# Newton's Cradle: Law of Conservation of Energy & Momentum

1. Feb 10, 2015

### Cascade

1. The problem statement, all variables and given/known data
Newton's cradle. Each ball is 50 g. First ball is raised to 3.0 cm, and the final ball reaches 2.6 cm after the collision.
1) Use the law of conservation of energy to calculate its velocity before impact.
2) Use the law of conservation of momentum to determine the velocity of the ball on the other side after the collision.

2. Relevant equations
Ek + Ep = Ek + Ep (+ W; is W relevant here?)
m1v2 + m2v2 = m1v2' + m2v2'

3. The attempt at a solution
1) Ek + Ep = Ek + Ep
1/2mvi2 + mgh1 = 1/2mvf2 + mgh2
0 + (0.050kg)(9.80m/s2)(0.030m) = 1/2(0.050kg)vf2 + 0
vf = 0.7668 m/s

2) p = p'
m1v2 + m2v2 = m1v2' + m2v2'
(0.050kg)(0.7668m/s) + 0 = 0 + (0.050kg)v2'
v2' = 0.7668 m/s

Is the height of the final ball involved in any of the calculations? I feel like it should be, but I can't figure it out.

2. Feb 10, 2015

### haruspex

The second question makes no sense to me.
You can find that velocity from the height reached by the final ball. We cannot find it by conservation of momentum because there are intervening balls, and we do not know what velocities they end up with. If everything were perfectly elastic, those velocities would be zero, but since the final ball does not reach the height the first ball started with, we know there are losses.
A better question would have been, assuming n intervening balls, all ending with the same velocity, find that velocity.

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