Chapter 6.2, Problem 15PP

To determine

To Calculate: The tension in the string.

Answer to Problem 15PP

0.744 N

Explanation of Solution

Given:

Mass of the ball, $m=16\text{ g = 0}\text{.016 kg}$

Radius of the circle, $r=1.4\text{ m}$

Time taken to complete one revolution, $t=1.09\text{ s}$

Formula used:

Centripetal force is given by:

  $F_c=\frac{m{v}^2}{r}$

Here, F is centripetal force, m is mass, v is velocity and r is radius.

Calculation:

Total distance cover by ball to complete one revolution of circle is:

  $\begin{array}{l}d=2\pi r\\ =2\times 3.14\times 1.4\\ =8.792\text{ m}\end{array}$

Now, velocity is given by,

  $v=\frac{d}{t}$

Here, d is distance t is time.

Therefore, velocity v is:

  $\begin{array}{l}v=\frac{8.792}{1.09}\\ =8.07\text{ m/s}\end{array}$

Tension in the string will be equal to centripetal force acting on the ball.

Therefore, tension in the string is:

  $\begin{array}{l}T=\frac{m{v}^2}{r}\\ =\frac{0.016\times {8.07}^2}{1.4}\\ =0.744\text{ N}\end{array}$

Conclusion:

So, the tension in string is 0.744 N.