Neglecting friction and the radius of the pulley, determine the tension in cable

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Explanation / Answer

tension (T) in the string at both points A and B is same. let angle CBD = b ; angle CAD = a. tan(b) = 2/2 = 1. => b= 45 degrees. tan(a) = 2/(1.5+1.5+2) = 21.8 degrees. let the force acting in vertical direction at joint C be Fy and the force acting in horizontal direction be Fx. since the body is in equilibrium, net force in vertical direction = 0 => T*sin(21.8) + T*sin(45) + Fy -40000 = 0 ---------->Equation 1 => 1.0784T + Fy = 40000 net force in horizontal direction = 0 =>T*cos(21.8)+T*cos(45) + Fx = 0. ------------>Equation 2 =>T*(1.6356) + Fx = 0 Torque at C = 0 =>T*sin(21.8)*7 + T*sin(45)*4 - 40000*5.5 = 0 => T = 40530.5674. =>Fx = -66291.7961 N ; Fy = -3708.1639.

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