A wooden block of mass M resting on a frictionless, horizontal surface is attach

Question

A wooden block of mass M resting on a frictionless, horizontal surface is attached to a rigid rod of length ? and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v hits the block and becomes embedded in it.

(a) What is the angular momentum of the bullet–block system about a vertical axis through the pivot? (Use any variable or symbol stated above as necessary.)

L = ?

(b) What fraction of the original kinetic energy of the bullet is converted into internal energy in the system during the collision? (Use any variable or symbol stated above as necessary.)

Explanation / Answer

a) angular momentum = of bullet + of mass

      = m v L + 0   = m v L

b) using angular momentum for collision,

before = after angular momentum

m v r = Iw

m v L = ((M+m) l^2 )w

w = m v / (M+m)L

initial KE = mv^2 /2

final KE = I w^2 /2 =((M+m) l^2 ) (m v / (M+m)L)^2 /2

KEf = m^2 v^2 / 2(M + m)

deltaK = KEi - Kef = mv^2/2 - m^2 v^2 / 2(M + m)

      = (Mm + m^2 - m^2 )v^2 / 2(M + m)

     = Mmv^2 / 2(M +m)

deltaK / Ki = [Mmv^2 / 2(M +m) ] / [mv^2 /2 ]

        = M / (M +m)

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