Moving mass on a platform from a beam in angular motion. Calculus based dynamics

Question

Moving mass on a platform from a beam in angular motion. Calculus based dynamics

A small block B is supported by a platform connected at A to rod OA Point A describes a circle in a vertical plane at constant speed vA, while the platform is constrained to remain horizontal throughout its motion by the use of a linkage (not shown in the figure). The coefficient of static friction between the block and the platform is must j = 0.4. Determine the maximum allowable speed v_A if the block is not to slide on the platform, and the values of theta for which sliding is impending at this speed. [v_A = 1.21 m/s; theta = 21.8degree and 158.2degree]

Explanation / Answer

us =0.4 , r =400 mm, g =9.8m/s^2

(a) vA = (us*r*g)^1/2 = (0.4*0.4*9.8)^0.5

vA =1.25 m/s

(b) tan (theta) = us = 0.4

theta = 21.8 degrees

theta =180 -21.8 = 158.2 degrees

(b)

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