30 N sign is suspended from a ceiling by two cables that are 2 m long.The cables are attached to the ceiling by bolts that are 3 m apart. Determine the tension in each cable.

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The weight of the sign is 30 N. It is suspended from a ceiling by two cables that are 2 m long and which are attached to the ceiling by bolts that are 3 m apart.

The tension in each of the cables can be divided into a component parallel...

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The weight of the sign is 30 N. It is suspended from a ceiling by two cables that are 2 m long and which are attached to the ceiling by bolts that are 3 m apart.

The tension in each of the cables can be divided into a component parallel to the horizontal and a component perpendicular to the horizontal. The net effect of the component parallel to the horizontal is 0 for the two cables.

The component perpendicular to the horizontal adds up to 30 N. As the cables are 2 m long and are attached by bolts 3 m apart the angle they make with the horizontal is arc cos (1.5/2) = 41.40 degrees.

If the tension in the cable is T, T*sin 41.40 = 15

=> T = 22.67 N

The tension in the cables is 22.67 N.

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