9TH

Force and laws of motion:-

Force:- To move a body we have to apply either a pull or push. This pull or push on a body is called force.

Force is an effort which makes the stationary objects move or moving objects stop. Force is needed in almost
all kinds of activities. Behind every motion or change in motion, a force is involved. It means force is the cause
of motion. We cannot see the force, but we feel it from its effect on the objects.

Effects of force:-

• Force can stop a moving body

Balanced and unbalanced forces:-

Balanced forces:- If the resultant of all the forces acting on a body is zero, then the forces are known as
balanced forces. If a number of balanced forces act on a body having uniform motion, then the body remains in
the uniform motion. Balanced forces do not change the state of rest or the state of uniform motion of a body.
Balanced forces can change the shape and size of a body.

Unbalanced forces:-If the net /resultant force/ total force of a number of forces acting on a body is not zero,
then the forces are known as unbalanced forces. Unbalanced forces can move a stationary object. Unbalanced
forces can change the velocity of a body.

Newton`s first law of motion:- Bodies at rest remain at rest and bodies in motion remain in motion until some
external force is applied on them. This behaviour of bodies at rest or in motion inspired Newton to formulate
his first law of motion.

According to Newton`s first law of motion, “ A body at rest will remain at rest and a body in uniform motion will
continue to move in a straight line with constant speed until and unless some external unbalanced force is
applied on it.”

Inertia:- Property of the body to resist any change in its state is termed as inertia. Inertia can also be defined as
the inability of a body to change its state of rest or of uniform motion in a straight line on its own. Newton`s
first law points towards this property (inertia) of a body. Hence, Newton`s first law of motion is also known as
`law of inertia`.

Mass is the measure of inertia:- Inertia of a body is measured by the magnitude of the force required to
change the state of the body. If a body is heavy, larger force is required to change its state and hence, greater is
its inertia. So mass of a body is the measure of its inertia. A 100 kg stone has more inertia than the 10 kg stone.
More fore is required to move a 100 kg stone than to move a 10 kg stone.
Types of Inertia

Inertia of a body is of three types-

1. Inertia of rest
2. Inertia of motion
3. Inertia of direction
Inertia of rest
It is the tendency of a body to oppose any change in its state of rest, or it is the inability of a body to change its
state of rest on its own.
Examples
• When a bus starts suddenly from rest, then the passengers tend to fall backwards. This is because the
sudden start of bus brings motion in the bus as well as in the feet of passengers as they are in contact
with the floor of the bus. But the upper part of the body opposes this motion due to inertia of rest and
wants to be in the previous state and hence the passengers tend to fall backwards on the sudden start
of the bus.
• When a carpet is beaten with stick, the dust particles in it come out. It is because on hitting, the carpet
comes in motion and moves backwards while the dust particles remain at rest due to inertia of rest and
hence, falls down.

Inertia of motion

It is the tendency of a body to oppose any change in its motion or it is the inability of a body to change its
speed on its own. It means if a body is moving with a constant speed, then the body wants to move with the
same speed and opposes any change in its speed.

Examples

• When a moving bus stops suddenly, the passengers in the bus tend to fall forward. It is because on
applying brakes the bus stops but the upper part of the body of the passengers still remains in motion
due to inertia of motion and hence, tends to fall forwards.
• When sudden brakes are applied to a fast moving bike, then the rider falls forwards because of inertia
of motion.
Inertia of direction
It is the tendency of a body to oppose any change in its direction of motion, or it is the inability of a body to
change its direction of motion on its own. It means a body wants to move in one direction only. We have to
apply some external force to change the direction of motion of the body.
Examples
• The sparks produced when knife is sharpened against a grinding wheel go tangentially to the rim of
wheel due to inertia of direction.
• When a bus or a car takes a sharp turn, then we tend to fall outwards. It is because when the car takes a
turn its direction of motion changes, but due to inertia of diretion we try to maintain our direction of
motion and feel to be thrown outwards.
Momentum:- The amount of motion contained in a moving body is known as momentum. The force required
to stop a moving body is directly propotional to the mass of that body, and also directly proportional to the
velocity of the body. Thus, the quantity of motion in a body is directly proportional to the mass and velocity of
that body. So the momentum of a body is equal to the product of its mass and velocity. If p is the momentum,
v is the velocity and m is the mass of a body, then momentum is defined as

p = mv

Momentum of a body is given by the product of mass and velocity of the body. Momentum is a vector quantity.

