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 ,
\(Tell\) \(me\) whether I use :
1) \(v-f=u\). ??
2) \(e=1\) ??
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 \(2.7108\).
I know it is applicable for pure rotating and pure translating objects whether extended or not because i can prove it)