**CBSE NOTES CLASS 9 SCIENCE CHAPTER 9**

**FORCE AND LAWS OF MOTION**

**Force**

A pull or a push is called force.

**Effects of Force**

- Force can make a stationary object move.
- It can stop a moving object.
- It can change the speed of a moving object.
- It can change the direction of a moving object.
- It can change the shape or size of an object.

**Balanced and Unbalanced force - Net Force**

- If two forces are acting on an object in the same direction,
Net force or the resultant force F = F

_{1}+ F_{2}Direction of resultant force will be in the same direction as the original forces.

- If two forces are acting on an object in the opposite direction,
Net force or the resultant force F = F

_{1}- F_{2}Direction of resultant force will be in the direction of the larger force.

- A body is supposed to be under
**unbalanced force**if the net force is not equal to zero.

**Galileo’s Experiment**

Take two smooth frictionless inclined planes arranged as shown. A marble is released from the top of one of the inclines.

When a marble is released from left, it would roll down the slope and go up on the opposite side to the same height from which it was released.

If the inclinations of the planes on both sides are equal then the marble will climb the same distance that it covered while rolling down.

If the angle of inclination of the right-side plane were gradually decreased, then the marble would travel further distances till it reaches the original height.

If the right-side plane were ultimately made horizontal (that is, the slope is reduced to zero), the marble would continue to travel forever trying to reach the same height that it was released from. The unbalanced forces on the marble in this case are zero.

**Conclusion**

An unbalanced (external) force is required to change the motion of an object but no net force is needed to sustain the uniform motion.

In practice it is not so due to presence of frictional force acting opposite to the direction of motion.

**NEWTONS LAWS OF MOTION**

**Newton’s First Law or Law of Inertia**

Every object continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.

Or

If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body.

**Inertia **

The property by virtue of which a body opposes any change in its state of rest or of uniform motion is known as inertia.

Greater the mass of the body greater is the inertia. That is mass is the measure of the inertia of the body.

If F = 0; u = constant (In the absence of external applied force velocity of body remains unchanged.)

**Examples of Inertia (Explain)**

- When brakes are suddenly applied to a moving vehicle, passenger’s head gets jerked in the forward direction. With the application of brakes, the vehicle slows down but our body tends to continue in the same state of motion because of its
**inertia.** - When a stationery vehicle suddenly starts moving, passenger’s head gets jerked in the backward direction.
- On hitting used mattress by a stick, dust particles come out of it. The mattress moves, but the particles tend to remain in their position.
- In order to catch a moving bus safely we must run forward in the direction of motion of bus.
- Whenever it is required to jump off a moving bus, we must always run for a short distance after jumping on the road to prevent us from falling in the forward direction.
- A spaceship out in interstellar space, far from all other objects and with all its rockets turned off, has no net external force acting on it. If it is in motion, it must continue to move with a uniform velocity.
- Only the carom coin at the bottom of a pile is removed when a fast moving carom coin (or striker) hits it. Other coins tend to remain at rest.
- If we place coin on a stiff card covering an empty glass tumbler and give the card a sharp horizontal flick with a finger, the coin falls in the tumbler. The inertia of the coin tries to maintain its state of rest even when the card flows off.
- Place a water-filled tumbler on a tray. Hold the tray and turn around as fast as you can. The water tends to remain at rest due to inertia and the water spills.

**Linear Momentum**

Momentum, **P **of a body is defined to be the product of its mass m and velocity **v**, and is denoted by **p**,

p = m v

Momentum is a vector quantity. SI unit is kg ms^{-1}

Physical Significance of Momentum

- Much greater force is needed to push a truck than a car to bring them to the same speed in same time. Similarly, a greater opposing force is needed to stop a heavy body than a light body in the same time, if they are moving with the same speed.
- If two stones, one light and the other heavy, are dropped from the top of a building, a person on the ground will find it easier to catch the light stone than the heavy stone. The mass of a body is thus an important parameter that determines the effect of force on its motion.
- A bullet fired by a gun can easily pierce human tissue before it stops, whereas the same bullet fired with moderate speed will not cause much damage. Thus for a given mass, the greater the speed, the greater is the opposing force needed to stop the body in a certain time.
- While catching a ball, cricketers allow a longer time for the hands to stop the ball by drawing the hands backwards in the act of catching the ball.
The greater the change in the momentum in a

**given time**, the greater is the force that needs to be applied.

**Newton’s Second Law of Motion**

The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which force acts.

**Mathematical Formulation of Second Law**

Consider an object of mass **m,** moving along a straight line with an initial velocity **u**. If it is uniformly accelerated to final velocity **v** in time **t;** by the application of a constant force **F** throughout the time **t**.

The initial and final momentum of the object will be, p_{i} = mu and p_{f} = mv respectively.

