A 500 lb spool with inner and outer radii ρ = 4 ft and R = 6 ft, respectively, is released...

A 500 lb spool with inner and outer radii ρ = 4 ft and R = 6 ft, respectively, is released from rest on an incline with θ = 30°. The center of the spool G coincides with its center of mass, and the radius of gyration of the spool is kG = 5 ft. Assume that the only forces acting on the spool after its release are the spool’s weight, the tension in the cord, and the contact force between the spool and the incline.

If the angular speed of the spool is ωs2 = 1.2rad/s after G has displaced a distance d = 10 ft from the release position, determine the work done by friction from the instant of release to when ωs2 is achieved.

Figure P8.34