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#1 2012-08-15 04:42:18

Registered: 2010-06-14
Posts: 30

Find the force that empties this bowl containing a liquid...

Here is a picture of the setup

The vessel is attached to a fixed axis (A-B) and has an inner radius of r and outer of R. The mass densities is p for the vessel and p1 for the liquid. Find the force F (at point C in the picture) that holds the vessel at rest with by a horizontal degree b (once again, see the picture).

M = F x L
Vsphere = 4*pi*r^3/3 = > Vvessel = 2*pi*(R^3-r^3)/3
Vliquid = pi*h^2*(3r-h)/3 (where h is the height of the liquid)
h = r(1-sin(b))

First solution wins!


#2 2012-08-15 19:32:07

bob bundy
Registered: 2010-06-20
Posts: 7,743

Re: Find the force that empties this bowl containing a liquid...

hi engrymbiff

Do you know the formula for the position of the centre of gravity for a hemisphere?  And how to work out the C of G for a segment?

Then take moments about the axis AB.


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei


#3 2012-08-16 00:01:11

Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

Re: Find the force that empties this bowl containing a liquid...

OP's post was kinda confusing. He posted this into the "Help me!" forum, but the last sentence of his post was "First solution wins!" Does this mean he doesn't want your help if you weren't the first to respond or did he not need help at all and the first post is just a problem for other members to try and do or...?

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