A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string is measured to be 6.0N . What would the tension be if the ball went around in only half a second?
The tension in the string balances out, and thus equals the centripetal force of the ball
T = mv^2/r if it only takes half the time to finish one orbit it has to be moving at twice the original speed. And since v is squared T will increase by 4 T' = m(2v)^2/r T' = 4mv^/r = 4T T' = 24.0 N
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