Unit3 Dynamics

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Unit 3 Dynamics

Dynamics:

The branch of mechanics that deals with the study of motion of an object and the causes of its

motion is called dynamics.

Force:

A force moves or tends to move, stop or tends to stop the motion of a body. The force can

also change the direction of motion of a body. It can also change the size or shape of a body

on which it acts.

Example of Force:

A goal keeper needs a force to stop a ball coming to him.

Inertia:

Inertia of a body is its property due to which it resists any change in its state of rest or

motion.

Momentum:

Momentum of a body is the uantity of motion it possesses due to its mass and velocity. It is

a vector uantity.

Formula of momentum:

Momentum ! of a body is given by the product of its mass m and velocity ".

Thus, ! # mv

Unit of Momentum:

In $I unit of momentum is %gms&' which is same as (ewton&second )(s*

Newton’s 1st law of Motion:

According to (ewton+s first aw of Motion “ A body continues its state if rest or of uniform

motion in a straight line provided no net force acts on it ”.


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For Example:

A book lying on a table remains at rest as long as no net force acts on it. $imilarly, a moving

object will not stop moving until a force is applied on it.

'st aw of Motion is also known as aw of Inertia.

Net Force:

(et -orce is the resultant of all the forces acting on a body.

Newton’s n! "aw of Motion:

According to (ewton+s nd aw of Motion “When a net force acts on a body, it produces

acceleration in the body in the direction of the net force. The magnitude of this

acceleration is directly proportional to the net force acting on the body and inversely

proportional to its mass”

Mathematical e/planation0

$uppose a force F produces acceleration a in a body of mass m, then we can state that

a 1 F and a 1 1#m

$r a % F#m it means F % ma

!utting % as proportionality constant, we get

- # %ma

In $I value of %#', therefore F & ma

Unit of force:

In $I unit of force is (ewton )(*.

2ne (ewton )'(* is a force that produces an acceleration of 'ms & in a body of mass ' kg.

That is0 '( # 'kg 3 'ms&

'( # kgms&


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Mass:

(ewton+s nd law of Motion tells us that “Mass is that characteristic of a body which

determines the magnitude of acceleration produced when a certain force acts upon it”.

It is a scalar uantity. 4eam balance is used to measure the mass. Mass of the body remains

the same everywhere.

'ei()t:

“The weight of a body is equal to the force with which the earth attracts that body towards

its centre”. It is a vector uantity. $pring balance is used to measure the force or weight of a

body. It varies depending upon the value of 5g6. 7nit of weight is (ewton.

8eight )8* of a body of mass )m* is related by the euation '& m(

(ewton+s third aw of Motion0

(ewton+s third aw of Motion states that “To every action there is always an equal but

opposite reaction”.

For Example:

8hen a rubber ball hits the ground it bounces back in the upward direction. The force which

the ball e/erts downward while hitting the ground is called 5action6 of the ball. At the same

time, the earth e/erts a force on the ball in upward direction due to which the ball rises up.

This force is called 5reaction6 of the earth.

$imilarly, a book is lying on a table. The weight of the book is acting on the table in

downward direction. This is the action. The reaction of the table acts on the book in the

upward direction.

*ension an! acceleration in a strin(:

9onsider a block supported by a string. The upper end of the string is fi/ed on a stand. et 8

be the weight of the block. The block pulls the string downwards by its weight, therefore

weight is acting downward. This causes a tension * in the string. The tension T in the string

is acting upward it the block. As the block is at rest, therefore the tension T in the string must

be eual and opposite of weight 8 of the block.


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Motion of +o!ies connecte! wit) strin(:

There are two cases of such a motion.

,ase 1: -ertical motion of two +o!ies attac)e! to t)e en!s of strin(s t)at’s passes o-er africtionless pulley

9onsider two bodies A and 4 of masses m' and m respectively. et m' is greater than m.

The bodies are attached to the opposite ends of an ine/tensible string. The string passes over

a frictionless pulley. As body A is heavier, it will move downward with some acceleration a.

at the same time, the body 4 will moves up with some acceleration a. as the pulley is

frictionless therefore the tension T will be the same throughout the string. et the tension in

the string be *.

$ince the body A moves downwards, hence its weight m'g is greater than the tension T in the

string.

... (et force acting on body A # m'g : T

According to (ewton+s nd aw of Motion;

m'g : T # m'a


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a # )m' : m* g

)m' = m*

>ivide euation by

T : mg # ma

m'g : T m'a

m' )T : mg* # m )m'g : T*

m'T : m' mg # m' mg : mT

m'T = mT # m' mg = m' mg

T )m' = m* # m' m g

* # m' m g

m' = m

-rom euation

( # )m' = m* a

)m' : m*

,ase : Motion of two +o!ies attac)e! to t)e en!s of a strin( t)at passes

o-er a frictionless pulley suc) t)at one +o!y mo-es -ertically an! t)e ot)er

mo-es on a smoot) )ori/ontal surface:

9onsider two bodies A and 4 of masses m' and m respectively attached to the ends of an

ine/tensible string. et the body A moves downward with an acceleration a. $ince the string

is ine/tensible therefore body 4 also moves over the horizontal surface with the same

acceleration a. As the pulley is frictionless therefore tension T will be same throughout the

string.

$ince body A moves downward therefore, its weight m'g is greater than the tension T in the

string.

2 1

A

A


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... (et force acting on body A# m'g : T

According to (ewton+s nd aw of Motion

m'g : T # m'a


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0elations)ip +#w Force an! momentum:

9onsider a body of mass m moving with initial velocity "i. et a force - acts on a body

which produces an acceleration a in it. This changes the velocity of the body. et its final

velocity after time T becomes "f . If !i and !f be the initial and final momentum of the body

related to initial and final velocities respectively, then

!i # m"i

!f # m"f

... 9hange in momentum # -inal momentum : Initial momentum

# !f : !i # m"f : m"i

Thus the rate of change in momentum is given by0

!f : !i # m"f : m"i

t t

# m )"f : "i*

t

$ince "f : "i is the rate of change of velocity eual to the acceleration a produced by

t the force -.

... !f : !i # t # ma

According to the (ewton+s nd aw of Motion,

- # ma

2r -# !f : !i # t


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Unit3 Dynamics

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