Help with a vector and tension problem?

A clothesline is tied between two poles, 8 m apart. The line is quite taut and has negligible sag. When a wet shirt with a mass of 0.8 kg is hung in the middle of the line, the midpoint is pulled down 8 cm. Find the tension in each half of the clothesline.
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My answer doesn’t agree with the text, so I am hoping to see what others get for the answer. Thanks in advance!
Each of your answers reminded me of what the calculus text didn’t mention in the section: that weight = m*g. Thanks for your help!

I am sorry I can’t draw a diagram for this; such a diagram would be very helpful.

When the shirt hangs on the line, the line is deflected. The shirt exerts a force down equal to its weight, and the y component of the tension in the wire equals the weight of the shirt (W=mg=7.8 N).

Now, from trig, you know that the angle the line makes with one edge is given by:

tan(theta) = 0.08m/4 m

you also know that tan(theta) will give you the ratio of tension in the y direction to tension in the x direction.

Knowing Ty and Tx you can use the Pythagorean theorem to find the total tension in the line. (You can do this simpler is you are familiar with the small angle approximation, but this step by step process will also give you the final answer)

hope this helps

Coollab ( Tshir Design / Vector progress)

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