newton's cradle

因為有2條 laws令到2個波撞起1個/3個波的情況唔可以發生
1)conservation of energy
2)conservation of momentum


The collision of Newton's cradle should be elastic. Therefore it follows both the law of conservation of momentum and law of conservation of energy.

Here I would show you why it is impossible for 2 balls to hit up 3 ball.














First of all, we start from law of conservation of energy



The point at which the sets of balls hit, their relative P.E. should be zero.

Now assume momentum is conserved,
i.e. 3(mv') = 2mv
v' = 2/3 v

K.E. of two ball just before collison (E) = 2*1/2 * mv2 = mv2

K.E. of three ball just after bollision (E') = 3 * 1/2 * m(v') 2=3 * 1/2 * m(2/3 v) 2
= 2/3 mv2

since E' < E, it implies some energy is destroyed.
But we all know it is not possible.
E should be equal to E' in theory
in theoretical calculation, there should not be any difference(loss)
but in pratice, E' < E as some K.E. in converted into sound.






Now we reconsider it from law of conservation of energy

Assume K.E. is conserved,
i.e. 3 * 1/2 * m(v')2 = 2 * 1/2 * mv2
v' = √(2/3) v

momentum of two balls just before collision (p)= 2mv

momentum of three balls just after collision (p')= 3mv'=√(6) mv


as p' < p it is also not possible
(remember momentum is a conserved physical quantity?)









The abouve argument is only rough proof. In strict speaking, you may put the difference in height of each ball in a set of ball into consideration.
(actully there is a difference in P.E. of a set of ball, when the two ball at A hits the three balls at B, the two ball at A do not have same machnical energy)



In real exam, it is not possible to do the above calculation, just memorize it hard.


You may try other cases yourself!!
參考資料:
我的解答
http://hk.knowledge.yahoo.com/question/?qid=7007073102031