2 (30 points): A block of mass m is pushed against a horizontal spring of neglig

Question

2 (30 points): A block of mass m is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The spring constant is k. When the block is released, it travels on a horizontal surface of distance d with a friction coefficient u to point A, the bottom of a vertical circular track, which is frictionless. The radius of the track is R. ?? 7n (a) What is the velocity of the block at point A? e x If the block can just reach the top, what force provides the centripetal force for the circular motion at the top point? What is the minimum velocity in terms of R?

Explanation / Answer

Solution :-

The energy stored in the spring after compression will be = (1/2)kd2
On launching this speed will transfer to the block , hence = (1/2)mv2
(1/2)kd2 = (1/2)mv2
k = mv2/d2
Now for second block
(1/2)kx2 = (1/2)(4m)(2v)2
(mv2/d2)x2 = 4m(4v2)
x = 4d

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