Center Of Gravity For Coca Cola Can

[Waxford]

I have a can of coke (there are soft drinks available and it works the same!). When it is full the centre of gravity is in the middle. If I take a mouthful out of the can the volume of liquid drops so does the centre of gravity. If I take another mouthful the centre of gravity drops again. However, when the can is empty the centre of gravity is back in the middle.

I can assume it is a simplified shape and the can is about 110mm tall, has a diameter of 63mm and a wall thickness of 0.5mm. Therefore, it holds about 330ml of liquid. If I assume the density of the Aluminium can is 2710kg/m3 and the density of the liquid is 1000kg/m3, what is the centre of gravity’s lowest point? And how much coke is left in the can at this point? Not necesarily looking for a formula. But a logical reason. Need to combine mass of can with mass of liquid? Or what's the logical way to deduce lowest point? How to explain in words?

[bobbinwales]

The centre of gravity must fall yes as the level of coke reduces but there must come a point before its empty where the weight of the coke is not enough to continue this and the centre of gravity rises again as the weight of the tin material above the coke line is more than the weight of the coke what's left plus the metal below. Depends on the densitys.

[THECORBYLOON]

Professor Google has the answer

https://www.lockhaven.edu/~dsimanek/puzzles/sodacan2.htm

[Peter Pedant]

yeah agree bo bo
the centre of er mass will be in the centre ( and mainly contributed to, by the liquid)

and this kinda drops to the midpoint of the cylinder of liquid

until the mass of the packing is of the same order ( not equal ) to the mass of the liquid.

sip sip sip - if you plot the centre of mass (y) as the can empties along the x axis, it will take up the shape of - - an inverted/backward tick mark.
( late steep upstroke)

lowest point - well it is the intersection of two straight lines
and will occur....
when the mass of the liquid ( NOT volume) is the same as the mass of the can. - this wouldnt be a bad skool maff 6th form exam q to be honest

[Peter Pedant]

there you are
reversed tick mark
not sure why it is quadratic and not linear ... ( because it is a linear combination....)