Solving Dynamics Problems with Burden's Self-Study: Momentum & Kinetic Energy

[apamnani1]

Good morning all. I wondered if anyone could assist me with the following dynamics problem.
The question is copied from Burdens Dynamics and Mechanical Sciece Self Study.

Question) Three balls of mass 2kg each, have a coefficient of restitution of k = 0.85. Ball A is released at a height of 1m from rest and strikes ball B and then ball B strikes ball C.

a) Determine the velocity of ball A just before it strikes ball B.
b) Write down the conservation of momentum equation for the analysis of the impact between ball A and ball B.
c) Calculate the velocity of each ball following the final impact.
d) What is the kinetic energy of the system just before the first impact.

Assume that the balls slide without friction. K is the ratio of relative speeds of balls after and before the impact K = v2-v1/u1-u2.

My conservation of momentum is the only piece I truly understand. After the final impact how would you go about analytically calculating the velocity as stated?

 

[NoPoke]

When in doubt simplify to a question that you can answer...

Ignore ball C

If stuck on part a) make an assumption (ie a reasonable guess) for the velocity of A before it hits B

Ignore gravity except where you *must* include it.
The question tells you to ignore friction so no need to apply that simplification

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But above all you have to show some working so that specific useful help can be given beyond the general one of when in doubt simplify..

 

[CWatters]

Hints:

Part a) Apply conservation of energy.

Part b and c) Perhaps read this..

http://en.wikipedia.org/wiki/Coefficient_of_restitution

Part d) See part a).