Chapter 5, Problem 18P

To determine

The maximum speed that Tarzan can tolerate at the lowest point of his swing

Answer to Problem 18P

Solution:

  $4.82\text{m/s}$

Explanation of Solution

Given:

Maximum exerting force $=\text{1150}\text{N}$

Mass $=\text{78}\text{kg}$

Length of vine $=\text{4}\text{.7}\text{m}$

Concept used:

Centripetal acceleration of Tarzan $=\frac{v^2}{r}$

v : speed of Tarzan

r : radius of the circular arc.

Newton’s second law of motion:

  ${\displaystyle \sum F}=ma$

Where, a is the acceleration and m is the mass.

Calculation:

  

Apply Newton’s law second law of motion:

  $\begin{array}{l}T-mg=\frac{m{v}^2}{r}\\ \text{1150-78×9}\text{.8 = 78×}\left(\frac{v^2}{\text{4}\text{.7}}\right)\\ \text{385}\text{.6=78×}\frac{v^2}{\text{4}\text{.7}}\\ v=\sqrt{\frac{385.6}{78}\times 4.7}\\ =\text{ 4}\text{.82}\text{m/s}\end{array}$

Conclusion:

The maximum speed of Tarzan, which can be tolerated at the lowest point of the swing $\text{= 4}\text{.82}\text{m/s}$ .