Force and Laws of Motion - class 9th Notes, Formulae, Numerical

Target: CBSE Board Exams | State Board Exams | NTSE | Olympiads | Foundation

Introduction:

बल और गति के नियम (Force and Laws of Motion) भौतिकी के सबसे महत्वपूर्ण अध्यायों में से एक है, जो वस्तुओं की गति और उस पर लगने वाले बल के प्रभाव को समझाता है। इस अध्याय में बल (Force), जड़त्व (Inertia), संवेग (Momentum) तथा Newton’s Laws of Motion जैसे प्रमुख सिद्धांत शामिल हैं। साथ ही, विभिन्न सूत्र (Formulae) और सॉल्व्ड न्यूमेरिकल्स छात्रों को इन अवधारणाओं को व्यावहारिक रूप से समझने में मदद करते हैं। यह अध्याय दैनिक जीवन की कई घटनाओं, जैसे वाहन का चलना या रुकना, को वैज्ञानिक दृष्टिकोण से समझाने में सहायक होता है।

Force:

Force is a push or pull upon an object resulting from its interaction with another object.
It has both magnitude and direction, making it a vector quantity.

Formula: F = m × a

Where:

F = Force (in Newtons, N)

m = Mass of the object (in kg)

a = Acceleration of the object (in m/s²)

Types of Force:

There are two basic types of force that we have learnt in class 8th

1) Balanced Force:

Definition:

Balanced forces are two or more forces acting on an object that are equal in magnitude but opposite in direction.
These forces cancel each other out, resulting in no change in the object's state of motion.
The Net/Total Force acting on an object is zero.

Effect:

No acceleration is produced.
If the object is at rest, it remains at rest.
If the object is in motion, it continues to move with the same speed and in the same direction.

Example:

A book resting on a table: The gravitational force pulling the book downward is balanced by the upward normal force from the table.
A person pushing a wall with equal force from both sides

2) Unbalanced Force:

Definition:

Unbalanced forces occur when the forces acting on an object are not equal in magnitude and/or not opposite in direction.
The net force is not zero, causing a change in the object's state of motion.

Effect:

Causes acceleration in the direction of the greater force.
Can start, stop, or change the direction of an object's motion.

Example:

A football being kicked: The applied force is greater than the opposing forces, causing motion.
Pushing a cart forward: If the forward force exceeds friction, the cart accelerates.

Newton’s Laws of Motion:

1) Newton's First Law of Motion (Law of Inertia):

Statement:

"An object will remain at rest, or in uniform motion in a straight line, unless acted upon by an external force."

Example: A book on a table will remain at rest unless someone pushes it.

Inertia:

Definition:

- Inertia is the tendency of an object to resist any change in its state of rest or of uniform motion in a straight line. It is not a force but a property of matter.

- In simple words, inertia means that an object will not change its motion unless a force is applied to it.

Origin of the Concept:

The concept of inertia was first clearly stated by Galileo Galilei in the 16th century and later included in Newton’s First Law of Motion.

Newton’s First Law & Inertia:

Newton’s First Law says:
“A body at rest will remain at rest, and a body in motion will continue in uniform motion in a straight line unless acted upon by an external force.”

This law actually describes inertia. It means:
- If an object is at rest, it will stay at rest unless a force moves it.
- If an object is moving, it will keep moving with the same speed and in the same direction unless a force slows it down, speeds it up, or changes its direction.

Types of Inertia:

1. Inertia of Rest

- Tendency of an object to remain at rest unless an external force acts on it.
Example: When you shake a tree, the leaves fall because the tree moves suddenly, but the leaves tend to remain in rest due to inertia.

2. Inertia of Motion

- Tendency of an object to continue moving with the same speed and direction unless a force changes it.
Example: A passenger in a moving bus falls forward when the bus stops suddenly, because his body tends to keep moving forward.

3.Inertia of Direction

- Tendency of an object to keep moving in the same direction unless a force changes its direction.
Example: When a car takes a sharp turn, passengers tend to lean sideways because their bodies try to keep moving in the original direction.

