Acantilever beam of length l = 70 in is made from two side-by-side structural-steel channels of size 3 in weighing 5.0 lbf/ft. the beam supports a uniform external distributed load of w = 6 lbf/in and a point load of f = 170 lbf at the end. including the weight of the channels, use castigliano's theorem to find the magnitude of deflection at a.

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?