Question

Please draw the forces acting on the free body diagram if necessary and answer the question clearly. Thank you.

4. A rod AB of mass M and length L is free to rotate about a horizontal axis through A. The rod is held horizontal and the endB is released. The rod rotates about A, and when it is vertical, the end B collides with a small mass M/2 and the mass gets attached to the rod. In the Sbsequent motion, the rod and the mass rise to a maximum angle (relative to the vertical). М, L в Show that (a) The angular speed of the rod when it is vertical, just before 3g the collision is given by a = L (b) Immediately after the collision the angular speed of the system is given by w'= (c) The maximum angle 0 is given by cos 0 =. M/2 EDNESDAY HELP SESSION

Answer 1

@ Consenring total mechanical energy of the rod between horizontal position and vertical position just before collision Mg 7 2 2 = 12 I w where I = moment of inertia of rod about A.' 2. Mght 2 = Low Tw=138 conserving Ananlar moment uni of the system of [Rod't body) about the hinge, . I w I w' where I and I are the est moment of inentia of the and system abant I just before an just after collision. ® conserving total mechanical thingy.. between the inihal. and final position of the system after collision, Mga (1-(020) + 494/1-603 0) = com * Mgh (1-cose) = x (M + 9.22 ) x 2 5 12 ) ti-Corso = ţ = 16030 = 1-5 - Ys