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M3 question

Dear all,

attached is a pic of an M3 question about volumes of revolution/centre of masses.

I've done the first parts, but don't understand how to do the last part.

Could someone please just tell me what to do...don't bother working through the whole question and posting the answering - I just need a method :smile:

Cheers,

Katie
M3.jpg91.3KB
Reply 1
Avatar for rockindemon
rockindemon
You need to find the angle at which it will topple. From this you can calculate the mass of liquid, given that you know where the centre of mass is in ordre for it to topple.
Reply 2
Avatar for JamesF
JamesF
1
I think this is how to do it.
Take moments about y=2 (the point where the cup stops touching the ground). Find the value of m such that the anticlockwise from the base is equal to the clockwise moment of the liquid and the cup together. Then the range of values is all the values larger than this.
Reply 3
Avatar for Jonny W
Jonny W
8
Work out the new COM. If the COM is strictly inside the dark-shaded region in Figure 3 then the cup cannot rest in equilibrium. ("Strictly" means not on the boundary.)
Reply 4
Avatar for Bezza
Bezza
2
You need to consider the horizontal position of the centre of mass of the whole system. When it is greater than or equal to 2cm from the base, it is above a point of contact with the table so the cup stays upright. When it is less than 2cm from the base it will topple.

You'll end up solving (1.55*300+5m)/(300+m) < 2
Reply 5
Avatar for k@tie
k@tie
OP
10
Bezza
You need to consider the horizontal position of the centre of mass of the whole system. When it is greater than or equal to 2cm from the base, it is above a point of contact with the table so the cup stays upright. When it is less than 2cm from the base it will topple.

You'll end up solving (1.55*300+5m)/(300+m) < 2

:frown: :frown: moments....I forget M3 assumes M2 knowledge...now I gotta relearn moments :frown: cheers everyone!!
Reply 6
Avatar for Bezza
Bezza
2
Katie Heskins
:frown: :frown: moments....I forget M3 assumes M2 knowledge...now I gotta relearn moments :frown: cheers everyone!!

I don't think you do really need to know moments (for this question at least), just that if the CoM is outside of the points of contact with the plane, it will topple

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