NCERT Class 9 Science Chapter 8: Force and Laws of Motion - Detailed Notes and Study Guide

Introduction to Force and Laws of Motion

In our daily lives, we observe objects at rest or in motion. A ball rolling on the ground eventually stops, a stationary bicycle moves when pedaled, and a hit cricket ball changes direction. What causes these changes? The answer lies in the concept of force and the fundamental principles governing motion. Chapter 8 of NCERT Class 9 Science, titled Force and Laws of Motion, builds upon basic kinematics concepts and introduces the underlying causes of motion as formalized by Sir Isaac Newton.

Understanding force and motion is essential not only for scoring well in CBSE examinations but also for understanding real-world physical events, ranging from driving automobiles to launching space rockets.

Understanding Force

In simple terms, a force is a push or pull applied to an object that results from its interaction with another object. Force is a vector quantity, meaning it possesses both magnitude and direction. The SI unit of force is the Newton (N) or kg·m/s².

Effects of Force

An applied force can produce several distinct effects on an object:

• Change state of motion: Move a stationary object or bring a moving object to rest.
• Change speed: Increase (accelerate) or decrease (decelerate) the velocity of a moving body.
• Change direction: Alter the path along which an object moves.
• Change shape and size: Deform an object temporarily or permanently (e.g., stretching a rubber band or squeezing clay).

Balanced and Unbalanced Forces

Forces acting on an object can be classified into two categories based on their net effect:

Newton's First Law of Motion and Inertia

Galileo Galilei first deduced that objects move with constant speed when no \texternal force acts on them. Sir Isaac Newton expanded on Galileo's ideas to formulate his First Law of Motion.

Statement of Newton's First Law

An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an \texternal unbalanced force.

This law implies that natural inclination of matter is to resist changes in its state of motion. Hence, Newton's First Law is also known as the Law of Inertia.

Inertia and Mass

Inertia is the inherent property of an object by virtue of which it resists any change in its state of rest or of uniform motion in a straight line.

The quantitative measure of inertia is mass. Heavier objects possess greater mass and, consequently, greater inertia. For example, pushing a massive boulder requires significantly more effort than pushing a small stone because the boulder has greater inertia.

Types of Inertia

• Inertia of Rest: The tendency of an object to stay at rest. Example: When a bus suddenly starts, passengers jerk backward because their feet move forward with the bus while their upper body tends to stay at rest.
• Inertia of Motion: The tendency of an object to maintain uniform motion. Example: When a moving bus stops suddenly, passengers lurch forward because their lower body stops with the bus while their upper body continues moving.
• Inertia of Direction: The tendency to maintain direction of motion. Example: When a vehicle takes a sharp turn, passengers lean outward due to their body's resistance to changing direction.

Newton's Second Law of Motion

While the first law explains what happens when forces are balanced or zero, Newton's Second Law quantifies force and describes how an unbalanced force changes the velocity of an object.

Concept of Momentum

Before defining the second law, we must understand momentum. The impact produced by a moving object depends on both its mass and its velocity. Momentum (p) is defined as the product of mass (m) and velocity (v):

p = m × v

• SI Unit of Momentum: kilogram-meter per second (kg·m/s).
• Momentum is a vector quantity having the same direction as the velocity.

Mathematical Statement of Newton's Second Law

The rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction in which the force acts.

Let an object of mass m have an initial velocity u. When a force F acts on it for time t, its final velocity becomes v.

• Initial momentum (p₁) = m × u
• Final momentum (p₂) = m × v
• Change in momentum = m(v - u)
• Rate of change of momentum = m(v - u) / t

Since acceleration a = (v - u) / t, we get:

Force (F) ∝ m × a

By setting the constant of proportionality to 1, we obtain the key formula:

F = m × a

Definition of 1 Newton

1 Newton (1 N) is defined as the force required to produce an acceleration of 1 m/s² in an object of mass 1 kg.

1 N = 1 kg × 1 m/s² = 1 kg·m/s²

Practical Applications of Newton's Second Law

• Catching a Cricket Ball: A fielder pulls his hands backward while catching a fast ball. This increases the time interval t over which momentum changes to zero, reducing the force F exerted on his hands.
• High Jump Athletes: Athletes land on a sand bed or cushioned mattress to increase impact time, thereby lessening the force of impact and preventing injury.
• Seat Belts in Cars: Seat belts \textend the time required for a passenger's momentum to drop to zero during sudden braking, lowering the force applied on the body.

Newton's Third Law of Motion

Newton's Third Law describes the mutual interactions between two bodies.

Statement of Newton's Third Law

To every action, there is always an equal and opposite reaction, and they act on two different bodies.

If object A exerts a force F_AB on object B, then object B simultaneously exerts an equal and opposite force F_BA on object A:

F_AB = -F_BA

Important Characteristics of Action-Reaction Pairs

• Action and reaction forces are equal in magnitude and opposite in direction.
• They act simultaneously.
• They act on two different objects and therefore never cancel each other out.

