A bob of mass m = 0.200 kg is suspended from a fixed point with a massless string of length L = 25.0 cm . You will investigate the motion in which the string traces a conical surface with half-angle θ = 24.0 ∘. What tangential speed v must the bob have so that it moves in a horizontal circle with the string making an angle 21°C with the vertical?

v= 0.667 m/s

Explanation:

M= 0200 Kg, L= 25.0 cm=0.25 cm, θ = 24.0°

To find: V=?

Solution:

according to the situation the formula after deducing the  result from the horizontal and vertical components of the force that is

∑(Fx) = Fc= mv²/r = T sinθ eqn 1

and ∑(Fy) = 0 N= T cosθ - W = T cosθ - mg

T cosθ = mgeqn 2

Dividing eqn 1 by eqn 2 we get

(mv²/r)/mg = T sinθ / T cosθ

⇒ v = square root ( gr tanθ)            (r is radius of the circular path that mass will move)

so to find radius r = L sin θ = 0.25 m  × sin 24° = 0.102 m

thus v = square root ( 9.81 m/s² × 0.102 m ×tan 24°)

v= 0.667 m/s