Question about momentum transfer

[WraithGlade]

Hi.

I'm trying to figure out how transfer of momentum works so that I can simulate it reasonably accurately and understand it on an intuitive level.

My intuition goes like this:

Momentum must be conserved. Therefore, if for example I had a 1 meter long Newton's Cradle with numerous polished steel balls on it, spanning the whole length, then if a steel ball moving at 1 meter/sec collides head on with the left side of the array then the ball furthest to the right in the array will begin swinging away from the array exactly 1 second after the first ball collided with the left side.

In other words, my intuition is that in momentum space it would be as if the original ball had never collided at all and just continued traveling along the space. Whereas, in contrast, in physical space, this would amount to the momentum being transferred along the line in order to achieve the equivalent effect.

Is my intuition correct?

Is the amount of time momentum transfer requires in the presence of collisions equivalent to the amount of time the original momentum would have taken to traverse the system without the presence of the colliding bodies?

This is all of course assuming that no energy is lost anywhere.

Thanks for reading.

 

[Dr_Morbius]

Your intuition is wrong. The momentum transfer occurs much faster than the speed of the balls. If the balls were perfectly elastic I'm guessing that the momentum transfer would happen at the speed of sound in whatever material the balls were made out of.

 

[jim hardy]

seeing is believing

 

[AlephZero]

There are two different mechanisms transferring the momentum here.

Before the impact, the momentum is being carried with the matter in the ball, as it moves. The "velocity of the momentum" is the same as the velocity of the ball, and could be anything.

The other mechanism is transferring momentum through a solid, by the forces acting between the atoms of the material. As #2 said, that always happens at the same speed, which is the speed of sound in the material. The speed of sound in most metals is about 5 times faster than in air.

But don't worry too much about being wrong here. The same sort of confusion can occur elsewhere in physics, for example the apparent speed of waves on the surface of water, compared with the motion of the water itself. The good thing is that you were thinking about what was going on.

 

[PJC01]

Hello,

Your intuition is correct in that momentum is conserved and that it can be transferred through collisions. The example of the Newton's Cradle is a good illustration of this concept. When the first ball collides with the left side, it transfers its momentum to the rest of the balls in the array, causing the ball on the far right to swing away. This is because the total momentum of the system must remain constant.

In terms of time, the amount of time it takes for momentum to transfer through collisions is not necessarily equivalent to the amount of time it would take for the original momentum to traverse the system without collisions. This is because the collisions themselves can affect the speed and direction of the objects involved, potentially slowing down the transfer of momentum. However, in a perfectly elastic collision where no energy is lost, the transfer of momentum would occur in the same amount of time as the original momentum would have taken to traverse the system.

I hope this helps clarify the concept of momentum transfer for you. If you have any further questions, please don't hesitate to ask. Keep up the good work in simulating and understanding this important concept in physics.