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Homework Help: Escape velocity sorta

  1. Dec 11, 2005 #1
    Q: In the absenceof air resistance, the least speed with which a body must be projected vertically upward from the earth's surface if it is to reach an altitude of 800km is...

    800km = 8.00x10^5 m
    radius of earth = 6.37x10^6 m
    mass of earth = 5.99x10^24 kg

    Kf +Uf = Ki + Ui
    0 + 0 = 1/2 mv^2 + (- G Me m / Re + 800km )
    1/2 mv^2 = G Me m / Re +800km
    m drops out
    v = square root of [ (2)(6.67x10^-11)(5.99x10^24)/(7.17x10^6) ]
    v = 1.06x10^4 m/s

    is this right? thanx in advance for the help
  2. jcsd
  3. Dec 11, 2005 #2


    Staff: Mentor

    Look at your Uf and Ui. Are you sure that Uf is 0? Are you sure about that expression for Ui?

  4. Dec 11, 2005 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    The change in kinetic energy = change in gravitational potential energy if one neglects air resistance (i.e. nonconservative forces).


    So the objective is to find the initial velocity at which a projectile will leave the earth's surface, r1 = re, and travel to a radius, r2 = re + 800 km.

    So there is an initial KE and GPE and a final KE and GPE, the total energy (KE + GPE) being equal. KE = kinetic energy and GPE being gravitational potential energy.

    The minimum speed coincides with KEf = 0, and thus KEi = 1/2 mvi2 = [itex]\Delta[/itex]GPE.
  5. Dec 11, 2005 #4
    Your initial potential energy muz include the energy of the body on the surface of the earth... It's not zero.
  6. Dec 12, 2005 #5
    ok i think i have it now

    Kf + Uf = Ki + Ui
    0 [because its a minimum velocity] + ( -G Me m / Re +800km ) [potential at 800km] = 1/2 m v^2 + ( -G Me m / Re ) [potential at the begining, the surface of the earth]

    then through some algebra we can solve for v

    2 [ {-(6.67x10^-11)(5.98x10^24)/(6.37x10^6)+(8.00x10^5)} + {(6.67x10^-11)(5.98x10^24)/(6.37x10^6)} ] = v^2

    v = 3.74x10^3 m/s is this right?

    hoping my arithmetic is right but i think i got it thanks in advancefor verification!
  7. Dec 12, 2005 #6
    Yup.. tat shld be the correct ans.
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