Member ABC is supported by a pin and bracket at C and by an inextensible cable o

Question

Member ABC is supported by a pin and bracket at C and by an inextensible cable of length L = 8.4 m that is attached at A and B and passes over a frictionless pulley at D. Assuming P = 800 N and ? = 20 degrees and neglecting the mass of ABC and the radius of the pulley, simplify the problem as much as possible analytically and, for 0 ? s ? 6 m, use MATLAB to:

(a) Calculate and plot the tension T in the cable as a function of s;

(b) Calculate and plot the magnitude of reactions Cx and Cy at hinge C as a function of s;

(c) Calculate and plot the magnitude of the reaction at hinge C as a function of s;

(d) Calculate the angle ? of the reaction at hinge C (with respect to +x-axis) as a function of s;

(e) Determine the maximum tension T-max and the corresponding value of s;

(f) Determine the (absolute) maximum reactions Cx & Cy and the corresponding values of s;

(g) Determine the (absolute) maximum reaction C and the corresponding value of s;

(h) If it exists, determine the value of s at which Cx = Cy and the corresponding value of Cy.

I'm really just stuck on the first one, part (a), the most, but a response to the rest would be very helpful, too. I've also attached a handwritten analysis of the problem on paper with equilibrium reactions, but I do not know if I analyzed the problem correctly. I labeled the angle adjacent to ? as ? and the rightmost angle ?, both of which vary as a function of0 ? s ? 6 m. First and foremost, I guess, is my assumption of the reaction at C correct? I appreciate any responses in advance; thank you!

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