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Definition of elastic collisionby i_island0
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#1
Aug2908, 09:30 AM

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I am a bit confused about the definition of elastic collision.
What i have studied is, elastic collision is one in which the kinetic energy is conserved. Now, some books also say that elastic collision is one in which both momentum and kinetic energy is conserved. But, is it true that momentum is always conserved in an elastic collision. I have an example where in the collision is elastic but the momentum is still not conserved. A rod of mass M is hanging from the hinge of the ceiling. Now a point mass 'm' collides elastically with the rod. Surely the energy is conserved. But is the momentum conserved? 


#2
Aug2908, 09:40 AM

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Why isn't momentum conserved in that case?



#3
Aug2908, 09:53 AM

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#4
Aug2908, 10:38 AM

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Definition of elastic collision
Momentum in any direction is instantaneously conserved in all collisions in which the external forces have no component in that direction … (either because there are no such forces, or because there are forces, but they are infinitesimal compared with the impulsive force of the collision) but there are plenty of exam problems in which you use momentum to find the velocity immediately after the collision, and then external forces take over, and you have to forget about momentum, and use energy. 


#5
Aug2908, 11:40 AM

P: 121

Ok, so please follow this link and please comment on it. Please take the collision to be elastic in nature.
http://www.flickr.com/photos/63184961@N00/2808272733/ Can we write momentum conservation equation for the system shown? If yes, can you tell me the equation. Of course angular momentum can be conserved about the hinge, but how about the momentum. 


#6
Aug2908, 12:55 PM

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Hi i_island0!
Yes … on second thoughts, you're right … linear momentum is not conserved. This is different from the usual exam problem, which I was expecting, of a ball or bullet hitting something on the end of a string. In that case, the external force is along the string, which is vertical, and so there will be conservation of horizontal components of momentum. In this case, the external force is at the hinge, and its direction is unknown, which prompted you to point out: hmm … so I should have added to my last post: Angular momentum about any axis is instantaneously conserved in all collisions in which the external forces have no torque about that axis … So you have two equations … conservation of energy, and of angular momentum … which should be enough to find the two unknowns. 


#7
Aug2908, 12:57 PM

P: 121

Sure boss, now things are falling on the right place...hehe
Do you mind looking at this post also: http://www.physicsforums.com/showthr...39#post1852439 


#8
Aug2908, 01:12 PM

P: 121

I would further want to comment on the definition of elastic collision.
Elastic collision is one in which translation Kinetic energy is conserved. IF during collision, some portion of energy is converted into vibrational or even rotational KE, then such a collision cannot be called elastic. 


#9
Aug2908, 01:28 PM

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I don't think I agree with that … "elastic" simply means that kinetic energy is conserved, and rotational KE is included. Of course, "elastic" isn't a word like "newton" that has an internationally recognised definition … it's just a customary word … but I'm pretty sure the people who set exams use it to include all KE. hmm … on the other hand, you were right the last time … so if you have any quotation to back up your claim, let's see it! 


#10
Aug2908, 01:32 PM

P: 121

sure i have, else why will i make such statements.
I was just reading a book, i forgot its name, i will look back again. But i was also shocked to see that elastic collision was defined as relating to only translation KE. Currently i am reading feyman's lectures on this and if i have very supportiv proof, i shall certainly write back on this. 


#11
Aug2908, 02:27 PM

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I'll be interested to see which book it is! 


#12
Aug2908, 07:47 PM

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I can mail you if i know your email address



#13
Aug2908, 11:29 PM

P: 333

Quite interesting to note that there are two different definitons of elastic collision. In classical mechanic we always begin with Newton laws while the conservation laws come later.
What are the quantities that we can calculate from this problem? I think we can always cross check the answers for consistency using Newton and consevation laws. 


#14
Aug3008, 04:29 AM

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#15
Aug3008, 08:08 AM

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#16
Aug3008, 08:46 AM

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#17
Aug3008, 09:46 AM

P: 121

i would agree with you both... because its not at all making sense to exculde rotational energy.
So, finally shall we conclude this thread with that: elastic collision is one in which KE (rotational + translation) is conserved. If some portion of KE goes in vibrational energy, then such collision shouldn't be called elastic. 


#18
Jan711, 05:48 PM

P: 2

Why would you say that the impulsive force exerted on the rod at the hinge is unknown? My understanding of the problem takes several assumptions but I am pretty sure they are already made and won't be repeating them. Here is my perception of things:  the hinge joint is a motion constraint which makes the attached end of the rod immobile in translational terms  the hinge will do its job of keeping the attached end of the rod immobile by applying an appropriate force in order to e.g. compensate the influence of gravitation  no matter what happens to the rod, what impulsive and nonimpulsive forces and their moments are applied to it, the hinge will act correspondingly doing anything that is needed to keep the attached end of the rod immobile  now, an object hits the rod and thus exerts an impulsive force in a known direction; all nonimpulsive forces are negligible since we're dealing with an impulse; due to the impulse, the rod will naturally try to gain velocity and the hinge will have to prevent that; therefore  the impulse at the hinge will be an exact opposite of the one at the collision point Voila. I would be grateful if you could comment on my interpretation of this thing and here is why: I came across this thread searching for angular momentum conservation at impact and found it very useful and making me think about it in a different way but I'm not really able to agree with all the remarks, which makes me feel uneasy. Thanks, k. 


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