(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ok, there's a cylindrical mug of mass m. When full of water it has a mass 4m. Assuming the base of the mug has no mass, how full is the water in the mug when the centre of mass is the closest to the base? (as a proportion of the height of the mug I'm guessing)

3. The attempt at a solution

I was trying to set up an equation with the sum of the bits equals the whole thing..

Moment of empty mug: mh/2

Moment of water: I think I get this bit wrong. it takes 3m of water to fill the cup, so 3m=h

But basically I then added the moments of the empty mug and water and equated it to total mass of the system multiplied by the COM.

I tried to differentiate to find a minimum but I had an h and a h^2 which didn't leave me with a nice answer in terms of h.

I rushed this, but if what I have said isn't clear I will make it clear when I come back to it later :)

Thanks

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# Homework Help: The lowest centre of mass while filling a cup of water?

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