Question

A pendulum Bob is 1.0kg is attached to a string of length 1.5m. The Bob moves in a horizontal circle in such a way that the sting is inclined at 60° to the vertical. Calculate (i) the radius of the circular path (ii) tension of the string (iii) period of them motion.

Answer 1

i)

$$r=\frac{l}{\sin{60}}=\frac{1.5}{\sin{60}}=1.7\ N$$

ii)

$$T=\frac{mg}{\cos{60}}=\frac{(1)(9.8)}{0.5}=20\ N$$

iii)

$$F=mg\tan{60}=1(9.8)\tan{60}=17\ N.$$

$$F=mr\omega^2$$

$$17=(1)(1.7)\omega^2$$

$$\omega=1\frac{rad}{s}$$

$$T=\frac{2\pi}{\omega}=\frac{2\pi}{1}=6.3\ s$$