Two Trolleys, One Push
Two students stand on low-friction trolleys and push against each other. Both roll backwards. Student A pushed B, and B pushed A — with forces equal in size and opposite in direction, even if one student is heavier. Set the size of the push and watch the two arrows stay equal.
force of A on B = 12.0 N · force of B on A = 12.0 N
The two forces are always equal in magnitude and opposite in direction, and they act on different bodies. That is Newton's third law.
Try each in your head before clicking an answer — this is a test, not a reveal. See how many you get first try. The clock starts on your first answer.
R1. A force is best described as:
R2. A body has zero resultant force. It will:
R3. Force is measured in:
If body A exerts a force on body B, then body B exerts a force on body A that is equal in magnitude, opposite in direction, and of the same type, acting along the same line. The two forces are a third-law pair.
| Property | A third-law pair |
|---|---|
| Magnitudes | equal |
| Directions | opposite |
| Type of force | the same (both pushes, both pulls, both gravitational, ...) |
| Bodies the forces act on | two different bodies |
These two ideas look similar but are not the same.
| Third-law pair | Balanced pair (equilibrium) | |
|---|---|---|
| Acts on | two different bodies | one body |
| Type of force | always the same type | may be different types |
| Example | table pushes book up; book pushes table down | weight of book down; normal reaction from table up |
| Can be added to find a resultant? | no — different bodies | yes — same body |
A book's weight and the normal reaction on the book are not a third-law pair: both act on the book. The partner of the book's weight is the pull the book exerts on the Earth.
The foot pushes the ground backwards; the ground pushes the foot forwards with an equal force. That forward force is what drives the walker.
The engine pushes gas backwards; the gas pushes the rocket forwards. No air is needed — the pair is between the rocket and the gas it carries.
The hand pushes water backwards; the water pushes the hand forwards.
Pairs: tap a force on the left, then its correct Newton's-third-law partner on the right to draw a line. When all six lines are drawn, press Check to score. Talk through each link — several of the right-hand cards are tempting but wrong.
Read each claim about a pair of forces and decide whether it is correct or contains an error, then read the explanation. Watch out for two balanced forces acting on one body being described as a third-law pair.
A book of weight $12\ \text{N}$ rests on a table. State the Newton's-third-law partner of (i) the weight of the book, (ii) the normal reaction from the table on the book. Explain why these two forces are not a third-law pair.
Ask which other body each force acts on. A partner force always acts on the other body of the interaction.
The weight is the Earth pulling the book down. Its partner is the pull of the book on the Earth: $12\ \text{N}$ upwards, acting on the Earth.
The normal reaction is the table pushing the book up. Its partner is the push of the book on the table: $12\ \text{N}$ downwards, acting on the table.
The weight and the normal reaction both act on the book. They balance because the book is in equilibrium, but a third-law pair must act on two different bodies. They are also different types of force — one gravitational, one contact.
A rocket of mass $3000\ \text{kg}$ is in deep space. Its engine pushes gas backwards with a force of $45\,000\ \text{N}$. State the third-law pair involved and find the initial acceleration of the rocket.
The force the gas exerts on the rocket is equal in magnitude to the force the rocket exerts on the gas. Use $F = ma$ for the rocket alone.
The rocket pushes the gas backwards with $45\,000\ \text{N}$; the gas pushes the rocket forwards with $45\,000\ \text{N}$. The pair acts on two different bodies, so the two forces do not cancel.
Considering the rocket alone, the only force is the push from the gas: $45\,000 = 3000a$.
$a = \dfrac{45\,000}{3000} = 15\ \text{m s}^{-2}$ forwards.
Answer, then check. Options are shuffled every load. The clock starts on your first answer.
Q1. Newton's third law states that if body A exerts a force on body B, then:
Q2. Which of these is a Newton's-third-law pair?
Q3. Two bodies collide. The forces they exert on each other are:
Q4. A rocket accelerates in deep space because:
Work each on paper, then reveal the solution to check your working.
A book rests on a table. State the Newton's-third-law partner of (i) the weight of the book, (ii) the normal reaction from the table on the book.
Reveal Solution
(i) The pull of the book on the Earth, acting upwards on the Earth. (ii) The push of the book on the table, acting downwards on the table.
A swimmer pushes water backwards with her hands. State the third-law pair and explain how she moves forwards.
Reveal Solution
The pair is: the hand pushes the water backwards, and the water pushes the hand forwards with an equal force. The forward force from the water acts on the swimmer, so she accelerates forwards.
A book of weight $8\ \text{N}$ rests on a table. Decide whether each of the following is a third-law pair, giving a reason: (a) the weight of the book and the normal reaction from the table on the book; (b) the normal reaction from the table on the book and the push of the book on the table.
Reveal Solution
(a) No. Both forces act on the book, so they are a balanced pair, not a third-law pair; they are also of different types. (b) Yes. They are equal in magnitude, opposite in direction, of the same type, and act on two different bodies.
Two ice skaters, of masses $60\ \text{kg}$ and $40\ \text{kg}$, stand facing each other on frictionless ice and push apart. During the push each experiences a force of $120\ \text{N}$. Find the magnitude of each skater's acceleration while they are pushing.
Reveal Solution
The two forces are a third-law pair, so both have magnitude $120\ \text{N}$. For the $60\ \text{kg}$ skater $a = \dfrac{120}{60} = 2.0\ \text{m s}^{-2}$; for the $40\ \text{kg}$ skater $a = \dfrac{120}{40} = 3.0\ \text{m s}^{-2}$. Equal forces, different accelerations, because the masses differ.
A rocket of mass $2000\ \text{kg}$ in deep space ejects gas to produce a forward thrust of $30\,000\ \text{N}$. (i) State the third-law pair involved. (ii) Find the initial acceleration of the rocket. (iii) Explain why the rocket does not need air to push against.
Reveal Solution
(i) The rocket pushes the gas backwards; the gas pushes the rocket forwards with an equal force. (ii) $a = \dfrac{30\,000}{2000} = 15\ \text{m s}^{-2}$. (iii) The pair is between the rocket and the gas it carries, so the rocket can accelerate even in a vacuum — there is nothing for the exhaust to push against.
Exit Ticket
Check the learning objectives you feel confident about: