Chapter 11, Problem 053 A uniform thin rod of length 0.63 m and mass 3.2 kg can

Question

Chapter 11, Problem 053 A uniform thin rod of length 0.63 m and mass 3.2 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 4.7 g bullet traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle 60° with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 9.00 rad/s immediately after the collision, what is the bullet's speed just before impact? Axis Number Units the tolerance is +/-290

Explanation / Answer

Angular momentum will be conserved,

mv L/2 sin theta = (ML^2/12 + m(L/2)^2)w, cancelling L on both sides,

0.0047*v*0.5 sin 60 degree = [3.2*0.63/12 + 0.0047*0.63/4] *9

  0.002035v = 1.51866

v = 1.51866/0.002035 = 746.27 m/s answer

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