Question

A traffic light weighing 16 pounds is suspended by two cables (see figure). Find the tension in each cable. (Round your answers to one decimal place.) lb (smaller value) lb (larger value)

Answer 1

Step 1: Draw an image to illustrate the problem

Consider the forces along the horizontal axis.

`\begin{gathered} -T_1\cos \theta_1+T_2\cos \theta_2=0 \\ \text{ therefore} \\ T_2\cos 20^0=T_1\cos 20^0 \end{gathered}`
`\text{ Dividing both sides by }\cos 20^0`
`\begin{gathered} (T_2\cos20^0)/(\cos20^0)=(T_1\cos 20^0)/(\cos 20^0) \\ \text{thus} \\ T_2=T_1 \end{gathered}`

Consider the forces along the vertical axis.

`\begin{gathered} T_1\sin 20^0+T_2\sin 20^0-16=0 \\ T_1\sin 20^0+T_1\sin 20^0-16=0\text{ (}T_1=T_2) \\ \text{ Thus} \\ 2T_1\sin 20^0=16 \\ T_1=(16)/(2\sin 20^0)\approx23.39\text{ pounds} \end{gathered}`

then T₁ = 23.39 pounds

Since T₁=T₂, then T₂ = 23.39 pounds

Hence, smaller value = 23.4 pounds to one decimal place and

larger value = 23.4 pounds to one decimal place