Physics Chapter 2 — Force and Laws of Motion

Section 2.1 – 2.2 · The Basics

The Concept of Force

A push or a pull on an object is called a force. We cannot see a force, but we can always see or feel its effect. The direction in which the object is pushed or pulled is the direction of the force.

Definition

Force is an external effort which tends to set a stationary body in motion, or stop a moving body, or change the speed or direction of a moving body, or change its size and shape. It may be a push, pull, stretch or squeeze.

The five effects of a force

1. Starts motion

🦶⚽

Moves a stationary body — kicking a still football.

2. Stops motion

🧤

Stops a moving body — a fielder catching a ball.

3. Changes speed

⏩

Speeds up or slows down a moving body.

4. Changes direction

↪️

A bat changing the path of a cricket ball.

5. Changes shape

🎈

Squeezing a balloon or pressing dough.

A push starts the ball moving; equal inward pushes change a body's shape.

Section 2.3 · Net Force

Balanced & Unbalanced Forces

Several forces often act on a body at once. What matters is their resultant (net) force — that decides whether the motion changes.

Balanced Forces

The resultant of all forces is zero. They cannot change the state of rest or of uniform motion, or the direction. (They can change the shape of a soft body.) Example: a heavy box that doesn't move when pushed — push, friction, weight and the normal reaction all cancel.

Unbalanced Forces

The resultant is not zero. They can start a body moving, stop it, change its speed or change its direction. When a body accelerates or retards, an unbalanced force must be acting on it.

Four forces on a box that won't move: push = friction and normal reaction R = weight mg, so the net force is zero (balanced).

Section 2.4 · The Opposing Force

Force of Friction

When one body slides over another, a force opposes their relative motion — this is friction. It arises from the tiny irregularities of the two surfaces interlocking; rougher surfaces → more friction.

Friction always acts opposite to the direction of (attempted) motion.

Static vs Sliding Friction

Static friction is the force to be overcome to start an object moving from rest. Sliding friction keeps a moving object moving at steady speed and is slightly smaller than static friction (once moving, the surfaces have less time to interlock).

Friction: friend & foe

Opposes motion — a rolling ball slows and stops.
Helps start motion — we can walk; tyres grip the road.
Helps control motion — brakes, writing with a pen.
Causes energy loss — parts heat up; machines lose efficiency.
Causes wear & tear — soles and tyres wear out.

💡

To move a stationary object you must push with a force greater than the opposing (static) friction.

Section 2.5 · The Big Idea

Galileo's Observations

Aristotle believed a body needs a continuous push to keep moving. Galileo disagreed — and his inclined-plane experiment changed physics forever.

⛷️ The double inclined-plane experiment

Galileo released a smooth marble down one frictionless slope and watched it climb the opposite slope. He noticed it always rose to nearly the same height it started from, whatever the steepness of the second slope. As he made the far slope gentler, the ball travelled further to reach that same height.

So if the far side were made flat, the ball — never reaching its starting height — would keep moving forever. Galileo concluded: an unbalanced force is needed to change motion, but no force is needed to keep a body moving uniformly. This is the seed of the law of inertia.

Gentler far slope → the ball travels further to reach the same height. A flat surface → it never stops.

Section 2.6 · Newton's First Law

Newton's First Law of Motion

Galileo's idea, stated precisely by Newton.

Newton's First Law (Law of Inertia)

A body at rest stays at rest, and a body in motion keeps moving in a straight line with uniform speed, unless acted upon by an external (unbalanced) force to change its state.

Three parts, three everyday truths

At rest stays at rest: a book on a table won't move until your hand (a force) pushes it.
In motion stays in motion: a rolling ball would never stop if friction and air resistance were removed.
Keeps its direction: a bike won't turn on its own — you must turn the handle (apply a force).

🧠

The first law tells us what a force does — it changes the state of rest or uniform motion. It defines force qualitatively.

Section 2.7 · The Lazy Property

Inertia & Mass

The property behind the first law is inertia — a body's reluctance to change its state of rest or motion.

