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)
= W/(1/5)
= 5W
On a vertical line, the tension is W.
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!
The tension in a clothesline refers to the force exerted on it when weight or force is applied. When you hang from a clothesline, your weight creates tension in the line. The tension in the clothesline will be greater when it is strung horizontally compared to when it hangs vertically. Let's understand why.
To explain this, we need to consider the concept of forces and vector components. When a clothesline is strung horizontally, the weight of the person hanging causes the line to stretch and create tension. In this case, the entire weight of the person is pulling directly downward, creating tension along the length of the clothesline.
However, when the clothesline is hanging vertically, the weight of the person is directed straight downward without any horizontal component. In this scenario, the tension in the clothesline is determined only by the weight of the person, since the force is acting vertically.
Mathematically, we can break down the force components acting on the clothesline. In the horizontal setup, the weight of the person is split into both the vertical and horizontal directions, leading to a greater overall force and tension. In the vertical setup, the weight only acts downward in the vertical direction, resulting in a lower overall tension in the clothesline.
To summarize, the tension in a clothesline is greater when it is strung horizontally because there is an additional horizontal component of force acting on the line due to the weight of the person hanging from it. This additional force component increases the overall tension in the clothesline.
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.