Why do 2 balls bounce in a Newton's Cradle instead of just one?

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Discussion Overview

The discussion centers on the mechanics of Newton's Cradle, specifically why lifting and releasing two balls results in two balls bouncing on the opposite side, rather than just one. The conversation explores concepts related to elastic collisions, momentum, and kinetic energy conservation.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that in Newton's Cradle, lifting one ball results in one ball bouncing out, while lifting two balls results in two balls bouncing out, questioning the underlying mechanics.
  • Another participant explains that this phenomenon involves elastic collisions where both momentum and kinetic energy are conserved, leading to the conclusion that the number of balls involved in the impact must match the number of balls that bounce out.
  • Some participants propose that it might be possible for two balls to equal one ball if the single ball had double the momentum, questioning how this would conserve energy and whether it makes sense.
  • A later reply elaborates on the conservation laws, stating that if two balls with mass m and velocity v collide, the total momentum and kinetic energy must remain consistent after the collision, which would not hold true if only one ball were to bounce out.
  • One participant asserts that the solution to this problem is well known and accepted in physics, referencing the implications for other scenarios like billiards, suggesting that many have attempted to find a different outcome without success.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the conservation laws, with some supporting the established explanation while others challenge the reasoning behind the necessity of two balls bouncing out. The discussion remains unresolved regarding the alternative perspectives on the mechanics involved.

Contextual Notes

Some assumptions about the nature of elastic collisions and the definitions of momentum and kinetic energy are implicit in the discussion. The mathematical steps involved in the conservation laws are not fully resolved, leaving room for interpretation.

Yuc4h
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Hello everyone

There is this device called Newton's Cradle

http://www.heurekashop.fi/files/magneetti/productpics/496picture2Upload.jpg

You lift one ball and let it impact with other balls, the impact is followed by other ball bouncing from the other side.

However, when you lift 2 balls, the impact is followed by 2 other balls bouncing. Why is that? I would initially guess that only one ball bounces, the answer can not be very simple since I actually asked a professor of physics about this and he didn't really know the answer.
 
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The simple answer is that this involves elastic collisions where no deformation occurs. Both kinetic energy and momentum are conserved. When you satisfy both conditions, you get 1 ball = 1 ball, 2 balls = 2 balls, etc as the only possible solution.
 
But also 2 balls = 1 ball would satisfy the conditions if the ball would get twice the momentum and it also would make more sense.
 
Yuc4h said:
But also 2 balls = 1 ball would satisfy the conditions if the ball would get twice the momentum and it also would make more sense.
How would that conserve energy? And why would it make more sense?
 
Both conditions have to be satisfied. If you have 2 balls, each of mass m, moving with velocity v before the collision, the combined momentum is 2mv and the combined kinetic energy is mv^2. After the collision, these must still be true.
If you had only one ball leaving, its momentum would have to be 2 mv. Since its mass is m, its velocity must be 2v. However, that would make the kinetic energy 2mv^2. So, this cannot be a solution.
This is a standard problem in Physics. The solution is well known and accepted. Thousands (millions?) of students have played with Newton's cradles and tried to get a different result. All have failed.
If this solution were not true, it would be impossible to play the game of pool (billiards) as we know it.
 

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