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Calculating Uncertainties of Measured quantities (Physics)

  1. Nov 11, 2013 #1
    1. The problem statement, all variables and given/known data
    d1 = 2.53 cm +/- .05 cm

    d2 = 1.753 m +/- .001 m

    0 = 23.5 degrees +/- .5 degrees

    v1 = 1.55 m/s +/- .15 m/s

    Using the measured quantities above, calculate the following. Express the uncertainty calculated value.


    2. Relevant equations

    d3 = 4 ( d1 + d2)

    3. The attempt at a solution

    d3 = 4 (2.53 cm +/- .05 cm) + (1.753 m +/- .001 m)

    d3 = 10.12 +/- .2 cm + 7.012 m +/- .004 m

    d3 = 10.32 cm + 7.016 m

    I don't understand this problem so I would appreciate some help.
     
  2. jcsd
  3. Nov 11, 2013 #2

    mfb

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    Staff: Mentor

    How did you get that?

    Try to convert both numbers to the same unit, either cm or m.

    Do you know how to combine uncertainties from multiple sources? This is certainly something you had in class and it is written in your textbook, too.
     
  4. Nov 11, 2013 #3
    Is there an equation involved in this problem? Like what do d1, d2, 0, v all have in common?
     
  5. Nov 11, 2013 #4
    You have to add your errors in quadrature.

    d3 = 4 ( d1 + d2)

    σd32 = σd12 + σd22

    You need to perform the calculation with just the values, and then calculate the error giving your answer in the form
    d3 +/- σd3

    ETA oops, you're not the question asker.
     
    Last edited: Nov 11, 2013
  6. Nov 11, 2013 #5
    response to uncertainties

    My textbook isn't very good and doesn't give an explanation about combining uncertainties. As for in class, my instructor doesn't explain the steps and there aren't any example given about the uncertainties. All it mentions is the definition of an uncertainty and the basic rules for uncertainties. I still don't understand how to do the problem.

     
  7. Nov 11, 2013 #6
    I added the numbers together and that is how I got it. I don't know how to convert to centimeters or meters. No, I don't know how to combine uncertainties from multiple sources.

     
  8. Nov 11, 2013 #7
    In response to your question, I am not sure what they have in common. I don't understand how to do the problem and this is how come I am asking for help.

     
  9. Nov 11, 2013 #8

    mfb

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    Staff: Mentor

    Good, you'll just need the most basic rule.
    How old is the captain?
    Then you can look that up.
     
  10. Nov 11, 2013 #9
    The following error propagation (sample calculations) consists of the ‘simple’ methods
    outlined in lab appendix (pages A7-A9). This method yields uncertainties which are
    slightly high, but still gives ‘reasonably good values’.


    For added/subtracted quantities, the uncertainties are obtained (propagated) by simply
    adding the absolute uncertainties (i.e., they are not added in quadrature).

    • Write correct significant figures based on the final uncertainty.

    For multiplied/divided quantities, the uncertainties are obtained by 1) converted to
    percent uncertainties (i.e., fractional uncertainties), and 2) the percent uncertainties are
    simply added (i.e., they are not added in quadrature).

    • Convert from percent to absolute uncertainties (to get correct significant figures for
    final answer).

    Important note for uncertainty calculations –Keep extra significant figures in
    uncertainties when doing computations. Convert to one significant figure in the final
    number (i.e., final answer)!!!

    This is what I have as a basic rule for uncertainties, but this doesn't mention the fact of showing me how to convert centimeters or meters in uncertainties. Please let me know if these are correct!

    d1 = 2.53 cm +/- .05 cm

    d2 = 1.753 m +/- .001 m

    0 = 23.5 degrees +/- .5 degrees

    v1 = 1.55 m/s +/- .15 m/s

    Using the measured quantities above, calculate the following. Express the uncertainty calculated value.

    1. d3 = 4 (d1 + d2)

    delta d3 = 4 * (0.05 + 0.001) = 0.204

    2. a = 4 v1^2 / d2

    delta a = 4 * (2 * 0.15 - 0.001) = 1.196

    3. d1 (tan (0))

    0

    4. Z = 4d1 (cos (0)) ^2

    4 * 0.05 = 0.2

    Are these right or are they still wrong? I did try to work on them. Please let me know as soon as you can!

     
  11. Nov 11, 2013 #10
    1 cm = 0.01m

    You should be able to figure the rest out from this.

    I shall give you an example of error propagation and you should be able to apply this to your problems.

    Two measured lengths, a and b.

    a = 106.0 ± 0.3 mm
    b = 58.3 ± 0.4 mm

    When we add these together we expect to see the final error is bigger than either of the contributing errors, but not larger than the sum of the errors.

    if x = a + b

    σ2x = σ2a + σ2b

    (where σ means uncertainty)

    a + b = 164.3 ± (0.32 + 0.42)1/2

    = 164.3 ± 0.5 mm

    All i've done is taken the square root of the errors added in quadrature to find the error in x.
     
  12. Nov 12, 2013 #11

    mfb

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    Staff: Mentor

    So you know about a proper way to combine errors: add them in quadrature.

    And this is all you need.

    It also does not mention that "5" is the number that follows "4". It is expected that you know the basics, or know where to find them.

    You just randomly add numbers that appear somewhere. That does not work.
     
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