Inertia & the mass link

Inertia is the property by which a body opposes any change in its state of rest or of uniform motion. The greater the mass, the greater the inertia — so mass is the measure of inertia. (That's why Newton's first law is also called the law of inertia.)

The three types of inertia

1 · Inertia of Rest

A body at rest resists being moved. Examples: passengers fall backward when a bus suddenly starts; fruits fall when a tree branch is shaken; dust is knocked out of a beaten carpet; only the bottom coin flies out when a carrom pile is struck.

2 · Inertia of Motion

A moving body resists being stopped. Examples: passengers fall forward when a bus stops suddenly; a person jumping off a moving bus tends to fall forward; luggage on a bus roof is tied down because it tends to keep moving.

3 · Inertia of Direction

A body resists a change in its direction of motion. Examples: passengers lean sideways when a car turns; a stone whirled on a string flies off tangentially when released; mud flies off a turning wheel along the tangent.

Section 2.8 · Mass in Motion

Momentum

Why is a fast cricket ball harder to stop than a slow one, and a heavy ball harder than a light one? Both mass and velocity matter. The quantity that combines them is momentum.

Linear Momentum

p = m × v

p = momentum, m = mass, v = velocity. SI unit: kg m/s (kg m s⁻¹); CGS unit: g cm/s.
Momentum is a vector — its direction is the same as the velocity. A body at rest (v = 0) has zero momentum.

What momentum depends on

Momentum is directly proportional to both mass and velocity. Double the mass → double the momentum; double the velocity → double the momentum. That is why a slow but heavy truck and a fast but light bullet can both carry large momentum — and why both can do great damage in a collision.

Given

A boy of mass 42 kg runs at 3 m/s. Find his momentum.

Formula

p = m × v

Substitute

p = 42 × 3

Answer

p = 126 kg m/s

Section 2.9 · The Master Equation

Newton's Second Law of Motion

The first law tells us a force changes motion; the second law tells us by how much — it gives a way to measure force.

Newton's Second Law

The rate of change of linear momentum of a body is directly proportional to the applied force, and the change takes place in the direction of the force.

From the law to F = ma

A body of mass m has its velocity changed from u to v in time t by a force F.

Initial momentum = mu; final momentum = mv; change = m(v − u).

Rate of change of momentum = m(v − u)/t. By the law, F ∝ m(v − u)/t.

Since (v − u)/t = a (acceleration), F ∝ ma → F = kma. Choosing units so that k = 1 gives the famous result:

Newton's Second Law — equation form

F = m a ⇔ a = F / m

Force = mass × acceleration. Also F = m(v − u)/t = rate of change of momentum.
Acceleration is directly proportional to force and inversely proportional to mass.

The unit of force — the newton

1 newton defined

One newton (N) is the force that gives a mass of 1 kg an acceleration of 1 m/s². So 1 N = 1 kg·m/s². In CGS, 1 dyne = 1 g·cm/s², and 1 N = 10⁵ dyne.

🛡️ The first law hides inside the second

If F = 0 in F = m(v − u)/t, then v − u = 0, i.e. v = u — the velocity does not change. So with no force, a body stays at rest or in uniform motion: that is exactly Newton's first law. The first law is a special case of the second.

Why we "increase the time" — everyday applications

Since F = Δp/t, spreading the same change of momentum over a longer time reduces the force. This single idea explains many safety designs:

A cricketer pulls the hands back while catching — longer time, smaller force, no injury.
Falling on a cushion or sand hurts less than on concrete — the stop takes longer.
Seat belts and shock absorbers stretch the stopping time, reducing the force on passengers.

