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# Three puzzles to ponder

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re: Three puzzles to ponder
2/19/2011 12:02:14 PM
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Darn... yeah 14.9cm from the bottom of the tank to represent 1/4 of the tank and 35.1cm from the bottom of the tank to represent 3/4 of the tank... Darn, I stand corrected,... I use the concept of Integral Calculus to calculate the area on the surface of one circular side of the tank covered by the fuel when the fuel occupies 1/4Volume and 3/4Volume of the tank... My solution was long actually... Techniques of Integration were applied: the "U substitution Method" and the "Trigonometric Substitution method"... sigh... But I enjoyed solving this puzzle... just to redeem myself... haahaha

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re: Three puzzles to ponder
2/19/2011 7:14:22 AM
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Good stuff. Again confirms the answers posted above 1/10/2011 9:30 PM EST obtained using a geometric method. Did you use a calculus method?

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re: Three puzzles to ponder
2/19/2011 5:57:43 AM
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Guess I'd post my answer... But not the solution... It's too complicated to write here... he should put the mark 14.1cm from the bottom of the tank to represent 1/4 fullness of the tank.... and he should put the mark 35.9cm from the bottom of the tank to represent 3/4 fullness of the tank...

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re: Three puzzles to ponder
2/15/2011 7:58:56 AM
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Ahw.. okay sir. :-D,.. I already have one solution for the puzzle...

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re: Three puzzles to ponder
2/14/2011 8:47:06 PM
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Good point about zeroing the scale -- I like that -- re the other ones I'll have to ponder them :-)

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re: Three puzzles to ponder
2/14/2011 7:03:03 PM
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Clarification - my answer above assumed (yeah I know what that makes me :-) that the strain gauge (spring) scale has a zero adjustment which gets set prior to use. If zeroed at the pole would read negative at the equator due to the reason you have given until re-adjusted. Anti-gravity! OK Max, since you asked in your first post here are a couple of puzzles along the same line as #3: 1) How fast would the earth need to rotate in order to exactly cancel weight at the equator? 2) The sun and moon cause the earth's tides. How much would the weight of the 100 Kg mass vary during a total solar eclipse between noon and at midnight with an ideal (perfect) strain gauge scale? To keep this less complicated, assume the mass in both cases is located directly in line with the gravitational centers of the earth, moon, and sun. For even more fun try it again for a total lunar eclipse. And no, I don't know the answers.

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re: Three puzzles to ponder
2/14/2011 6:02:35 PM
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That was covered by zeeglen's answer, distinguishing between a balance scale and a spring scale. Although even a spring scale would show some slight error, as the platform and mechanism have non-zero mass. When I first read Max's #3, I was expecting a question about acceleration forces. Even over five years, would it be noticeable? Dave

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re: Three puzzles to ponder
2/14/2011 2:24:56 PM
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This is why I ordered that DVD course on Calculus (see my other blog on "Teaching an old dog new tricks")

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re: Three puzzles to ponder
2/14/2011 2:14:13 AM
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Just figured out last night before going to bed that I was wrong... hahahaha... I thought the answer was easy... I just typed in what was on my mind the instant after I read the puzzle... Then later I formulated another solution... The solution involves integral calculus... "sigh"... thought the puzzle was easy...

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re: Three puzzles to ponder
2/14/2011 2:09:09 AM
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Now that's amazing

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