1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proton moving from infinity

  1. Feb 19, 2016 #1
    1. The problem statement, all variables and given/known data
    A proton is moving at speed v from infinity toward a second stationary proton, as shown below. Determine the minimal distance between them.

    http://s27.postimg.org/lmw3d21j7/Untitled.png


    2. Relevant equations
    [tex] W = \frac{kq_1q_2}{r} [/tex]
    [tex] E_k = \frac{mv^2}{2} [/tex]
    3. The attempt at a solution

    Let's say that the minimal distance between two protons is x and at that moment their speeds are v_1. Then the initial energy would be E_1 and the final E_2:
    [tex]E_1 = \frac{mv^2}{2} [/tex]
    [tex] E_2 = \frac{ke^2}{x} + mv_1^2 [/tex]
    According to the law of conservation of energy: [tex] E_1 = E_2 [/tex]
    And now I just don't know how to find the speed v_1.
     
  2. jcsd
  3. Feb 19, 2016 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Can you think of any other conserved quantities?
     
  4. Feb 19, 2016 #3
    Maybe an electric field or potential will remain constant at some point?
     
  5. Feb 19, 2016 #4
  6. Feb 19, 2016 #5
    So, I see that I can use conservation law of linear momentum. But how to include a given distance r?
     
  7. Feb 19, 2016 #6
    good

    that was my problem too....
    been away from solving any of these for, well 50 plus years,

    amazing I can remember my own name!!

    https://en.wikipedia.org/wiki/Momentum#Conservation

    "If the velocities of the particles are u1 and u2 before the interaction, and afterwards they arev1 and v2, then

    dccfa0969fdbd08e06981e85f2813970.png "

    Think about whether you can use these as a second set of equations.....m's are all the same, only proton is moving initially, right?? two equations, two velocity unknowns

    the stationary proton accelerates, reaches some velocity which you'll know.....
    so you'll need another equation relating velocity to minimal distance....unsure what that is
     
  8. Feb 19, 2016 #7

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Is the second proton free to move or is its location fixed? I think you're supposed to assume the latter.
     
  9. Feb 19, 2016 #8
    Of course....duh!!
    thank you
     
  10. Feb 20, 2016 #9
    Yes, the second proton is fixed. Then I suppose I could use conservation law of angular momentum.
     
  11. Feb 20, 2016 #10

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, but only if you choose the axis carefully.
    Linear momentum is not conserved because the second proton is being held in place by some external force. How do you avoid that being a problem for angular momentum?
     
  12. Feb 20, 2016 #11
    Let's say I choose an axis going through the second proton which is fixed. Vector of electrical force creating external forces momentum goes through the axis, so the momentum of external forces equals zero. Then the initial and final angular moments would be:

    [tex] L_i = mvr [/tex]
    [tex] L_f = mv_1x [/tex]
    [tex] L_i = L_f [/tex]

    According to the law of conservation of energy:

    [tex] \frac{mv^2}{2} = \frac{mv_1^2}{2} + \frac{ke^2}{x} [/tex]



    Am I right?
     
  13. Feb 20, 2016 #12

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Looks right.
     
  14. Feb 20, 2016 #13

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    This doesn't really make sense. I know what you're trying to say, but what you've written is nonsense.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted