find out the expression of final velocities  of two  bodies in an one dimensional elastic collision

Asked by dekakokil | 3rd Mar, 2021, 06:43: PM

Expert Answer:

Let a mass m1 which is moving with initial velocity u1 is colliding with another mass m2 moving with intial velocity u2 .
After collision, let the respective velocities be v1 and v2
 
By conservation of momentum , we get
 
m1 v1 + m2 v2 = m1 u1 + m2 u2  = α  ............................... (1)
 
( it is assumed u1 and u2 are known )
 
Since collision is elastic , we get by conservation of energy
 
(1/2) m1 v12 + (1/2) m2 v22 = (1/2) m1 u12 + (1/2) m2 u22
 
from above expression, we get ,  m1 v12 + m2 v22 = β  .........................(2)
 
From eqn.(1) , we get ,  v1 = (1/m1 ) [ α - ( m2 v2 ) ]  ...............(3)
 
 
By substituting eqn.(3) in en.(2) , we get a quadratic equation in v2 . Hence we get v2 from the solution of quadratic equation.
 
After getting v2 , we get value of v1 from eqn.(3)

Answered by Thiyagarajan K | 5th Mar, 2021, 10:26: AM

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