A uniform horizontal strut weighs 380.O N. One end of the strut is attached to a

Question

A uniform horizontal strut weighs 380.O N. One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs 210.0 N. The strut is also supported by a cable attached between the end of the strut and the wall. Assume that the entire weight of the sign is attached at the very end of the strut. 30° Restaurant Find the tension in the cable (in N). Find the force (in N) at the hinge of the strut. (Give the direction in degrees counterclockwise from the +x-axis. Assume that the +x-axis is to the right.) magnitude direction counterclockwise from the +x-axis

Explanation / Answer

weight of strut = wstrut = 380 N

weight of sign = wsign = 210N

net torque about hinge is zero

T*L*sin30 - Wstrut*L/2 - Wsign*L = 0

T*sin30 - Wstrut/2 - Wsign = 0

T*sin30 - 380/2 - 210 = 0

T = 800 N

B) ON horizantal direction

Fx - Tx = 0

Fx = Tx = T*cos30 = 693

on vertical direction
Fy - Wstrut - Wsign + Ty = 0

Fy = 380 + 210 - 800*sin30 = 190

magnitude = sqrt(Fx^2/+Fy^2) = 718.6 N

direction = tan^-1(Fy/Fx) = 15.3

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