Answer to Question #308211 in Classical Mechanics for Sam

Question

1)A wedge of mass 2and angle 60slides freely along a smooth horizontal floor. A uniform circular disk of mass and radius rolls along the rough surface of the wedge with its centre attached to the top of the wedge by a spring of natural length and spring constant . A second uniform circular disk of mass and radius rolls along the rough surface of the wedge with its centre attached to the centre of the first disk by a second spring of natural length and spring constant . The entire system undergoes planar motion. Take as generalized coordinates the displacement of the wedge along the floor, x, the displacement of the upper disk from the top of the wedge, y, and the displacement of the lower disk from the upper disk, z.

A)Determine expressions for the total kinetic energy and the total potential energy of the system.

B)Determine the Lagrangian of the system and obtain Lagrange’s equations for the system.

Answer 1

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