Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 204: 27a


Vine doesn't break

Work Step by Step

Lets calculate the speed at the end of the descent ( initial speed is zero so kinetic energy will be zero too). The total energy of tarzan initially is: $E_{tot}=E_{k0}+E_{p0}=0+mgh(1)$ $E_{k0} $ and $E_{p0}$ are initial kinetic and potential energies of tarzan. After the descent, the potential energy will be zero and all potential energy will be converted to kinetic energy. Therefore, $ E_{tot}=E_{k_{1}}+E_{p1}=\dfrac {mv^{2}_{1}}{2}+0\left( 2\right)$. So from (1) and (2), we get: $E_{tot}=E_{k_{1}}+E_{po}=\dfrac {mv^{2}_{1}}{2}+0=mgh+0\Rightarrow v^{2}_{1}=2gh(3)$ Lets assume the vine doesn't break until tarzan reaches the lowest point. The force applied to vine by tarzan at the lowest point (trajectory of tarzan will be circular) will be: $F_{tot}=mg+\dfrac {mv^{2}_{1}}{L}\left( 4\right) $ where $L$ is the length of the vine Lets calculate this using (3). We get: $F_{tot}=mg+\dfrac {mv^{2}_{1}}{L}=mg+\dfrac {2mgh}{L}=mg\left( 1+\dfrac {2h}{L}\right) \approx 932.62N < F_{vine}=950N$ $F_{vine} $ is the minimum force to break the vine so vine doesn't break.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.