Another Physics Brain Teaser

Discussion in 'All Things Boats & Boating' started by DGreenwood, Jan 27, 2007.

  1. MikeJohns
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    MikeJohns Senior Member

    Thats a planing hull. Would be very impressive.:)
     
  2. MikeJohns
    Joined: Aug 2004
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    MikeJohns Senior Member

    Simple static bouyancy questions thrown at first year students are suposed to test understanding. Here's one out of a final year exam that caused more problems than it should have:

    A solid steel sphere 1m in diameter floats in a bath of Mercury. Calculate the total submerged depth given the SG of Steel is 8 and SG of mercury is 13.6

    Pure water at 4 degrees (sg of 1) is introduced to a depth of 1m above the surface of the mercury. Calculate the new immersion depth relative to the mercury surface.

    Give the pressure acting on the extreme top and bottom of the sphere.
     
  3. Frosty

    Frosty Previous Member

    Jeeeesus I throw the towel in. I couldnt work that out to save my life.

    Probably need Poida and his vacuum cleaner.

    I tell you what --after youve debated this I would really like to see some one --any one explain the maths involved.
     
  4. Poida
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    Poida Senior Member

    Mike, does a barge have to actually plane to pressurise the water underneath it. A barge, not common here, I would have thought has a straight bow wedge shaped towards the bottom.

    My interpretation of a planing hull is one that can lift out of the water not one that is trying.

    Even take into consideration an olympic swimming pool has to be a specified depth as there is a reaction between the swimmer and the bottom of the pool. (just to change the subject completely)

    I'll get back to the sphere in the murcury later gotta go shopping.

    Poida
     
  5. antoineb
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    antoineb Junior Member

    the bulldozer one is too easy

    if hanging below the barge it displaces some water i.e. weighs less on the barge, so the barge will obviously be floating higher.

    i'm not sure this qualifies as a brain teaser, sorry ;-)
     
  6. Frosty

    Frosty Previous Member

    There is a part B to the barge over the bridge question.

    I think we have established that the scales of the bridge would not move as the barge passed over it

    The Aquaduct was built with lock doors, I didnt tell you this but it was.

    You then shut the doors as the barge is on the bridge and seal in the water and the barge.

    You then drain away all the water in the canal, and remove the canal.

    You are left with a 2000 ton bridge-2000 tons of water and a 1000 ton barge. Ok the water will be more than 2000 tons due to the displacement of the barge when it was launched anywhere along the canal but not 1000tons more on the scales. Where is the weight of the barge?
     
  7. Raggi_Thor
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    Raggi_Thor Nav.arch/Designer/Builder

    I don't get it :)
    I thought we had less water in the aqueduct after the barge displaced some of it.
     
  8. Frosty

    Frosty Previous Member

    Ah---- that might be the answer then. I dont know the answer its something I always wondered about. Mmmm that explains it. Of course!!
     
  9. PI Design
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    PI Design Senior Member

    Putting my head on the line with this one:

    Initial draft = 0.559m
    Draft after adding water = 0.559m
    Pressure at TDC = 5.48 Pa
    Pressure at BDC = 84.39 Pa
     
  10. Raggi_Thor
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    Raggi_Thor Nav.arch/Designer/Builder

    Seems reasonable since 8/13.6 = 0.588.
    Do you remember a formula for the volume of a sliced sphere, or do you integrate (is that the name in English?).
     
  11. PI Design
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    PI Design Senior Member

    Raggi,

    I used the volume of a sliced sphere, but it still wasn't all that easy, because the formula requires you to know the depth of slice and the radius at that depth to calculate the volume. In this case, I knew the volume required, but obviously not the depth, nor the radius at that depth. However, being a sphere, the radius is a function of the depth, so I could combine the two with a bit of trigonometry.
    I guess you could do it from first principles and use calculus to integrate, but this seemed easier.
     
  12. Raggi_Thor
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    Raggi_Thor Nav.arch/Designer/Builder

    Good work :)
     
  13. Poida
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    Poida Senior Member

    Back from shopping but I see that PI has already worked out the steel sphere in the mercury bath problem.

    Yes of course using the old "volume of a sliced sphere formula" and a bit of trigonometry.

    Bit of a bugger really since while I was out shopping I bought myself a metre diameter steel ball and a bath of mercury. I thought the physical experiment would have proved more accurate.

    Now I've got to find a use for a steel ball and a bath of mercury.
     
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  14. Raggi_Thor
    Joined: Jan 2004
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    Raggi_Thor Nav.arch/Designer/Builder

    Maybe you can make yourself a very accurate and quite decorative thermometer in the garden, preferably seen from the kitchen window?
     

  15. PI Design
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    PI Design Senior Member

    Sorry mate! I've no idea if I'm right though, so feel free to have a go yourself. Do you agree that the the draft (relative to the mercury) is unaffected by the addition of the water?

    Balls of steel in the bath, eh? Yup, I think a giant thermometer is the way to go. Or some kind of decorative mercury fountain, balancing the ball on top.
     
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