forces physics problem - Please Help ASAP

Question

A 0.70 kg stone attached to a string is whirled in a horizontal circle of radius 28 cm as in the figure below. The string makes an angle of 30° with the vertical.

(a) Find the speed of the stone.

(b) Find the tension in the string.

Answer 1

The store travels in a 38cm radius (0.38m).   Strangely enough, we must find forces in the vertical direction to solve this problem.

The centrifugal force in the horizontal direction is mV^2/r.   This is also the horizontal component of the string tension.   The vertical component is then (mv^2/r)*tan 30.

The vertical component must equal mg so that the string does not accelerate upwards or downwards.

mg = (mv^2/r)*tan 30.   V^2 = gr/tan 30.

Then to find the string tension, we have the horizontal and vertical components of the tension. 

Vertical = mg, horizontal = mg * tan 30.  Use pythagorean theorem to find the result Tension.