# What is the magnitude of the tension on the ends of the clothesline if a horizontal clothesline is tied between 2 poles, 10 meters apart and when a mass of 2 kilograms is tied to the middle of the clothesline, it sags a distance of 3 meters?

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To find the tension on the ends of the clothesline, you can use the formula for the tension in a horizontal rope with a sag:

[ T = \frac{W}{2} \left( \frac{4L - S}{L} \right) ]

Where:

- ( T ) = tension in the clothesline
- ( W ) = weight of the mass (2 kilograms in this case)
- ( L ) = distance between the poles (10 meters)
- ( S ) = sag distance (3 meters)

Substitute the given values into the formula:

[ T = \frac{2}{2} \left( \frac{4 \times 10 - 3}{10} \right) ]

[ T = \frac{1}{2} \left( \frac{40 - 3}{10} \right) ]

[ T = \frac{1}{2} \left( \frac{37}{10} \right) ]

[ T = \frac{37}{20} ]

[ T = 1.85 , \text{Newtons} ]

So, the magnitude of the tension on the ends of the clothesline is 1.85 Newtons.

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