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What happens if there is a underweight or overweight pool ball in this shot?
First see this question:
http://answers.yahoo.com/question/index?qid=20080122105042AAOOQbS&r=w#RZcsX2S8Vjcv9ccfz0VGGJTmyzS0qZbfHvcQ1jHuYj9ZdncEPbLZ
12 balls are lined up in a perfect row all in contact. All are identical except for 1, which could be underweight or overweight. A cue ball hits the end of this row dead on, no English. What happens, and why? I’d like a Newtonian physics answer, not just a guess.
The cue ball is identical to the other 11, of course.
The cue ball is shot in line with the row of 12 balls. If all 12 were identical, what will happen is that the cue ball will “stick” to the end of this row, and the last ball will shoot off. You’d still have 12 balls stuck together.
To answer the reference question…
If you could hit the balls with the same force, the one that weighs differently will have a different velocity after impact. If we treat the system as being conservative, then we can assume the momentum is maintained between collisions.
Intial momentum = final momentum…
If the que ball is hit with the same velocity with no english then the following would hold true…
m1*v1i + m2*v2i = m1*v1f + m2*v2f
We are assuming that the intial velocity of the 2nd ball is zero.
m1*v1i = m1*v1f + m2*v2f
Solving for v2f…
v2f = m1/m2*(v1i – v1f)
In the masses were the same it should be easy to see that after impact the velocity should be the same as the other balls. However, the one with a different mass would effect the m1/m2 term and thereby would have a different final velocity. So, a larger mass for the oddball would result in a slower velocity and vice versa for a smaller mass.
Hope that helps.
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