# 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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Quote:
 Original post by kelchargeTwo people got it right. It was 137 degree's, but at least I know I'm not the only one. No offense jjd. :)

You're kidding aren't you? jjd got it absolutely right, the chain doesn't start wrapping around the cylinder until it hits 90 degrees. Where did you get the question from?

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It first takes 90 degrees until the chain catches and begins to wrap around the cylinder. As jjd explained, that leaves 7 inches left. The formula for arc length is:

s = n * pi * r / 180

And solving for n we have

7 = n * pi * 5 / 180
n = 80.3 degrees

Adding that to 90 leads us to 170.2 deg.

Ergo, what jjd said.

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

haha! no way! [wink] Those answers assume that the chain sticks to the cylinder all the way. But since the chain starts at the bottom, that can't be the case until the cylinder rotates through 90 degrees. If I were to use that rationale, I could raise the bar by 5 inches by only rotating the cylinder through 57.2 degrees [smile]

-Josh

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I think kelcharge's logic would work if the chain had no length...

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Quote:
 Original post by skittleoI think kelcharge's logic would work if the chain had no length...

Ooh! I like that [smile]

-Josh

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Quote:
 Uproar over this question

This is why I hate geometry

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The way the math works out. This would be be correct if the metal bar was hanging in a hole or something that keep it from moving horizontally.

The way physics and jjd would work it out. The chain won't touch the cylinder until after the cylinder was rotated more than 90 degrees.

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Quote:
 Original post by skittleoI think kelcharge's logic would work if the chain had no length...

...and if we knew how long the bar was
...and how far from the ground it started

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The question is not explicitely clear. We assume that the bar sits on the ground at the start of the rotation. This is not specificied. So it is possible the bar is already one foot off the ground and no rotation is necessary. This question is moot.

Edit:

Quote:
Original post by Neil Kerkin
Quote:
 Original post by skittleoI think kelcharge's logic would work if the chain had no length...

...and if we knew how long the bar was
...and how far from the ground it started

Too fast for me. =P

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Quote:
 Original post by skittleoThe question is not explicitely clear. This question is moot.

Agreed. Kelcharge, you really should talk to your teacher about the ambigouity of this problem if by chance you answered the 170.2° Now unless a diagram was provided, I think you can have a valid argument.

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It's also not specified how high off the ground the cylinder is and how long the chain is. Clearly if the top of the cylinder is less than a foot off the ground, it will be impossible to raise the bar more than a foot. And if the chain isn't long enough, you might never be able to raise it in the first place. And if the chain is too long, it'd take a good deal more turning of the cylinder to raise it above the ground.

[Edited by - kSquared on September 7, 2005 10:04:45 PM]

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Plus it's not specified in which axis the cylinder turns. If you turn the cylinder in the vertical plane, then the answer will depend on how long the cylinder is and at which point you rotate it (both of which weren't specified). So everyone's answer can be deemed correct [smile].

This is why you need to think like a lawyer when you write mathematics questions. Students always try to weasel their way through everything. [wink]

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Quote:
 Original post by Trapper ZoidStudents always try to weasel their way through everything. [wink]

Rascally students!

When I first read it I was confused by the chain being on the bottom; If the cylinder is lying on its side, shouldn't one of the ends be the bottom? [smile]

Kelcharge, you bring that teacher here so we can keelhaul him! [wink]

-Josh

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It also depends on whether the chain winds over itself on the cylinder, the thickness of that chain, as well as the point on the metal bar at which the chain is attached, and the length of that bar. We may also need the chain's modulus of elasticity, moment of inertia, and linear mass, as well as the mass of the bar.

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Quote:
 Original post by FrunyIt also depends on whether the chain winds over itself on the cylinder, the thickness of that chain, as well as the point on the metal bar at which the chain is attached, and the length of that bar. We may also need the chain's modulus of elasticity, moment of inertia, and linear mass, as well as the mass of the bar.

[lol]

GameDev.net, turning even the simplest problems into rocket science.

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