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Gravitation energy 2

  1. Jun 21, 2014 #1
    1. The problem statement, all variables and given/known data
    Mass m is left to fall from height h above the surface of a star with radius R. derive an expression for the velocity it hits the ground, using R, h and the acceleration g

    2. Relevant equations
    The energy: ##E=\frac{1}{2}mv^2-\frac{GMm}{r}##
    The acceleration: ##g=\frac{GM}{r}##

    3. The attempt at a solution
    $$\frac{GMm}{R+h}=\frac{1}{2}mv^2-\frac{GMm}{R}$$
    $$\frac{GM}{R+h}=\frac{v^2}{2}-g$$
    This expression doesn't give the desired one: ##\sqrt{\frac{2Rgh}{R+h}}##
     
  2. jcsd
  3. Jun 21, 2014 #2

    SammyS

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    The term on the left above is missing a negative sign.

    What does your expression give for a result?
     
  4. Jun 21, 2014 #3
    oo

    $$-\frac{GM}{R+h}=\frac{v^2}{2}-g$$
    $$-\frac{RGM}{R(R+h)}=\frac{v^2}{2}-g$$
    $$-\frac{Rg}{(R+h)}=\frac{v^2}{2}-g$$
    $$v^2=2g\left( \frac{R}{R+h}+1 \right)$$
     
  5. Jun 21, 2014 #4
    I solved it thanks to your remark, bye
     
  6. Jun 21, 2014 #5

    Orodruin

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    *removed* posted at same time as Karol solved it.
     
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