1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triple integral to find the gravity inside a solid sphere

  1. Nov 4, 2008 #1
    gravity inside a solid sphere

    1. The problem statement, all variables and given/known data
    I'm having a hard time setting up a triple integral to find the force of gravity inside a solid sphere. I've done a similar proof in physics before with gravity inside a spherical shell, but it only required a single integral. In this problem the answer must be derived using a triple integral.


    2. Relevant equations
    Newton's law of gravity:

    |[tex]\vec{F_{grav}}[/tex]|= [tex]\frac{GmpdV}{r^{2}}[/tex]

    3. The attempt at a solution
    I believe i found a way to set up the triple integral using spherical coordinates on another physics forum thread, but I don't understand how to get the integrand. Can someone please explain the way the intergrand was derived in the following integral?

     
    Last edited: Nov 5, 2008
  2. jcsd
  3. Feb 2, 2017 #2
    http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell.html#wtls
     
  4. Feb 2, 2017 #3
  5. Feb 5, 2017 #4
    • Poster reminded to watch the attitude, and not to post in all capital letters (yelling)
    THANK FOR NOTICING . ALSO SEE GRAVITATION CHAPTER IN HALLIDAY RESNICK INTRO PHYSICS USED TEXTBOOKS
     
  6. Feb 5, 2017 #5
    THIS PROOF IS FOR INVERSE SQUARE MATH EQUATIONS.
    DIVIDE BY DISTANCE r BETWEEN
    CENTER OF MASS 1 AND
    CENTER OF MASS 2
    SQUARED.
    YOUR WEIGHT F ON PLANET EARTH SURFACE IS
    m1 = YOUR BODY MASS
    m2 = PLANET EARTH MASS

    r = 6378 KM = 4000 MILES = NOT 0 KM = NOT 0 MILES =
    PLANET EARTH RADIUS + HEIGHT OF m1

    NOW CALC F = WEIGHT

    ALSO APPLIES TO ELECTRIC FORCE
    INVERSE SQUARE MATH EQUATION

    EXCEPT
    GRAVITY IS ONLY ATTRACTION FORCE BUT
    ELECTROSTATIC CAN BE
    ATTRACTION FORCE OR
    REPULSION FORCE
     
  7. Feb 5, 2017 #6
    Has your shift button stuck or are you normally a loud person?
     
  8. Feb 8, 2017 #7

    TeethWhitener

    User Avatar
    Science Advisor
    Gold Member

    Here's a link to the page on how to use the open practice problem forums:
    https://www.physicsforums.com/threads/read-me-how-to-use-this-forum.855656/
    It's a repository of old unanswered threads that are open for anyone to respond to, without the typical limitations that are generally placed on responses in the homework forums. Many of us in the forum like to solve these problems in our spare time. To keep our knives sharp, so to speak.
     
  9. Feb 8, 2017 #8

    berkeman

    User Avatar

    Staff: Mentor

    Thread is closed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Triple integral to find the gravity inside a solid sphere
Loading...