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Dimensional analysis question

  1. Sep 24, 2008 #1
    1. The problem statement, all variables and given/known data
    determin the dimensions of [tex]\alpha[/tex] in the following
    a)Sin([tex]\alpha[/tex]X[tex]^{}2[/tex]) (alpha* X squared) (X is a distance)
    b)10[tex]\alpha[/tex]t3
    c)cot([tex]\alpha[/tex]X2/R) (R is a radius)
    d)e(hf/[tex]\alpha[/tex]T - 1 (h is plancks constant with units J*s) ( f is frequency


    2. Relevant equations



    3. The attempt at a solution
    so are these all supposed to be dimensionless?

    attempt at a: [L2 [tex]\alpha[/tex] ] = 1 therefore [tex]\alpha[/tex]= [1/L2 ] (where L is length)

    id appreciate some help :)
     
  2. jcsd
  3. Sep 24, 2008 #2
    Yes, you're right and the solution is correct. All of those example functions must have dimensionless arguments, otherwise they don't make sense, sort of "apples plus oranges = peaches" or something like that.
     
  4. Sep 24, 2008 #3
    just to clarify for b & d, does it matter that the dimensions are in the exponent?
     
  5. Sep 24, 2008 #4
    anyone?
     
  6. Sep 24, 2008 #5

    tiny-tim

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    Hi mjolnir80! :smile:

    (have an alpha: α and a squared: ² and a cubed: ³ :smile:)
    No, it's all the same … 10αt³ and sin(αt³) need the αt³ to be dimensionless for exactly the same reason. :smile:
     
  7. Sep 24, 2008 #6
    one more quick thing about dimensional analysis :)
    in an equation lets say X=Vit + 1/2 a t2

    if we wanted to prove that this equation is dimensionally correct, how would the + between the 2 terms on the r.h.s effect the analysis would we have to ignore the + and just try to make it so that the overall dimensions canel each other out to give lenghth?
     
  8. Sep 25, 2008 #7

    tiny-tim

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    Hi mjolnir80! :smile:

    No … with one or more +s, each part must have the same dimensions …

    in this case, X must have the same dimensions as Vit and as 1/2 a t2 :smile:
     
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