Worked examples

Example A

What acceleration does a 200 N force give a 5 kg body? [2 Marks]

Given

F = 200 N, m = 5 kg; find a

Formula

a = F / m

Substitute

a = 200 / 5

Answer

a = 40 m/s²

Example B

Find the force needed to give a 1500 kg car a velocity of 30 m/s in 10 s, starting from rest. [3 Marks]

Given

m = 1500 kg, u = 0, v = 30 m/s, t = 10 s

Formula

F = m(v − u)/t

Substitute

F = 1500 × (30 − 0)/10

Answer

F = 4500 N

Example C

Find the change in momentum of a 1500 kg car when its speed rises uniformly from 36 km/h to 72 km/h. [3 Marks]

Convert

u = 36×5/18 = 10 m/s; v = 72×5/18 = 20 m/s

Formula

Δp = m(v − u)

Substitute

Δp = 1500 × (20 − 10)

Answer

Δp = 15000 kg m/s

Example D

A bullet of mass 4 g moving at 50 m/s enters a wall to a depth of 10 cm. Find the average resistance of the wall. [3 Marks]

Given

m = 4 g = 0.004 kg, u = 50 m/s, v = 0, s = 0.10 m

Formula

first find a from v² = u² + 2as, then F = ma

Substitute

0 = 50² + 2a(0.10) → a = −2500/0.2 = −12500 m/s²

Force

F = 0.004 × (−12500) = −50 N

Answer

Average resistance = 50 N

Section 2.10 · Forces Come in Pairs

Newton's Third Law of Motion

The first law defines force, the second measures it — the third tells us where forces come from: forces always occur in pairs.

Newton's Third Law

To every action there is an equal and opposite reaction. When body A exerts a force on body B, body B exerts an equal and opposite force on A at the same instant.

⚠️ The detail everyone forgets

Action and reaction are equal in magnitude and opposite in direction, but they act on two different bodies — so they never cancel each other. Because the two bodies can have different masses, the same-sized force can produce very different accelerations (a = F/m): the lighter body accelerates more.

The boy on skates pushes the wall; the wall pushes back equally — and the boy (lighter, free to move) rolls away.

Everyday examples of the third law

Walking

🚶

Foot pushes ground back; ground pushes us forward.

Recoil of a gun

🔫

Bullet shoots forward; gun kicks backward.

Rocket / jet

🚀

Gases rush down/back; craft is pushed up/forward.

Hose pipe

💧

Water rushes forward; pipe pushes back.

Man & boat

🚣

Man steps forward; boat slides backward.

Swimming

🏊

Swimmer pushes water back; water pushes swimmer forward.

Extension · Follows from the Third Law

Conservation of Momentum

Putting the second and third laws together gives one of physics' most powerful rules — used everywhere from collisions to rockets.

Law of Conservation of Momentum

In the absence of an external unbalanced force, the total momentum of a system stays constant. For two interacting bodies: total momentum before = total momentum after, i.e. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

🔫 The recoil of a gun — worked through

Before firing, both gun and bullet are at rest, so total momentum = 0. After firing, the bullet (mass m) moves forward at velocity v and the gun (mass M) recoils at velocity V. By conservation of momentum:

0 = mv + MV ⟹ V = − (m v) / M

The minus sign shows the gun moves opposite to the bullet. Because M ≫ m, the recoil speed V is small.

Worked Example

A 4 kg rifle fires a 20 g bullet at 400 m/s. Find the recoil velocity of the rifle. [3 Marks]

Given

M = 4 kg, m = 0.02 kg, v = 400 m/s, initial momentum = 0

Formula

0 = mv + MV → V = −mv/M

Substitute

V = −(0.02 × 400) / 4 = −8/4

Answer

V = −2 m/s (the rifle recoils at 2 m/s)

Problem-Solving Masterclass

F = ma, Applied Step by Step

Each problem follows the same routine — Given → Formula → Substitute → Calculate → Answer. Learn to spot which form of the law a problem needs.

M1 · F = ma

A force of 40 N acts on a 5 kg mass for 2 s. Find the velocity gained (from rest).

Step 1

a = F/m = 40/5 = 8 m/s²

Step 2

v = u + at = 0 + 8×2 = 16 m/s

Answer

Velocity = 16 m/s

M2 · F via momentum

A motorcycle (with rider) of mass 200 kg moving at 90 km/h is stopped in 5 s. Find the braking force.

