1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Uncertainity Problems

  1. Sep 27, 2004 #1
    I just did a physics lab and now I have to fill up this uncertainity data sheet. I finished the sheet but I am having doubts about some of my answers. So I am just going to state how I solved the problems, if any of you can just tell me if I did them right or wrong (if wrong, what did I do wrong?) it would be much appreciated. ( I know..this stuff can be a pain to read over forum)

    3 of us measured 3 aspect of one same object and we received the following data

    D1 = 51.56 mm , 51.68mm and 51.60mm +- 0.01 mm (<==uncertainity)

    Average D1 = 51.61mm = .5161cm
    (not sure about the formula) Uncertainity of Average D1 = ((max-Average) + (average-min) )/2 = +- .06mm = +- .0006cm (it asks us to put the uncertainty as cm).

    % relative error of the average uncertainty (again not sure about the formula) - (uncertainity of Average D1/ Average D1) * 100 = .12%

    I am not gonna go through D2 and T (the other two objects) but let me just give their average and uncertainty of their average

    Average D2 = .2041cm +-.0001 cm
    Relative Uncertainty = .0005

    Average T = .0312 +- .0007cm
    Relative Uncertainty = .0224

    Now it Asks for

    Average D2^2, it's uncertainty and %relative error

    Since AverageD2^2 = Avg D2*Avg D2

    $$$ (not sure if the method of getting the relative error for D2^2 is correct) To

    So - .0005+.0005 = .001 = .1 % (relative error %)

    $$$ (not sure if the method of getting the absolute uncertainty here is correct) And to get the absolute uncertainty I have to multiply relative uncertainty by the quantity, so = (Avg D2 * Avg D2) * (relative uncertainty) = (.2041 cm * .2041 cm ) * (.001) = .00004 cm^2 .

    Now it asks for

    D1^2 - D2 ^ 2 's relative error % and uncertainty.

    To get that I have to add the absolute uncertainty of D1^2 to absolute uncertainty of D2^2. Average D1 ^ 2's absolute uncertainty was .0006 cm.

    So Absolute uncertainty for D1^2 - D2 ^ 2 = .001+.001 = +-.002.

    Now it asks for the volume of the object for which we have to use the following formula = pie ( (D1 ^2 - D2 ^ 2)t )/ 4 (i am sure about this formula as it was given in the sheet) and it asks us to find it's uncertainty.

    This is where it got a little more confusing for me. However, I realized I will only have to find the uncertainty of the following part - (D1 ^2 - D2 ^ 2)t.

    I need to know the relative uncertainty of D1 ^ 2 - D2 ^ 2 , and since I already know the absolute uncertainty for that which is .002, I will just have to divide that by the product of D1 ^2 - D2 ^ 2 which is .225, so the relative uncertainty is = .002/.225 = .008

    Now i have to multiply the product of (D1^2 - D2^2) (t) with (.008+relative uncertainty of T, which is .0224) and that will give me the the volume.

    Wow..ok I am just gonna stop there. If all these are right, then I am probably never gonna have problem with uncertainties again.
  2. jcsd
  3. Sep 28, 2004 #2
    Ok made a silly mistake there, in all those figures given in centimeters, the decimal goes one time to the right. I accidentally divided by 100 instead of 10.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook