Simple challenging fluid mechanics question(buoyancy)

  • #1
hello fluid knowers!
here is a question i have asked from several students every time a different answer was given to me.
now lets see what is your answer mechanicals!

question:
we have a steel block floating in mercury as shown below:
http://www.pikipimp.com/pp/pimped_photo/s/image/41/662/573/1.JPG?ts=1235241467627

now we bring the block out of mercury and cut a piece of block for example EFHG and then again put it in the mercury,the question is how pressure on the lower surface of block named CD changes?
here is possible answers:
-it is equal in both states
-it is lower in second state
-it is lower in first state
-it depends on how we cut the block
 
Last edited by a moderator:

Answers and Replies

  • #2
russ_watters
Mentor
20,577
7,241
It is lower in the second state. Basically, you have a block with the same dimensions and a lower weight in the second state than in the first. It floats higher and the pressure on the bottom surface is lower.
 
  • #3
you were near the right answer but i have another opinion, i will give it away tonight.
 
  • #4
1,564
7
Russ is right. Its a simple statics problem. Less weight means there is less mass to be supported against gravity and since the geometry of CD didn't change the pressure will be lower.
 
  • #5
1
0
Second way the pressure would be less.
 
  • #6
i can confirm that your answers were right,but i think there is an exception,if you cut the piece in this way:
-EF and HG can have any length
-Eh and FG are cut so that their length is equal to AC or BD,i mean if AC and BD are for example 1 [m],EH and FG are cut so that their length is 0.99999 [m]
in this way the pressure would be very very near to first state and we can take them equal.
what's your opinion?
 
  • #7
djeitnstine
Gold Member
614
0
They can be approximated to be equal but are not.
 
  • #8
Q_Goest
Science Advisor
Homework Helper
Gold Member
2,974
39
i can confirm that your answers were right,but i think there is an exception,if you cut the piece in this way:
-EF and HG can have any length
-Eh and FG are cut so that their length is equal to AC or BD,i mean if AC and BD are for example 1 [m],EH and FG are cut so that their length is 0.99999 [m]
in this way the pressure would be very very near to first state and we can take them equal.
what's your opinion?
If the slot is cut such that mercury can flow into this cut slot, then if you do what you're suggesting, then yes, the pressure is effectively the same with only some small deviation due to the volume of material left between the two remaining sections.

I think that looking at your diagram, it is assumed that mercury won't ever be able to enter this volume (EFGH) that was removed. If that were the case, then the block would only ever float higher and result in lower pressure.
 
  • #9
2,017
85
Thats a pretty ******** ambiguous question if you ask me.

Very very near does not make them equal. Bottom line remove material = lower pressure.

And for another thing cutting EH to = AC would remove that section ACEH from the main block.
 
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