Chapter 5, Problem 79GP

To determine

To find: The speed of train.

Answer to Problem 79GP

  $26.9$ m/s

Explanation of Solution

Given Data:

  $r=235$

  $\theta =17.5°$

Formula Used:

  

From above force diagram,

X component $F_r\sin \theta -a_{R}m=0$

  $F_T\sin \theta =m{v}^2/R\to (1)$

Y component $F_T\cos \theta -mg=0$

  $F_r\cos \theta =mg\to (2)$

Dividing eqn (1) by (2)

  $v=\sqrt{rg\tan \theta }$

Calculation:

Substituting the value we get

  $\begin{array}{l}{v}^2=rg\tan \theta \hfill \\ =235\times 9.8\tan {(17.5)}^{\circ }\hfill \\ v=26.9\text{m}/\text{s}\hfill \end{array}$

Conclusion:

Therefore, we conclude that the speed of train will be $26.9$ m/s