1. Limited time only! Sign up for a free 30min personal 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!

Two equations, a few unknowns

  1. Dec 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Could someone help me get from these two equations to E'/E=[(A-1)/(A+1)]2

    http://postimg.org/image/m5zi9ha19/

    2. Relevant equations

    E = v^2=E' = v'2 + AV^2
    p=v=p' = v' + AV = v


    from conservation of energy, momentum

    E'/E= (v'2 + AV^2)/(v^2)

    3. The attempt at a solution

    Three or four pages in my binder with no progress.
     
  2. jcsd
  3. Dec 15, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    $$mv = mv' + AmV$$ can be written as $$mv - mv'= AmV$$ and this gives $$(mv - mv')^2= (Am)^2 V^2$$
    You can use this in the equation for the conservation of energy and get rid of V, so just v' and v' are left as unknown, and their ratio is related to E'/E.
     
  4. Dec 15, 2013 #3
    Ok from what you wrote I've solved for $$V^2=(mv-mv')^2/(Am)^2$$.

    Now I then plugged that V^2 into my $$E'/E= (v'2 + AV^2)/(v^2)$$

    I am left with something like

    $$(v'(A-1)+v^2-2vv')/(Av^2)$$

    so far so good?
     
  5. Dec 15, 2013 #4
    I've figured it out, thank you
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted