Problem 2 points) A block of mass 2m sits at rest on a frictionless track that f

Question

Problem 2 points) A block of mass 2m sits at rest on a frictionless track that forms a circular vertical loop or radius r. A bullet of mass m strikes the block horizontally with initial speed v, and remains embedded in the as the block and bullet circle the loop. Determine parts (a) and (c) in terms of some or all of the quantities m, r, and g: (a) Find the speed of the block and bullet immediately after impact. (b) What fraction ofthe kinetic energy of the bullet & block system before impact remains as kinetic energy of the bullet and block system immediately after impact? Thi answer should be a number only, with no variables.) is What happened to the rest of the kinetic energy? (c) Find the work done by gravity after the collision as the bullet & block move to point P. In terms of gandronly (do determine the minimum initial speed vm of the bullet if the block & bullet are to successfully execute a complete circuit of the loop.

Explanation / Answer

Ans:-

Part d

At the top of the loop mg = mv² /r

v² = rg

Vertical distance between the top and bottom point is 2r
Conservation of energy

½ mv^2 + mgh = ½ m*Vmin^2 + mgh

½ rg + g 2r = ½ Vmin^2

Vmin^2 =2* (5/2 gr) = 5gr

Vmin =sqrt (gr)

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