A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 3 years 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
  1. theEric
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'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 \(r\).

  2. theEric
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    As for the surface, I guess \(a^2\) is constant and so we'd have a surface like|dw:1374850120317:dw|It'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.

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.