Archimedes Paradox

aim1732

We are preparing a physcs quiz and are planning to use the following problem

If we have a wooden block balanced at the junction of two immiscible liquids then we have the buoyancy of the two liquids balance the weight of the block.The lower liquid will exert your normal upthrust but the upper liquid also exerts an upthrust even though it is above the block.How does it happen?

We are thinking of a hypothetical situation in which we remove the upper liquid.If we now pour the other liquid then it tends to increase the hitting of the molecules of the lower liquid hence increasing the pressure.That is to say the upper liquid indirectly exerts that pressure using the lower liquid.

I am looking for an alternative approach or verification of the above explanation.

jim hardy

If i've got the question right,
make your block have vertical sides so the geometry is simple, i.e. there's vertical force applied only to the bottom and top surfaces.

What's force up on bottom?
What's force down on top?

P X A both places , of course.
P_bottom = ρ₁gh₁ +ρ₂gh₂

Dont forget that the liquid above the block also exerts force down on the top of block, so raising level above block does not increase bouyant force. It remains equal to weight of fluid displaced.

vikrambij

first thing this is not a paradox at all.... u shud go thru d basics of fluid mechanics,,,, Archimedes principle is nothing but net upward force due to pressure difference.,,,
in ur problem the net force on the curved surface is zero (balanced),,, net force on the upper part is downward which is equal to p₁xarea; where p₁ is the pressure at upper surface,,,,
while net force on the lower surface is upward which is equal to p₂xarea ; where p₂ is the pressure at the lower surface,,,

the relation between p₁ and p₂ is :
p₂ = p₁+ρ₁gh₁+ρ₂gh₂

so eventually net upward force(thrust force) comes out is
F_thrust = F_upward - F_downward
F_thrust = (ρ₁gh₁+ρ₂gh₂) x area
where
h₁ = height of cylinder in liquid A (upper liquid)
h₂ = height of cylinder in liquid B
take obvious meaning of other symbols

gmax137

[rant]
Sorry, Vik, I didn't read past that. I find the real newspeak to be double-plus ungood...
[/rant]

vikrambij

didn't mean dat,,only if u catch that thing,,,,