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A bullet of mass m B = 1.69 ? 10 ? 2 kg is moving with a speed of 102 . m / s wh

ID: 2262054 • Letter: A

Question

A bullet of mass mB=1.69?10?2kg  is moving with a speed of 102.m/s  when it collides with a rod of mass mR=7.69kg  and length L=1.05m  (shown in the figure). The rod is initially at rest, in a vertical position, and pivots about an axis going through its center of mass. The bullet embeds itself in the rod at a distance L4  from the pivot point. As a result, the bullet-rod system starts rotating.

a) Find the magnitude of the angular velocity, ? , of the bullet-rod system after the collision. You can neglect the width of the rod and can treat the bullet as a point mass.

Please include a multiplication sign (*) to indicate that two units are being multiplied.

?= [Num] [Units]

b) What is the change in kinetic energy in the collision?

Please include a multiplication sign (*) to indicate that two units are being multiplied.

?K= [Num] [Units]

Explanation / Answer

apllying conservation of angular momentum

before collision

A.M of bullet=l=mB*v*L/4--------1

after collision AM of bullet=l'=mb*(L/4)^2*w-------2

where w if angular velocity of rod fater collision

AM of rod=L=Iw

I=1/3m(L/2)^2

I=MI of rod=1/3 ML^2--------3

from 1,2,3,

l=L+l'

from above

w=mB*v*L/4/(I+m(L/2)^2)

w=mB*v/(4L(M/12+mB/16))=.638 rad/sec