Two identical stell balls, each of mass 4.0 kg, are suspendedfrom strings of len

Question

Two identical stell balls, each of mass 4.0 kg, are suspendedfrom strings of length 33 cm so that they touch when in theirequilibrium position. We pull one of the balls back until itsstring makes an angle =34 degrees with the vertical and letit go. It collides elastically with the other ball.
(a) How high will the other ball go? (b) Suppose that instead of steel balls we use putty balls.They will collide inelastically and remain stuck together after thecollision. How high will the other ball rise after thecollision? Two identical stell balls, each of mass 4.0 kg, are suspendedfrom strings of length 33 cm so that they touch when in theirequilibrium position. We pull one of the balls back until itsstring makes an angle =34 degrees with the vertical and letit go. It collides elastically with the other ball.
(a) How high will the other ball go? (b) Suppose that instead of steel balls we use putty balls.They will collide inelastically and remain stuck together after thecollision. How high will the other ball rise after thecollision?

Explanation / Answer

Case 1. Elastic balls.. In this case we apply two equations at the time ofcollision. 1. Conservation of momentum as there would be noforce in horizontal direction, since the string would bevertical. 2. Elastic collision leads to conservation ofenergy/or can use the coefficient of restitution. Applying these two equations we get the ball withvelocity coming to at rest and the other ball getting exactly thesame speed as the first ball, and hence by theconservation of energy would go to the same height as the firstball.
Case2 . For pure inelastic collision at thetime of collision two balls would become one and net speed of thecombined structure would be according to conservation ofmomentum. mv = (m+m)*V...where V is the new speed. On solving V = v/2. And now applying the conservation of energy 1/2(2m)*V2 = 2mgH On solving it gives H = V2/2g =v2/8g And since v2 = 2gh....where h was the earlierheight, we have H = h/4. Angle can be calculated appropriately

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