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Constant of proportionality

  1. Feb 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Can anyone translate what k would be? I have never had to deal with a constant of proportionality before, and am not quite sure how to deal with it..

    The resulting aggregates therefore
    each have a net charge Q that is directly proportional to their molecular weight M:
    Q= K1 M
    where K1 (and in subsequent steps of this derivation K ) is a constant of proportionality.
     
  2. jcsd
  3. Feb 27, 2008 #2
    You've dealt with them, you just didn't know what they were called

    When I say y is directly proportional to x, what I mean is that if I double x, I double y. If I halve x, I halve y. If I square root x, I square root y, etc.

    so y=x? No, I said if I double x it doubles y, but I didn't say they're the SAME number! So if y and x are proportional you'd say y=k*x (or whatever letter) so all those things I said are true, if you double x, for that equation to still be equal you must double y

    For a counterexample what if they AREN'T directly proportional? So say y=k*x^2, if I double x, for the equation to hold, I have to quadruple y!

    You'll note that y=k*x results in the graph of a line with slope k, so you'll also hear that y and x are linearly related, which means the same thing as directly proportional

    You'll also commonly hear "inversely proportional", which means y=k/x, so if I double x, I take half of y, if I triple x, a third of y

    Counterexample again when it's NOT inversely proportional, y=k/x^2, if I double x, I take a fourth of y!

    ADDENDUM: The constant of proportionality that you're likely most familiar with is probably pi!

    What is pi exactly?(3! Wait no...) A bajillion years ago(1 jiggayear)some ancient Greeks or Carthaginians or whoever were looking at circles and thinking "hey the circumference and diameter are directly proportional!" Meaning if you took a circle with diameter of 1 m(well ancient greeks so like...1 hand?), it would have some circumference. If you took a circle with diameter 2(same unit), well the circumference is twice as much as before!

    So C=k*d they figured. So what was k? They had to take an actual circle that they could measure the circumference and diameter of, and find the ratio(so if C=k*d, then k=C/d) and they found it was a little more than 3. About .14 more than 3. And they called it pi since they were Greeks and the latin letter k probably didn't exist then >_>

    That's how Newton figured out his law of gravitation. He figured that the net force(which he had already figured out was directly proportional to acceleration, with that particular constant of proportionality being the mass)was directly proportional to the product of the two masses involved, and inversely proportional to the distance squared(so if you double either mass, you double the force, but if you double the distance between them you cut the force by a FOURTH)

    And that's the meat of the law, the part that really matters. The constant of proportionality (G, so F=G*m1*m2/d^2) is just some fundamental constant which he didn't have the tools to measure at the time

    So for the equation in your question, if you're not given K1, you're not really expected to care then. The POINT is that charge is directly proportional to M, so you understand the relationship between the two. As the molar mass of the aggregates increases, Q increases, and the nature of their relationship is linear
     
    Last edited: Feb 27, 2008
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