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Determining work of a 3 particle system

  1. Oct 9, 2016 #1
    1. The problem statement, all variables and given/known data
    on a spherical astroid with a radius of 500km and an acceleration due to gravity of 3.0m/s2
    How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000m/s?
    2. Relevant equations
    conservation of energy
    Ui + ki=Uf +kf
    U=-(GmM)/r
    K=(1/2)mv2
    -------------------------
    f=ma
    -(GmM)/r2=ma
    -(GM)/r2=a
    -(GM)/r=ar
    (can apply to h height)

    r=radius of astroid
    h=height above center
    m=mass of rocket
    M=mass of astroid
    G=gravitational constant
    a=acceleration due to astroids gravity
    3. The attempt at a solution
    Ui + ki=Uf +kf
    Ui + ki=Uf + 0
    -(GmM)/r +(1/2)mvi2=-(GmM)/h
    the m masses cancel
    -(GM)/r +(1/2)vi2=-(GM)/h
    -ar +(1/2)vi2=-ah
    r-(1/2)(1/a)vi2=h
    plugging in the values gives me
    500000m+(1/2)(1/(3m/s2)(1000m/s2)2=h

    5166666.667meters from the center of the astroid. so 166666.667 meters above its surface. Which is the incorrect answer. the right answer is 250000 meters above the surface.

    I know this should be a pretty simple problem, Not too sure where I went wrong. Thanks ahead of time
     
  2. jcsd
  3. Oct 9, 2016 #2
    Okay so I realized that I cannot use mgh fro the U final because the acceleration due to gravity is different here. So I found the mass of the astroid. If I use U=-(GmM)/r and solve for h will I get the correct answer?

    and btw the title is wrong for this post.
     
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