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Questions on buoyancy

  1. Feb 1, 2012 #1
    1)How can a fluid exert pressure in all directions ?The only force that a fluid exerts is its weight (as far as I know) and as weight acts downwards, fluids should only exert pressure in the downward direction. Also why do they say fluids exert pressure in all directions ? Why can't they say fluids exert force in all directions?

    2)Why do liquids exert an upward force on objects ? Is it because the object exerts a downward force on the liquid, so the liquid exerts a reaction force on the object ? If that is true then since action = reaction, the upward force should push the object up with a force equal to the objects weight which means that all objects should float. Also,if the reaction force is not the upward force then what happens to the reaction force ?

    3)If we push a cork to the bottom of a bucket of water it shoots back up. My textbook says that this is due to the upward force of water on the object, but if that is true then why doesn't water exert a downward force on the object (maybe the downward force could be its weight ?) because water exerts pressure in all directions, including downwards ?

    4)In my textbook there is a picture of a guy underwater picking up a treasure chest or something that looks like a treasure chest and under the picture they have written that it weighs less underwater so he can easily pick it up. But how would it be easier to pick it up as it would be lying on the floor so there would be no water underneath it so how could could the water exert an upward force on it ? Is it through the irregularities on its surface ? If yes, then what if it was a perfectly smooth box?

    After doing a bit of research on the internet I think I understand a bit ( but I'd still like my previous questions to be answered ) and I also have a few more questions -

    5)From what I gathered an object immersed in water experiences a net upward force because the "pressure a liquid exerts increases with depth" so the upward force at the bottom will be more than the downward force at the top resulting in a net upward force.But won't there also be a downward force at the bottom of equal magnitude as the upward force at the bottom.This would mean that the upward force of greater magnitude would be cancelled resulting in no net force ? The only explanation I could come up with is that the downward force of equal magnitude has no surface area on which to act. Is this correct?

    6)But what if the object was shaped like a very,very thin disc ? Then the pressure difference would also be extremely small meaning that the difference between the upward force and the downward force would also be very small. And if a long rod like object was placed vertically in water the pressure difference would be very high resulting in a much greater upward force. So, this means that buoyancy depends on the shape of the object.

    7)Another question I have is that if the pressure a liquid exerts increases with depth then if you take a object shaped like a upside down pyramid then the pressure at the top will be less but it will have more surface area meaning bigger force whereas at the bottom there will be less surface area therefore less force.So, again buoyancy depends on shape.

    Please make the answers as simple as possible.
    Last edited: Feb 1, 2012
  2. jcsd
  3. Feb 1, 2012 #2
    Imagine a balloon that you squeeze with your hand. The balloon expands in all directions, not just the direction you push it in. If it's just the weight of the fluid pushing down, the same principle applies...the fluid pushes down, but the fluid below wants to get out of the way in all directions, producing a force in all directions. I suppose you can say "force", but the magnitude of the force depends on the area. Pressure takes both these variables into account.

    It does exert a downward force as well, but the downward force can only act against the upper surface of the cork, which is under less pressure than the lower surface. Remember, the pressure always acts perpendicular to the surface.

    Yeah, you're kind of right. We must assume that there are irregularities in the box and the floor. Most likely water will get in there unless there's a perfect seal. Also the box is probably flooded with water which acts to llift its contents. Either way, if there's gold and metals in there I doubt he's going to "easily" lift that.

    You're correct, there's no surface for the pressure to act on. This is where using the word pressure becomes important. Since Pressure x "surface" = force, no "surface" gives you no force. The pressure also only acts perpendicular to the surface....and it's going to press it, not pull it.

    You would think so, but then if you go through the math you realize that a very thin disk might have a small pressure difference between the upper and lower surfaces....but then the surfaces are large, giving you a force. If you orient the disk so that it's vertical, the pressures then act on smaller surfaces (just the edges), but then the pressure differences are larger, giving you an identical force.

    The pressure at the bottom doesn't just act at the tip, but perpendicular to each face. That's ALOT of area that it has to act on. It might not act straight up and it might diminish as you go up the pyramid, but then there's more of the pyramid to act against, giving the same result. You can play it any way you want...you can add ribs to an object to maximize the downward area and minimize the upward area. But for an object to make sense, the area facing down has to be equal to the area facing up. Otherwise the object simply can't exist. Then if you try to solve for all the forces on each face, you will see that no matter what you do and how you orient it, the end result is that the shape doesn't matter. Just volume.
    Last edited: Feb 1, 2012
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