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Question:

Physics center of mass help!!! :(?

A cylindrical concrete silo is 4 m in diameter and 32 m high. It consists of a 6000 kg concrete base and 38000 kg cylindrical concrete walls. Neglect the thickness of the silo walls and base.I need to find how high the center of mass is of the silo and then also how high the center of mass is off the ground when it is 2/3 full of something with a density of 780 kg/m^3....I have no idea and I've been at it for a while answers are much appreciated and if you could show how you got the answers or what equations to use that would be most excellent. thanks.

Answer:

Hmmm, I'm not an expert but perhaps the location of the center of mass doesn't change with respect to the pier but does change with respect to the canoe's center. The boat moves 46.5 cm in order to keep the location of the center of mass unchanged with respect to the pier. If this is so, calculating Carmelita's mass should be straightforward.
Ycg = (ΣM*y)/ΣM Let the bottom of the silo be y = 0; then Ycg = (6000*0 + 38000*16)/(6000+38000) = 13.818 m The top of the fill material will be 2/3*32 = 21.333 m and the CM of the fill will be half than height. The fill mass = (π/4)*4?*21.333*780 = 209104.4 kg. So, Ycg(filled) = (44000*13.818 + 209104.4*21.333/2)/(44000+209104.4) = 11.2145 m

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