Unit of momentum=unit of mass×unit of velocity

Unit of momentum=kg×m/s=kgms-1

If a body is at rest, then v=0 and hence, linear momentum, p=mv=0. It means a body at rest does not possess
any momentum.

Newton`s second law of motion:-

According to newton`s second law of motion,’’The rate of change of linear momentum of a body is directly
proportional to the applied unbalanced force on the body in the direction of the net force.’’

External force applied α change in linear momentum/time taken

It means if a larger force is applied on a body, then rate of change of linear momentum will be larger. If F is the
external force applied, dp is the small change in linear momentum and dt is the small time taken for that
change, then

Fαdp/dt

F=kdp/dt

K is the constant of proportionality.

In SI unit the value of k=1.

F=dp/dt .........1

Mathematical relation for Newton`s second law of motion:-

Let a body of mass `m` be moving with an initial velocity `u`. If an external force `F` is applied on it, then its final
velocity becomes `v` after time `t`.

Now,

Initial momentum of the body p1 =mu

Change in momentum of the body = p2 - p1 = mv- mu =m(v-u)

Rate of change of momentum of the body = m(v-u)/t .......2

We know that, (v-u)/t = a (acceleration)

Using this in equation (2), we get

Rate of change of linear momentum of the body=ma......3

From Newton`s second law of motion,

Rate of change of linear momentum= Applied force(F).......4

Thus, from equation 3 and 4 we have

Force=mass×acceleration=ma........5

Mathematical relation of Newton`s second law of motion F =m(v-u)/t ...... 6

Also F=ma

Therefore, a=F/m

It means that the acceleration produced in a body is directly proportional to the force aplied on it and inversely
proportional to the mass of the body. If the same amount of force is applied on two bodies of different masses,
then the acceleration produced will be less in the heavier body and more in the lighter body.

Unit of force:-

F=ma

Unit of force=Unit of mass×Unit of acceleration=kgm/s 2

Unit of force= kgm/s2. This unit is known as newton

SI unit of is newton which is represented by N.

It is a vector quantity.

One newton is that force which when applied on a body of mass 1 kg produces an acceleration of 1ms -2 in it. In
CGS system of units,`dyne` is the unit of force.

1 dyne= 1g×1cms-2

1 dyne is that force which when applied on a body of mass 1g produces an acceleration of 1 cms -2 in it.

Relation between newton and dyne:

1 newton=1000g×100cms-2

1 newton=105 gcms-2

1 newton=105 dyne

Applications of Newton`s second law of motion:-

From Newton`s second law of motion,

F =m(v-u)/t

In some practical situations we have to reduce large momentum of a body suddenly. It would lead to a large
force which may cause injury or damage. To pevent this, the time taken to reduce the momentum of body is
increased, due to which, the amount of force acting on the body decreases.

Examples

• The momentum of a fast moving ball is large. In catching the ball the momentum of ball has to be
reduced to zero. When a cricketer lowers his hands while catching the ball, then the time taken to
reduce the momentum of the fast moving ball increases. The force exerted by the ball on the hands of
the player decreases. Thus, the hands of the player do not get hurt.
• The use of seat belts in a car prevents injuries to the passengers in case of an accident or in case of
sudden application of brakes. It is because when car stops suddenly in an accident or in case of an
emergency brake, the belt worn by the passenger of the car increases the time of fall of the passenger
forward. Due to this the rate of change of momentum of the passenger reduces. Hence, the passenger
may not get injured due to less force acting on him.

Newton`s third law of motion:-

According to Newton`s third law of motion, ‘’ When a body applies some force on another body, then the
second body also applies equal force on the first body but in opposite direction simultaneously.’’ It means that
the forces between two bodies are equal in magnitude but opposite in direction. One force is called action and
the other force is called reaction.

Newton`s third law of motion may also be stated as, ‘’To every action there is an equal and opposite reaction.”

Examples of Newton`s third law of motion

• When we walk on the ground, we push the ground backwards. This force of push is action.
Simultaneously, the ground applies an equal and opposite force on our feet, this force is reaction. It is
the force of reaction of the ground on us which enables us to walk on the ground.
• During swimmimg, a person pushes the water backwards, by hands (action). Simultaneously, the water
applies an equal force(reaction) in forward direction which enables the person to swim.
• When a ball hits the floor, it applies force(action) on the floor. Simultaneously, the floor exerts equal
reaction force on the ball which enables it to bounce upward.