Factors Affecting Inertia:

The inertia of a body depends only on its mass:
- Greater the mass → greater the inertia.
- Smaller the mass → lesser the inertia.

Daily Life Examples of Inertia:

- Dust particles are removed from clothes by shaking them (inertia of rest).
- A moving train stops, and passengers are pushed forward (inertia of motion).
- A cyclist turns suddenly, and his body leans outward (inertia of direction).

Key Points to Remember:

- Inertia is not a force; it is a property of matter.
- It explains why objects resist changes in their motion.
- Newton’s First Law of Motion is also called the Law of Inertia.

2) Newton's Second Law of Motion :

statement:

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

This law explains how the velocity of an object changes when a force is applied.

Momentum:

Definition:

Momentum is the measure of the motion of a body.
It depends on both the mass of the body and its velocity.
It is a vector quantity, which means it has both magnitude and direction (same as the direction of velocity).

In simple terms:

A heavier or faster-moving object has more momentum than a lighter or slower object.

Example:

a moving truck has more momentum than a moving bicycle at the same speed.

Formula for Momentum:

P = m × v

Where:

P = momentum

m = mass of the body (kg)

v = velocity of the body (m/s)

SI Unit: kg·m/s

Characteristics of Momentum:

Vector quantity – has both magnitude and direction.
Direction – same as the direction of velocity.
If velocity is zero, momentum is also zero.
Momentum changes if either mass or velocity changes.
A force is required to change the momentum of a body.

Examples:

A cricket ball moving at 20 m/s has more momentum than the same ball moving at 5 m/s.
A loaded truck moving slowly can have more momentum than a small car moving fast because of its large mass.

Derivation for Newton's Second Law of Motion :

3) Newton's Third Law of Motion :

Statement:

"For every action, there is an equal and opposite reaction".

This means that forces always occur in pairs. When one object applies a force on another, the second object applies a force of the same magnitude but in the opposite direction on the first object.

Mathematical Form:

F₁₂ = - F₂₁

The negative sign indicates opposite directions.

Where:
F₁₂ = Force exerted by object 1 on object 2
F₂₁ = Force exerted by object 2 on object 1

Key Points:

Mutual Interaction: Forces exist only due to interaction between two bodies.
Equal Magnitude: Action and reaction forces are always equal in size.
Opposite Direction: They act in exactly opposite directions.
Different Bodies: Action and reaction forces act on different objects.
Simultaneous: Action and reaction occur at the same instant.

Examples:

Walking: Your foot pushes the ground backward (action), and the ground pushes your foot forward (reaction).
Rowing a Boat: The oar pushes water backward (action), and water pushes the oar forward (reaction).
Recoil of a Gun: The bullet is pushed forward by the gun (action), and the gun is pushed backward by the bullet (reaction).
Jumping off a Boat: You push the boat backward (action), and the boat pushes you forward (reaction).
Bird Flying: Wings push air downwards (action), and air pushes wings upwards (reaction).

Applications in Daily Life & Technology:

Rocket Propulsion: Hot gases expelled backward push the rocket forward.
Swimming: Hands push water backward, and water pushes the swimmer forward.
Jet Engines: Air is pushed backward; engine gets thrust forward.
Sports: High jump, long jump, and kicking a ball.

Law of Conservation of Momentum:

Statement:

"The total momentum of an isolated system remains constant if no external force acts on it".

In other words,

"Total Momentum before collision is equal to the total momentum after collision".

When two or more bodies interact, the total momentum before the interaction is equal to the total momentum after the interaction, provided there is no external force like friction or air resistance.

Mathematical Form:

Let,

m₁, v₁= mass and velocity of first body

m₂, v₂= mass and velocity of second body

Before collision;

Total Momentum = m₁u₁ + m₂u₂

After collision:

Total Momentum = m₁v₁ + m₂v₂

According to the law:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Key Points:

Momentum is conserved in the absence of external forces.
Applies to isolated systems only.
Valid for elastic and inelastic collisions.
Momentum of conservation is vector qauantity.