Convert

u = 90×5/18 = 25 m/s, v = 0, t = 5 s

Formula

F = m(v − u)/t = 200(0 − 25)/5

Answer

F = −1000 N (the minus sign = opposing/braking force)

M3 · uses v² = u² + 2as

A 250 kg motor car is stopped in 18 m by a resistance of 1000 N. Find its initial speed.

Acceleration

a = F/m = −1000/250 = −4 m/s²

Then

v² = u² + 2as → 0 = u² + 2(−4)(18) → u² = 144

Answer

u = √144 = 12 m/s

M4 · F = ma + s = ut + ½at²

A constant 6 N force acts on a 2 kg body at rest. How long does it take to travel 54 m?

Acceleration

a = F/m = 6/2 = 3 m/s²

Distance

s = ut + ½at² → 54 = 0 + ½×3×t² → t² = 36

Answer

t = 6 s

M5 · masses tied together

A 5 N force gives mass m₁ an acceleration of 8 m/s² and mass m₂ an acceleration of 24 m/s². What acceleration would it give if both are tied together?

Find masses

m₁ = F/a₁ = 5/8 = 0.625 kg; m₂ = 5/24 ≈ 0.208 kg

Combined

m = 0.625 + 0.208 = 0.833 kg

Acceleration

a = F/m = 5/0.833

Answer

a = 6 m/s²

M6 · v–t graph → force

A ball of mass 50 g has a velocity–time graph falling from 30 m/s to 0 in 6 s. Find the force on the ball.

Acceleration

a = slope = (0 − 30)/6 = −5 m/s²

Force

F = ma = 0.05 × (−5)

Answer

F = −0.25 N (a retarding force)

M7 · JEE-style (conservation)

A 60 kg astronaut, floating at rest in space, throws a 2 kg tool at 9 m/s. Find the astronaut's recoil speed.

Given

total initial momentum = 0; M = 60 kg, m = 2 kg, v = 9 m/s

Formula

0 = mv + MV → V = −mv/M = −(2×9)/60

Answer

V = −0.3 m/s (astronaut drifts back at 0.3 m/s)

Textbook Exercise · Fully Solved

Exercise — Worked with Formula & Alternate Methods

Representative numericals from the chapter exercise, each solved in full with the formula shown and, where useful, a second method to cross-check.

Q1 · 3 Marks

A force acting on a 12 kg body produces an acceleration of 2 m/s². Find the force, and the new acceleration if the force is doubled.

Force

F = ma = 12 × 2 = 24 N

Doubled

a = F/m = 48/12 = 4 m/s² (mass same → a doubles too)

Answer

Force = 24 N · new acceleration = 4 m/s²

Q2 · 3 Marks

A constant force acts on a 5 kg object for 2 s and raises its velocity from 3 m/s to 7 m/s. Find the force, then the final velocity if the same force acts for 5 s.

Acceleration

a = (v − u)/t = (7 − 3)/2 = 2 m/s²

Force

F = ma = 5 × 2 = 10 N

For 5 s

v = u + at = 3 + 2×5 = 13 m/s

Answer

Force = 10 N · final velocity = 13 m/s

Q3 · 5 Marks

The speed–time graph of a 1200 kg car: speed rises 0→15 m/s in 2 s (O→A), stays at 15 m/s (A→B), then is braked to rest in 1 s. Find (a) the distance in the first 2 s and (b) the braking force.

(a) area

distance = area of triangle OAE = ½ × 2 × 15 = 15 m

(b) F

F = m(v − u)/t = 1200(0 − 15)/1 = −18000 N

alternate (b)

a = (0 − 15)/1 = −15 m/s²; F = ma = 1200 × (−15) = −18000 N ✓

Answer

(a) 15 m · (b) 18000 N (braking)

Q4 · 3 Marks

A 20 N force acting on a body at rest for 2 s gives it a velocity of 10 m/s. Find the mass of the body.

