How does Newton's Cradle work? I know it has something to
do with gravity and his 3rd law, and possibly the conservation of energy.
I would like some formula's if possible.
The only reason to bring gravity in is for the pendulum motion. Newton's
Cardle involves both momentum and energy conservation. If one ball strikes
from hieght y, one ball flies up from the other side to height y. Both
energy and momentum are conserved. If we drop the initial ball from 2y,
why is it that we always get one ball going to 2y and not 2 balls going to
y? How does it know?
Momentum would certainly be conserved since one ball strikes with momentum
m(2v) and two pop up with momentum (2m)v giving m2v = 2mv. But we must
consider kinetic energy. One ball would strike with 1/2 m(2v)^2 while the
two balls would have energy 1/2 (2m)v^2. This would give us an equation of
2mv^2 = mv^2 which violates conservation of energy. The only way that
momentum and energy can both be conserved is if the same number of balls
are ejected as hit, and return to the same height.
---Nathan A. Unterman
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Update: June 2012