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Physics problem, why is my answer wrong? HELPPP

  1. Jan 25, 2005 #1
    Two neutron stars are separated by a distance of 10^13 m. They each have a mass of 10^30 kg and a radius of 10^5 m. They are initially at rest with respect to each other.


    (a) How fast are they moving when their separation has decreased to one-half its initial value?


    My answer is 3.652 x 10^3 m/s , and it is wrong again (sigh).

    here is my computations

    1/2(mass)(final velocity)^2 - G(M1)(m2)/Final distance = 1/2(mass)(initial velocity)^2 - G(M1)(m2)/(initial radius)




    Since they are initially at rest, the vi term is zero, and that kinetic energy term vanishes. Then i plug in the values and solve for final velocity:

    1/2(10^30)(final velocity)^2 - (6.67x10^-11)(10^30)^2/(5x10^12) = -(6.67x10^-11)(10^30)^2/(10^13)



    so I isolate for final velocity and i get (final velocity)^2 = 1.33 x 10^7

    and i get final velocity = 3.652 x 10^3, when i input it it says it is wrong. Can someone help me, where did i go wrong? I did it multiple times already.
     
  2. jcsd
  3. Jan 25, 2005 #2
    you have a 2 different ways to approach this problem
    1. use reduced mass and the centrifugal force=gravitational force
    2. use conservation of energy

    both with end up with the same answer :wink:
     
  4. Jan 25, 2005 #3
    I used conservation of energy, so where did i go wrong?
     
  5. Jan 25, 2005 #4
    I used

    Potential Energy Final + Kinetic Energy final = Potential energy initial + kinetic energy initial
     
  6. Jan 25, 2005 #5
    the neutron starS are orbiting around each other..... and the both have velocity and contain KE
     
  7. Jan 26, 2005 #6
    In this problem, are you are they are orbiting around each other? Cauase in part B they collide, so I assumed they are in a straight line path toward each other. WTF
     
  8. Jan 26, 2005 #7
    part b? you didn't mention that....
    even if they are moving in a straight line, both neutron stars are moving (with same speed).
     
  9. Jan 27, 2005 #8
    Part A: Your equation is set up right, however you need to multiply the final kinetic energy by 2 since you have 2 neutron stars. final distance = 1/2 initial distance, subsitute that into the equation. Also you shouldn't really label r as the initial radius, because this part of the problem uses the distance (10^13m).

    Part B: uses the same equation, but the distance is now 2x the radius which would be the diameter.

    Should really work with variables first to simplify the equation, then start plugging in values.


    Also what school do you go to? I was working on this same problem a couple of hours ago.
     
    Last edited: Jan 27, 2005
  10. Jan 27, 2005 #9
    my part B) says: how fast are they moving just before they collide?

    _____ m/s
     
  11. Jan 27, 2005 #10
    ahhh, i see, i didn't realize i had to multiply the final kinetic energy by 2...i missed that key point. Ok leme try to do my computations , brb TY.
     
  12. Jan 27, 2005 #11
    check ur pm box tekno
     
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