Everyday Examples of Newton's Third Law

• Walking on Ground: We push the ground backward with our feet (action), and the ground pushes us forward with an equal force (reaction).
• Recoil of a Gun: When a bullet is fired from a gun, the gun exerts a forward force on the bullet (action), and the bullet exerts an equal backward force on the gun (reaction), causing recoil.
• Swimmer in Water: A swimmer pushes water backward (action), and the water exerts a forward force on the swimmer (reaction).
• Rocket Propulsion: Hot gases exhaust downwards at high velocity (action), propelling the rocket upward (reaction).

Conservation of Momentum

The Law of Conservation of Momentum is a fundamental conservation principle in physics that directly follows from Newton's second and third laws.

Statement

In an isolated system (where no \texternal unbalanced force acts), the total momentum of colliding bodies remains constant or conserved.

Mathematical Derivation

Consider two balls A and B of masses m_A and m_B moving in a straight line with initial velocities u_A and u_B (where u_A > u_B). They collide for a time duration t and move with final velocities v_A and v_B.

• Force exerted by A on B: F_AB = m_B(v_B - u_B) / t
• Force exerted by B on A: F_BA = m_A(v_A - u_A) / t

According to Newton's Third Law, F_AB = -F_BA:

m_B(v_B - u_B) / t = -m_A(v_A - u_A) / t

Simplifying the equation yields:

m_Au_A + m_Bu_B = m_Av_A + m_Bv_B

This shows: Total momentum before collision = Total momentum after collision.

Important Formula Summary

Important Questions and Answers

Question 1: Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Answer: When a branch of a tree is shaken vigorously, the branch comes into immediate motion. However, due to inertia of rest, the attached leaves tend to remain in their initial state of rest. As a result of this sudden relative movement between the moving branch and stationary leaves, a force acts on the leaf stems, causing some leaves to break off and fall down.

Question 2: A bullet of mass 20 g is horizontally fired with a velocity 150 m/s from a pistol of mass 2 kg. What is the recoil velocity of the pistol?

Answer:
Given:
Mass of bullet (m₁) = 20 g = 0.02 kg
Initial velocity of bullet (u₁) = 0 m/s
Final velocity of bullet (v₁) = 150 m/s
Mass of pistol (m₂) = 2 kg
Initial velocity of pistol (u₂) = 0 m/s
Let final recoil velocity of pistol = v₂

According to the law of conservation of momentum:
Total initial momentum = Total final momentum
(m₁ × u₁) + (m₂ × u₂) = (m₁ × v₁) + (m₂ × v₂)
0 + 0 = (0.02 kg × 150 m/s) + (2 kg × v₂)
0 = 3 + 2v₂
2v₂ = -3
v₂ = -1.5 m/s

The negative sign indicates that the pistol recoils in the direction opposite to the bullet's motion with a speed of 1.5 m/s.

Question 3: State Newton's Second Law of Motion and derive the formula F = ma.

Answer: Newton's Second Law states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction of the force.

Derivation:
Let an object of mass m have initial velocity u and final velocity v after time t under force F.
Initial momentum p₁ = mu
Final momentum p₂ = mv
Change in momentum Δp = mv - mu = m(v - u)
Rate of change of momentum = m(v - u) / t
By definition, Force F ∝ m(v - u) / t
Since acceleration a = (v - u) / t, we get F ∝ ma.
Using constant k = 1: F = ma.

Question 4: Why does an athlete take a long run before taking a high jump?

Answer: An athlete runs before taking a high jump to gain inertia of motion. The velocity acquired during the run adds to the athlete's body momentum, helping them jump higher and cover a longer distance through the air easily.

Question 5: A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration and the force acting on it if its mass is 7 tonnes (1 tonne = 1000 kg).

Answer:
Given:
Initial velocity (u) = 0 m/s
Distance (s) = 400 m
Time (t) = 20 s
Mass (m) = 7 tonnes = 7000 kg

Using second equation of motion: s = ut + ½ at²
400 = (0 × 20) + ½ × a × (20)²
400 = ½ × a × 400
400 = 200a
a = 2 m/s²

Now, Force F = m × a
F = 7000 kg × 2 m/s²
F = 14,000 N

Chapter Summary

• Force: A push or pull that can change an object's state of rest, motion, speed, direction, or shape.
• Balanced Forces: Net force is zero; does not alter motion state.
• Unbalanced Forces: Net force is non-zero; produces acceleration.
• Newton's First Law: Objects preserve state of rest or uniform motion unless acted on by \texternal unbalanced forces (Law of Inertia).
• Inertia & Mass: Inertia is resistance to change in state of motion. Mass is the direct quantitative measure of inertia.
• Momentum (p = mv): Vector quantity representing quantity of motion in an object. Unit: kg·m/s.
• Newton's Second Law (F = ma): Rate of change of momentum is proportional to applied force. 1 Newton = 1 kg·m/s².
• Newton's Third Law: For every action force, there is an equal and opposite reaction force acting on different bodies.
• Conservation of Momentum: Total momentum of an isolated system remains constant before and after collisions.