Question

1. The small mass m is to slide down the large mass M without friction. The track along which the small block slides is a quarter circle with radius R. The large mass itself is free to move on a frictionless horizontal surface. Initially both masses are at rest with the small mass at the top of the quarter circle, as shown in the figure. (a) (5 Pts.) What is the initial total mechanical energy with respect to the horizontal surface? (b) (10 Pts.) What will be the velocity of the mass m when it reaches the horizontal surface? (c) (10 Pts.) What distance does mass M move as the mass m moves from m the top to the horizontal surface? R/ Solution:

Answer 1

initially when small block m is at top then it is at rest so it's total mechanical energy is it's potential energy, if we take horizontal surface to be at 0 potential energy then total mechanical energy with respect to horizontal surface is = mgR

as height of m is R

velocity of m as it reaches horizontal surface = v

as

u is speed of M towards left and M moves a distance y towards left when m moves R towards right so that their center of mass does not move as there is no external force acting on the system

so M moves    distance towards left

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