The system in the figure is in equilibrium. A mass of 365 kg hangs from the end
ID: 1464836 • Letter: T
Question
The system in the figure is in equilibrium. A mass of 365 kg hangs from the end of the uniform strut whose mass is 95 kg. The strut makes an angle of 45° with the ground and the cable makes an angle of 30° with the ground. Find the tension T in the cable.
Find the horizontal force component exerted on the strut by the hinge.
Find the vertical force component exerted on the strut by the hinge.
Compute torque about bottom to get T, torque about top to get (Fv-Fh) and horizontal forces for Fh = T cos(angle).Explanation / Answer
net torque = 0
T*cos30*L*sin45 = T*sin30*L*cos45 + m*g*L*cos45 + M*g*L/2*cos45
T*cos30*sin45 = T*sin30*cos45 + (95*9.8*cos45)+(365*9.8*0.5*cos45)
T = 7429.8 N
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along horizantal
net Fx = 0
Fh - T*cos30 = 0
Fh = T*cos30 = 6434.4 N
along vertical
Fv - m*g - M*g - T*sin30 = 0
Fv - (365*9.8)-(95*9.8)-(7429.8*sin30) = 0
Fv = 8222.8 N
++++
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