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Algebraic unknowns problem

  1. Dec 25, 2012 #1
    1. The problem statement, all variables and given/known data

    The unknowns below read as "m sub 1", "rub sub 2" etc.
    The maths part of a physics problem states:

    r1/v1 = r2/v2

    Combining these with equation :

    m1r1 = m2r2

    gives:

    v1/v2 = r1/r2 = m2/m1



    2. Relevant equations



    3. The attempt at a solution

    Would anyone be able to explain to me how they have gone to the final line of

    v1/v2 = r1/r2 = m2/m1

    Thank you!
     
    Last edited: Dec 25, 2012
  2. jcsd
  3. Dec 25, 2012 #2

    mfb

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    2016 Award

    Staff: Mentor

    You can re-write
    r1/v1 = r2/v2 as v1/v2=r1/r2
    and
    m1r1=m2r2 (I think you mean this) as r1/r2=m2/m1.
     
  4. Dec 25, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This is the same as saying that v1/v2= r1/r2 as you have below.

    Combining these with equation :

    m1r1/m2r2[/quote]
    This is not an equation and does not say anything. What did you mean to say?

    If you meant to say "m1r1= m2r2" above, yes, that is correct.



    2. Relevant equations



    3. The attempt at a solution

    Would anyone be able to explain to me how they have gone to the final line of

    v1/v2 = r1/r2 = m2/m1[/quote]
    You had, initially, r1/v1 = r2/v2. Multiply both sides by v1/r2 to get (r1/v1)(v1/r2)= (r2/v2)(v1/r2). On the left, the "v1" terms cancel leaving r1/r2. On the right the "r2" terms cancel leaving v1/v2. That is, r1/r2= v1/v2.

    If you also have m1r1= m2r2, then dividing both sides by m1r2 gives (m1r1)/(m1r2)= (m2r2)/m1r2). The "m1" terms cancel on the left and the "r2" terms cancel on the right leaving r1/r2= m2/m1. Thus r1/r2= v1/v2= m2/m1.

     
  5. Dec 25, 2012 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This is not an equation. Did you mean "m1r1= m2r2"?

    You have initially, r1/v1 = r2/v2. Multiply both v1/r2. On the left the "v1" terms cancel and you get (r1/v1)(v1/r2)= r1/r2 and on the right the "r2" terms cancel and you get (r2/v2)(v1/r2)= v1/v2 so v1/v2= r1/r2.

    If you actually meant m1r1= m2r2, then divide on both sides by m1r2. On the left, (m1r1)/(m1r2), the "m1" terms cancel and you get r1/r2. On the right, (m2r2)/(m1r2), the "r2" term cancel and you get m2/m1: v1/v2= r1/r2= m2/m1.
     
  6. Dec 25, 2012 #5
    Yes.

    Apologies for that. I have now corrected the initial question.
     
  7. Dec 25, 2012 #6
    I understand it now. Thank you.

    Sorry for the confusion earlier!
     
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