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change
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Force
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(iü) Force can change the direction of motion of an
object.
(iv) Force can change the shape of an object.
Inertia
The inherent property ofa material body by virtue of
which it remains in its state of rest or of uniform motion in
astraight line. This term was first used by Galileo.
Thevarious types of inertia are as below
(0) Inertia of Rest
It is defined as the tendency of a body to remain in its
position of rest.
C.g. A person standing in a train flls backward when
the train suddenly starts moving forward. It depicts,
when train moves, the lower part of his body beginsto
move alongwith the train while the upper part of his
body continues to remain at rest due to inertia.
() Inertia of Motion
Ir is defined as the tendency of a body to remain in its
state of uniform motion in a straight line.
ce. When a moving bus suddenly stops or apply brakes,
e-g.
aperson standing in it falls forward. As the bus stops, the
lower part of his body comes to rest alongwith the bus
while upper part of his body continues to remain in
motion due to inertia and falls forward.
(ii) Inertia of Direction
It is defined as inability of a body by virtue of which it
tries to resist the change in its direction of motion.
C.g. An umbrella protects us from rain.
The rain drops falling vertically downwards cannot
change their direction of motion and wet us, with the
umbrella on.
Newton's Lows of Motion
Sir Isaac Newton (1642-1727) made a systematic study
of motionof bodies. He arrived at three laws of motion
which are called Newton's laws of motion. These laws
are as follows

Newton's First Law of Motion

This law states that every body continues in its state of
rest or of uniform motion in astraight line unless it is
compelled by some external force to change that state.
Momentum
Momentum of a body is defined as mass in motion
along a straight line path. The amount of
omentum depends on the mass and the velociry of
the body. So, numerically it is the product of it
mass m and velocity v and is denoted by P.
Momentum, p = mv
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Newton's Second Law of Motion
This law states that the rate of change of momentum
of a body is directly proportional to theexternal force
applied on the body and the change takes place in the
direction of the applied force.
 Let F be external force applied on the body in the
direction of motion of the body for time
interval At.
then the velocity of a body of mass mchanges from v
- Av, i.c. change in momentum Ap= mAv.
to v +,
According to Newton's second law.
Foc Ap or Fk Ap

where. k is a constant of proportionality.

If limit A ’0, then the term Ap becomes the

derivative
dp
di
Thus, F=k dp
dt
For a bodyof fixed mass m, we have
d (mv) = km dy
F=k
dt dt
du
F= kma - = a
dt
Let, k=1
So, Force, F= ma
In scalar form, this equation can be written as
F= ma
:.l unit force = I unit mass xl unit acceleration
A unit force may be defined as the force which
produces unit acceleration in a body of unit mass.
Units of Force
" Ihe force is a vector quantity and its SI unit is
newton (N).
One newton is defined the force which produces an
acceleration of l m/s in a body of mass 1 kg.
1N=1kg x l ms
1N=1kg m/s
Impulse
The larger force which acts on an object for a very
short time producing a finite change in momentum of
theobject is called impulsive force. Hence, impulse of
aforce is defined as the product of the average force
and the time interval for which the force acts on the
body. It is denoted by I.
Thus, Impulse = Average force x time
Impulse is a vector quantity. The direction of impulse
1S same as that of the force.
Its SI unit is newton-second (N-s).
Its dimensional formula is (MILT)
Expression for an Impulse
Consider a constant force F which acts on a body for
time dt. The impulse is given by
dI = Fdt
If the force acts on the body for a time interval from
to t,, the impulse is given by
I= [dl= Fd
IfF, is the average force, then
I=F av dt = F, (t?
 Impulse, I =F, At
According to Newton's second law of motion,
F= dp ’ Fdr = dp
dt
Integrating both sides with limits, we get
P2
[Fd = | dp PI

