1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Digging a hole through the earth

  1. Feb 5, 2010 #1
    have examined how g varies with distance from the Earth's surface. but how to change g if, instead dig down to the center of the earth?
    if we do Start in the center of the Earth (see picture) how will the value of g varies from there to 2r height above the Earth's surface. Suppose that Earth's density is constant throughout the Earth's volume.

    http://www.pluggakuten.se/wiki/images/5/5a/Martin.jpg [Broken]

    i do sow:
    [tex]M = \rho \cd V = \rho \fr{4\pi r^3}{3}\\ F_1=m\cdot g\\ F_2=G\frac{mM}{r^2}\\ F_1=F_2\rightarrow \\ g=G\frac{M}{r^2}\rightarrow g=G\frac{\fr{\rho 4\pi r^3}{3}}{r^2 }\rightarrow \\ g=G\frac{\rho 4\pi r}{3}[/tex]

    but its WRONG,
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 5, 2010 #2


    User Avatar
    Science Advisor

    Re: gravitational

    Why do you say it's wrong? It looks correct to me. The gravitational force due to any mass above you is canceled by a corresponding mass in the opposite direction so you only use the mass below you which is [itex](4/3)\pi r^3 \rho[/itex]. Since we can treat that mass as if it were all at the center of the earth the acceleration is [itex]g= (4/3)\pi r^3 \rho G/ r^2= (4/3)\pi\rho G r[/itex], exactly what you have.
    Last edited by a moderator: May 4, 2017
  4. Feb 5, 2010 #3
    Re: gravitational

    but what is r? in this formula [itex]g= (4/3)\pi r^3 \rho G/ r^2= (4/3)\pi\rho G r[/itex]
    r must be distance between celestial bodies, but in the formula are the r=radius.
  5. Feb 5, 2010 #4
    Re: gravitational

    Now I'm mixing up all sorts of things in each other. What is meant by the change of g instead dig down to the center of the earth?
    it means that we have different masses for the Earth?like;
    http://www.pluggakuten.se/wiki/images/6/6b/3.JPG [Broken]

    But what happens to gravity when earth curvature is half instead, see picture below;
    http://www.pluggakuten.se/wiki/images/7/75/2.JPG [Broken]

    does I thinking right? sorry, my english is bad
    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook