10 min readConcept sheetSection A MCQ (1 mark) and true or false (2 marks, two parts); Section B very short answer (2 marks)

Newton's third law and impulse

Forces come in pairs: action and reaction are equal, opposite and act on different bodies. Impulse = force × time = change in momentum.

Newton's third lawWhen two bodies interact, F₁₂ = −F₂₁: the two forces are equal in size and opposite in direction

Action-reaction pairThe two forces act on two different bodies at the same time, so they never cancel each other

ImpulseJ = F Δt = Δp = mv − mu; a vector in the direction of the force

Unit of impulseN s, which is the same as kg m s⁻¹

Forces always come in pairs

The Earth pulls a falling mango. The mango also pulls the Earth, with an equal force. When you push an almirah, it pushes back on you. A single force never exists alone. Whenever two bodies interact, each pushes or pulls the other. We call one force the action and the other the reaction. They happen at the same instant; the reaction does not come later. Newton's third law: when two bodies interact, the force by the first on the second is equal in size and opposite in direction to the force by the second on the first. In vectors, F₁₂ = −F₂₁.

Spotting action and reaction pairs

Situation	Action	Reaction
A book on a table	Book presses down on the table	Table pushes up on the book
Walking	Foot pushes the ground backward	Ground pushes the foot forward
Swimming	Hands push the water backward	Water pushes the swimmer forward
Firing a gun	Gun pushes the bullet forward	Bullet pushes the gun backward (recoil)
The Earth and the Moon	Earth pulls the Moon	Moon pulls the Earth

Why action and reaction do not cancel

A third-law pairThe book pushes the table down, and the table pushes the book up. These two forces act on different bodies, so they can never cancel each other.

Balanced forces on one bodyOn the book alone, its weight acts down and the table's normal force acts up. Both act on the same body, so they cancel and the book stays at rest. They are not a third-law pair.

Why does a person pushing an almirah not slide backward? Friction from the floor holds the feet. On a slippery wet floor, the person could not push the almirah at all.

Impulse equals the change in momentum

1
A bat hits a ball, or a hammer hits a nail: a large force acts for a very short time. Such a force is hard to measure, so we measure its effect.
2
Impulse is the product of the force and the time for which it acts: J = F Δt.
3
By the second law, F = (mv − mu)/Δt, where u and v are the velocities before and after.
4
Multiply both sides by Δt: F Δt = mv − mu.
5★
So, impulse = final momentum − initial momentum = change in momentum. Its unit is N s.

★ key step

Impulse in daily life: same change in momentum, longer time, smaller force

A cricket fielder draws the hands back while catching a fast ball. The stopping time grows, so the force on the hands is smaller.
Long jumpers land in sand, and high jumpers on a thick foam mattress.
Cars have crumple zones and airbags. They make the stopping time longer, so the force on passengers is smaller.
Glass, eggs and mobile phones are packed in foam, straw or bubble wrap.
Shock absorbers in scooters and buses spread a jolt over a longer time.
The opposite use: a hammer or a karate chop makes the contact time very short, to get a very large force.

Worked example: catching a cricket ball

Problem

A fielder catches a 0.16 kg cricket ball moving at 25 m s⁻¹. Find the impulse on the ball. Find the average force if she stops it in 0.05 s, and if she draws her hands back and stops it in 0.2 s.

Working

Change in momentum = 0 − (0.16 kg × 25 m s⁻¹) = −4 kg m s⁻¹. So the impulse has size 4 N s.
With stiff hands: F = Δp/Δt = 4 N s ÷ 0.05 s = 80 N.
Drawing the hands back: F = 4 N s ÷ 0.2 s = 20 N.
The time is 4 times longer, so the force is 4 times smaller.

Answer

Impulse 4 N s; average force 80 N with stiff hands but only 20 N when the hands are drawn back

In real life

A cricketer draws the hands back while catching, and phones come packed in foam, because a longer stopping time means a smaller force. Walking, swimming and every rocket launch from Sriharikota work by the third law.

Exam angle

2 marks: “Why does a cricket fielder pull the hands back while catching a fast ball?” The ball's change in momentum is fixed. Pulling the hands back makes the stopping time Δt longer. Since F = Δp/Δt, the force on the hands is smaller, so they are not hurt.

2 marks: “State Newton's third law of motion. Why do action and reaction forces not cancel each other?” When two bodies interact, the force by one on the other is equal in size and opposite in direction to the force by the other on the first. They act on different bodies, so they cannot cancel.

1 marks: “What is the SI unit of impulse?” N s, which equals kg m s⁻¹.

Remember it

Action and reaction: equal, opposite, on DIFFERENT bodies. Impulse: F × t = change in momentum.