A block of mass m is moving with speed v along a horizontal surface when it collides with a uniform rod of mass 2m and length L attached at one end to a pivot. The surface and pivot have negligible friction. The rod is vertical when the block collides with the end of the rod. The block sticks to the rod, and the block-rod system rotates so that the end of the rod reaches a height h, as shown above. The total rotational inertia of the rod about the pivot is 2mL^2 /3. Express answers in parts a, b, and c in terms of m,L,v and physical constants as appropriate.
a. Derive an expression for the angular speed of the block-rod system immediately after the collision.
b. Show that the change in height h of the bottom of the rod can be given by the equation h=(3v^2)/(20g)
c. Derive an expression for the mechanical energy dissipated during the collision.
