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B Rate of sinking objects

  1. Oct 13, 2016 #1
    Hi All,

    I have a problem (with 3 separate instances) to which I believe I have the answers, but would like check with those more knowledgeable than myself. They revolve around 3 blocks sinking through water and which falls quicker. I am ignoring friction.

    Instance 1:
    All blocks are exactly the same shape and size. They have different masses however. Which falls quicker?

    Instance 2:
    All blocks are of different sizes (short/medium/long), but have the same mass. Which falls quicker?

    Instance 3:
    All blocks are made of the same material but are different sizes (short/medium/long). Which falls quicker?

    My understanding of the answers is based upon Newton's second law, buoyancy and free body force diagrams:
    W(obj) - W(wat) = mass of object x acceleration (where Weight of water is equal to its density x volume of object x gravity):

    a- ( m(o) - m(w) ) g = m(o) a
    b- ( p(o) - p(w) ) vg = p(o) v a (mass = density x volume)

    1. Using eqn a: Although m(o) increases, m(w) remains constant, therefore acceleration increases and heavier mass falls quicker

    2. Using eqn a: As they have the same mass, m(o) remains constant, but m(w) increases as the size of the object increases. Therefore, the smaller object falls quicker

    3. Using eqn b: All densities are equal, but as the volume on both sides of the equation cancel each other out, they fall at the same rate

    Is this the correct understanding? I believe it is, but it does do your head in!!!
  2. jcsd
  3. Oct 13, 2016 #2


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    Hello jr, :welcome:

    If you want to ignore friction, you are back to Galileo Galilei's experiments.
    You equations are hard to read and understand. are the a and the b enumerators or variables ?

    [edit] all right, enumerators.

    Instance 1 and 2: I agree. Some can even move upwards...
    Instance 3: agree also.

    In all cases it's pretty straightforward to write an expression for the acceleration.
  4. Oct 13, 2016 #3
    Thanks BvU,
    It basically comes down to density. Those with greater densities sink faster than those with smaller densities.
    It's basic physics but something I haven't needed to think about or do for ages - when they come up in aptitude tests you forget the equations and logic behind the reasoning!
  5. Oct 13, 2016 #4


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    Same here: Galilei had to do with non-vacuum and was genius enough to reason through that limitation. For a fish such luck isn't there :smile:
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