FXt= P2-P1
|Impulse, I=P:-P1
Thus, the impulse of a force is equal to the total change
in momentum produced by the force.
EXAMPLE6. Abatsman hits back aball straight in the
direction of the bowler without changing its initial speed
of 12 m/s. If the mass of the ball is 0.15 kg, determine the
impulse imparted to the ball. (Consider a ball in linear
motion). (NCERT)
Sol Given, m =0.15 kg, v=12 m/s,u=-12 m/s
Change in momentum = p, -p, = m[v- u]
=0.15 (12- (- 12)) =0.15x 24
P2 -Pi =3.60 kg-m/s
Impulse, I=P2 P1 ’ I=3.6 N-s
Newton's Third Law of Motion
Newton's third law states that for every action, there is
always an equal and opposite reaction.
In simple terms, the third law can be stated as follows
Force in nature always occurs in pairs. Force on body
Abybody B is equal and opposite to the force on
the body B by A.
Some important implications about the third law of
motion
(i) Newton's third law of motion is applicable
irrespective of the nature of the forces. The
forces of action and reaction may be mechanical.
gravitational, electric or of any other nature.
(ii) Action and reaction always act on two different
bodies If they acted on the same body, the
resultant force would be zero and there could
never be accelerated motion.
(ii) The force of action and reaction cannot cancel
cach other This is because action and reaction,
though equal and opposite forces always act on
different bodies and so cannot cancel each other.
(iv) No action can occur in the absence of a reaction
In atug of war, one team can pull the rope only
if the other team is pulling the other end of the
rope, no force can be exerted if the other end is
free.
One team can exert the force of action because
the other team provides the force of reaction.
(i) Rotatory lawn sprinkler The action of rotatory
lawn sprinkler is based on third law of motion.
As water forces way of the nozzle, it exerts an
equal and opposite force in the backward
direction, causing the sprinkler to rotate in the
opposite direction. Thus,water is scattered in all
directions as shown in following figure.

Water Rotatory lawn sprinkler

Explonation of Conservation of Momentum
Let us consider the momenta of two particles system of
masses m, and m, arep, and p, respectively, then the
net momentum of the whole system
P=Pt P: ...()
Suppose E and F, are two forces acting on particles of
masses mand m,. Let in aasmall time interval At, the
change produced by the forces F, and F, are Ap, and
Ap,.
Thus, net change in momnentum
Ap = Ap, + Ap,
Ap_ Ap,+ Ap,
At At At
or dp dpi P2
dp, (as
ArAt ’0]
dt dt dt
or dp =F, +E, ...(i1)
dt
where, F, =}ex tFint
and F, =Fzet +Fzint
dp = (F ex tFint)+ (F,ext t F2int)
dt
dp
or
dt
= (Fexx tF2)t Fint t Fzin) ....(ii)
From Newton's third law, the internal forces always
Occur in pair so
(F in t Fio)=0
or
(F int =- Fzin,)
From Eg. (i1), we get
Thus, dp
dt
=(-Fzin, + Fin)t( Ee + Fe)
dp
or
dt
=0+ F, +F;eu or dp =Ft
dt
where, F=Ea t+Fa Fa =0
Then, dp =) Momentum, p =
dt
Or
constant
. n mechanics, we encounter several kinds of
forces.
() Gravitational Force The force of
arises between two bodies having attraction that
called force of gravitation or definite masses is
is a non-contact force. gravitational force. It
(G) Contact Force It is a force that is
objects in contact with cach other. applied by
Some of the
contact forces are given below.
(a) Frictional Force It is a type of
contact force
which is parallel to surfaces in contact and
resists the relative motion of the bodies in
contact.

(b) Normal reaction It is a type of

which is normal to the surfaces incontact force
contact.
(c) Buoyant Force The upward force exerted by
the fluid on the solid immersed in the fluid is
called buoyant force. It is equal to the weight of
the fluid displaced by the solid.
(d) SpringForce The force
generated in the spring when
it is either elongated or
compressed for a small
displacement. It is expressed
as F = kx, where k is spring
constant and x is either mg
elongation or compression of Spring force
spring.
(iii) Tension force When a body of mass m is fastened
with the string, then the weight of the body acts
downward while a force acts just opposite to the
downward force for balancing the downward force,
this force is called tension.
T= mg
where. g= acceleration due to gravity,
T= tension in the string.

mg
Tension force
 Friction
Whenever a body moves or tends to move over the
surface of another body, a force comes into play
which acts parallel to the surface of contact and
opposes the relative motion. This opposing force is
called friction.
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