Question

A rock (mass = 150g) is being swung in a circle. The length of the string is 0.5 m. If the string makes an angle of 30 degrees with the horizontal, what is the tension in the string and what is the velocity of the rock? Please show and explain as much work as possible. Thank you!

Answer 1

Tension of the string for a circular motion at an angle is given by,  $T = \frac{W}{\cos \theta}$

$\Rightarrow T = \frac{mg}{\cos 30^o} = \frac{0.150 * 9.8}{ \cos 30^o} = 1.7 N \rightarrow Answer$

Centripetal Acceleration,  

T sin R m

$\Rightarrow \frac{v^2}{L \sin \theta} = \frac{T \sin \theta}{m }$

Rearranging, Velocity, $v = \sqrt{\frac{T \sin \theta* L\sin \theta}{m }}$

$\Rightarrow v = \sqrt{\frac{1.7 \sin 30^o* 0.5\sin 30^o}{0.150 }} = 1.19 m/s \rightarrow Answer$