2019-03-01_Physics_Times

dm M (mass of the body)

1

rCM rdm.

M

 

 

1 1 2 2 3 3.......... n n

CM

m v m v m v m v

v

M

  



   



1 1 2 2 3 3.......... n n

CM

m a m a m a m a

a

M

  



   



(I) Addition of mass

Due to addition of mass, the C.M of a system

generally shifts towards or into the region

where mass is added. If C 1 is C.M before

addition and C 2 is the C.M of added mass

and C C d1 2 ,then

int

shift added ,

ial added

m d

X

M m

  

  

   C.M shifts

towards the side of added mass.

(II) Removal of mass

Due to removal of mass the C.M of a system

shifts away from the region where mass is

removed. If C 1 is C.M of the body before

removal and C 2 is the C.M of the removed part

and C C d1 2 then

removed

shift

initial removed

m d

X

M m

   

  

  

‘’ indicates CM shifts opposite to the side of

removed mass

ext

dP

F

dt







If ext^0 ; constant

dP

F P

dt

  



 

P P P 1    2 ......... Pn constant.

   

Impulse of a force F acting on a body is defined

as:-

J



= Fdt



=

dv

m

 dt



dt =m dv



J m v v ( 2  1 )

 

It is also defined as change in momentum

J P 

 

J F dt P P P    f i

    

Impulse on a body for a time interval is equal to

the area under force time (F-t) graph in the same

time interval.

It is a vector quantity.

Magnitude is equal to area under the F-t. graph.

J = Fdt = Fav (^) dt = F tav
Collision is an event in which a strong force acts
between two or more bodies for a short time, which
results in change of their velocities.
The line passing through the common normal
to the surfaces in contact during impact is called
line of impact. The force during collision acts
along this line on both the bodies.
Line of impact in different collisions
(i) Two balls A and B are approaching each other
such that their centres are moving along line
CD.

4. Velocity of centre of mass of a system

5. Acceleration of centre of mass of system

6. Shift in the position of centre of mass

7. Conservation of momentum

8. Impulse

Instantaneous Impulse :

9. Collision

10. Line of Impact

11. Elastic collision

Head on Collision

In an elastic collision, the particle regain their

shape and size completely after collision, i.e., no