Question

A bob of mass m = 0.300 kg is suspended from a fixed point with a massless string of length L = 21.0 cm . You will investigate the motion in which the string traces a conical surface with half-angle θ = 22.0

What tangential speed v must the bob have so that it moves in a horizontal circle with the string making an angle 22.0 ∘ with the vertical?

Express your answer numerically in meters per second.

Answer 1

Given,

m = 0.3 kg ; L = 21 cm ; theta = 22 deg

Let v be the required speed. T be the tension in the string.

We know that,

T cos(theta) = w (1)

where W = mg, weight. Also:

T sin(theta) = Fc (2)

where, Fc is the centripital force

T sin(theta) = m v^2/r

Dividing (2)/(1)

T sin(theta)/ T cos(theta) = m v^2/L x mg

tan(theta) = v^2/gr

v = sqrt (g r tan(theta))

but r = L sin(theta)

v = sqrt (g L sin(theta)tan(theta))

v = sqrt (9.81 x 0.21 x sin22 x tan22) = 0.558 m/s

Hence, v = 0.558 m/s