Examples:

Gun and Bullet: Before firing, total momentum = 0. After firing, bullet moves forward and gun recoils backward, total momentum remains zero.
Two Skaters Pushing Each Other: Both move in opposite directions with equal and opposite momentum.
Rocket Propulsion: Expelling gases backward gives equal forward momentum to the rocket.
Colliding Balls: In billiards, the total momentum before and after collision is the same.

Applications:

Rocket and jet engine design.
Sports such as billiards, cricket, and boxing.
Space travel including satellite ejection and spacecraft docking.
Vehicle crash analysis.

Recoil of Gun:

- When a bullet is fired from a gun, the bullet is pushed forward and the gun moves backward. This backward motion of the gun is called recoil.

- It occurs due to Newton’s Third Law of Motion: For every action, there is an equal and opposite reaction.

• Action: Force exerted on the bullet to propel it forward.
• Reaction: Force exerted by the bullet on the gun in the opposite direction.

Physics Explanation:

The recoil of a gun can be explained using the Law of Conservation of Momentum.

           Before firing:
           - Gun and bullet are at rest.
           - Total momentum = 0.

           After firing:
           - Bullet moves forward with high velocity.
           - Gun moves backward with small velocity.
           - Total momentum remains zero (if no external force acts).

Mathematical Form:

Let,

m_g = mass of the gun

m_b = mass of the bullet

v_g = Recoil velocity of the gun

v_b = velocity of the bullet

Before firing:

Total momentum = 0

After firing:

m_bv_b + m_gv_g = 0

Key Observations:

Recoil velocity is inversely proportional to the mass of the gun.
Bullet's velocity is much greater than the gun's recoil velocity due to small bullet mass.
Recoil is felt as a backward 'kick' against the shoulder.

Applications:

Gun design includes recoil-absorbing mechanisms.
Rocket propulsion works on a similar principle.
Sports shooters brace themselves to counter recoil.

Solved Numerical:

1) A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s². Determine the mass of the encyclopedia.

Solution:

Given:
Force (F) = 15 N
Acceleration (a) = 5 m/s²
Mass (m) = ?
From Newton’s Second Law of Motion:
F = m × a
Rearranging the formula to find mass:
m = F ÷ a
Substitute the values:
m = 15 ÷ 5
m = 3 kg

2) Car A of mass 1500 kg travelling at 25 m/s collides with another car B of mass 1000 kg travelling at 15 m/s in the same direction. After collision, the velocity of car A becomes 20 m/s. Calculate the velocity of car B after collision.

Solution:

Given:
Mass of car A (m_a) = 1500 kg                            Mass of car B (m_b) = 1000 kg
Initial velocity of car A (uₐ) = 25 m/s                 Initial velocity of car B (u_b) = 15 m/s
Final velocity of car A (v_a) = 20 m/s                   Final velocity of car B (v_b) = ?
Solution:
Using the Law of Conservation of Momentum:
mₐ uₐ + m_bu_b = mₐ vₐ + m_b v_bSubstitute the values:
1500 × 25 + 1000 × 15 = 1500 × 20 + 1000 × v_b37500 + 15000 = 30000 + 1000 × v_b52500 = 30000 + 1000 × v_b52500 - 30000 = 1000 × v_b22500 = 1000 × v_bv_b = 22500 ÷ 1000
v_b = 22.5 m/s

3) A cat of body mass 2.5 kg running with a speed of 2 m/s jumps on a stationary skateboard of mass 0.5 kg. Will the skateboard move with the cat on it? If yes, find the velocity of the combined (cat + board) system.

Solution:

Given:
Mass of cat (m_c) = 2.5 kg
Initial velocity of cat (u_c) = 2 m/s
Mass of skateboard (m_s) = 0.5 kg
Initial velocity of skateboard (u_s) = 0 m/s
This is a perfectly inelastic collision (they move together after contact), so we use conservation of linear momentum:
m_c u_c + m_s u_s = (m_c + m_s) v
Substitute values:
2.5 × 2 + 0.5 × 0 = (2.5 + 0.5) v
5 = 3.0 v
v = 5 ÷ 3 = 1.67 m/s (approximately)

Answer:
Yes, the skateboard will move. The combined velocity of the cat and skateboard is approximately 1.67 m/s in the cat’s original direction.

