Probably a silly buoyancy question.

[hferdjal]

Okay, the buoyancy equation is this:

Fb = (pV)g = mg

Now, as far as I know:

(1) - An object will float if buoyancy force > "weight of the object".
(2) - And vice-versa, the object will sink if "weight of the object" > buoyancy force.

Now, looking at (2), I'm pretty sure that the object will stop sinking if the buoyancy force eventually ends up exceeding the object. My question is this. What aspect of the buoyancy equation (Fb = pVg) increases in relation to depth (so that it'll eventually exceed the weight of the block)? Density stays the same, the volume of the water displaced stays the same (does it not?), and gravity stays the same.

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[axp107]

The Buoyancy force does not change with depth. I remember reading this in EK.

An object that sinks in general.. will continue to sink

the Buoyancy force doesn't keep increasing or anything.. if this did happen... an object would slow down until it just "floats" in the middle of the liquid. That's not possible in an ideal liquid..

maybe if you had something with "viscosity" or thickness, it would have some effect. But don't worry about it. Just know that Fb does not change with depth.

The equation also can prove this.. Fb = pvg

Gravity is constant, density is constant, volume can't increase as an object is sinking. Hope that helped.

 

[UCDavisdude]

f bouyancy increases until the object is fully submerged(v sub). at that point, it is constant regardless of depth.

 

[hferdjal]

Yea, it helped tremendously. Thanks.

Edit - (deleted rest of post) I was going to ask about "apparent weight", but I figured it out myself ^_^.

Thanks again though guys.

 

[_T_]

I actually had this same question so just to clarify.

Lets say at the top Fb = X
X increases until Vdis = Vobj after that it remains constant?

This is probably my weakest point on the whole exam..

 

[twopiradian]

sorry

 

[Zoom-Zoom]

If an object is sinking, Fb is already less than the weight of the object. If outside pressures reduce it's volume and lower Fb even more, then the object will accelerate to the bottom, not suspend.

This is how submarines reach neutral buoyancy. They flood, sink, then pump the water back out until the weight equals Fb.

 

[Zoom-Zoom]

I actually had this same question so just to clarify.

Lets say at the top Fb = X
X increases until Vdis = Vobj after that it remains constant?

This is probably my weakest point on the whole exam..

Yes, Fb is directly proportional to the volume of the object that is submerged. The more water something displaces, the more force the water will exert back on that object. Once it's full submerged, though, the force is constant. So to go back to the OP's question, the variable part of the question is volume. Density is constant for a given liquid and g is always the same. The volume of liquid that is displaced depends on how far down the object is submerged, which usually depends on it's mass.

Fb > Weight of object when the object is less dense than the liquid
Fb < Weight of object when the object is more dense.

You can prove this by setting pvg (object) equal to pvg (liquid), and assuming the object is fully submerged so that the volumes are equal (ie: it's surface is perfectly aligned with the surface of the liquid), the density determines whether or not it will float. Hope that makes sense

 

[BlackSails]

Doesnt the pressure(and density) of a liquid increase with depth?

 

[x10694]

Okay, the buoyancy equation is this:

Fb = (pV)g = mg

Now, as far as I know:

(1) - An object will float if buoyancy force > "weight of the object".
(2) - And vice-versa, the object will sink if "weight of the object" > buoyancy force.

Now, looking at (2), I'm pretty sure that the object will stop sinking if the buoyancy force eventually ends up exceeding the object. My question is this. What aspect of the buoyancy equation (Fb = pVg) increases in relation to depth (so that it'll eventually exceed the weight of the block)? Density stays the same, the volume of the water displaced stays the same (does it not?), and gravity stays the same.

I am not exactly sure but i don't think 1 is true. Buoyant force equal weight of the object if it floats. and the buoyant force increase when V is increasing buy once the object is totally submerged and still not float it will sink all the way down

 

[werd]

Doesnt the pressure(and density) of a liquid increase with depth?

the pressure as you go down is equal to the weight of the column of (water+air) above you... so the pressure does increase a lot as something sinks. however, liquids are relatively noncompressable and even huge pressures will only affect density by a very small amount. for mcat purposes, changes in water density with things like depth, temperature, and solute concentration are probably beyond the scope of what they're looking for. these considerations are, however, crucial for effective participation in david letterman's "will it sink?" game 😉