A string under a tension of 50.5 N is used to whirl a rock in a horizontal circl

Question

A string under a tension of 50.5 N is used to whirl a rock in a horizontal circle of radius 2.30 m at a speed of 20.8 m/s on a frictionless surface as shown in the figure below. As the string is pulled in, the speed of the rock increases. When the string is 1.00 m long and the speed of the rock is 52.5 m/s, the string breaks. What is the breaking strength, in newtons, of the string?

Explanation / Answer

In first case T = m v^2 / R ==> m = T R / v^2 = 50.5 * 2.30 / 20.8^2 = 0.2684 kg Therefore T' (breaking strength ) = m v'^2 / R' = 0.2684 * 52.5^2 / 1.00 = 740 N

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