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1) A disk and a ring, both of mass M and radius R, are placed atop an incline an

ID: 1697868 • Letter: 1

Question

1) A disk and a ring, both of mass M and radius R, are placed atop an incline and allowed to roll down. Give an expression for the kinetic energy of the disk at the bottom of the inclind in terms of its mass, radius and translational velocity, vdisk. how does this kinetic energy compare to the kinetic energy of the ring at the bottom of the incline?

2) A block, also of mass M, is placed atop an incline with the same slope and height as the one in teh first question. Assuming this incline is frictionless, give an expression for the kinetic energy of the block at the bottom of the incline in terms of its mass and its velocity, vblock. How does this kinetic energy compare to the kinetic energy of the ring and the disk at the bottom of the incline?

3)how do the velocities of teh disk, ring and block compare at the bottom of the incline? which one reaches bottom first? (hint: think about how much of the kinetic energy of each object is associated with the translational velocity of the object.) why?

Explanation / Answer

When the disk reach the bottom of the incline, the potential energy convert into kinetic energy

      then the kinetic energy at the bottom

                K = 1/2Mv^2 + 1/2I^2

                   = 1/2MV^2 + 1/2 (1/2MR^2) (V/R)^2

                    = 1/2MV^ + 1/4MV^2

                    = 3/4MV^2

similarly when the ring reaches

The kinetic energy

              K = 1/2Mv^2 + 1/2I^2

                   = 1/2MV^2 + 1/2 (MR^2) (V/R)^2

                    = 1/2MV^ + 1/2MV^2

                    = MV^2

Therefore the kinetic energy of the disk is 3/4 time of the ring

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