NTNUJAVA Virtual Physics Laboratory
Enjoy the fun of physics with simulations!
Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
September 17, 2019, 12:02:48 pm *
Welcome, Guest. Please login or register.
Did you miss your activation email?

Login with username, password and session length
 
   Home   Help Search Login Register  
An interdisciplinary approach. ...Wisdom
Google Bookmarks Yahoo My Web MSN Live Netscape Del.icio.us FURL Stumble Upon Delirious Ask FaceBook

Pages: [1]   Go Down
  Print  
Author Topic: Minimum energy problem  (Read 4809 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
Administrator
Hero Member
*****
Offline Offline

Posts: 3082



WWW
«
Embed this message
on: February 22, 2010, 02:36:55 pm » posted from:Taipei,T\'ai-pei,Taiwan

Assume a partciel A is moving in a confined circular orbit (with radius a), another particle B is located away from the center (at r=b).
And there is a gravitation field between particles \vec{g}=\frac{k}{r^2}\hat{r}
where \hat{r} is the unit vector between those two particles.
What is the minimum initial velocity for particle a to circular the orbit?

Because the field is \vec{g}=\frac{k}{r^2}\hat{r} so the potential energy is V(r)=\frac{-k}{r}

From consevation of energy

\frac{1}{2}mv^2-\frac{mk}{a-b}=\frac{1}{2}mu^2-\frac{mk}{a+b}
v^2-u^2\ge \frac{2k}{a-b}-\frac{2k}{a+b}=\frac{4kb}{a^2-b^2}
So the minimum velocity is v=\sqrt{\frac{4kb}{a^2-b^2}}

What if we want the particle always touch the inner surface at r=a (i.e. the Normal force provided by the circular orbit is always pointing into the center of the circle)

Do you know how to solve it?

The following is the simulation for you to play with.
You can drag particle B ( to change b)
Mode:
1. N out the normal force is always pointing away from the center of the circle and v is the minimum velocity to reach another end.
2. N inthe normal force is always pointing into the center of the circle and v is the minimum velocity
3. You can change cst to change the velocity ratio.

The red arrow is the velocity of the particle a (You can drag the arrow to change velocity)
The blue arrow is the gravitation force between particle A and B.
The magenta arrow is the required Centripetal force.
Another black arrow is the normal force supplied by the circular orbit.

The kinetic energy/potential energy and total energy as function of angle are drawn as red/blue and green curves.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
  • Please feel free to post your ideas about how to use the simulation for better teaching and learning.
  • Post questions to be asked to help students to think, to explore.
  • Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!


* circularOrbitNgravity.gif (13.78 KB, 839x535 - viewed 383 times.)
Logged
Pages: [1]   Go Up
  Print  
An interdisciplinary approach. ...Wisdom
 
Jump to:  


Related Topics
Subject Started by Replies Views Last post
Energy conservation: potential/kinetic energy
Kinematics
Fu-Kwun Hwang 2 24068 Last post June 17, 2008, 03:09:47 pm
by Fu-Kwun Hwang
Field control with minimum and maximum
Questions related to EJS
Edward 2 8442 Last post June 20, 2008, 03:56:18 pm
by Edward
potential energy
Dynamics
deepika.physicslover 6 16806 Last post February 15, 2009, 10:59:52 pm
by deepika.physicslover
Minimum energy problem
dynamics
ahmedelshfie 0 3170 Last post June 01, 2010, 01:18:38 am
by ahmedelshfie
Problem with Extra energy in vertical spring simulation
Question related to Physics or physics related simulation
mickey2times 3 7088 Last post April 12, 2012, 07:04:55 am
by mickey2times
Powered by MySQL Powered by PHP Powered by SMF 1.1.13 | SMF © 2006-2011, Simple Machines LLC Valid XHTML 1.0! Valid CSS!
Page created in 0.592 seconds with 22 queries.since 2011/06/15