Buoyant Force

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MedPR

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Really having trouble with fluids.

A bathtub duck floats in water with one third of its volume above the water line. What is its specific gravity?

The explanation is that since one third of the duck is shown above the water, the displaced volume is 2/3V.

That means that the volume of displaced water is equal to 2/3 the volume of the duck? So Vwaterdisplaced = 2/3Vduck

Also, since the duck is floating, that means that Fb = mg?

Fb=dVdisplacedg

d=m/v so m=vd so mg = dvg

So dVdisplacedg = dVduckg

vdisplaced = vduck

Since 2/3 of the duck is submerged, the displaced volume = 2/3Vduck.

So the specific gravity of the duck is 2/3? Since the density of water is 1000kg/m^3, does that mean the density of the duck is 667kg/m^3?

I think I understand this problem, and I know it's the most simple fluid problem there is, but I want to be sure I'm not missing any of the important systematic problem solving steps.

Thanks!

milski

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Yes and yes. You're doing fine.

MedPR

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Yes and yes. You're doing fine.

Thanks.

In the case of a fully submerged object, Vdisplaced = Vobject?

milski

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Thanks.

In the case of a fully submerged object, Vdisplaced = Vobject?

Yes. And if it's not sinking futher, Fb=mg.

FearlessHyena

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Thanks.

In the case of a fully submerged object, Vdisplaced = Vobject?

Well since it's completely submerged, by definition the volume displaced matches the volume of the object. So, when is the buoyant force of an object the greatest?

MedPR

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Well since it's completely submerged, by definition the volume displaced matches the volume of the object. So, when is the buoyant force of an object the greatest?

I thought buoyant force was a property of the fluid, not the object.

chiddler

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Well since it's completely submerged, by definition the volume displaced matches the volume of the object. So, when is the buoyant force of an object the greatest?

Buoyant force is greatest when displacement of fluid is greatest, or when it is completely submerged.

I thought buoyant force was a property of the fluid, not the object.

It is a property of both fluid density and object volume.

milski

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I thought buoyant force was a property of the fluid, not the object.

Fb = density * V * g

So it depends on the fluid, volume displaced and gravity.

PS: SDN seriously needs a better way to type greek letters/formulas.

FearlessHyena

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Fb = density * V * g

So it depends on the fluid, volume displaced and gravity.

PS: SDN seriously needs a better way to type greek letters/formulas.

Excellent. Now what happens to buoyancy of an object if the temperature of fluid increases? We are assuming an expansion of liquid.

ljc

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Excellent. Now what happens to buoyancy of an object if the temperature of fluid increases? We are assuming an expansion of liquid.

Density of the fluid decreases, so the duck would sink slightly. For instance, if water decreased to 3/4th of its normal density, the duck would sink until 75% was underwater. The buoyant force, though, would not change. It'd still be equal to the mass of the duck * gravity.

snow, PBR, and bears
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We also have to assume that the duck expands more slowly that the liquid.

Liquids and solids (usually) both grow when heated. As long as the liquid expands faster, the duck will ride lower.

MedPR

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Buoyant force is greatest when displacement of fluid is greatest, or when it is completely submerged.

It is a property of both fluid density and object volume.

Fb = density * V * g

So it depends on the fluid, volume displaced and gravity.

PS: SDN seriously needs a better way to type greek letters/formulas.

If you put 3 objects, each of different density, in a tub of water, the water exerts the same buoyant force on all 3 objects.

Doesn't that mean the buoyant force is a property of the water?

milski

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If you put 3 objects, each of different density, in a tub of water, the water exerts the same buoyant force on all 3 objects.

Doesn't that mean the buoyant force is a property of the water?

It does, and that's what we are saying too.

If your argument is that it is property only of the fluid density, consider objects with the same same density but submerged to different levels. The buoyant force will be different even with the same fluid.

MedPR

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It does, and that's what we are saying too.

If your argument is that it is property only of the fluid density, consider objects with the same same density but submerged to different levels. The buoyant force will be different even with the same fluid.

No, my argument is that the buoyant force on different objects in the same medium is the same. Fb is a property of the medium.

Which of the following are TRUE regarding thre balls of equal size that are fully submerged in water, if ball A sinks, ball B is stationary, and ball C rises?

