Centre of mass of a coke can

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The centre of mass of a full coke can obviously is at the centre and will go down as the level of coke in the can is decreased. When the can is empty, however, the centre of mass is back at the centre.

If you know the weight of the empty can and the weight of the full can, can you determine at what level of coke the centre of mass will be at its lowest point?

To make the calculations in your head easier assume that the can is a perfect cylinder and that the empty can weighs 40 grams. It holds 320 ml, therefore the total weight when full is 360 grams. The can is 12 cm high.

Determine the level of coke at which the centre of mass will be lowest. It is possible to solve this without calculus.

Have Fun!


Problem adapted from problem 4:
Gardner, Martin. 1972. Mathematical Games. Scientific American, volume 226, no. 4, p. 101. 
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