thanks The crate A of weight W = 32 lb is being pulled to the right by the winch

Question

thanks

The crate A of weight W = 32 lb is being pulled to the right by the winch at B. The crate starts at x = 0 and is pulled a total distance of 15 ft over the rough surface for which the coefficient of kinetic friction is muk = 0.5. The force P in the cable due to the winch varies according to the plot, where P is in lb, b is in lb/ ft, and x is in ft. The coefficient of static friction is insufficient to prevent slipping. Using the work-energy principle, determine the speed of the block which A = 11 lb/ ft and at = 15 ft.

Explanation / Answer

so work enrgy principle

work done by external force=int(20+11sqrt(x))dx,x=0,15)

=726.028 lb-ft

friction force=coeff*W=16 lb

so work done by external force =friction loss+gain in K.E

=726.028=16*15+0.5*(32/32)*v^2

so v=31.17 ft/s

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