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.