Spinning object: how much faster to increase string tension by factor of 4

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StaticShock
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Alright here's the problem. An object that has 20 grams of mass and is siwnging horizontally with a 2 meter ratius. it makes 10 rotations within 12 seconds.

the question is How many times faster would the stopper have to be spun to increase the tention of the string by a factor of 4?


now, i know Fc=M (V sq'ed)/R.

Mass stays the same, so does the radious(I belive) and the tention force is = to FC so fc has to be increased by a factor of 4 . So the only real thing to change is the V.

I just don't see how.
 
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i think you just answered your own question...

"how much faster does the stopper have to be spun" not how do you make it spin faster?
 
yes, but i don't know how to do it

Do I can't simply multiply V by 4 as the Square would throw it off
 
well i actually worked it out through the full calculations but there is a much simpler way i noticed afterwards.. Anyhoo

I started by finding the period of the motion

T = 10/12

Then the angular velocity
w = 2pi/T

then it was really plug and chug.

Fc = Mw^2r
Fc = 2.23 or somewhere around that, did in head soz.

Now you know your Force, multiply that by 4 and solve for V.

answer should be exactly 2x the intial velocity.