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math question

Lasagna
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9/22/2011 3:42:30 AM
Posted: 5 years ago
Let's say you have a one-meter string. Point a, one end of the string, is stapled to a table. Point b, the opposite end, is moved through the air in an arc, of say .25 meters (we'll only deal with a two-dimensional plane). If I take one more point (c) half-way through the string, is there a formula that establishes a relationship between points b and c? IOWs, if I move the end of the string through a .25 meter arc, how far has point c moved? I have a friend who needs to know this for a construction job.
Rob
Ore_Ele
Posts: 25,980
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9/22/2011 9:41:27 AM
Posted: 5 years ago
At 9/22/2011 3:42:30 AM, Lasagna wrote:
Let's say you have a one-meter string. Point a, one end of the string, is stapled to a table. Point b, the opposite end, is moved through the air in an arc, of say .25 meters (we'll only deal with a two-dimensional plane). If I take one more point (c) half-way through the string, is there a formula that establishes a relationship between points b and c? IOWs, if I move the end of the string through a .25 meter arc, how far has point c moved? I have a friend who needs to know this for a construction job.

If c is 1/2 way between a and b, then it will move 1/2 the distance.

This is because you are moving along a partial circumfrence of the circle, where distance is expressed as theta*r (I don't know how to make the theta symbol on the computer, but it is the "o" with the line through the middle [1]), where theta (we'll call "o") represents the angular radians and r is the radius of rotation.

So let's look at the two arcs, we'll call them arc_b (arc made by point b) and arc_c (arc made by point c). arc_b = .25 meters, we know this because it was defined. what we are trying to find is arc_c.

arc_c = o*r_c (where "r_c" = the radius to point c). Since "r_c" = 1/2*r this can be subed in, so arc_c = o*(1/2*r) or arc_c = 1/2*o*r.

Since o*r = arc_b we can now say that arc_c = 1/2*arc_b. or .125 meters

[1] http://www.google.com...
"Wanting Red Rhino Pill to have gender"
Lasagna
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9/22/2011 10:06:53 AM
Posted: 5 years ago
So what you're saying is that the % of the way up the string is exactly equal to the % of the arc that the point goes through? So if the point is 1/4 the way up the string, and the end arc is 1 foot, then the point goes through a 1/4 foot arc?
Rob
Ore_Ele
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9/22/2011 10:08:56 AM
Posted: 5 years ago
At 9/22/2011 10:06:53 AM, Lasagna wrote:
So what you're saying is that the % of the way up the string is exactly equal to the % of the arc that the point goes through? So if the point is 1/4 the way up the string, and the end arc is 1 foot, then the point goes through a 1/4 foot arc?

Yes.
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Lasagna
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9/22/2011 2:48:41 PM
Posted: 5 years ago
That's funny, because if you think about it, it couldn't be any other way. A point at 99.99% of the length would have to go through just under the full length, and a point right near the bottom would almost not move. So logically it would have to be a scale, starting at 0% at the bottom and 100% at the top, which is directly proportional to the % distance it is from the top point. I probably would have assumed this, but the person who asked me seemed to indicate that it might be more complicated and I never bothered to think it through. Thanks for clarifying that for me.
Rob