. What is its mass on Mars?
- A swimmer pushes the water backwards with her hands. Explain, using Newton's third law, why she moves forwards. Name both forces in the pair.
- A bus brakes suddenly and a standing passenger lurches forwards. Explain this with Newton's first law. (Higher: use the word inertia.)
Print the worksheet with working space and homework. Teacher answers come with your Library copy.
Teaching newton's laws of motion: common questions
How do I get students past the idea that a moving object needs a force?
Ask about something they know moves steadily, a car on a motorway, and ask what would happen if the driving force were bigger than the forces against it: it would speed up. So at a steady speed they must be equal. Then take friction away in their heads, an ice rink or deep space: nothing slows it, so it keeps going with no force at all. Coming back to it in later lessons matters: the idea returns.
What is the difference between balanced forces and a third-law pair?
Balanced forces act on one object and cancel, so it doesn't accelerate: the book's weight and the table's push up on it. A third-law pair acts on two different objects and never cancels: the Earth pulls the book, the book pulls the Earth. A pair is always the same type of force; ask "on which object does each act?"
What are the virtual block scenes, and do they replace required practical 7?
They don't replace it. Students change the push or the angle on a model of a block with friction; the scene works out the friction, the resultant and the acceleration, and checks what they set. It shows friction holding a block still and letting go, and F = m a with friction, quickly. Required practical 7 measures real accelerations of a trolley for different forces and masses; do it as well.
Is Newton's laws on Foundation and Higher tier?
Both. Resultant force, the first law, F = m a, weight and the third law are on both tiers. Inertia and inertial mass are Higher only: they appear on one slide and in the stretch, marked Higher.
Should students use g = 9.8 or 10 N/kg?
AQA exam questions give the value of g whenever it is needed, usually 9.8 N/kg near the Earth's surface. This lesson uses 9.8 throughout; tell students to use the value the question gives, even if they met 10 N/kg elsewhere.
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Yes. Read the lesson, print the worksheet and open its slides without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the quizzes, the virtual scenes, the answers and the answer slides.
Curriculum reference: AQA GCSE Physics 8463: 4.5.6.2.1 (Newton's first law, inertia), 4.5.6.2.2 (Newton's second law, F = m a) and 4.5.6.2.3 (Newton's third law), with 4.5.1.3 (gravity: weight, W = m g) and 4.5.1.4 (resultant forces).
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