Acceleration

a = (v − u)/t = 10/2 = 5 m/s²

Mass

m = F/a = 20/5 = 4 kg

Answer

Mass = 4 kg

Q5 · 3 Marks

A car moving at 108 km/h is stopped in 4 s by the brakes. If its mass with passengers is 1000 kg, find the braking force.

Convert

u = 108 × 5/18 = 30 m/s, v = 0, t = 4 s

Formula

F = m(v − u)/t = 1000(0 − 30)/4

Answer

F = −7500 N (braking force)

Q6 · 3 Marks

A 2.5 kg body undergoes a change of velocity of 10 m/s in 5 s. Find the force acting on it.

Acceleration

a = Δv/t = 10/5 = 2 m/s²

Force

F = ma = 2.5 × 2 = 5 N

Answer

Force = 5 N

Quick Reference

Formula & Fact Sheet

Everything in one place for a 5-minute revision.

Concept	Formula / Statement	Note
Force	a push or a pull	vector; changes state/shape
Momentum	p = m v	vector, kg m/s
Second law	F = m a	also F = m(v−u)/t = Δp/t
Acceleration	a = F / m	more mass → less a
1 newton	1 N = 1 kg·m/s²	1 N = 10⁵ dyne
First law	no force → no change in motion	law of inertia
Inertia	∝ mass	rest · motion · direction
Third law	action = − reaction	act on different bodies
Conservation of p	m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂	no external force
Recoil	V = − m v / M	gun/astronaut recoil
Balanced forces	net = 0	no change in motion
Unbalanced forces	net ≠ 0	cause acceleration
km/h → m/s	× 5/18	—

Smart Study

10 Exam & JEE-Foundation Tips

Where students gain — and lose — marks in this chapter.

Write F = ma first

State the formula, then substitute. The formula line itself earns a mark.

Convert km/h → m/s

Always × 5/18 before using F = m(v−u)/t. A unit slip is the most common error.

Mass in kg, not grams

A 50 g ball is 0.05 kg. Forgetting this throws the force off by 1000×.

Negative force = opposing

A minus sign on F or a means braking/retarding. State the magnitude in your final line.

Action ≠ reaction cancel

They act on different bodies, so they never cancel. A favourite 1-mark trap.

Inertia depends on mass only

Not on speed or shape. "Inertia of a moving object depends on its mass."

Momentum is a vector

Direction matters; before firing, total momentum of gun + bullet = 0.

Link to motion graphs

v–t slope = a, so F = m × (slope). Many force questions are graph questions in disguise.

"Increase time → reduce force"

The reasoning behind catching, cushions, seat belts and shock absorbers (F = Δp/t).

Cross-check by a 2nd method

JEE habit: confirm a force with F = ma and F = Δp/t. Two routes, one answer.

CBSE Pattern Practice

Practice Question Bank

MCQ · Assertion–Reason · VSA (1M) · SA (2M / 3M) · LA (5M) · Application (4M) — covering every question type in the chapter exercise, each with a step-by-step solution.

⚡ Beyond the Textbook

JEE Foundation Challenge Set

Original problems built on the same Class 9 toolkit (F = ma, momentum, conservation, third law) but with sharper reasoning. Try each before opening the solution.

Bonus problems — tap a card's button to reveal the worked solution.

Force & Laws of Motion

Balanced Forces

Unbalanced Forces

Static vs Sliding Friction

Friction: friend & foe

⛷️ The double inclined-plane experiment

Three parts, three everyday truths

1 · Inertia of Rest

2 · Inertia of Motion

3 · Inertia of Direction

What momentum depends on

🛡️ The first law hides inside the second

⚠️ The detail everyone forgets

🔫 The recoil of a gun — worked through

Write F = ma first

Convert km/h → m/s

Mass in kg, not grams

Negative force = opposing

Action ≠ reaction cancel

Inertia depends on mass only

Momentum is a vector

Link to motion graphs

"Increase time → reduce force"

Cross-check by a 2nd method