Chapter 5, Problem 5P

To determine

The maximum speed that the ball can have.

Answer to Problem 5P

Solution:

The maximum speed of the ball $\text{=13}\text{.31m/s}$ .It will happen when the tension in the stringis $\text{75}\text{N}$ .

Explanation of Solution

Given:

Mass of ball, $m=\text{0}\text{.55}\text{kg}$

Radius of circle, $r=\text{1}\text{.3m}$

Maximum tension force in the string, $T_{\max }=\text{75N}$

Formula Used:

Centripetal acceleration $\left(a_c\right)=\frac{v^2}{r}$

Where, v is the velocity and r is the radius of the circular path.

The tension in string provides necessary centripetal force because it acts in the horizontal direction.

  $T=\frac{m{v}^2}{r}$

  

Calculation:

  $\begin{array}{l}{T}_{\max }=\frac{m{v}_{\max }{}^2}{r}\left(\text{speed increase, then tension force also increase}\right)\\ v_{\max }=\sqrt{\frac{T_{\max }.r}{m}}\\ v_{\max }=\sqrt{\frac{\left(75\right)\left(1.3\right)}{0.55}}\\ \text{ =13}\text{.31m/s}\end{array}$

Conclusion:

As the speedof ball increases,the tension in the string also increases. The maximum speed of the ball $\text{=13}\text{.31}\text{m/s}$ .It will happen when the tension in the stringis $\text{75}\text{N}$ .