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Question about dimensional analysis

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    I have an equation for motion:
    x(t) = x(0) + x(0) * k * t[itex]^{1.5}[/itex]
    x is in meters and t is in seconds. I have to determine the unit of k.

    2. Relevant equations



    3. The attempt at a solution

    x(t) = x(0) + x(0) * k * t[itex]^{1.5}[/itex]
    [x(t)] = meters
    Therefore, [x(0)] = meters and [x(0) * k * t[itex]^{1.5}[/itex]] = meters
    meters * [k] * seconds[itex]^{1.5}[/itex] = meters
    meters * (1/seconds[itex]^{1.5}[/itex]) * seconds[itex]^{1.5}[/itex] = meters

    Does this mean the the unit of k is 1/seconds[itex]^{1.5}[/itex], 1/seconds, or something completely different?
     
  2. jcsd
  3. Nov 27, 2011 #2
    You first option is correct 1/s^1.5
     
  4. Nov 27, 2011 #3
    Thanks, I didn't know if that was possible. I have another question if you could please check:

    A force F is equal to k*x^n, where x is in centimeters.

    [k*x^n] = N
    [k]*(cm^n) = N
    [k] = N/(cm^n)

    The unit of k is N/(cm^n), is this correct?
     
    Last edited: Nov 27, 2011
  5. Nov 27, 2011 #4
    Yes, you seem to have it sorted out!!
     
  6. Nov 27, 2011 #5
    Great, thanks. I've done far better in more difficult subjects like multivariable calculus, but the lack of a proper instructor for physics has me making stupid mistakes these days. :frown:

    Would you happen to know of any online resource where I can practice graphical analysis of equations like these? What I have to do is to take a non-linear data set and convert it to a straight-line equation, determine appropriate units for slope and intercept, and determine values for the constants based on slope and intercepts. I only have two practice problems to work with.
     
  7. Nov 27, 2011 #6
    I have never looked for any online resources for these types of problems.
    If you know the power law for the equation (t^1.5 in your first example, n in your second example) Then the graph to plot is x against t^1.5 for the first and F against x^n for the second.
    These would give straight lines with gradient k in each case.
    If you do not know the power law.... I think that is the case in your second example, you only know it as n then you must take logs :
    F = k * x^n
    LnF = Lnk + n*Lnx

    A graph of LnF against Lnx will be a straight line with gradient n and intercept Lnk from which k can be calculated

    Does this make any sense for you, have you met log ~ log graphs
     
  8. Nov 27, 2011 #7
    I get the hang of those graphs, but I would feel more comfortable with practice. The other problem I have which I can't work is finding the resistivity p of a wire whose resistance R = (4pL)/(pi*d^2)

    Plot R on the y-axis and 1/(d^2) on the x-axis to get gradient = 4pL/pi, and then p = gradient/(4L/pi). But I didn't get a correct graph:
    https://www.physicsforums.com/showpost.php?p=3618742&postcount=3

    Hence, that is why I would feel more comfortable with more to practice with. But I understand what you said about log ~ log graphs, I have this problem (the one I made this thread for, not the previous one) fitted into a linear form properly, all the points rest on a straight line.
     
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