NCERT Class 9 Science Chapter 9: Force and Laws of Motion - A Complete Guide

Introduction to Force and Laws of Motion

Welcome, students! In the previous chapter on 'Motion', we learned to describe the movement of objects using terms like position, velocity, and acceleration. We saw how objects can move in a straight line or a circular path, and we learned to calculate their speed and the rate at which their speed changes. But have you ever wondered what causes motion? Why does an object speed up, slow down, or change its direction? What makes a stationary football move when kicked, and what makes a moving ball stop? The answers to all these fundamental questions lie in the concept of Force. This chapter, 'Force and Laws of Motion', delves into the cause of motion. We will explore the brilliant work of scientists like Galileo Galilei and Sir Isaac Newton, whose laws form the bedrock of classical mechanics. Understanding these principles is crucial not just for your exams, but for comprehending how the physical world around you operates, from the simple act of walking to the complex launch of a rocket into space.

Balanced and Unbalanced Forces

In our everyday language, a force is simply a push or a pull. We push a door to open it, we pull a drawer to take something out, we lift a book from the table. All these actions involve a force. In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (which includes starting to move from a state of rest), i.e., to accelerate. Let's dig deeper into the types of forces based on their effect.

What are Balanced Forces?

Imagine a heavy box on the floor. You and a friend push it from opposite sides with exactly the same amount of strength. What happens? The box doesn't move. This is a classic example of balanced forces. Balanced forces are two or more forces of equal magnitude acting on the same object but in opposite directions. Since the forces cancel each other out, their net effect is zero. A state of balanced forces does not cause any change in the object's state of motion. If the object is at rest, it remains at rest. If it is moving at a constant velocity, it continues to do so.

• Example 1: Tug of War. If both teams pull the rope with equal force, the rope and the central marker do not move in either direction. The forces are balanced.
• Example 2: A book on a table. A book lying on a table is acted upon by two forces: the force of gravity pulling it downwards and the normal force from the table pushing it upwards. These forces are equal and opposite, so the book remains stationary.

What are Unbalanced Forces?

Now, let's go back to the tug-of-war game. What happens if one team starts pulling harder than the other? The rope and the opposing team will start moving in the direction of the stronger pull. This is due to an unbalanced force. An unbalanced force is a force that causes a change in the motion of an object. When the forces acting on an object are not equal and opposite, there is a net force, and this net force causes the object to accelerate. Acceleration means the object can speed up, slow down, or change its direction of motion.

• Example 1: Pushing a Box. If you push a box and it starts to slide across the floor, the force you are applying is greater than the opposing force of friction. This unbalanced force causes the box to move.
• Example 2: Kicking a Football. A football at rest will only move when an unbalanced force (the kick) is applied to it. The force of the kick overcomes the ball's inertia and causes it to accelerate.

It's important to understand the role of friction here. The force of friction always opposes motion. When you push a heavy box, you must apply a force greater than the frictional force between the box and the floor to get it moving. If your push is equal to the frictional force, the forces are balanced, and the box won't move.

First Law of Motion

Sir Isaac Newton, building upon the ideas of Galileo, formulated three fundamental laws of motion that govern the physical world. The first law addresses what happens to an object when no unbalanced force acts on it. It is also famously known as the Law of Inertia.

Newton's First Law of Motion states: An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied unbalanced force.

This law has two parts:

1. An object at rest will stay at rest unless an unbalanced force acts on it. (A book on a table will not fly off on its own.)
2. An object in motion will stay in motion with the same speed and in the same direction unless an unbalanced force acts on it. (This is harder to observe on Earth due to friction and air resistance, but a satellite in the vacuum of space will keep moving.)

Inertia and Mass

The First Law of Motion introduces the concept of inertia. Inertia is the natural tendency of an object to resist a change in its state of motion or of rest. It's like the object's inherent 'laziness' or reluctance to change what it's doing. The key point here is that inertia is not a force; it's a property of matter.

How do we measure inertia? The inertia of an object is measured by its mass. The more mass an object has, the more inertia it has, meaning it's harder to change its state of motion.

• It's easier to push a small toy car than a real car. The real car has much more mass, and therefore, much more inertia. A much larger unbalanced force is needed to get the real car moving.
• Similarly, it is harder to stop a moving truck than a moving bicycle, even if they are moving at the same speed. The truck has more mass and thus more inertia.

Everyday Examples of Inertia:

• Riding a Bus: When a bus at rest starts moving suddenly, you feel a jerk backwards. This is because your body, due to inertia, wants to remain in its state of rest, while the bus (and your feet in contact with it) moves forward. Conversely, when a moving bus stops suddenly, you lurch forward. Your body, due to inertia, wants to continue moving forward, while the bus has stopped.
• Shaking a Carpet: When you hang a dusty carpet and beat it with a stick, the dust particles fall out. The stick sets the carpet in motion, but the dust particles, due to their inertia of rest, tend to remain where they are. They separate from the carpet and fall down due to gravity.
• Fruits falling from a Tree: Vigorously shaking a tree branch causes the fruits to fall. The branch is set into motion, but the fruits, due to inertia, try to remain at rest and thus get detached from the branch.

