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 2m(L^2)/3. Express answeers in parts (a), (b), and (c) in terms of m, L, v, and physical constants as approapriate.
(a) Derive an expression for the angular speed omega 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=3(v^2)/20g.
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 2m(L^2)/3. Express answeers in parts (a), (b), and (c) in terms of m, L, v, and physical constants as approapriate.
(a) Derive an expression for the angular speed omega 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=3(v^2)/20g.
