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## A boy of weight, W, hangs from the center of a clothesline and distorts the line so that it makes 30 degrees angles with the horizontal at each end.

Find the tension in the clothesline in terms of W.

In this problem, the center of the clothesline is a point in equilibrium, i.e., the sum of all forces equals zero. There are two tension forces of the same magnitude T directed at 30° above the horizontal pointing left and right from the center, as well as the weight W pointing straight down. The vertical or y-component of either tension force is the opposite side in a right triangle whose hypotenuse is T and is therefore given by T sin(30). Then the sum of the forces in the vertical direction equals zero:

∑ Fy = 2Tsin(30) -W = 0

Since 2 sin(30) = 2 (1/2) = 1, we have

T-W=0, or T=W.

The tension in the clothesline equals the weight.
The weight is not given as a value.  It is merely labeled as "W".
do you mean 30 degree angles?

i am assuming the clothesline is shaped like a triangle. you divide the triangle in half with a line thru it and now you have  2 right triangles ( 30-60-90). there are two hypotenuses and their tension is found by W/sin30deg. Since there are two hypotenuses, it should be 2 times W/sin30deg; since the tension it supported by the two sides of the clothesline.