A cylindrical concrete silo is 4 m in diameter and 27 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.
(a) How high off the ground is the center of mass of the silo when it is empty?


(b) How high off the ground is the center of mass of the silo when it is two-thirds full of silage whose density is 780 kg/m3?

i need some help, not nessasarily the answers (although that'd help) but where to start would be great.

9/29/2008 11:03:42 PM

Is the base solid concrete, IE not able to be filled with stuff? What are the dimensions of the base?

9/30/2008 1:58:36 PM

i've done this same problem like 4 or 5 times helping people. i never understand what's so hard about it.

i don't feel like explaining it, but the answers are

a) 11.66 m

b) 9.53 m

[Edited on September 30, 2008 at 3:48 PM. Reason : let me know if they're right]

9/30/2008 3:46:38 PM

Separate it into parts. Find the CG of the cylinder (hint: it's in the middle). Find the CG of the base (hint: it's in the middle). Do a mass weighted average of the two positions.
Part two: Find total mass of the grain. Then find the CG of the grain (hint: it's in the middle). Do a mass weighted average of the three positions.

[Edited on September 30, 2008 at 3:52 PM. Reason : ]

9/30/2008 3:50:12 PM

wraith and tl both missed the "neglect the thickness of the base"

9/30/2008 3:51:53 PM

no i didn't

9/30/2008 3:54:24 PM

i see what you're saying, but "it's in the middle" doesn't really matter when finding the vert. CG for a base whose thickness is negligible. the CG of the base is at h=0.

[Edited on September 30, 2008 at 3:59 PM. Reason : 3333]

9/30/2008 3:59:25 PM

right, it's in the middle of the circle, and it's also in the middle of the height. but since the height is zero, the middle is also zero.
and the cg is in the middle of the circle all three times, so there's no need for any sideways dimensions in the calculation.



Walls: CG is 13.5m up. 38000 kg
Base: CG is 0m up. 6000 kg

Mass weighted average:
(13.5m*38000kg + 0m*6000kg)/(38000kg + 6000kg)

Silage: h is 2/3*27 = 18m. V is pi*r^2*h = 226m. m is dens*V = 176431 kg. CG is halfway up it: 9m.

Mass weighted average of all three:
(13.5m*38000kg + 0m*6000kg + 9m*176431kg)/(38000kg + 6000kg + 176431kg)


omfsignificantdigits


(your answers are correct, rvrrat)

[Edited on September 30, 2008 at 4:06 PM. Reason : how can you possibly need help with this question? this is the easiest CG question you'll ever do.]

9/30/2008 4:05:31 PM