posted by Kelsea on .
The clothesline is under tension when you hang from it. Why is the tension greater when the clothesline is strung horizontally than whe is hangs vertically?
Assuming the horizontal line of 10 ft sags 1 ft when clothes are on it.
The force in the y-direction (vertical) is W, the horizontal force is
H = W/tan(θ)
On a vertical line, the tension is W.
because tension is proportional to 1/sinAngle of the wire when a mass is hung from it.
so, if the weight is mg, the tension can be much higher, as in mg/sinangle and horizontal the angle of depression is near zero.
I differ on Mathmate on the trig function, the wire is not ever horizontal under weight, the wire is sagging, but the principle is the same, the force is magnified greatly. Tension in wire is proportional to 1/sinAngle.
Bob, you're right, the horizontal component calculated using W/tan(θ) does not equal to the tension of the (initially) horizontal line. W/sin(θ) is more accurate after sagging occurs.
Thank you guys!