The change in momentum

p_{f} – p_{i} ∝ mv – mu

Δp ∝ m × (v – u)

$$\mathrm{Rate\; of\; change\; of\; momentum}\propto \mathrm{m}\frac{\left(\mathrm{v}-\mathrm{u}\right)}{\mathrm{t}}$$

$$\mathrm{Or\; the\; applied\; force,\; F}\mathrm{}\propto \mathrm{m}\frac{\left(\mathrm{v}-\mathrm{u}\right)}{\mathrm{t}}$$

$$\mathrm{Or\; F\; =}\mathrm{k}\mathrm{}\mathrm{m}\frac{\left(\mathrm{v}-\mathrm{u}\right)}{\mathrm{t}}=\mathrm{k}\mathrm{}\mathrm{m}\mathrm{}\mathrm{a}$$

Here **k** is a constant of proportionality.

The unit of force has been defined in such a way that **k = 1**.

$$\mathrm{So,\; F\; =}\mathrm{}\mathrm{m}\frac{\left(\mathrm{v}-\mathrm{u}\right)}{\mathrm{t}}=\mathrm{}\mathrm{m}\mathrm{}\mathrm{a}$$

The SI unit force, Newton (**N**) and is equal to that force, which causes an acceleration of **1** **m s**^{-2} to a mass of 1 kg,

i.e. 1 N = 1 kg × 1 m s^{-2}. = 1 kg m s^{-2}

- The second law is consistent with the First law, i.e. F = 0 implies a = 0.
- If v = 0 at an instant, i.e., if a body is momentarily at rest, it does not mean that force or acceleration are necessarily zero at that instant. For example, when a ball thrown upward, reaches its maximum height, its velocity is zero, but the force continues to be equal to its weight
**mg**and the acceleration is**‘g’**, the acceleration due to gravity. - If a body is accelerating under two horizontal forces,
**(**F_{1}> F_{2}**)**,F = F

_{1}- F_{2}=*m a*

**Impulse**

The change in momentum of an object, when a force acts on it for a short duration, is called impulse.

J = p_{2 }- p_{1} = mv – mu

$$\mathrm{F}\mathrm{}=\frac{\mathrm{m}\mathrm{v}\mathrm{}\u2013\mathrm{}\mathrm{m}\mathrm{u}}{\mathrm{\Delta}\mathrm{t}}\mathrm{}\mathrm{}\mathrm{}$$

$$\Rightarrow \mathrm{}\mathrm{}\mathrm{}\mathrm{F}\mathrm{}\mathrm{\Delta}\mathrm{t}\mathrm{}=\mathrm{}\mathrm{m}\mathrm{v}\mathrm{}\u2013\mathrm{}\mathrm{m}\mathrm{u}$$

A large force, acting for a short time to produce a finite change in momentum is called an **impulsive force**.

**Examples of Impulsive Forces **

- Force applied by foot on hitting a football.
- Force applied by boxer on a punching bag.
- Force applied by bat on a ball in hitting it to the boundary.
- While catching a ball a player lowers his hand to save himself from getting hurt.
- A person falling on a cemented floor receives more jerk compared to that falling on a sandy floor.

**Third Law of Motion**

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

Here action refers to the force applied by first body on the second body and reaction refers to the force applied by second body on the first one.

Or

Forces always occur in pairs. Force on a body A by B is equal and opposite to the force on the body B by A.

- There is no cause effect relation implied in the third law. The force on A by B and the force on B by A, act at the same instant.
- Action and reaction forces act on different bodies, not on the same body. Consider a pair of bodies A and B. According to the third law,
**F**_{AB}(force on A by B) = –**F**_{BA}(force on B by A)

**Examples**

- When a bullet is fired from the gun, the gun pushes the bullet forward and the bullet pushes the gun in backward direction (recoil).
- When we push any block in the forward direction then block pushes us in the backward direction with an equal and opposite force.
- Horse pulls the rod attached to the cart in the forward direction and the tension of the rod pulls the cart in the backward direction.
- Earth pulls the body on its surface in vertically downward direction and the body pulls the earth with the same force in vertically upward direction.
- While walking, we push the ground in the backward direction using static frictional force and the ground pushes us in the forward direction using static frictional force.
- When a person sitting on the horse whips the horse and horse suddenly accelerates, the saddle on the back of the horse pushes the person in the forward direction using static frictional force and the person pushes the saddle in the backward direction using static frictional force.

**Principle of Conservation of Momentum**

The total momentum of an isolated system of interacting particles is conserved.

Or

When two bodies collide, the total momentum of the system before the collision is equal to the total momentum of system after the collision,

**Proof**

Consider two bodies A and B, with initial velocities **u**_{A} and **u**_{B}. The bodies collide for a duration of time Δt and get apart, with final velocities **v**_{A} and **v**_{B }respectively.

By the second Law

F_{AB }= m_{A}(v_{A} – u_{A})/Δt

and

F_{BA }=_{ }m_{B}(v_{B} – u_{B})/Δt

By third law, **F**_{AB}** = −F**_{BA}, we have

m_{A}(v_{A} – u_{A})/Δt = - m_{B}(v_{B} – u_{B})/Δt

This could also be written as,

m_{A}u_{A }+ m_{B}u_{B }= m_{A}v_{A} + m_{B}v_{B}