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Two planets colliding

  1. Nov 25, 2015 #1
    1. The problem statement, all variables and given/known data

    Two spherical pieces of rock, of masses m1=1.0×1010kg and m2=2.0×1010kg and both of radius r=1500m (2.s.f.) are in deep space a distance of R=1000km (2.s.f.) apart. The only force between them is gravity and they are initially stationary. Find the speed of m1 at collision ? and how much distance m1 travells before colliding.
    2. Relevant equations
    F=Gm1m2/R^2
    U=Gm1m2/r
    E=0.5mv^2

    3. The attempt at a solution
    For the first part i tried to find the difference in potential then equate that to the kinetic energy but its was in vain
     
  2. jcsd
  3. Nov 25, 2015 #2

    Doc Al

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    Staff: Mentor

    That's certainly part of the solution. Hint: Besides energy, what else is conserved?

    Show what you did.
     
  4. Nov 25, 2015 #3
    momentum is conserved so m1v1=-m2v2

    But how do you calculate the potential energy?

    Thanks for the reply
     
  5. Nov 25, 2015 #4

    Doc Al

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    Right.

    You gave the formula yourself:
    It's missing a minus sign, by the way.
     
  6. Nov 25, 2015 #5
    so is it Gm1m2/(2r+R)=0.5m1v1^2

    where R is the distance between the surface of the two rocks
     
  7. Nov 25, 2015 #6

    Doc Al

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    You need the change in potential energy, as the rocks move from initial to final position. And that will equal the total kinetic energy of both rocks, not just m1.

    You need to combine that with conservation of momentum to solve for the final speed of m1.
     
  8. Nov 25, 2015 #7
    Thats what is confusing me so is it
    Gm1m2/(2r+R) -Gm1m2/(2r)=0..5m1v1^2+0.5m2v2^2
     
  9. Nov 25, 2015 #8

    Doc Al

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    Almost. You have the sign wrong on the left-hand side. (What you have now is negative.)
     
  10. Nov 25, 2015 #9

    jbriggs444

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    Since we are not told whether the separation is center to center or edge to edge, it is not clear whether you need to account for the 2r in the starting separation. In any case, to two significant figures, 2r is negligible compared to R. So you may as well simplify the equation now and save yourself some work later.
     
  11. Nov 25, 2015 #10
    OMG !!! I got the answer. Thanks alot.

    So for the second part i got the answer by guessing that m1/m2=d2/d1
    where d1 is the distance travveled by m1 and likewise for d2

    and the answer was correct but i dont know why
     
  12. Nov 25, 2015 #11

    Doc Al

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    Excellent.

    No guessing allowed! :-)

    Hint: Where is the center of mass of this system? Does it change when they approach?
     
  13. Nov 25, 2015 #12
    I got it. But why doesnt the CM change ?
     
  14. Nov 25, 2015 #13

    jbriggs444

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    If the two masses start at rest, the total momentum of the system is zero, yes? The total momentum of a composite system can (at least classically) also be computed as total mass multiplied by velocity of the center of mass.

    If total mass is non-zero and momentum is zero, what does that tell you about the velocity of the center of mass?
     
  15. Nov 25, 2015 #14
    Thanks !!!
     
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