Physics, please show steps how to solve

Question

A 0.90 kg stone attached to a string is whirled in a horizontal circle of radius 43 cm as in the figure below. The string makes an angle of 30° with the vertical.

(a) Find the speed of the stone.

 m/s

(b) Find the tension in the string.

 N

Answer 1

We start by applying Newton's 2nd Law in both the radial and vertical directions. In the radial direction we have Tsin(θ) = ma = mv²/r. In the vertical direction we have no acceleration so Tcos(θ) = mg ⇒ T = mg/cos(θ). Plugging this into the radial equation gives mgtan(θ) = mv²/r ⇒ v = (rg tan(θ))^1/2.