Question

Discuss elastic collision jn 1 dimension obtain exdression for velocities of the 2 bodies after such a collision

Answer 1

Elastic collision are those in which the momentum of the body remains conserved .

let there are two bodies having mass m1 and m2 
u1 =initial velocity of body first
u2=initial velocity of body second 
v1 = final velocity of body first 
v2= final velocity of body second 

m1u1 + m2u2 = m1v1+m2v2 ---------------( ! )

now energy also conserved in elastic Collison
 
1/2m1u1 + 1/2m2u2 =1/2 m1v1+ 1/2m2v2 ---------------------( !! )

from equation ( !) 

m1(u1-v1 ) =m2(v2-u2 )____________( * )

from equation ( !! )

m1(u1²-v1² ) =m2(v2²-u2² )________________(**)

dividing equation ( * ) AND (** )
$\frac{ u1^{2}-v1^{2} }{u1- v1} = \frac{v2^{2}-u2^{2}}{v2-u2}$

u1+v1= v2+u2

v2 velocity after collision 
v2 = u1 + v1 -u2 

subsitiute the value of the v2 in equation ( !) 

v₁= (m₁ - m₂ ) u₁+ 2 m₂ u₂ / m₁ + m₂

similarly we can find v2