A traffic light hangs from a pole as shown in the figure . The uniform aluminum

Question

A traffic light hangs from a pole as shown in the figure . The uniform aluminum pole AB is 7.10 m long and has a mass of 11.0 kg. The mass of the traffic light is 22.0 kg.

T=_____N

Please do not only show the answer but how you arrived at the answer as I solved it and keep getting the answer of 385.42 N but it tells me that I may have used the wrong significant figures or rounding as I'm close but not close enough to the answer. I did no rounding or significant figures in the formula as I just calculated it directly so there's not really much any way I can try plugging it in differently. I appreciate everyone's help who helps me to figure this out.

A traffic light hangs from a pole as shown in the figure . The uniform aluminum pole AB is 7.10 m long and has a mass of 11.0 kg. The mass of the traffic light is 22.0 kg. Determine the tension in the horizontal massless cable CD. T=_____N Please do not only show the answer but how you arrived at the answer as I solved it and keep getting the answer of 385.42 N but it tells me that I may have used the wrong significant figures or rounding as I'm close but not close enough to the answer. I did no rounding or significant figures in the formula as I just calculated it directly so there's not really much any way I can try plugging it in differently. I appreciate everyone's help who helps me to figure this out.

Explanation / Answer

length AD = (3.8m)/sin(37*) = 6.32m So, lenght DB = AB - AD = 7.10m - 6.32m = 0.78 m center of mass of the rod will be at a distance = 7.10m/2 =3.55m
Equating torque about pivot A to zero T = (305.629 +1222.519)/3.8034
T = 401.777 N tension in the cable is 401.77 N.

T = 401.777 N tension in the cable is 401.77 N.

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