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Uncertainty problem

  1. Jun 4, 2006 #1
    Imagine playing baseball in a universe where planck's constant was 0.60 J-s. What would be the uncertainty in the position of a .50 kg baseball that is moving 20 m/s with an uncertainty of 1.0 m/s?
    so i know, delta X*delta P=(plancks constant/2pi)/2
    I solve for x. and it will tell me the uncertainty for position in the x,
    my question is, how do i find out the percent uncertainity for this problem?
    Do i do, 1/20 and that will give me % uncertainty? i know basic question..but any help is appreciated.
     
  2. jcsd
  3. Jun 5, 2006 #2
    You almost have it. When you divide the uncertainty by the actual value it is called the relative uncertainty. So 1/20 will give you the relative uncertainty and it isn't the percentage uncertainty. The percentage uncertainty is simply found by multiplying the relative uncertainty by 100.

    ie [tex]\\frac{\Deltax}{x}(100)=% uncertainty[/tex]

    Edit: I still don't see the above latex properly so I will just put it in text here.

    % unc = [delta(x)/x]*100

    So obviously once you find the momentum ([tex]p=mv[/tex]), multiply by the RELATIVE uncertainty (will be 1/20 in your case) to find the uncertainty in momentum. You then solve for x like you said, but remember this will give you the absolute uncertainty in the position...so unless you know the inital value for x you can't find the percentage uncertainty for the position.

    That last paragraph was probably not necessary, but I thought it might explain a bit more ??
     
    Last edited: Jun 5, 2006
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