A community for students.
Here's the question you clicked on:
 0 viewing
gorica
 one year ago
A smooth surface of revolution is hyperbolic with equation z=a^2/r, the axis Oz pointing vertically downwards and r, θ and z being cylindrical polar coordinates. A small particle mass m slides on the interior of the surface. Calculate potential energy.
gorica
 one year ago
A smooth surface of revolution is hyperbolic with equation z=a^2/r, the axis Oz pointing vertically downwards and r, θ and z being cylindrical polar coordinates. A small particle mass m slides on the interior of the surface. Calculate potential energy.

This Question is Closed

theEric
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure if I can help, but here are my thoughts that you and others can dispute. Is this potential energy just the potential energy due to gravity? It looks like mass is the only data on this particle. Then \(E_{potential}=m\ g\ z\) if you consider the particle to have \(0\ [J]\) at \(z=0\). And \(a^2\) and \(r\) are unknown? Then the potential energy could not be known, but could be put in terms of \(a\) and \(r\).

theEric
 one year ago
Best ResponseYou've already chosen the best response.0As for the surface, I guess \(a^2\) is constant and so we'd have a surface likedw:1374850120317:dwIt's inside that, on the interior, I guess. That is because it is a hyperbola whose \(z\)value does not depend on \(\theta\), but only \(r\). So \(\large z=\frac{a^2}{r}\) at every value for \(\theta\) in those cylindrical coordinates.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.