A homogeneous structural steel (ASTM A36) rectangular bar moves on a non-smooth plane, inclined at an angle of 40?with respect to the horizontal (see figure). The block is of length, ? lx=7? in, of height, ly=2 in, and of width (into the plane of the figure), lz=?4? in. The coefficient of (kinetic) friction between the steel bar and the plane is 0.2?. The coordinate system to be used is as shown in the figure.

a) Determine the average normal stress (including sign; if positive, no sign is needed) acting on the bar at the interface of the bar and the plane.

b) Determine the average shear stress (including sign; if positive, no sign is needed) acting on the bar at the interface of the bar and the plane.

c) At what distance along the plane from the lower left corner of the bar does the resultant normal reaction force on the bar act?

d) If at one instant the velocity of the bar has a magnitude of 2.6 ft/s, what is the magnitude of the velocity after it has moved farther down the incline a distance of 3.4? ft?

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