# Homework Help: Uncertainity Problems

1. Sep 27, 2004

### Freeze

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 .

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. Sep 28, 2004

### Freeze

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.