A string can withstand a force of 135 N before breaking. A 2.0 kg mass is tied to the string and whirled in a horizontal circle with a radius of 1.10 m. What is the maximum speed that the mass can be whirled at before
the string breaks?

The mass would have centripetal acceleration a given by

a = v ² / R

where

v = tangential speed of the mass

R = length of the string

By Newton's second law, a maximum tension of F = 135 N would apply an acceleration of

135 N = (2.0 kg) a   →   a = 67.5 m/s²

which requires a tangential speed v of

67.5 m/s² = v ² / (1.10 m)   →   v = √((67.5 m/s²) (1.10 m)) ≈ 8.62 m/s

resonant frequency

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