Force and Laws of Motion Class 9 Science Chapter 9 NCERT Notes

Force and Laws Motion Short Notes | Class 9

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Introduction

Force is an interaction that, when unopposed, changes the motion of an object. It can cause an object to move, stop, or change direction. Forces can also change the shape of objects.

• Types of Forces

(i) Balance Force

(ii) Unbalance Force

Balance Force

When two or more forces acting on an object are equal in magnitude but opposite in direction, they cancel each other out. This results in no change in the object’s motion.

Example: Imagine a book resting on a table. The gravitational force pulling the book down is balanced by the normal force of the table pushing the book up. Since these forces are equal and opposite, the book remains stationary.

Unbalance Force

When the forces acting on an object do not cancel each other out, the net force is not zero. This causes the object to accelerate in the direction of the resultant force.

Example: Consider pushing a toy car. If you apply a force to the car, and there is no equal and opposite force to balance it, the car will start moving in the direction of the applied force.

Laws of Motion

Newton’s First Law of Motion (Law of Inertia)

• Definition: 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.
• Example: A book on a table will remain at rest until someone pushes it. Similarly, a moving car will continue to move at the same speed and direction unless brakes are applied or it hits an obstacle.

 Mass and Inertia

Mass

Mass is a measure of the amount of matter in an object. It is also a measure of an object’s inertia. The greater the mass of an object, the greater its inertia, meaning it will be more resistant to changes in its state of motion.

Inertia

Inertia is a property of matter that describes its resistance to any change in its state of motion. This means that an object will remain at rest or continue to move at a constant velocity unless acted upon by an external force. This concept is encapsulated in Newton’s First Law of Motion, also known as the Law of Inertia.

Momentum

Momentum is the product of an object’s mass and its velocity. It is a vector quantity, which means it has both magnitude and direction. The formula for momentum is:

$$\text{Momentum}(p)=\text{Mass}(m)\times \text{Velocity}(v)$$

Units

The SI unit of momentum is kilogram meter per second (kg·m/s).

Properties of Momentum

1. Vector Quantity: Momentum has both magnitude and direction. The direction of momentum is the same as the direction of the object’s velocity.
2. Conservation of Momentum: In a closed system, the total momentum before and after an event (like a collision) remains constant, provided no external forces act on the system. This is known as the Law of Conservation of Momentum.

Examples

• Sports: When a football is kicked, its momentum changes due to the force applied by the player’s foot.

Newton’s Second Law of Motion (Law of Acceleration)

• Definition: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is ( F = ma ), where ( F ) is the force, ( m ) is the mass, and ( a ) is the acceleration.
• Example: Pushing a shopping cart. The harder you push (more force), the faster it accelerates. If the cart is heavily loaded (more mass), it accelerates less for the same amount of force.

Mathematical expression

Newton's second law of motion is mathematically expressed as:

$$\mathrm{<span\; style="font-family:\; Kanit;"><span\; style="font-size:\; medium;">F</span></span>}<span\; style="font-family:\; Kanit;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; Kanit;"><span\; style="font-size:\; medium;">m</span></span>}\mathrm{<span\; style="font-family:\; Kanit;"><span\; style="font-size:\; medium;">a</span></span>}$$

where:

• $F$ is the net force acting on an object (in newtons, N),
• $m$ is the mass of the object (in kilograms, kg),
• $a$ is the acceleration of the object (in meters per second squared, m/s²).

This equation states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The direction of the force is the same as.

$$\vec{F}=m\cdot \vec{a}$$

where $\vec{F}$ and $\vec{a}$ are vector quantities that indicate direction in addition to magnitude.

Newton's First Law of Motion from Second Law

First law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.

∴ F = 0

We know, F = m(v-u)/t

(i) A body is moving with initial velocity u then,

m(v-u)/t = 0 ⇒ v – u = 0

∴ v = u

Thus, final velocity is also same.

(ii) A body is at rest i.e., u = 0

Therefore, from above u = v = 0

So, the body will continue to be at rest.

Newton’s Third Law of Motion (Action and Reaction)

• Definition: For every action, there is an equal and opposite reaction.
• Example: When you jump off a small boat, you push the boat backward as you move forward. The force you exert on the boat is matched by an equal and opposite force exerted by the boat on you.

Law of Conservation of Momentum

Definition

The Law of Conservation of Momentum states that in an isolated system, the total momentum of two or more bodies acting upon each other remains constant, provided no external forces are acting on them. This means that the momentum before and after an event (like a collision) is the same.

Mathematical Expression

Consider two objects with masses ( m_1 ) and ( m_2 ), and initial velocities ( u_1 ) and ( u_2 ). After a collision, their velocities change to ( v_1 ) and ( v_2 ). According to the law:

                                        m1​u1​+m2​u2​=m1​v1​+m2​v2​

This equation shows that the total momentum before the collision (left side) is equal to the total momentum after the collision (right side).

Explanation

• Isolated System: A system where no external forces (like friction or air resistance) are acting.
• Momentum: The product of mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

Examples

1. Collisions: When two cars collide, the total momentum of the system (both cars) before and after the collision remains the same.
2. Rocket Propulsion: The momentum of the gases expelled backward is equal and opposite to the momentum gained by the rocket moving forward.

Derivation Using Newton’s Third Law

Newton’s Third Law states that for every action, there is an equal and opposite reaction. This principle helps derive the conservation of momentum. When two objects collide, the force exerted by object A on object B is equal and opposite to the force exerted by object B on object A. This results in the conservation of momentum in the system.