Recently during a weekend part at a fraternity, a keg of sweetened iced tea was

Question

Recently during a weekend part at a fraternity, a keg of sweetened iced tea was donated by some friends from another. However, a tap for the keg could not be located. Being resourceful, the partygoers drilled holes on the top and bottom of the keg in order to drain the keg of its contents. However, an argument about the center of mass (com) of the keg broke out and the hosts set about to calculate the com of the keg as a function of the height of the iced tea in the keg. The hosts were able to determine that the keg had a mass of 7.00 kg, and was in the shape of a cylinder of height L=0.600 m. The total mass of iced tea before the holes were drilled was 17.7 kg.

(a) What was the com, h, of the keg and its contents before the holes were drilled?

(b) What was the com, h, of the keg after all of the iced tea had drained out?

(c) Describe qualitatively what happens to the com, h, of the keg and iced tea combination as the iced tea is drained from the keg.

(d) Starting from the definition of the com, write down an expression for the com as a function of y, the height of the remaining iced tea.

(e) Find y when the com reaches its lowest point.

I'm looking for theory as well as methodology so I can learn for future problems.

Explanation / Answer

a) 0.3 m

b) 0.3m

c) it first moves down and then move up finally to reach same height

d) h = [(y*10.7/0.6)(y/2) + 7(0.3)] / ((y*10.7/0.6)+7) = [18.92(y^2) + 2.1] / (17.83y+7)

e) dh/dy = 0

differentiate above equation and equate it to zero, you will get y.

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