Questions relating to elastic collisions:
Given the equations
(1) m1v1 + m2v2 = m1v1' + m2v2'
(2) (v1 - v2) = - (v1' - v2')
In the case where two objects are of equal mass (m1 = m2) and one object is initially at rest (v2 = 0) before an elastic collision, use the above equations and conservation of momentum to show that v1' = 0 and v2' = v1. All working must be shown.
Now consider two objects of different mass, where one object is initially at rest (v2 = 0). In this case the objects stick together as a result of the collision and move away together. Use conservation of momentum to derive an expression for their common velocity after the collision (v'). All working must be shown.
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