18-51 - 1851 A spring having a stiffness of k = 300 N> m is...

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18–51.A spring having a stiffness of is attached tothe end of the 15-kg rod, and it is unstretched when .If the rod is released from rest when , determine itsangular velocity at the instant . The motion is in thevertical plane.u=30°u=u=k=300 N>mk300 N/mBA0.6 muSOLUTIONPotential Energy:With reference to the datum in Fig.a, the gravitational potentialenergy of the rod at positions (1) and (2) isSince the spring is initially unstretched,. When , the stretch of thespring is . Thus, the final elastic potential energy of thespring isThus,Kinetic Energy:Since the rod is initially at rest,. From the geometry shown inFig.b,. Thus,. The mass moment of inertiaof the rod about its mass center is .Thus,the final kinetic energy of the rod is

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