1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Stability of object

  1. Mar 5, 2016 #1
    1. The problem statement, all variables and given/known data
    is it necessary to find the meta center for this question ? the formula of meta center is I /Vd , the I ( moemtn of inertia ) for rectangle is (ab^3) / 12 , but what is a ? what is b ? i'm confused now

    2. Relevant equations


    3. The attempt at a solution
    ρ
    gVsubmerged = weight(579N)
    1025(9.81)Vsubmerged = weight(579N)
    Vsubmerged = 0.058m^3

    0.058m^3 = (1.2x0.9x hsubmerged)
    hsubmerged =0.054m

    center of buoyancy = 0.054/2 = 0.027m
    metacenter = I / Vd = [(ab^3) / 12 ] /Vd
     

    Attached Files:

  2. jcsd
  3. Mar 5, 2016 #2

    Buzz Bloom

    User Avatar
    Gold Member

  4. Mar 5, 2016 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    For a rectangle measuring a by b, the second moment of area about an axis through the mid points of the sides of length b is ##\frac 1{12}ab^3##.
     
  5. Mar 11, 2016 #4
    what is the value of a and b ? is the second moment about x -axis(Ixx) , right ? IMO , a is 0.9m , b is 1.2m , am i correct ?
     
    Last edited: Mar 11, 2016
  6. Mar 11, 2016 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In principle, you should consider each axis as a potential axis for tipping. However, it is obvious that one of ab3, a3b is the larger. Which gives the greater danger of tipping, the larger or the smaller?
     
  7. Mar 11, 2016 #6
    how to know which axis is more danger of tipping ?

    the hydrostatic pressure act on the top and the bottom surface of the object , so i am consdiering the moment about x of tipping
     
  8. Mar 11, 2016 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Is tipping more likely with a high metacentre or a low one?
     
  9. Mar 11, 2016 #8
    low metccenter , right ?
     
  10. Mar 11, 2016 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  11. Mar 11, 2016 #10
  12. Mar 11, 2016 #11
  13. Mar 11, 2016 #12

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes.
    To get a low metacentre, does "I" need to be large or small? If a>b, which of ab3 and a3b will give that less stable i?
     
  14. Mar 12, 2016 #13
    to get low metacenter , the I has to be small. since the water pressure act on the bottom of the box , the b is 1.2m , a is 0.9m , am i right ?
     
  15. Mar 12, 2016 #14

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It depends how you are defining a and b. Is that using the a3b form or the ab3 form?
     
  16. Mar 12, 2016 #15
    I am using
    ab3
     
  17. Mar 12, 2016 #16

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Does a=.9, b=1.2 give a lower I than the other way around?
     
  18. Mar 12, 2016 #17
    a=1.2 , b = 0.3 , i would get lower metacenter , but the formula is yp = yc + Ixx / (ycA) , Ixx is the second moment of inertia about x-axis . Ir cant be changed , right ?
     
  19. Mar 12, 2016 #18

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The object in question could tip about either of two axes. If you fix one direction as x and apply that formula you will only be considering one axis of tipping.
     
  20. Mar 12, 2016 #19
    why not 3 axes? since the object is 3d ( as shown in the diagram )
     
  21. Mar 12, 2016 #20
    for a = 1.2 , b = 0.3 , i will get metacenter = 1.25m , but , which value to choose ? 1.25m or 2.22m( a = 0.3, b = 1.2 ) ?
    if metacenter = 1.25m or 2.22m , G located at 0.86m +0.3m =1.16 m , object is stable
     
  22. Mar 12, 2016 #21

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, it's 3D, and you are right that in principle it could tip over any axis. But it is fairly obvious that the most likely tip is about the natural axes. Feel free to analyse the general case.:wink:
    To check for stability, consider the worst case, i.e. the least metacentric height.
    The metacentric height you calculated, 1.25m, is the height from the centre of buoyancy, not from the base.
    But that only makes it even more stable than you concluded.
     
  23. Mar 12, 2016 #22
     
    Last edited: Mar 12, 2016
  24. Mar 12, 2016 #23
    i thought when we consider the center of pressure , we only need to consider the Ixx ( second moment of inertia about x -axis) , y -axis is the vertical axis ..... this is the first question i ever encountered that we need to find the second moment of inertia about 2 axes
     
  25. Mar 12, 2016 #24
    Why do we wanna consider 2 axes for rotation of object?
    Normally we consider only 1 axis of rotation of object, right?
     
  26. Mar 12, 2016 #25

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You're getting confused here.

    We're talking about the stability of this platform. The center of pressure, etc. has no bearing on this analysis.

    The location of the metacenter M depends on the inertia of the waterplane cut by the hull of the platform. Using b = 0.3 would make no sense, since this dimension represents the depth of the platform's hull.

    The Ixx used in the equation for yp represents something else and is not applicable here.

    For the stability of this platform, BM = I / V, but I can be calculated about an axis which either runs parallel to the length of the platform or parallel to the breadth of the platform, which ever choice leads to the least value of I. V = volume of displacement and remains the same in any event.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted