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Dimensional Analysis

Discussion in 'FAC & Stats Pack' started by gdmiccc, Jul 2, 2013.

  1. gdmiccc

    gdmiccc Member

    Hi,
    In the Dimensions section of Chapter 5, one of the examples states that since "exp(x) is dimensionless, we know that lambda(t) must be dimensionless, in other words t has the same dimension as 1/lambda"

    Also, in the solution explanation of Question 5.7 is states that "Since the argument of exp(x) is dimensionless, we know that x has the same dimension as 1/lambda"

    If anyone could elaborate or explain how "we know" these statements, I would greatly appreciate it. Thanks.
     
    gdmiccc, Jul 2, 2013
    #1
  2. John Lee

    John Lee ActEd Tutor Staff Member

    Yeah - it's not particularly clear. I guess the way I think about it is that if it wasn't then the power series expansion would cause problems:

    \( e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ... \)

    So if x is measured in cm then:

    1 is dimensionless, x is cm, x² is cm² and so on...
     
    John Lee, Jul 3, 2013
    #2

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