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

Answer:

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

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

        $Tan \theta = \frac{ 4}{6}$

=>     $\theta = tan^{-1}[\frac{4}{6} ]$

=>     $\theta = 33.70^o$

   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

          $T = \frac{m*g}{sin (\theta )}$

substituting values

           $T = \frac{1 *9.8}{2 * sin (33.70 )}$

           $T = 8.83 \ N$