Second Law of Motion

Newton's First Law tells us what happens when there is no net force. The Second Law of Motion tells us what happens when there is a net force. It provides a quantitative relationship between force, mass, and acceleration.

Before we state the law, we need to understand a new concept: Momentum.

What is Momentum?

Momentum is the 'quantity of motion' possessed by a moving body. It is defined as the product of an object's mass and its velocity. Momentum is a vector quantity, meaning it has both magnitude and direction. The direction of momentum is the same as the direction of the velocity.

The formula for momentum (denoted by 'p') is:

p = m × v

• p = momentum
• m = mass of the object
• v = velocity of the object

The SI unit of momentum is kilograms-meter per second (kg m/s). Since momentum depends on both mass and velocity, even a small object moving at a very high speed (like a bullet) can have a large momentum. Similarly, a very massive object moving at a low speed (like a train) also has a very large momentum.

Mathematical Formulation of Second Law of Motion

Newton's Second Law of Motion states: 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's derive the famous equation from this law.

Consider an object of mass 'm' moving with an initial velocity 'u'. A force 'F' is applied to it for a time 't', causing its velocity to change to 'v'.

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

We know from the first equation of motion that acceleration 'a' = (v - u) / t. Substituting this in the above expression, we get:

Rate of change of momentum = m × a

According to the Second Law, Force (F) is proportional to the rate of change of momentum.

F ∝ m × a

F = k × m × a

Here, 'k' is a constant of proportionality. The units of force, mass, and acceleration are chosen in such a way that the value of k becomes 1. One unit of force is defined as the amount that produces an acceleration of 1 m/s² in an object of 1 kg mass.

Thus, we get the fundamental equation:

F = m × a

The SI unit of force is the newton, symbolized as N. From the equation F = ma, we can define one newton:

1 N = 1 kg × 1 m/s²

So, one newton is the force required to cause an acceleration of 1 m/s² in a body of mass 1 kg.

Applications of the Second Law of Motion:

• Catching a Cricket Ball: A fielder moves his hands backwards while catching a fast-moving cricket ball. Why? The ball has a high momentum. To stop the ball, its momentum must be reduced to zero. By moving his hands back, the fielder increases the time (t) over which the change in momentum occurs. Since F = (change in momentum) / t, increasing the time decreases the force exerted by the ball on the fielder's hands, preventing injury.
• High Jump Athletes: Athletes in a high jump event are made to land on a cushioned bed or a sand bed. The soft landing surface increases the time it takes for the athlete's momentum to become zero, thus reducing the force of impact on their body.

Third Law of Motion

Newton's first two laws explain how forces affect the motion of a single object. The third law describes a fundamental symmetry in nature: forces always occur in pairs. You cannot have a single isolated force.

Newton's Third Law of Motion states: To every action, there is an equal and opposite reaction.

This means that whenever one object exerts a force on a second object (the 'action'), the second object simultaneously exerts a force back on the first object that is equal in magnitude and opposite in direction (the 'reaction').

Key points to remember about the Third Law:

• The action and reaction forces are always equal in size.
• The action and reaction forces are always opposite in direction.
• Crucially, the action and reaction forces act on different objects. Therefore, they never cancel each other out.

Examples Illustrating the Third Law:

• Walking: When you walk, you push the ground backwards with your feet (action). In response, the ground pushes you forward with an equal and opposite force (reaction). It is this reaction force from the ground that makes you move forward.
• Recoil of a Gun: When a bullet is fired from a gun, the gun exerts a forward force on the bullet (action). The bullet, in turn, exerts an equal and opposite backward force on the gun (reaction). This backward push is what is known as the gun's 'recoil'.
• Rocket Propulsion: A rocket expels hot gases downwards at high velocity (action). These gases exert an equal and opposite upward force on the rocket (reaction), which pushes the rocket into the sky.
• A Sailor Jumping from a Boat: When a sailor jumps from a boat to the shore, he pushes the boat backwards with his feet (action). The boat, in turn, pushes the sailor forward (reaction), helping him reach the shore. You might notice the boat moves away from the shore in this process.

Conservation of Momentum

The law of conservation of momentum is a direct consequence of Newton's Third Law of Motion. It is one of the most fundamental conservation laws in physics.

The Law of Conservation of Momentum states: In an isolated system (where there are no external unbalanced forces), the total momentum of the system remains constant or conserved.

Let's understand this with the example of a collision of two balls.

Consider two balls, A and B, with masses m_A and m_B. They are moving in the same straight line with initial velocities u_A and u_B, respectively (let's assume u_A > u_B so they will collide).

