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Force and Laws of Motion

CBSE Class 9 Science • Chapter 8 • Detailed Master Notes

Chapter Overview:

Force is an external effort in the form of push or pull. It can change state of motion, shape, or direction. This chapter explains Isaac Newton's three laws of motion, Inertia, Momentum, and the Principle of Conservation of Momentum.

1. Balanced and Unbalanced Forces

Balanced Forces: Resultant force is zero. Equal and opposite. Do not change state of motion. Can change shape.
Unbalanced Forces: Resultant is non-zero. Causes acceleration (change in speed/direction).

2. First Law of Motion (Law of Inertia)

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 force.

Inertia: The natural tendency of an object to resist a change in its state of motion or rest. Mass is measure of inertia.

Real Life Examples:

Falling backward: When a bus starts suddenly, our feet move forward with bus but upper body remains at rest due to inertia.
Falling forward: When a moving bus brakes, feet stop but upper body continues to move forward.
Dusting carpet: Beating carpet moves fibres, dust remains at rest due to inertia and falls off.

3. Second Law of Motion

The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.

Momentum ($p$): Product of mass and velocity. $p = mv$. SI unit: $kg m/s$.

Mathematical Formulation:

Force $\propto$ Rate of change of momentum.
$F \propto \frac{p_2 - p_1}{t}$
$F \propto \frac{mv - mu}{t}$
$F \propto m (\frac{v - u}{t})$
$F = kma$. (Putting $k=1$).

$$ F = ma $$

Force = Mass $\times$ Acceleration. SI Unit: Newton ($N$).

Application: A cricket player lowers his hands while catching a ball to increase time of impact ($t$). Since $F \propto 1/t$, increasing time reduces the force exerted by the ball on hands, preventing injury.

4. Third Law of Motion

To every action, there is an equal and opposite reaction.

Action and Reaction act on two different bodies.
They act simultaneously.

Examples:

Walking: We push ground backward (Action), ground pushes us forward (Reaction).
Gun Recoil: Gun exerts force on bullet (Action), bullet exerts equal force on gun (Recoil).
Rocket Propulsion: Exhaust gases pushed down (Action), Rocket pushed up (Reaction).

5. Conservation of Momentum

In an isolated system (no external unbalanced force), the total momentum remains conserved.

Derivation:

Two balls A and B with masses $m_A, m_B$ and velocities $u_A, u_B$ collide.
After collision, velocities are $v_A, v_B$.
Force by A on B ($F_{AB}$) = Force by B on A ($-F_{BA}$) (3rd Law).
$m_B \frac{v_B - u_B}{t} = - m_A \frac{v_A - u_A}{t}$
$m_A u_A + m_B u_B = m_A v_A + m_B v_B$

$$ \sum p_{\text{initial}} = \sum p_{\text{final}} $$

Practice Zone

Q1: A force of 5 N gives a mass $m_1$ an acceleration of $10 m/s^2$ and mass $m_2$ an acceleration of $20 m/s^2$. What acceleration would it give if both masses were tied together?

Ans: $m_1 = F/a_1 = 5/10 = 0.5 kg$. $m_2 = F/a_2 = 5/20 = 0.25 kg$.
Total mass $M = 0.75 kg$.
New acceleration $a = F/M = 5 / 0.75 = 6.67 m/s^2$.