4) What is the recoil velocity of the gun of mass 8 kg when a bullet of mass 10 g is fired from it with a velocity of 400 m/s?

Solution:

Given:
Mass of gun (M) = 8 kg
Mass of bullet (m) = 10 g = 0.01 kg
Velocity of bullet (v) = 400 m/s
Recoil velocity of gun (V) = ?
Initially, the system (gun + bullet) is at rest, so initial momentum is zero. By conservation of momentum:
0 = m v + M V
V = - (m v) ÷ M
V = - (0.01 × 400) ÷ 8
V = - 4 ÷ 8 = -0.5 m/s
Answer:
The recoil velocity of the gun is 0.5 m/s backward (opposite to the bullet’s motion).
Real also: Light-Reflection and Refraction class 10 (Part-1)
Read also: Light-Reflection and Refraction class 10 (Part-2)

Practice Numerical:

1) What magnitude of net force is required to give a 135 kg refrigerator an acceleration of magnitude 1.40 m/s² (Answer : 189 N)

2) Determine the acceleration that result when a 12 N net force is applied to a 3 kg object and then to a 6 kg object. (Answer : 4 m/s² and 2 m/s²)

3) There are cars with masses 4 kg and 10 kg respectively that are at rest. The car having the mass 10 kg moves towards the east with a velocity of 5 m/s. Find the velocity of the car with mass 4 kg with respect to ground. (Answer : -12.5 m/s)

4) Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m/s and 1 m/s respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. determine the velocity of the second object. (Answer : - 1.165 m/s)

5) From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an velocity of 35 m/s. Calculate the recoil velocity of the rifle. (Answer : 0.4375 m/s)

6) A bullet is fired from a gun of 15 kg with a velocity of 100 m/s, if mass of the bullet is 50 g, what will be the velocity of the gun and in which direction. (Answer : 0.333 m/s)

7) A bullet of mass 40 g is fired from a gun of mass 10 kg, if velocity of bullet is 400 m/s then the recoil velocity of the gun will be: (Answer : 1.6 m/s)

8) When a bullet of mass 50 g is fired from a gun of mass 10 kg, the gun recoils with a velocity 2 m/s. Find the muzzle velocity of the bullet. (Answer : 400 m/s)

9) Find the velocity of a bullet of mass 5 gram which is fired from a pistol of mass 1.5 kg, the recoil velocity of the pistol is 1.5 m/s. (Answer : 450 m/s)

10) A bullet is fired from a gun with a velocity of 600 m/s, the recoil velocity of the gun is 3 m/s. What is the ratio of the mass of the gun and bullet? (Answer : 200:1)

Conclusion:

अंत में, Force and Laws of Motion अध्याय का अध्ययन छात्रों के लिए अत्यंत आवश्यक है, क्योंकि यह भौतिकी की मजबूत नींव तैयार करता है। नोट्स, सूत्रों और सॉल्व्ड न्यूमेरिकल्स का नियमित अभ्यास करने से छात्रों की अवधारणाएँ स्पष्ट होती हैं और समस्या-समाधान क्षमता में सुधार होता है। निरंतर अभ्यास और सही समझ के साथ छात्र इस अध्याय में अच्छी पकड़ बना सकते हैं और परीक्षा में उत्कृष्ट प्रदर्शन कर सकते हैं।

Read also: New way of Education

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Comments

SarthakAugust 22, 2025 at 8:57 AM
Explain the ans of practice numericals of force and laws of motion
SarthakAugust 22, 2025 at 8:58 AM
Determine the acceleration that result when a 12 N net force is applied to a 3 kg object and then to a 6 kg object. (Answer : 4 m/s2 and 2 m/s2)