Why does Newton's Cradle behave the way it does?

[sungholee]

If you pull and let go three "balls" from one side of a Newton's cradle, three will be pushed from the other side. But why is that? Why can't one ball be pushed three times as fast (or far?) as a result of the three balls? Or 2, for that matter?

 

[Simon Bridge]

That's a very good question - in fact: how does the cradle know how many balls to send off the far side?
Have you tried tapping the cradle with a hammer too? What happens?

What have you done so far to try to figure it out ;)

Other things to try
- hold the fifth ball still when the first drops.
- raise one ball from each end and drop them at the same time
- raise one ball from one end and two balls from the other end...

- raise all five balls: why doesn't just one ball go five times as high?

 

[rcgldr]

There have been previous threads about this. The reason has to do with how the force is distributed and transmitted through the balls, which compress slightly (like a very stiff spring) during the collision. Link to web page:

http://www.lhup.edu/~dsimanek/scenario/cradle.htm

 

[bobie]

Why can't one ball be pushed three times as fast

how does the cradle know how many balls to send off the far side?

The reason has to do with how the force is distributed and transmitted through the balls, which compress slightly

The answer is very simple: just because a ball doesn't know how many balls are behind it. Each collision takes place separately between a ball at rest and a ball with KE and with same mass.

 

[Simon Bridge]

@bobie: simple aye? Have you visited rclgdr's link?

What you've described it the "series of 2-ball collisions" approach - the only way "[e]ach collision takes place separately...", physically, is if there is a small gap between each ball - which is not required for the result.
Please read the link if you have not already done so.

 

[AlephZero]

Why can't one ball be pushed three times as fast (or far?) as a result of the three balls? Or 2, for that matter?

Things like that can happen, but only if the balls have different masses. In most "toy" cradles the balls are all identical, but there is no reason why you can't make your own where you can change the pattern of different sized balls. Steel ball bearings work well. The bigger and heavier, the better.

 

[Simon Bridge]

Steel ball bearings work well. The bigger and heavier, the better.

Up to a point ... the bigger and heavier they are the more rigid they need to be. At some point you won't find steel (or other material) rigid enough.

Seen the demolition-ball Newton's cradle thing?

But, the bigger the balls, the more likely you will see other solutions pop up.
That link in post #3 is essential reading.

 

[bobie]

@bobie: simple aye? Have you visited rclgdr's link?.

I have, I think last ball cannot be pushed 2 or 3 times faster because it starts moving before the energy of the first or second ball is discharged. the third balls discharges its energy and stops , then takes the energy of the second ball. discharges it to the penultimate... and so on .
Isn't time delay the main reason?

 

[sophiecentaur]

The answer is very simple: just because a ball doesn't know how many balls are behind it. Each collision takes place separately between a ball at rest and a ball with KE and with same mass.

I notice that the concept of Momentum hasn't been brought into the discussion and this sort of problem is best treated inn terms of Impulse. For any collision, an equal and opposite impulse is applied to each of a colliding pair. For equal mass balls, this will stop the first and send the second off at the same velocity.
If you want to treat the intermediate balls as a single mass then it gets more complicated and you need to consider the first and last collisions together but you can still consider the impulses in each collision. Equal times again and equal contact forces (as long as incoming and outgoing balls have the same mass). Two simple simultaneous equations can be obtained for each collision and the velocity of the middle mass drops out - giving the same overall result.