Question

An object of mass 5 kg is secured by a string and set to rotate round a vertical circular path of 2 m radius . when the object is at the lowest possition its tangential speed is 6 m/s , calculate the tension in the string.

Answer 1

Question#14603

An object of mass $5\,\mathrm{kg}$ is secured by a string and set to rotate round a vertical circular path of $2\,\mathrm{m}$ radius. When the object is at the lowest position its tangential speed is $6\,\mathrm{m/s}$, calculate the tension in the string.

Solution:

Let:

$$m = 5\,\mathrm{Kg}$$ $$r = 2\,\mathrm{m}$$ $$v = 6\,\mathrm{m/s}$$ $$F - ?$$

$F = mg + Ft$, where $Ft$ – centrifugal force

$$F = mg + m\omega^2 r, \text{ where } \omega \text{ – angular velocity}$$

As: $v = \omega r$; $\omega = \frac{v}{r}$

$$F = mg + m(\frac{v}{r})^2 r = mg + m\frac{v^2}{r}$$ $$F = 5 * 9.8 + 5 * \frac{6^2}{2} = 139\,\mathrm{N}$$

Answer: 139 N.