Chapter 6, Problem 83A

To determine

Tension in the chord at bottom.

Answer to Problem 83A

  $F_T=24.1\text{N}$

Explanation of Solution

Given:

Mass of the ball, $m=1.13\text{kg}$

Radius of cord, $r=0.5\text{m}$

Speed of ball, $v=2.4\text{m/s}$

Formula Used:

Tension in the chord at bottom is

  $F_T=F_g+F_c=m{a}_{\text{grav}}+\frac{m{v}^2}{r}$

Here,

  $m$ is mass of object revolving, $v$ is velocity, $r$ is radius and $a_{\text{grav}}$ is acceleration due to gravity.

Calculation:

Put the given values in above relation and solve

  $\begin{array}{c}{F}_T=\left(1.13\times 9.8\right)+\frac{1.13\times {2.4}^2}{0.5}\\ =11.084+13.0176\\ =24.0916\\ \approx 24.1\text{N}\end{array}$

Conclusion:

Therefore, the tension in the cord at the bottom of the circle is

  $F_T=24.1\text{N}$