Question

Angular Momentum and Inelastic Collisions Two balls, each with mass M/2, are attached to the ends of a thin rod of length L = 0.45 m and negligible mass. The rod is free to rotate in a horizontal plane without friction about a fixed vertical axis through its center. With the rod initially at rest (as shown), two wads of wet putty hit the balls at the same time and stick to them. Assume that the wads of putty have different masses m, = 0.100 kg and m2 = 0.0500 kg. Just before they hit the balls, the wads are moving horizontally with speeds v; = 3.00 m/s and v, = 5.00 m/s. Assume further that M = 4.5 kg Putty wad #1 Putty wad #2 Rotation axis (a) Determine the numerical value of the angular speed after of the system just after the putty wads hit. In which direction does the rod spin after the putty wads hit? Clockwise or counterclockwise? (b) Determine the ratio of the kinetic energy of the system after the collision to that of the putty wads just before? KEater KE before

Answer 1

ca) cale celore the moment of ivernia of rod + Peetty system. about ceurer 164.4)*(3+61 +) (•)? -$=(4,5 +0:1) *(0-49)*+(4:5 +0.05) x(045)? - I= 0.2354 Kg. n? consider the conservation of auguor womentin Linitial . Lfinal., (counter clockwise is positive) - mieh-mg Usb + Wo Is = I Wafter - - 0.1 X3 X0:45 -0.05 X 5 X0.45 toxh 0.2354 Wation Wapsen: 0.0478 ross counter clockcerise Keattes KE before Emner? tanque? Ą I Wafter O.1 x3 + 0.05x5? 0.2354-x(0.0478) ? Reather Kebefon Reatter, 3997.39 a Ke before t