Velocity of bodies in contact

[darkelf]

If both bodies are in motion and come into contact, say a ring sliding on a block in motion as well. The speed of the ring (RPM) and the speed of the block in motion would both change once the bodies come into contact.

Is there a way of calculating what the speeds of both bodies would be while they are in contact? If one knows the speeds of both bodies before contact, can one calculate what the speeds would be when they come into contact?

 

[tiny-tim]

Hi darkelf!

Momentum is always conserved in a collision,

so if the velocities of the two bodies are the same afterwards (that's called a perfectly inelastic collision ), then that velocity is the total momentum beforehand divided by the total mass

 

[darkelf]

Thanks Tiny Tim. What if you don't have the mass of one of the bodies as its suspended. I am able to calculate the force applied but don't know how to relate that to find the reduction in speeds during contact.

Is there an equation one can use to calculate this. I'm assuming that after contact speeds return to initial instantaneously.

Thanks again.

 

[Dr.D]

I would suggest that you post a figure. It is possible for us to give you a lot of irrelevant information because of not understanding your case.

Tiny-tim, I have to disagree with your general statement
"Momentum is always conserved in a collision."

Consider a physical pendulum striking a fixed obstacle. In this case, there is an impulsive reaction at the pendulum pivot and linear momentum is not conserved. Angular momentum may, or may not be conserved, depending on the nature of the impact.

 

[tiny-tim]

Tiny-tim, I have to disagree with your general statement
"Momentum is always conserved in a collision."

Consider a physical pendulum striking a fixed obstacle. In this case, there is an impulsive reaction at the pendulum pivot and linear momentum is not conserved. Angular momentum may, or may not be conserved, depending on the nature of the impact.

No such thing as a "fixed obstacle" …

if the obstacle is attached to the Earth, then the Earth recoils slightly, and momentum is conserved

Thanks Tiny Tim. What if you don't have the mass of one of the bodies as its suspended.

(If it's not a free collision, and if you don't want to take the recoil of the Earth into account, then: ) the suspended body will move in a circle, or on a sphere, and angular momentum about the top of the string will be conserved (immediately after the collision).

 

[Dr.D]

Tiny-tim, first of all, I mentioned a physical pendulum, meaning a solid body such as a beam, not a string, rotating as a pendulum.

You are, of course, correct when you say that there is no such thing as a "fixed obstacle," but have you ever tried to quantify the momentum of a bolder sitting on the Earth when struck by a pebble? Most of us, at least most folks I know, would call the bolder a fixed obstacle. How would you describe that interaction?

 

[tiny-tim]

Hi Dr.D!

How would you describe that interaction?

hmm … i wouldn't call it an interaction (or a collision) between two bodies …

i'd call it a one-body problem … the boulder is just a restraint!

 

[Dr.D]

No impact then, just a sudden change in the equation of motion with new boundary conditions? Great idea!

 

[darkelf]

Thanks for the help guys. I understand that there are some software out there that can help me model out the problem taking into account the material properties.
I not very good with the internet so drawing out the problem here isn't all that easy.
Basically, a rotating cylindrical body is comes in contact with a moving square body. Like say rollers coming into contact with a metal sheet.
Does this description help?

 

[Dr.D]

Presumably the roller is supported on an axle, so that there will be reactions at the axle. Is the metal sheet supported, or is it flying through the air?

You need some careful free body diagrams showing all of the (impulsive) forces that act, remembering that you will have both normal contact forces and friction forces in this impact. Could get messy!

 

[darkelf]

yes the roller is supported by an axle and the metal sheet is supported by a frame. Elastic and plastic deformations take place.

Is there a software that I can use to develope a numerical solution modeling the free body diagram on it and let it take into account all the forces and material properties?

 

[Dr.D]

I'm sure that Algor will claim to be able to do this, provided you model just about half the universe that includes your system. Realistically, I doubt it.

PS: I would have grave doubts about the Algor results, just like I have about Algore.

 

[darkelf]

There isn't any other Finite Analysis software I could try?

 

[Dr.D]

Sure, try any of them you want.