As part of a carnival game, a 0.653-kg ball is thrown at a stack of 17.3-cm tall

Question

As part of a carnival game, a 0.653-kg ball is thrown at a stack of 17.3-cm tall, 0.423-kg objects and hits with a perfectly horizontal velocity of 10.3 m/s. Suppose the ball strikes the very top of the topmost object as shown to the right. Immediately after the collision, the ball has a horizontal velocity of 4.35 m/s in the same direction, the topmost object now has an angular velocity of 2.03 rad/s about its center of mass and all the objects below are undisturbed. If the object's center of mass is located 12.1 cm below the point where the ball hits, what is the moment of inertia of the object about its center of mass? What is the center of mass of the tall object immediately after it is struck? Answers to three sig figs please.

Explanation / Answer

L1 = mv1l = 0.653*10.3*0.173

L2 = mv2*l + IW = 0.653*4.35*0.173 + I*2.03


0.653*10.3*0.173 = 0.653*4.35*0.173 + I*2.03

I = 331.116e?3 kg m^2


ycm = ((0.653*17.3) + (0.423*(17.3-12.1))/(.423+.653)= 12.5432 cm

i.e = 17.3 - 12.5432 = 4.76 from top

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