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Need help ;)

  1. Feb 13, 2007 #1
    Hi, Im a student from norway, and im strugeling with this problem, hope someone can help me og guide me in the direction:

    A object is brought out in space in a distance of 3(6,37*10^6) from the senter of the earth. not any velocity when the object is released in space.
    1) What is the objects velocity when it hits the earth ( this Ive solved)
    2)
    i)how long does the object use halfway towards the earth?
    ii)how log does it take untill the object hits the earth?

    HELP PLEASE!!
     
  2. jcsd
  3. Feb 13, 2007 #2

    George Jones

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    Write down the equation for conservation of energy, with speed written as a derivative.
     
  4. Feb 13, 2007 #3
    how do i do that?
    so far Ive come up with this:

    2*R(radius of the earth)=3R-integrate from 0 to t(1/2(integrate from 3R to 2R(-G*M(Earth)/r^2)) *t^2
     
  5. Feb 13, 2007 #4

    George Jones

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    I'm not sure what you're doing here.

    To make sure things are OK, just write down the conservation of energy equation, and leave the integrals until later.
     
  6. Feb 13, 2007 #5
    I use : 1/2 mv^2
    and Gravital Potential energy, and unerversial of gravety = Gm(1)m(2)/r^2
     
  7. Feb 13, 2007 #6

    George Jones

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    Let R be the radius of the Earth, and suppose that the object is a distance r from the centre of the Earth. If the object starts at rest from 3R, what is the *equation* for conservation of energy.
     
  8. Feb 13, 2007 #7
    :cry: I dont know, ive sat down with a teacher and he didnt know eather , just the equation i told you about
     
  9. Feb 13, 2007 #8

    George Jones

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    ???

    Let K be kinetic energy and V be gravitational potential energy.

    K_initial + V_intitial = K_final + V_final

    Can you substitute expressions for each of the terms in this equation?
     
  10. Feb 13, 2007 #9
    I know, but i toght i was suppose to use potentional energi in this ? Im not sure... im about to give up now. As far as i know Im supose to end up with an integral I have to use Maple to solve ....
     
  11. Feb 13, 2007 #10

    George Jones

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    :confused: Again, I'm confused. My equation involves potential energy.

    If you'll substitute expressions (that I think you know) into the equation that I wrote previously, I'll help you get the integral, but, since this is homework (and thus should be in the homework section), I'm, at this point, not going to write down the answer.
     
  12. Feb 13, 2007 #11
    hehe, no its not homework, I dont have to do this .... Its voluntary

    I come jp with this :

    1/2mv(0)^2+ G M(earth) m(object) (1/r1-1/r2)=1/2mv^2+ G M(earth) m(object) (1/r1-1/r2)
    Im sure its wrong :(
     
  13. Feb 13, 2007 #12

    George Jones

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    Almost.

    If the object starts from rest, then, initially, v = 0, so K_initial = 0. This gets rid of one of the terms in the equation.

    Also, the gravitation potential energy (of the system) when the object is a distance r from Earth's centre is

    V = - G M m/r^2.

    Use r_initial and r_final to get V_initial and V_final.

    Because of work and family commitments, I might not be able to get back to this thread until tomorrow.
     
  14. Feb 13, 2007 #13
    V initial = 0 and Vfinal is 2GM(E)/3radius of the earth ...
    Thank u for yore time , Ill let you know by tomorrow if Ive solved the problem!
     
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