# Think your smart, I thought I was...

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Here is a math problem that I failed to solve correctly, let's see if you can. There is a metal cylinder 10 inches in diameter. The cylinder is suspended in the air on its side. At the bottom of the cylinder is a chain and at the bottom of the chain is a metal bar. It needs to be lifted 1 foot off the ground. How many degree's does the cylinder need to turn? I do not need this as an answer to homework as it was on a quiz and I missed the point, but now that I have the right answer I want to see how dumb/smart I am compared to other people and not a teacher with a book.

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I am not smart, but I like puzzles.

First rotate the cylinder through 90 degrees. This will have the chain hanging directly down from the side. In other words, the bar has been raised by the radius of the cylinder, 5 inches. We need another 7 inches to raise the bar by a foot. The circumference of the cylinder is 10*pi so 7/(10*pi) is the fraction of a revolution we need to continue turning the cylinder by. Since there are 360 degrees in a complete revolution this means we need to turn the cylinder by (7*360)/(10*pi) or 2520/(10*pi) degrees, which is about 80.2 degrees. So, in total the cylinder has to rotate 170.2 degrees.

Anyway, that's my spin on it [smile]

-Josh

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Sorry but your wrong, but I'll give you a hint, it has something to do with arc length of a circle.

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My guess is ~137°

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Answer reversed to not spoil it for the rest of you mathletes.

.ytxis derdnuh eerht semit net revo owt sulp yteniN

Could be wrong, too. This is just my first impulse.

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Quote:
 Original post by Drew_BentonMy guess is ~137°

Better not be! I'll have to beat the OP with my logic stick! [wink]

-Josh

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My probaly wrong solution.
137.51 degrees

C=2*r*pi

10*pi=31.42'

12'/31.42'=0.382 or 12' would equal a 38.2% turn of the cylinder.

38.2% * 360 degrees = 137.51 degrees.

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Quote:
 Original post by jjdBetter not be! I'll have to beat the OP with my logic stick! [wink]

Well, I should have put my "educated guess" - which now thinking about is wron I think. Here's what I did:

Arc Len = 2*pi*r*arc measure/360
So I solved for when the arc length is 12 (inches) and got that answer. However, I'm thinking that the wrapping of the chain around the cylinder would require more turns then I have accounted for. I don't know, we'll see!

At least someone else, Kestrel, got what I did [wink]. I just used pi as 3.1415 and didn't bother with accurate decimals.

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Two people got it right. It was 137 degree's, but at least I know I'm not the only one. No offense jjd. :)

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I think that it you take into account gravity pulling the chain away from the bottom of the cylinder as it turns it should be 170.2. If the chain and cylinder were magnetized then it would wrap tightly around it and you get 137.

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