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December 21, 2014

December 21, 2014

Posted by **David** on Wednesday, April 21, 2010 at 7:24pm.

- Physics -
**Damon**, Wednesday, April 21, 2010 at 7:30pmm v^2/r

v the same

r the same

twice m

- Physics -
**Damon**, Wednesday, April 21, 2010 at 7:32pmWait a minute, this horizontal circle does not mean the string is horizontal.

r will not be constant in the real case.

- Physics -
**Damon**, Wednesday, April 21, 2010 at 7:47pmSay string at angle A from vertical.

Then r of circle = R sin A if R is string length

Inward force on mass by string = T sin A

so

T sin A = m v^2/r = m v^2/(R sin A)

T sin^2 A = m v^2/R

Vertical force on mass by string = T cos A

so

T cos A = m g

period = p = 2 pi r/v = 2 pi R sin A/v

so

v = 2 pi R sin A/p

and

v^2 = 4 pi^2 R^2 sin^2A/p^2

so

T sin^2 A = m v^2/R = m * 4 pi^2 R^2 sin^2A/p^2

so

T = m 4 pi^2 R^2/p^2

interesting, if p is the same when you double m you double the tension

I suppose that makes sense in the limit of very slow and hanging just about straight down, the tension is mostly m g and has to be double for twice the mass.

- Physics -
**Damon**, Wednesday, April 21, 2010 at 7:58pmAnd we already did the limit for very fast, string horizontal also gives twice the tension for twice the mass.

Cute problem !

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