Problem 5-57 Translational Equil.- Part 6 - B

A sign outside a hair stylist's shop is suspended by two wires. The force of gravity on the sign has a magnitude of \(55.7\; N.\) If the angles between the wires and the horizontal are as shown in the figure, determine the magnitude of the tensions in the two wires.
[Ans. \(T_1 = 49.9\; N;\) \(T_2 = 40.8 \;N\)]

Diagram of sign suspended by two wires.

Accumulated Solution

Diagram of vectors with all directions and angles indicated.

\(a = 0 \\ \sum F_x = 0, \; \sum F_y = 0\)

\(x - \text{components}\) \(y - \text{components}\)
\(T_{1x} = -T_1 \cos45 = -0.7071 \;T_1\) -
\(T_{2x} = T_2 \cos30 = 0.8660 \;T_2\) -
\(0\) -
\(\text {Sum:} -0.7071 \;T_1 + 0.8660\; T_2 + 0 = 0\) -

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