Class 9th || Science || Notes || Chapter 9: Force and Laws of Motion

Introduction to Force

A force is a push or pull acting upon an object. Force can cause an object to move, stop, or change its velocity (speed and direction). Force can also change the shape of an object. It is a vector quantity, meaning it has both magnitude and direction.

• Unit of Force: The SI unit of force is the Newton (N).
• Formula: $$\text{Force}=\text{mass}\times \text{acceleration}$$
• $$F=m\times a$$

Effects of Force

• Force can change the speed of an object.
• Force can change the direction of motion.
• Force can change the shape of an object.
• Force can cause an object to start or stop moving.

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Balanced and Unbalanced Forces

1. Balanced Forces:

   • When two or more forces acting on an object cancel each other out, the object does not move, or it remains in a state of uniform motion.
   • In the case of balanced forces, the net force acting on an object is zero.
   • Example: A book resting on a table experiences balanced forces (gravity pulling it down and the table pushing it up).

2. Unbalanced Forces:

   • When the forces acting on an object do not cancel each other out, the object accelerates or changes its state of motion.
   • The net force is not zero in the case of unbalanced forces.
   • Example: If you push a book on a table, it starts moving because the applied force is unbalanced.

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Newton’s Laws of Motion

Sir Isaac Newton formulated three fundamental laws that describe the relationship between force and motion. These laws explain how objects behave when forces are applied.

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

• Statement: An object remains in a state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.

• Explanation: Objects do not change their state of motion (whether at rest or moving uniformly) on their own. It requires an external force to bring about a change.

• Inertia: The tendency of an object to resist changes in its state of motion is called inertia. The greater the mass of an object, the greater its inertia.

  • Examples:
    • A book lying on a table will remain at rest unless you push it.
    • A car in motion continues moving forward even when you turn off the engine, until friction or another force slows it down.

Newton's Second Law of Motion (Law of Force and Acceleration)

• Statement: The force acting on an object is equal to the mass of the object multiplied by its acceleration.

  $$F=m\times a$$

  Where:

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

• Explanation: The second law relates the net force acting on an object to its mass and the acceleration produced. This means that for a given mass, the greater the force applied, the greater the acceleration. Similarly, for the same force, a heavier object will have less acceleration than a lighter one.

  • Examples:
    • Pushing a heavy box requires more force to achieve the same acceleration as pushing a lighter box.
    • A car accelerates faster when more force is applied by pressing the accelerator pedal.

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

• Statement: For every action, there is an equal and opposite reaction.

• Explanation: When one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first object. These forces are called action and reaction forces, and they always occur in pairs.

  • Examples:
    • When you jump off a boat, the boat moves backward (reaction) while you move forward (action).
    • A rocket propels forward by expelling gas backward. The backward force of the gas is the action, and the forward movement of the rocket is the reaction.

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Inertia and Mass

• Inertia: The tendency of an object to resist any change in its state of motion.
  • Inertia of Rest: A body at rest will remain at rest until an external force is applied. Example: A stationary car will not move unless you push it.
  • Inertia of Motion: A moving body will continue moving in a straight line with uniform speed unless a force acts on it. Example: A moving bus continues to roll forward when the engine is turned off.
• Mass: The quantity of matter in an object. It is also a measure of an object's inertia. A larger mass means greater inertia and requires more force to change its state of motion.

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Momentum

Momentum is the quantity of motion an object possesses. It is the product of an object’s mass and velocity.

• Formula: $$\text{Momentum}=\text{mass}\times \text{velocity}$$
• $$p=m\times v$$
• Where:
  • $p$ is momentum,
  • m is the mass of the object (in kg),
  • $v$ is the velocity (in m/s).
• SI Unit: kilogram meter per second (kg·m/s).

Law of Conservation of Momentum

• Statement: In an isolated system (where no external forces are acting), the total momentum before and after an event (such as a collision) remains constant.

• Explanation: When two or more objects interact (e.g., collide), their total momentum before the interaction is equal to their total momentum after the interaction, provided no external forces act on them.

  • Example: When two billiard balls collide, the total momentum of both balls before and after the collision remains constant.

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Applications of Newton’s Laws of Motion

1. Seatbelts and Car Safety:

   • Inertia explains why passengers in a moving vehicle continue to move forward when the vehicle suddenly stops. Seatbelts apply an external force to stop the passengers and prevent injury.

2. Rockets and Spacecrafts:

   • Rockets rely on Newton’s third law of motion. The action force is the expulsion of gases from the rocket’s engine, and the reaction force propels the rocket forward.

3. Sports and Momentum:

   • In sports like cricket or football, players try to reduce the impact by moving their hands or body backward while catching or receiving the ball. This increases the time of contact and reduces the force, minimizing injury.

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Numerical Problems in Force and Motion

1. Example Problem 1:
   • A car has a mass of 1000 kg and accelerates at 2 m/s². What is the force required?
   • Solution:
     Using $F=m\times \mathrm{a,}$
     $F=1000\text{kg}\times 2{\text{m/s}}^2=2000\text{N}$.
2. Example Problem 2:
   • A ball of mass 0.5 kg is moving with a velocity of 10 m/s. What is its momentum?
   • Solution:
     Using $p=m\times v$,
     $p=0.5\text{kg}\times 10\text{m/s}=5\text{kg}\text{m/s}$