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Breaking rules of Algebra?

  1. Jul 13, 2009 #1
    Breaking rules of Algebra???

    1. The problem statement, all variables and given/known data
    I am copying this problem from my textbook. It is about momentum and Kinetic energy




    3. The attempt at a solution

    My problem lies in part B. According to Part A, v₁'=v₁‐kv₂'
    But in part B, (v₁‐kv₂')²+kv₂'²=v₁'², see the problem? v₁‐kv₂' has been plugged into v₁'² and it reappeared again on the right hand side.

    Right I need help. KEEP IN MIND THAT "K" IS THE RATIO OF M2/M1
    ALSO[/SIZE] PLEASE SHOW ME HOW TO GET TO PART C
     
    Last edited: Jul 13, 2009
  2. jcsd
  3. Jul 13, 2009 #2

    Pengwuino

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    Re: Breaking rules of Algebra???

    What do you mean it reappeared again on the right hand side? It looks fine. I'm not sure about the jump to part C though...
     
  4. Jul 13, 2009 #3
    Re: Breaking rules of Algebra???

    Shouldn't it have been this?

    (v₁‐kv₂')²+kv₂'²=v₁²
     
  5. Jul 13, 2009 #4

    Pengwuino

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    Re: Breaking rules of Algebra???

    Yes, you're right, I need glasses. It has to be unprimed on the right side. Sounds like a typo (prime's are easy to mess up :rofl:). The jump to part C makes sense now.
     
  6. Jul 13, 2009 #5
    Re: Breaking rules of Algebra???

    What should I do? What the general solution?

    I am suppose to get a result of this

    v₁'=(m₁‐m₂)v₁/(m₁+m₂)
    v₂'=2m₁v₁/(m₁+m₂)
     
  7. Jul 13, 2009 #6

    Pengwuino

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    Re: Breaking rules of Algebra???

    Where are these masses coming from? You have part C, it should be immediate what v2' is and from the first equation, you can determine v1'.
     
  8. Jul 13, 2009 #7
    Re: Breaking rules of Algebra???

    It's a momentum question. Basically it states an object with velocity collides a stationary object that is heavier than the object clashing in. The result is both objects repelling and heading the opposite direction of each other. I am suppose to find the velocity using the conversation of energy - KE.
     
  9. Jul 13, 2009 #8

    Pengwuino

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    Re: Breaking rules of Algebra???

    I mean what is the equation for the masses? I assume it's k = something about masses.
     
  10. Jul 13, 2009 #9
    Re: Breaking rules of Algebra???

    Sorry, I don't know what you are talking about? K (in post 1) is the ratio of M2/M1
     
  11. Jul 13, 2009 #10

    Pengwuino

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    Re: Breaking rules of Algebra???

    So k=m2/m1. Part C shows you exactly what v2' is so you should be able to solve for it immediately with no tricks or substitutions other then k=m2/m1. To solve for v1', use the very first equation you have after you solve v2'.
     
  12. Jul 13, 2009 #11
    Re: Breaking rules of Algebra???

    Can you show me the algebra...? Because I am still stuck on Part B.
     
  13. Jul 13, 2009 #12

    Pengwuino

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    Re: Breaking rules of Algebra???

    You were correct in noticing it was a typo in the third and subsequently 4th line. The [tex]v_1 '^{^2 } [/tex] should have been a [tex]v_1 ^2 [/tex] on the right side. The line after it is also incorrect. You have the right idea to plug in v1' from the first equation. Now expand the left side and its a simple cancellation. Subtract [tex]v_1 ^2 [/tex] from both sides and you get part C and you can solve for v2' immediately.
     
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