A traffic light hangs from a pole as shown in the diagram. The uniform aluminum pole $AB$ is of length $7.20\,\text{m}$ and has a mass of $12.0\,\text{kg}$. The mass of the traffic light is $21.5\,\text{kg}$. The point $C$ is located $3.80\,\text{m}$ vertically above the pivot $A$. A massless horizontal cable $CD$ is attached at $C$ and connects to the pole at point $D$, where the pole makes an angle of $37^{\circ}$ with the cable.

Question

A traffic light hangs from a pole as shown in the diagram. The uniform aluminum pole $AB$ is of length $7.20\,\text{m}$ and has a mass of $12.0\,\text{kg}$. The mass of the traffic light is $21.5\,\text{kg}$. The point $C$ is located $3.80\,\text{m}$ vertically above the pivot $A$. A massless horizontal cable $CD$ is attached at $C$ and connects to the pole at point $D$, where the pole makes an angle of $37^{\circ}$ with the cable.(a) Determine the tension in the horizontal massless cable $CD$.
, (b) Determine the vertical and horizontal components of the force exerted by the pivot $A$ on the aluminum pole.
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Jason · Accepted Answer

$4.08\times10^{2}\,\text{N}$
$4.08\times10^{2}\,\text{N}$
$3.28\times10^{2}\,\text{N}$

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