Collision in 1-D
o If the initial velocities and final velocities of both the bodies are along the same straight line , then it is called a one-dimensional collision , or head-on collision .
Elastic collision :
( A ball of mass m1 with initial velocity v1 strikes a ball of mass m2 initially at rest and after collision ball 1 moves with velocity v ’ 1 and ball 2 moves with velocity v ’ 2 , in the same direction )
o Momentum conservation : m1 v1 + m2 v2 = m1v1 ’ + m2 v2 ’
o KE conservation : m1 v1 2 + m2 v2 2 = m1v ’ 1 2 + m2 v ’ 2 2 o Where m1 , m2 are the masses of the two blocks
v1 is initial velocity of block 1 , v2 = 0 here v ’ 1 is final velocity of block 1
o After solving these two equations we get ,
Special cases in elastic collision : o
Case 1 – If the two masses are equal m1 = m2 , then , v1 ’ = 0 & v2 ’ = v1 The first mass comes to rest and pushes off the second mass with its initial speed on collision .