Chapter 8, Problem 50P

To determine

To Find: The speed of upper end of pole.

Answer to Problem 50P

Speed of upper end of pole is $8.22\text{m/s}$ .

Explanation of Solution

Given Information:

Length of pole is $2.30\text{m}$ .

Formula used:

By the law of conservation of energy

  $\begin{array}{l}{E}_I=E_F\\ U_I=K_F\\ mgh=\frac{1}{2}I{\omega }^2\\ \frac{mgl}{2}=\frac{1}{2}\left(\frac{1}{3}m{l}^2\right){\left(\frac{v_{end}}{l}\right)}^2\\ v_{end}=\sqrt{3gl}\end{array}$

Here,

  $m$ is the mass of pole,

  $l$ is the length of pole,

  $v_{end}$ is the velocity of upper end of pole,

Calculation:

  $\begin{array}{l}{v}_{end}=\sqrt{3gl}\\ v_{end}=\sqrt{3\times 9.8\times 2.30}\\ v_{end}=8.22\text{m/s}\end{array}$

Conclusion:

Speed of upper end of pole is $8.22\text{m/s}$ .