ch11-p066 - 66. We make the unconventional choice of...

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66. We make the unconventional choice of clockwise sense as positive, so that the angular velocities (and angles) in this problem are positive. Mechanical energy conservation applied to the particle (before impact) leads to mgh mv v gh = ¡ = 1 2 2 2 for its speed right before undergoing the completely inelastic collision with the rod. The collision is described by angular momentum conservation: mvd I md =+ rod 2 c h ω where I rod is found using Table 10-2(e) and the parallel axis theorem: IM d M d Md rod F H G I K J = 1 12 2 1 3 2 2 2 . Thus, we obtain the angular velocity of the system immediately after the collision: 22 2 (/ 3 ) md gh M dm d = + which means the system has kinetic energy () rod /2 Im d + which will turn into potential energy in the final position, where the block has reached a height
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