Question

A horizontal clothesline is tied between 2 poles, 12 meters apart. When a mass of 1 kilograms is tied to the middle of the clothesline, it sags a distance of 4 meters. What is the magnitude of the tension on the ends of the clothesline

Answer 1

The tension on the clotheslines is
`T = 8.83 \ N`

Step-by-step explanation:

The diagram illustrating this question is shown on the first uploaded image

From the question we are told that

The distance between the two poles is
`d = 12 \ m`

The mass tie to the middle of the clotheslines
`m = 1 \ kg`

The length at which the clotheslines sags is
`l = 4 \ m`

Generally the weight due to gravity at the middle of the clotheslines is mathematically represented as

`W = mg`

let the angle which the tension on the clotheslines makes with the horizontal be
`\theta` which mathematically evaluated using the SOHCAHTOA as follows

`Tan \theta = ( 4)/(6)`

=>
`\theta = tan^(-1)[(4)/(6) ]`

=>
`\theta = 33.70^o`

So the vertical component of this tension is mathematically represented a

`T_y = 2* Tsin \theta`

Now at equilibrium the net horizontal force is zero which implies that

`T_y - mg = 0`

=>
`T sin \theta - mg = 0`

substituting values

`T = (m*g)/(sin (\theta ))`

substituting values

`T = (1 *9.8)/(2 * sin (33.70 ))`

`T = 8.83 \ N`