I. Density of Ball C is less than that of Ball B
II. The buoyant force on Ball C is greater than that on Ball A.
III. The density of Ball A is greater than that of water.

The answer is I and III only. In other words, the buoyant force is the same.

Explanation for why II is wrong.

The buoyant force a fluid exerts on an object depends on the density of the surrounding medium, the volume of the object, and the gravitational force constant. Because ball A has the same volume as ball C, they experience the same buoyant force. The reason Ball A sinks and ball C floats has to do with their differences in weight despite the fact that they experience the same buoyant force. It is false that the buoyant force on Ball C is greater than that on Ball A.

milski

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Not according to this TBR question.

Which of the following are TRUE regarding thre balls of equal size that are fully submerged in water, if ball A sinks, ball B is stationary, and ball C rises?

I. Density of Ball C is less than that of Ball B
II. The buoyant force on Ball C is greater than that on Ball A.
III. The density of Ball A is greater than that of water.

The answer is I and III only. In other words, the buoyant force is the same.

All the balls are fully submerged, hence the submerged volume is the same. Same volume, same fluid - same force for all the balls.

milski

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The buoyant force a fluid exerts on an object depends on the density of the surrounding medium, the volume of the object, and the gravitational force constant. Because ball A has the same volume as ball C, they experience the same buoyant force. The reason Ball A sinks and ball C floats has to do with their differences in weight despite the fact that they experience the same buoyant force. It is false that the buoyant force on Ball C is greater than that on Ball A.

Is not that exactly what I said? The precise definition would be 'submerged volume' but for a fully submerged ball, they are the same.

umdnjmed

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So dVdisplacedg = dVduckg

vdisplaced = vduck

Can someone please go over this and check if it is correct? I thought the density on the left was the density of the fluid, while that on the right was the density of the duck (from his/her derivation) Why did both cancel out?

Can someone please confirm the following for me so I can determine if my understanding of fluids is correct. I may have over analyzed/complicated it and gotten myself confused so please bear with me.

1) Buoyant force is always equal to m(fluid displaced) * g, if the object is floating or submerged/suspending in the fluid.

i'll use fd for fluid displaced

2)In the 2 scenarios above; partially or fully submerged (but not sinking) m(fd) * g is always equal to mg (object)

3) When the object sinks, mg (object) > m(fd) * g Therefore the object sinks, since the buoyant force cannot overcome the downward gravitational force.

4)When an object is fully submerged but suspended in the fluid, mg (fd) = mg (object), If g is canceled from both sides, both masses are equal. Because the volume of fluid displaced is equal to the volume of the object in this case, and both masses are the same, both object must have the same density...?

5) Is it right to say the density of the fluid is equal to m (fd)/ V(fd)? Since the density of the fluid is uniform, this derivation will be correct, right?

6) So I tried to apply the following logic to a partially submerged object; I equated the two known equations for buoyant force
mg (fd) = Rho (fluid) * V (obj) * g ...g cancels out
Instead of mass, substitute Rho (fluid) * V (fd) for m
Rho will cancel out on both sides
Yet I am left with V(fd) = V(obj)
But this would be wrong for a partially submerged object. Did I make a wrong assumption somewhere?

I have wracked my brain but I'm still missing something, and I have missed all the buoyancy questions on my practice exams.

umdnjmed

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Please don't bother. An aleve pill did the trick. I went online and figured everything out . The assumption I made in 2 was wrong. It applies only to partially submerged objects.

Also I didn't realize that if the object and fluid have different densities, the object cannot simply suspend in the fluid. it will eventually rise or sink, therefore there will be a net force acting on it. This net force can be calculated from the buoyant force and mg (object)

Finally, I was using V (object) in the equation for buoyant force, when it was actually the volume of fluid displaced.

Thanks all the same to anyone who even bothered to read my previous post. I'll do more research before posting next time.

milski

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Hey, no problem, asking is ok. I just read through what you've posted and if we ignore the first post, you have a good grasp of what's going on in the second one.

Full Member
Well since it's completely submerged, by definition the volume displaced matches the volume of the object. So, when is the buoyant force of an object the greatest?

Think about pulling an inflated balloon underneath the water.....at first its easy, but as you pull more and more of it underwater, its tougher to submerge....FB is greatest when volume is fully submerged.

umdnjmed

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Thanks for the confidence boost Milski