Question

A 0.152 kg ball is attached to a string that is 62.2 cm long. The string will break if subjected to a tension force of 4.8 N. If a small child swings the ball in a horizontal circle around her head, at what velocity will the string break?

Answer 1

Answer:

The value is  $v = 3.68 \ m/s$

Explanation:

From the question we are told that

   The mass the ball is  $m = 0.152 \ kg$

    The length of the string is $l = 62.2 \ cm = 0.622 \ m$

      The tension of force that will break the string is $T = 4.8 \ N$

Generally the radius of the circle made by swinging the  string is  $r = l = 0.622\ m$

     Generally the centripetal force acting on the ball is mathematically represented as  

              $F_c = \frac{mv^2}{r}$

Generally this centripetal force is mathematically represented as

          $F_c = T - mg$

=>       $T - mg = \frac{mv^2}{r}$

=>      $4.8 - 0.152 * 9.8 = \frac{0.152 * v^2}{0.622}$

=>      $v = 3.68 \ m/s$