A girl having a mass of 15 kg sits motionless relative to th

A girl, having a mass of 15 kg, sits motionless relative to the surface of a horizontal platform at a distance of r = 5m from the platform\'s centre., If the angular motion of the platform is slowly increased so that the girl\'s tangential component of acceleration can be neglected, determine the maximum speed which the girl will have before she begins to slip off the platform. The coefficient of static friction between the girl and the platform is mu = 0.2.

Solution

As the girl is on the verge of slippingN

F = mu_s N - 0.2 N

sigma Fb = 0

N - (15 * 9.8) = 0

N = 147 N

sigma Fn = m a_n

(0.2 * 147) = 15 (v² / 5)

v² = (0.2 * 147 * 5) / (15)

v = 3.13 m/s