[ilovemath]

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

This is a good animation of how Newton's Cradle works

There was a question in an exam paper, Ed Jan 2011.

A student obsereved that when the raised ball collided weith the nearest stationary ball and stops. The ball furthest to the right moves away and the three middle balls remain stationairy. As time progressed the middle balls are also observed to be moving.

My question is: why initially don't the middle balls appear to move but eventually they do appear to move?
Also, if momentum is ALWAYS consereved, why do the balls stop moving?

thanks

[burning-ape]

I'm not a physicist or in any way educated about physics, but I can have an uneducated guess.

When the kinetic energy travelling backwards and forwards through the cradle begin to lessen significantly, maybe it becomes less of a striking action and more of a pushing motion. Sort of like when you're playing pool and the difference between jabbing the ball and pushing the ball along with your pool cue.

Once again, I'm probably wrong but it's a guess nonetheless.

[Manitude]

I reckon part of the answer will revolve around the momentum being transmitted to air molecules - it is conserved, just not within the system of the cradle alone.

In a vacuum it would take much longer to slow down, but eventually energy loss through thermal energy* would cause it to slow down.

*arguably this is also kinetic energy. Last year we were introduced to the concept that all energy is kinetic energy. So in the case of thermal energy is can be the vibration of molecules in the balls, or the kinetic energy of photons transmitting radiation.

[Imposition]

(Original post by ilovemath)
http://www.lhup.edu/~dsimanek/scenario/newton.htm


My question is: why initially don't the middle balls appear to move but eventually they do appear to move?
Also, if momentum is ALWAYS conserved, why do the balls stop moving?

thanks

The balls are close together and so that's why it appears like they don't move.

some of the energy is lost due to air resistance and friction.

[ilovemath]

(Original post by Manitude)
I reckon part of the answer will revolve around the momentum being transmitted to air molecules - it is conserved, just not within the system of the cradle alone.

In a vacuum it would take much longer to slow down, but eventually energy loss through thermal energy* would cause it to slow down.

*arguably this is also kinetic energy. Last year we were introduced to the concept that all energy is kinetic energy. So in the case of thermal energy is can be the vibration of molecules in the balls, or the kinetic energy of photons transmitting radiation.

ok, so I get the momentum argument...thanks for that

I am still a little unclear though as to why the balls initially don't move and then do move

[Manitude]

(Original post by ilovemath)
ok, so I get the momentum argument...thanks for that

I am still a little unclear though as to why the balls initially don't move and then do move

One of the people above me talked about how the sudden impulse becomes more of a push. This seems reasonably plausible.
Also I wouldn't discount the possibility of the balls always moving ever so slightly - it takes a non-zero length of time between one ball hitting the pack and the one on the end being propelled up. I reckon the balls move in that very short time, and maybe the movement becomes more pronounced as time goes on. That's just speculation though, Google probably (by which I mean definitely) knows more than I

[ilovemath]

(Original post by Manitude)
One of the people above me talked about how the sudden impulse becomes more of a push. This seems reasonably plausible.
Also I wouldn't discount the possibility of the balls always moving ever so slightly - it takes a non-zero length of time between one ball hitting the pack and the one on the end being propelled up. I reckon the balls move in that very short time, and maybe the movement becomes more pronounced as time goes on. That's just speculation though, Google probably (by which I mean definitely) knows more than I

cheers for your help

[Blutooth]

(Original post by Manitude)
One of the people above me talked about how the sudden impulse becomes more of a push. This seems reasonably plausible.
Also I wouldn't discount the possibility of the balls always moving ever so slightly - it takes a non-zero length of time between one ball hitting the pack and the one on the end being propelled up. I reckon the balls move in that very short time, and maybe the movement becomes more pronounced as time goes on. That's just speculation though, Google probably (by which I mean definitely) knows more than I

My thoughts exactly. Nice exposition.

[ilovemath]

(Original post by Blutooth)
My thoughts exactly. Nice exposition.

would another way to think about it be as follows:

Kinetic energy is NOT consereved as collisions are in-elastic BUT momentum is still conserved.
as total KE decreases more balls have to move to allow momentum to be consereved ??

[Blutooth]

(Original post by ilovemath)
would another way to think about it be as follows:

Kinetic energy is NOT consereved as collisions are in-elastic BUT momentum is still conserved.
as total KE decreases more balls have to move to allow momentum to be consereved ??

In this system momentum is not conserved. The cradle eventually comes to a stop.

[Blutooth]

(Original post by ilovemath)
would another way to think about it be as follows:

Kinetic energy is NOT consereved as collisions are in-elastic BUT momentum is still conserved.
as total KE decreases more balls have to move to allow momentum to be consereved ??

irrelevant

Spoiler:

Show

In inelastic collisions Kinetic energy is not conserved because some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed.

However momentum is not conserved in this system because there are external forces acting on our system of objects. I suspect that the scratching of the wires against the hooks they are tethered to will produce a retarding frictional force that will cause the system to loose momentum . Ofc there will also be air molecules but this force is likely to be less significant.

Law of conservation of momentum states that the momentum of a system is conserved as long as there are no external forces acting on the system.

[Blutooth]

(Original post by ilovemath)
would another way to think about it be as follows:

Kinetic energy is NOT consereved as collisions are in-elastic BUT momentum is still conserved.
as total KE decreases more balls have to move to allow momentum to be consereved ??

The last line is most correct. Sorry that's probably what you wanted an answer to in the first place.

[Blutooth]

(Original post by ilovemath)
would another way to think about it be as follows:

Kinetic energy is NOT consereved as collisions are in-elastic BUT momentum is still conserved.
as total KE decreases more balls have to move to allow momentum to be consereved ??

This might be a mathematician's way of looking at the problem.

Let's say a ball on the end of the cradle is drawn back and set in motion at time t=0. Suppose the cradle as a time period of roughly 2 seconds during it's first oscillation. After 2 seconds what will it mean if the end ball is moving at it's initial speed, u?

Well, it will have meant that the kinetic energy was conserved!!! But this is not the case since the collisions are inelastic. Hence the ball must be travelling at a smaller speed lets say v. But then we find the momentum of that ball is smaller than it was at time , t=0 as mu>mv. Hence the other balls must have gained some momentum in the collisions...

[Arekkusu]

(Original post by ilovemath)
ok, so I get the momentum argument...thanks for that

I am still a little unclear though as to why the balls initially don't move and then do move

I am no physicist but would imagine the transition to a "soft" pushing motion occurs as some function of the elasticity of the balls.

[ilovemath]

ah well, I think I have come up with another answer:

as KE is lost, it is transferred to the middle balls so there motion is attentuated on each collision hence they don't start moving but eventually they move