CBSE Science Notes & Video lectures Class 9 | Force and Laws of Motion Class 9

Force and Laws of Motion

When we want to open a door, we have to push the door handle. And when we want to close the door, we have to pull the door handle with our hand. This means that to move a body, it has either to be pushed or pulled. A push or pull on a body is called force. The direction in which a body is pushed or pulled is called the direction of the force.

➤ Force is that cause that produces acceleration in the body on which it acts.

Effects of force

A force cannot be seen. A force can be judged only by the effects which it can produce in various bodies (or objects) around us. A force can produce the following effects.

1. A force can move a stationary body.

2. A force can stop a moving body.

3. A force can change the direction of a moving body.

4. A force can change the speed of a moving body.

5. A force can change the shape (and size) of a body.

A force is an influence that tends to set a stationary body in motion or stop a moving body; or which tends to change the speed and direction of a moving body; or which tends to change the shape (and size) of a body.

Balanced and Unbalanced Forces.

➤ If a set of forces acting on a body produces no acceleration in it, the forces are said to be balanced. If it produces a nonzero acceleration, the forces are said to be unbalanced.

If two forces balance each other, they must be in opposite directions and have equal magnitudes.  

Some common forces

a) Contact forces

b) Normal forces

c) Friction

d) Forces exerted by spring 

e) Forces exerted by a string

f) Weight

a) Contact forces

When body A is in contact with another body B then A can exert a force on B and B can exert a force on A. These forces are called contact forces. Push or pull exerted by a person, forced by the wind, force exerted by a load on the head of a porter, etc are examples of contact forces. 

b) Normal forces

If the contact forces between forces two bodies are perpendicular to the surfaces in contact, the forces are called the normal force. 

Newton has given three laws to describe the motion of bodies. These laws are known as Newton's laws of motion. Newton's laws of motion give the precise definition of force and established a relationship between the force applied to a body and the state of motion acquired by it.

 Newton's First Law of Motion

According to Newton's first law of motion: A body at rest will remain at rest, and a body in motion will continue in motion in a straight line with uniform speed unless it is compelled by an external force to change its state of rest or of uniform motion.

The inability of a body to change on its own its state of rest or of uniform motion is known as inertia. Inertia is that property of a body due to which it resists a change in its state of rest or of uniform motion.

Inertia may be thought of as having two forms: the inertia of rest, due to which a body at rest remains at rest, and inertia of motion, due to which a moving body keeps moving without any change in its velocity.

Mass is a measure of the inertia of a body. If a body has more mass, it has more inertia. That is heavier objects have more inertia than lighter objects.

 Examples of Newton's First Law

a) Inertia of rest If we keep a body at rest at a place, it remains there for any length of time if no force is applied to it.

b) Jerks while traveling When we stand on a bus and the bus starts suddenly, we tend to fall backward. This is because our feet are in contact with the floor of the bus and the friction at the contact is high. This force does not allow the feet to sleep on the floor. The feet, therefore move forward with the floor. The upper part of the body does not feel the forward force immediately and remains at rest for a while. So, the upper part of our body gets jerked backward.

Similarly, when the bus stops suddenly, the feet come to rest immediately, but the upper part of the body continues to move in the forward direction. So, we tend to fall forward.  We also tend to fall sideways when the bus turns sharply. This is because the feet turn with the floor, but the upper part of the body continues to move for a while in the original direction.

Initially, there are two forces on the coin. The earth pulls the coin downwards (weight) and the card pushes it upwards (normal force). The forces balance each other and the coin remains at rest.

When we apply a horizontal force on the card, it is accelerated and it moves away. Since the friction between the card and the coin is negligible, there is no force on the coin in the horizontal direction.  It remains in its original position due to the inertia of rest. 

Newton's Second Law of Motion

`F_1` produces an acceleration of  `5ms^-2` and `F_2` produces an acceleration of  `10ms^-2`

in the same body then,   

`F_2 = 2F_1`  (mass fixed)

Suppose we apply a force `F_1` on a body of `2kg` which produces an acceleration of of `5ms^-2`. To produce same acceleration in a `4kg` body, we have to apply a force twice as strong as `F_1`.   

`F_2 = 2F_1`   (a is fixed)

👉  The magnitude of the net force acting on a body is proportional to the product of the mass of the body and its acceleration. The direction of the force is the same as that of the acceleration.

If we denote the magnitude of the force by F and acceleration by a,

          

`F\propto a`  (i)

Mass m is fixed.

