A small block of mass 2m initially rests on a track at the bottom of the circula

Question

A small block of mass 2m initially rests on a track at the bottom of the circular, vertical loop-the-loop shown above, which has a radius r. The surface contact between the block and the loop is frictionless. A bullet of mass m strikes the block horizontally with initial speed vo and remains embedded in the block as the block and bullet circle the loop. Determine each of the following in terms of m, v0 r, and g.

Pic of scenario: http://tinypic.com/view.php?pic=2whp7p2&s=9#.VxYcCsfKe8U

a. The speed of the block and bullet immediately after impact

b. The kinetic energy of the block and bullet when they reach point P on the loop

c. The minimum initial speed vmin of the bullet if the block and bullet are to successfully execute a complete circuit of the loop

Explanation / Answer

c)

At the top of the loop mg = mv² /r

v² = rg

Vertical distance between the top and bottom point is 2r

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b)

Find the velocity at the point P knowing the vertical distance and calculate 1/2 m.v²

Using v² = u² - 2as =rg and noting that u = V0/3


(V0/3 )² - 2*g(2r) = g r


(V0/3 )² = 5rg

V0 /3 = [5rg ]

V0 = 3* [5rg ]

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