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Rigid Body Dynamics

Please solve problems 6/140 and 6/127 only. Refer attachment for fig.

Problem 6/140 : The sheave of 400 mm radius has a mass of 50 kg and a radius of gyration of 300 mm. The sheave and its 100 kg load are suspended by the cable and the spring which has a stiffness of 1.5 kN/m. If the system is released from rest with the spring initially stretched 100 mm, determine the velocity of O after it has dropped 50 mm.

Problem 6/127 : The drum of 375 mm radius and its shaft have a mass of 41 kg and a radius of gyration of 300 mm about its axis of rotation. A total of 18m of flexible steel cablewith a mass of 3.08 kg per m of length is wrapped around the drum with one end secured to the surface of the drum. The free end of the cable has an initial overhang x = 0.6m as the drum is released from rest. Determine the angular velocity of the drum for the instant when x = 6m. Assume that centre of mass of the portion of cable remaining on the drum lies on the shaft axis when x = 6m. Neglect friction.

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