• Initial momentum of ball A = m_A * u_A
• Initial momentum of ball B = m_B * u_B
• Total initial momentum of the system = m_A * u_A + m_B * u_B

During the collision, which lasts for a time 't', ball A exerts a force F_AB on ball B. According to the third law, ball B exerts an equal and opposite force F_BA on ball A. So, F_AB = -F_BA.

After the collision, let their velocities become v_A and v_B.

• Final momentum of ball A = m_A * v_A
• Final momentum of ball B = m_B * v_B
• Total final momentum of the system = m_A * v_A + m_B * v_B

Using the second law, the force F_AB causes a change in the momentum of ball B:

F_AB = m_B * (v_B - u_B) / t

Similarly, the force F_BA causes a change in the momentum of ball A:

F_BA = m_A * (v_A - u_A) / t

Since F_AB = -F_BA:

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

Canceling 't' from both sides:

m_B * v_B - m_B * u_B = -m_A * v_A + m_A * u_A

Rearranging the equation to group initial and final momenta:

m_A * u_A + m_B * u_B = m_A * v_A + m_B * v_B

This equation shows that the total momentum before the collision is equal to the total momentum after the collision, provided no external force acts on the system. This is the principle of conservation of momentum.

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: This phenomenon can be explained by Newton's First Law of Motion, specifically the concept of inertia of rest. Initially, both the branch and the leaves are in a state of rest. When we vigorously shake the branch, we apply a force to it, setting it into motion. However, due to their inertia, the leaves tend to resist this change and try to remain in their state of rest. This opposition between the moving branch and the stationary leaves creates a strain at the point where the leaves are attached. If the shaking is strong enough, this strain overcomes the attachment strength, and the leaves get detached and fall down.

Question 2: An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 m/s²?

Answer: This is a direct application of Newton's Second Law of Motion (F = ma).
Given:

• Mass of the vehicle (m) = 1500 kg
• Acceleration of the vehicle (a) = -1.7 m/s² (The negative sign indicates that the acceleration is in the opposite direction to the vehicle's motion, which is why it's stopping. This is also known as deceleration or retardation.)

F = 1500 kg × (-1.7 m/s²)

F = -2550 kg m/s²

F = -2550 N

Question 3: If action is always equal to the reaction, explain how a horse can pull a cart.

Answer: This is a classic question about Newton's Third Law. It's true that the horse exerts a force on the cart (action), and the cart exerts an equal and opposite force on the horse (reaction). If we only considered these two forces, it would seem impossible for the horse-cart system to move. However, the key is to analyze all the forces acting on the horse and the cart as separate objects within a larger system.

• The horse pushes the ground backwards with its feet. As per the third law, the ground pushes the horse forward with an equal and opposite force.
• The cart experiences a backward pull from the horse, but it also experiences a forward pull from the horse.
• There are also opposing forces, like friction on the cart's wheels and air resistance.

Question 4: A hockey ball of mass 200 g travelling at 10 m/s is struck by a hockey stick so as to return it along its original path with a velocity of 5 m/s. Calculate the magnitude of change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.

Answer: To calculate the change in momentum, we need to find the initial and final momentum of the ball.
Given:

• Mass of the hockey ball (m) = 200 g = 0.2 kg (It's crucial to convert to SI units)
• Initial velocity (u) = 10 m/s
• Final velocity (v) = -5 m/s (The negative sign is very important here. Since the ball returns along its original path, its final velocity is in the opposite direction to its initial velocity.)

Step 1: Calculate the initial momentum (p₁).

p₁ = m × u = 0.2 kg × 10 m/s = 2 kg m/s

Step 2: Calculate the final momentum (p₂).

p₂ = m × v = 0.2 kg × (-5 m/s) = -1 kg m/s

Step 3: Calculate the change in momentum (Δp).

Change in momentum (Δp) = Final momentum - Initial momentum

Δp = p₂ - p₁

Δp = (-1 kg m/s) - (2 kg m/s)

Δp = -3 kg m/s

Chapter Summary

Here are the key takeaways from our deep dive into Force and the Laws of Motion:

• Force: A push or a pull that can change an object's state of motion or rest.
• Balanced Forces: Equal forces acting in opposite directions, resulting in zero net force and no change in motion.
• Unbalanced Forces: Forces that are not equal and/or opposite, resulting in a net force that causes acceleration.
• Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction, unless acted upon by an unbalanced force.
• Inertia: An object's natural tendency to resist changes in its state of motion. It is measured by the object's mass.
• Momentum (p): The product of an object's mass and velocity (p = mv). Its SI unit is kg m/s.
• Newton's Second Law: The rate of change of momentum of an object is proportional to the applied unbalanced force. This gives the equation F = ma.
• Unit of Force: One newton (N) is the force needed to accelerate a 1 kg mass by 1 m/s².
• Newton's Third Law: For every action, there is an equal and opposite reaction. These forces act on different bodies.
• Law of Conservation of Momentum: For an isolated system, the total momentum before a collision is equal to the total momentum after the collision (m_A u_A + m_B u_B = m_A v_A + m_B v_B).