Producing the same acceleration in two objects of unequal masses. Then,

`F\propto m`     (ii)

Here, acceleration is constant.

From (i) & (ii)

`F\propto ma`

F = kma

Where k is a constant.

Linear Momentum

👉The product of the mass of a body and its velocity is called the linear momentum of the body.  Quite often we only use the word momentum for linear momentum.

If m be mass and v be the velocity, the linear momentum p is 

`p = mv`

A bullet fired at a wooden board can destroy it. But a small stone of the mass as the bullet when thrown at the board will hardly cause any damage. Although their masses are the same, the high velocity of the bullet gives it a large momentum, which causes damage.

 Newton's Second Law in terms of Momentum

👉The rate of change of momentum of an object is proportional to the net force applied to the object. The direction of the change of momentum is the same as the direction of the net force.

Suppose the linear momentum at time `t_1` is `p_1` = `mv_1` and that at time `t_2` is `p_2` = `mv_2`

The rate of change of momentum is `\frac{p_2-p_1}{t_2-t_1}` or `\frac{\triangle p}{\triangle t}`

According to the second law  `\frac{p_2-p_1}{t_2-t_1}\propto F`

`F=k\frac{p_2-p_1}{t_2-t_1}`

where k is constant

`F=k\frac{mv_2-mv_1}{t_2-t_1}`

`F=km\left(\frac{v_2-v_1}{t_2-t_1}\right)`

 or  `F=km\left(\frac{\triangle v}{\triangle t}\right)`

`F= kma`

If a force acting on a body of mass 1 kg produces an acceleration of 1 `ms^{-2}` in it, the force is called one Newton.

If we substitute F =1N, m = 1kg, a = 1 `ms^{-2}` in equation  F = kma  we get k = 1 then becomes 

`F = ma`

This equation is taken to be the statement of Newton's second law in the mathematical form.

Note that unit 'Newton' is identical to kg `ms^{-2}`. The Newton is denoted by N. It is the SI unit of force.  

With the definition of the Newton, we got k = 1,

The equation `

                                           `F=k\frac{p_2-p_1}{t_2-t_1}` then becomes 

`F=\frac{p_2-p_1}{t_2-t_1}` or  `\frac{\triangle p}{\triangle t}`

The second law of motion is often seen in action in our everyday life.

Catching a fast-moving cricket ball, a fielder in the ground gradually pulls his hands backward with the moving ball.

If the ball is stopped suddenly then its high velocity decreases to zero in a very short interval of time. Thus, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.

Third Law of Motion

👉To every action, there is an equal and opposite reaction and they act on two different bodies. 

These two forces are always equal in magnitude but opposite in direction.

The two opposing forces are also known as action and reaction forces.

It is important to note that even though the action and reaction forces are always equal in magnitude, these forces may not produce accelerations of equal magnitudes. This is because each force acts on a different object that may have a different mass.

When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite force on the gun. This results in the recoil of the gun. Since the gun has a much greater mass than the bullet, the acceleration of the gun is much less than the acceleration of the bullet.

Conservation of Momentum

👉In an isolated system (where there is no external force), the total momentum remains conserved.

Suppose two objects (two balls `A` and `B`, say) 

Before collision

Let the masses be `m_A` and `m_B`

Let the velocities be `u_A` and `u_B`

and `u_A > u_B`

After collision 

Let the velocities be `v_A` and `v_b`

Two forces are `F_{AB}` and `F_{BA}`

The rate of change of its momentum (or `F_{BA}`) during the collision will be 

`F_{BA} =m_A \frac {(v_A-u_A)}{t}`

Similarly 

`F_{AB} =m_B \frac {(v_B-u_B)}{t}`

According to the third law of motion, the force `F_{AB}` exerted by ball `A` on ball `B` and the force `F_{BA}` exerted by the ball `B` on ball `A` must be equal and opposite to each other. Therefore, 

`F_{BA} = -F_{AB}`

or   `m_A \frac {(v_A-u_A)}{t} =  m_B \frac {(v_B-u_B)}{t}`

`m_A u_A + m_B u_B  =  m_A v_A + m_B v_B` 

Since `(m_A u_A + m_B u_B )` is the total momentum of the two balls `A` and `B` before the collision and `(m_A v_A + m_B v_B )` is their total momentum after the collision, we observe that the total momentum of the two balls remains unchanged or conserved provided no other external force acts.

References

1. S. Chand Class IX physics 
2. Foundation Science  Physics Class IX 
3. NCERT Science Class IX