The system in the figure is in equilibrium. A mass of 345 kg hangs from the end

Question

The system in the figure is in equilibrium. A mass of 345 kg hangs from the end of the uniform strut whose mass is 80 kg. The strut makes an angle of 45° with the ground and the cable makes an angle of 30° with the ground. (1) Find the tension T in the cable.

(2) Find the horizontal force component exerted on the strut by the hinge.

(3) Find the vertical force component exerted on the strut by the hinge.

Please provide a detailed answer as if I were a 2nd grader trying to do this. Also I might add that forms of this question have been answered before however, the answers were wrong and the steps to recieve them were unclear. Thanks in advance!

Explanation / Answer

first

W is the weight of the strut that acts at the center of mass

0 = (L / 2)*W * sin(135) + L * m*g * sin(135) - L * T sin(165)

T = (L /2) * W * sin(135) + L *m*g *sin(135) / L*sin(165)

T = 0.5 * 80 * 9.8 * sin(135) + 345 * 9.8 * sin(135) / sin165

T = 10308 N

now we can balance forces in each direction . the angle between T and the horizontal direction is 30deg

x direction

0 = Fh - Tcos(30)

Fh = 10308 * cos(30deg) = 8926.98 N

then

0 = Fv - W - m * g - T * sin(30)

Fv = W + m * g + T * sin(30)

Fv = 80 * 9.8 + 345 * 9.8 + 10308 *sin(30)

Fv = 9319 N

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