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Find L if

  1. May 15, 2013 #1
    Find L if....

    1. The problem statement, all variables and given/known data

    [tex]\omega=\frac{1}{h}In(\frac{L}{Lo}-1)[/tex]

    Find L if omega - -2.6, Lo = 16 and h = 1.5
    2. Relevant equations



    3. The attempt at a solution

    -2.6*1.5=In(L/16-1)
    -3.9=In(L/16-1
    e^-3.9=L/16-1
    0.02024=L/16-1
    1.02024=L/16
    so L=16.32384
     
  2. jcsd
  3. May 15, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The correct abbreviation for the natural log is 'lower case L' and 'lower case N'. You have 'Upper case I' and 'lower case N', which is incorrect. Otherwise, your algebra appears to be correct.
     
  4. May 15, 2013 #3
    Ok thanks for the help I will use the correct abbreviation in future
     
  5. May 15, 2013 #4

    Mark44

    Staff: Mentor

    It's best to substitute the constants at the end of your algebraic manipulation. Doing so sooner can lead to round-off errors.

    This is the way I would have done it.
    $$\omega=\frac{1}{h}\ln(\frac{L}{L_0}-1)$$
    $$\Rightarrow h \omega = \ln(\frac{L}{L_0}-1)$$
    $$\Rightarrow e^{h \omega} = \frac{L}{L_0}-1$$
    $$\Rightarrow e^{h \omega} + 1 = \frac{L}{L_0}$$
    $$\Rightarrow L_0 (e^{h \omega} + 1) = L$$
    Now you can replace the constants.
     
  6. May 16, 2013 #5
    this makes a lot of sense thanks Mark44
     
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