What best describes the buoyant force on the objects?

[Bogus_Roads]

Homework Statement

Two objects made from the same material with the same mass are placed in a liquid, base first. The base of Object 2 is three times that of Object 1. What best describes the buoyant force on the objects?

A) Object 1 has a greater buoyant force acting on it because it has a larger volume submerged.

B) Object 2 has a greater buoyant force acting on it because it has a larger volume submerged.

C)Object 2 has a greater buoyant force acting on it because it has a larger area at its base.

D)The buoyant force acting on both objects is the same.

Homework Equations

F_B=$$\rho$$V_sg

The Attempt at a Solution

if ($$\rho$$_o/$$\rho$$_f)=(V_s/V), doesn't that mean that V_s depends on V? Aren't the two submerged volumes different, and then the two buoyant forces different?

 

[ehild]

Does the volume change if both the mass and the density stays the same?

ehild

 

[Bogus_Roads]

ehild,

So the volumes are the same, but the shapes are different? I just assumed that if one's base was larger than another's, one volume would be larger than the other's.

 

[gneill]

ehild,

So the volumes are the same, but the shapes are different? I just assumed that if one's base was larger than another's, one volume would be larger than the other's.

That would be an excellent trick, one that could make you very wealthy! A single gold coin molded appropriately and repeatedly would become an infinite volume of gold!

But seriously, the problem I have with this question as it is posed is that it doesn't explicitly state that both objects are completely immersed in the liquid. If one or the other or both are floating, then the answers would be different.

 

[kuruman]

But seriously, the problem I have with this question as it is posed is that it doesn't explicitly state that both objects are completely immersed in the liquid. If one or the other or both are floating, then the answers would be different.

Sorry, the objects displace the same amount of fluid regardless of whether they float or sink.

 

[gneill]

Sorry, the objects displace the same amount of fluid regardless of whether they float or sink.

The question is about the buoyant force. A hollow object may be made of the same amount of material as a solid one (and so present a lower effective density). The first can displace its weight in fluid and float (the buoyant force is equal to the weight), the second will not displace its weight in fluid and will sink (the buoyant force is less than the weight).

The amount of fluid displaced will not be the same for the same mass of material; the floating one displaces its weight in fluid, the sinking one displaces its volume in fluid.

 

[ehild]

That would be an excellent trick, one that could make you very wealthy! A single gold coin molded appropriately and repeatedly would become an infinite volume of gold!

Well, as far as I know, gold objects are valued according to their weight, not volume. :)

One thinks of a block if the base is mentioned - maybe it is my bad English. Also, "the objects are made of the same material" does not imply that they are not hollow? A hollow one is "made" partly of air, and has got a different effective density than a solid one, and the problem is undefined.

But seriously, the problem I have with this question as it is posed is that it doesn't explicitly state that both objects are completely immersed in the liquid. If one or the other or both are floating, then the answers would be different.

When both objects are solid, having the same mass and made of the same material, then their densities are identical and so are their volumes. If the density is less than that of the fluid, both objects will float and the buoyant force is equal to their weight, mg. That also means that the immersed volumes are the same.
If the density of the objects is higher than that of the fluid, both will sink. Assuming that the fluid is deep enough to cover both objects, the buoyant force is equal for both of them: volume of the objects multiplied with the density of the fluid and g.

ehild

 

[ehild]

ehild,

So the volumes are the same, but the shapes are different? I just assumed that if one's base was larger than another's, one volume would be larger than the other's.

The objects are of the same mass and made of the same material. For me, same material means also same density. Mass/density is volume, {same mass}/{same density} means the same volume. If you have two blocks and the base of one block is three times the base of the other, and the height of the first one is one third of the height of the other one, the volumes are equal. Or you have a block and a pyramid, both of equal height but the base of the pyramid is three times the base of the block, their volumes will be the same again. Objects of different shape can have the same volumes and same masses if they are made of the same material.

Floating or sinking in a fluid depends also on the shape: if the object is hollow like an empty can, or concave like a boat, it can float even it is made of a higher density material. But then you can say that it is made partly of air, and the effective density is lower than the density of the liquid. ehild

 

[gneill]

The objects are of the same mass and made of the same material. For me, same material means also same density. Mass/density is volume, {same mass}/{same density} means the same volume. If you have two blocks and the base of one block is three times the base of the other, and the height of the first one is one third of the height of the other one, the volumes are equal. Or you have a block and a pyramid, both of equal height but the base of the pyramid is three times the base of the block, their volumes will be the same again. Objects of different shape can have the same volumes and same masses if they are made of the same material.

Floating or sinking in a fluid depends also on the shape: if the object is hollow like an empty can, or concave like a boat, it can float even it is made of a higher density material. But then you can say that it is made partly of air, and the effective density is lower than the density of the liquid.


ehild

I suspect that it is a personal convention to assume that the given objects are not shaped to change their effective densities. Arguing that it is "made partly of air" so that it is no longer made from the same material seems to me to be a questionable rationalization for excusing a loosely written question.

Anyways, just to carry things to an absurd end, if you beat an object thin enough and large enough in area, it'll float by dint of surface tension! Yet it's still "made from" one material and has the same density!

 

[ehild]

Anyways, just to carry things to an absurd end, if you beat an object thin enough and large enough in area, it'll float by dint of surface tension! Yet it's still "made from" one material and has the same density!

You are right, but this was a multiple choice question for high school, I suspect, and it was meant not too complicated. So the surface tension can be excluded. I agree, the question was loosely written, not excluding hollow objects. It would have been better to write "blocks" instead of "objects". Anyway, the answers A,B,C have no sense. If you have to choose from the given answers, D can be the only sensible one.


ehild