There are several several instances when we can use the fact that \(e=1\). to simplify collision problems which saves us from having to apply conservation of energy.

The result \(e=1\). is fairly obvious for head-on collisions, and for collisions of extended objects involving pure translation and for those involving pure rotation.

But my doubt is can I in general use the result for any collision among extended bodies too which might involve a combination of both rotation and translation ??

Can I say that if an object elastically collides with another,,, then the velocities of the points of contacts of both objects satisfy the relation \(e=1\). ??

example in the image,, if the collision between ball and rod is elastic,, can i say that the point of collision of the rod after collision necessarily moves at a speed v such that,, if the balls initial and final velocities are \(u\). and \(f\). respectively ,

then ,

\(Tell\) \(me\) whether I use :

1) \(v-f=u\). ??

or

2) \(e=1\) ??

or

3) Do I have to use the usual way of energy conservation and momentum conservation and angular momentum conservation independently ??

Please any one who has the knowledge I seek help me ,, if possible also provide a qualitative or quantitative explanation

\(Be\) \(Careful\). :

e is the coefficient of restitution, not to be confused with \(2.7108\).

\(NOTE\). :

I know it is applicable for pure rotating and pure translating objects whether extended or not because i can prove it)

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## Comments

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TopNewestWhy do you put two commas

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where ever you have used them ?Log in to reply

I had edited Them For \(Saketh\).

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Yes you can in general use the result e=1 for any kind of collisions.

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My question Challenges in mechanics by Ronak Agarwal (Part3) is based on this concept only.

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gotta try it then,, i saw it before but it seemed to lengthy,, either way can you prove that e=1 for all sorts of elastic collisions? or is it just a general result you know and apply ? :)

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Yes it is a general result that \(e=1 \Rightarrow\) Energy is conserved.

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