Determine the x- and y-coordinates of the centroid of the shaded area. (10) (b) Calculate the moment of inertia of the shaded area about the x- and y-axes. (10)

(a) Determine the x- and y-coordinates of the centroid of the shaded area. (10) (b) Calculate the moment of inertia of the shaded area about the x- and y-axes. (10) 2. See figure below for a truss structure. (a) Find the reactions at the supports. (5) (b) Find the axial force in member CD. (10) (c) Point out at least 5 zero-force members. (5) 3. See figure below. Neglect the weight of the beam. a) Find the reactions at the left end of the beam. (5) b) Find the internal shear force and bending moment at x = 1 m measured from the left end of the beam. (10) c) Draw the shear force and bending moment diagrams for the entire beam. (5) q = 10 kN/m 2 m 1 m 20 kN 4. Determine the range of cylinder mass m for which the 50-kg block is in equilibrium. Neglect the mass of the pulley. (a) Assume frictionless contact between the belt and the pulley. (15) (b) Re-do your calculation with the coefficient of friction between the belt and pulley µ = 0.1. (5) Hint: the equation for belt friction is  T  T e 2 1 . 5. See figure below. The natural length of the spring is 2 ft. (a) Find the magnitude and direction of the force exerted

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