Uniform circular motion: A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution?
A) 4.8 s
B) 3.8 s
C) 4.5 s
D) 5.2 s

Question

Quizplus · Accepted Answer

Explanation:The centripetal force is provided by the tension in the string.$$F_c=ma_c=\frac{mv^2}{r}$$$$T=\frac{mv^2}{r}$$$$v=\sqrt{\frac{Tr}{m}}=\sqrt{\frac{(51	ext{ N})(1.3	ext{ m})}{23	ext{ kg}}}=3.8	ext{ m/s}$$$$T=\frac{2\pi r}{v}=\frac{2\pi(1.3	ext{ m})}{3.8	ext{ m/s}}=\boxed{4.8	ext{ s}}$$

Uniform Circular Motion: a 23 Kg Mass Is Connected to a Nail