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two bodies of masses 5kg and 3kg moving in the same direction along the samestraight ine with velocity 5m/s and 3m/s respectively sufering 1-d elastic collision.Find velocity after collisions?
Asked by sarojarma | 25 Sep, 2019, 19:42: PM
answered-by-expert Expert Answer
Since the collision is elastic, both momentum and energy are conserved.
 
By momentum conservation :-  m1 u1 + m2 u2 = m1 v1 + m2 v2  ...........................(1)
 
where m's are masses , u's are initial velocities and v's are final veleocities.
 
we have m1 = 5 kg , u1 = 5 m/s , m2 = 3 kg , u2 = 3 m/s
 
hence from eqn.(1), we have,  5 v1 + 3 v2 = 34  kg-m/s   ........................(2)
 
By energy conservation :-   (1/2) m1 u12 + (1/2) m2 u22 = (1/2) m1 v12 + (1/2) m2 v22  ...................(3)
 
by substituting values for masses and initial velocities,
 
we get,  5 v12 + 3 v22 = 152   J   .........................................(3)
 
we substitute v2 using eqn.(2) , and rewrite eqn.(1) as
 
5 v12 + (3/9) ( 34 - 5 v1 )2 = 152  
 
Above eqn. can be simplified as,   2v12 -17 v1  + 35  = 0  ...................(4)
 
Solution for the above eqn. :-   v1 = 5  or  v1 = 3.5
 
v1 = 5 is not acceptable solution, because it imples no velcity changeafter collision which is not true
 
Hence acceptable solution, v1 = 3.5  m/s
 From eqn.(2), by substituting for v1 , we get v2 = 5.5 m/s
Answered by Thiyagarajan K | 26 Sep, 2019, 12:28: PM

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