Hey guys. I had a question on elasticity which looked something like this.
We have small beads of mass say and Mass of rod say . Now we need to find the extension in the rod after the beads collide with the the perfectly elastic rubber. Given that it rotates with angular speed and
and . [And if you need more variable you can take it. I think the given variables are enough]
No friction is there between the beads.
Now see my solution.
We have a rotating rod. So we will find out the extension for rotation (Say ) and for the collision say .
So is it that we need to find out .
Now we can find easily as follows.
Lets take a differential portion of the rod as .
Now the mass of the differential mass =
As rod is uniform we have
Now We Stress=
Integrating from we get
Now we have the part.
For . Can we say that the force exerted by each mass on the rod is and then
So We can take
But i am confused if i can take the sum or if the beads play any role in extension or not.