If the ball revolves twice every second, what is the tension in the string?

AI Thread Summary
To determine the tension in the string of a rotating ball, first calculate the velocity using the formula v = 2πr/T, where T is the period of rotation. Given that the ball revolves twice per second, the period T is 0.5 seconds. This velocity is then used to find the centripetal acceleration with the formula a_c = v^2/r. The relationship between centripetal acceleration and tension in the string is expressed through the equation m * a_c = F_T + F_g, where F_g is the gravitational force. The discussion highlights the need for step-by-step calculations to arrive at the correct tension value.
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A 0.25-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m. If the ball revolves twice every second, what is the tension in the string?
 
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1) How can you figure out the velocity of the ball by the information given?
2) How is that velocity related to the centripetal acceleration experienced by the ball?
3) How is the centripetal acceleration of the ball related to the tension in the string?
 
v = \frac{2 \pi r}{T}
a_c = \frac{v^2}{r^2}=\frac{4 \pi^2 r}{T^2}
m \cdot a_c = F_T + F_g
i don't know if that's it, because I am kind of limited on my sources. I am at work, and I am not even supposed to be on this site. :smile: the last equation is probably wrong, but i know the first two are right. well, i think. :smile:
 
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i don't think that is right, i need the step by step help
 
all you have to do is plug in the numbers.
 
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