# Density Question

Discussion in 'MCAT Study Question Q&A' started by niranjan162, May 12, 2008.

1. ### niranjan162

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Came across this question:

[FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif]Another block of identical dimensions to the first is held half immersed in the water. When released, it sinks. When the block was released, which of the following must be true?

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1. [FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif]
[*]A. weight of fluid displaced > weight of block[URL="http://javascript%3Cb%3E%3C/b%3E:strikeq%281734,1%29;"][x][/URL]
[*]B. Density of fluid < density of block[URL="http://javascript%3Cb%3E%3C/b%3E:strikeq%281734,2%29;"][x][/URL]
[*]C. Buoyant force < maximum buoyant force [URL="http://javascript%3Cb%3E%3C/b%3E:strikeq%281734,3%29;"][x][/URL]
[*]D. Maximum buoyant force = half the weight of the block
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Answer is C for this reason

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[FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif]"Tricky! You must recognize that the half immersed block would sink as long as its density is greater than that of the original wood block which floats half immersed (see Q32). Thus the second block may: (i) have a specific gravity between 0.5 and 1.0 (which means the block's density would be less than that of water); or (ii) it could have a density equal to that of water; or (iii) it could have a density greater than that of water: either way, it would sink from a position of being held half immersed [thus answer choice B. is not the best answer because of the preceding points (i) and (ii)]. When the block sinks, it will certainly displace more water than it did initially; therefore, the buoyant force increases to its maximum.{cf. Archimedes Principle, Q31}"

I dont get it. I thought the fact that the density was greater made it sink.
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3. ### Kaustikos Archerize It

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The point it's trying to make is that you do not know that it is necessarily more dense than the fluid upon initial release. The idea that it "sinks" initially is that it's more dense than the other block, hence why it sinks more. But you do not know for sure if it will completely submerge in the fluid. The question never states that it submerges (or that it stops for that matter), that's why in the explanation it talks about the 3 possibilities. Since we do not know if it submerges or floats, we cannot honestly say that it is more dense than the water. For all we know, the block may float once the block becomes 2/3 submerged instead of 1/2 like the other block, thus making it more dense than the block for sure. That is the definitive in this "experiment".

I do have a question that hopefully someone else can answer:
For buoyant forces, how does one know when we have reached maximum force? I guess I am asking if a submerged/sinking ever reaches "maximum" buoyant force when it is falling underwater? Is that basically F = pgV and that when completely submerged you have maximum buoyant force? And in the case of a floating object, it's just the volume displaced?

4. ### physics junkie

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Word play is lame. You generally don't say something sank when you put it in water and it floats with 2/3 submerged.

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