- #1
Hamiltonian
- 296
- 190
- Homework Statement
- A ball of mass M and radius R is placed inside a spherical shell of the same mass M and the inner radius 2R. The combination is at rest on a tabletop in the position shown in the figure. The ball is released, and it rolls back and forth inside the shell. Find the maximum displacement of the shell.
- Relevant Equations
- -
I was able to solve this problem easily by using the fact that the center of mass of the system is stationary as ##\sum F_{ext} = 0## for the ball and shell system. since COM's of both objects can be replaced with point masses at there center, the shell will have maximum displacement when its COM is in the position of the ball and the ball's in the place of the shell's COM, by the given geometry, we can conclude when the COM's of both the bodies exchange positions the shell's COM would have been displaced by ##R##
I wanted to know if there is a way to write the equation of motion of the shell and from that evaluate its maximum displacement.
also, it's given in the problem that the ball rolls inside the shell(i.e. no slipping condition applies) hence I feel that the question was expected to be solved in this manner?
I am unable to come up with any equations in terms of the ##x##-coordinate of the shell.
a hint to get started with this problem will be amazing! :)