A wad of sticky clay of mass m = 5.0 g and velocity vi = 106 m/s is fired at a s

Question

A wad of sticky clay of mass m = 5.0 g and velocity vi = 106 m/s is fired at a solid cylinder of mass M = 15.0 kg and radius R = 25 cm (Figure P11.41). The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through the center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d = 23 cm, less than R, from the center. Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. Is mechanical energy conserved in this process? Yes No

Explanation / Answer

(a)     for the given problem for simplicity let usconsider that the system to consist of the wad of clay and thecylinder     no external forces acting on this system have atorque about the center of the cylinder thus the angular momentumof     the system is conserved about the axis of thecylinder     Lf = Li     I = m vi d     [(1 / 2) M R2 + m R2] = m vi d     = 2 m vi d / (M + 2 m)R2 (b)     no, some mechanical energy changes to internalenergy in this perfectly inelastic collision

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