Question

Problem , (20%) A 0.9 kg block of negligible size is located a d-0.8m from the center of a rotating platlorm with an outer radius of D-2m, as shown in the picture to the right The platforn starts rotating from rest, and its angular speed increases at a constant rate of 1.2 rad's The coefficient of static friction between the block and the platform is Ah-02. Draw two clear, complete, and appropriate free body diagrams of the situation in the designated spaces below: a top view and a side view. b. What is the velocity of the block when it just begins to slip? c. How much time passes after the platform begins to rotate before the block just begin to slip? Top view FBD Side view FBD

Answer 1

(b) F_L = mu_s N = mu_s mg at the time of slipping F_L = m a_c material implication mu_s kg = m w^2 r material implication w^2 - mu_s g/r = 0.2 times 9.8/0.8 w^2 = 2.45 material implication w = 1.56 rad/s v = r w = 0.8 times 1.56 material implication v = 1.25 m/s (c) w = w_0 + alpha t 1.56 = 1.2 t material implication t = 1.56/1.2 material implication t = 1.3 sec