Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_65

6/65 Repeat Prob. 6/64 for the case where the cable configuration has been changed as shown in the figure. [From Prob. 6/64: The 30-kg spool of outer radius $r_o = 450 \text{ mm}$ has a centroidal radius of gyration $\bar{k} = 275 \text{ mm}$ and a central shaft of radius $r_i = 200 \text{ mm}$. The spool is at rest on the incline when a tension $T = 300 \text{ N}$ is applied to the end of a cable which is wrapped securely around the central shaft as shown. Determine the acceleration of the spool center $G$ and the magnitude and direction of the friction force acting at the interface of the spool and incline. The friction coefficients there are $\mu_s = 0.45$ and $\mu_k = 0.30$. The tension $T$ is applied parallel to the incline and the angle $\theta = 20^\circ$.]