The discussion focuses on calculating the overall uncertainty of the variable R, defined as R = (h² + l²) / 2h. The uncertainties provided are ±0.57% for h, ±1.14% for h², and ±7% for l². Participants clarify that the uncertainty in h² is derived from the uncertainty in h, specifically by multiplying the percentage uncertainty of h by 2. The conversation emphasizes the distinction between actual uncertainty and percentage uncertainty, highlighting the importance of using differential calculus to compute uncertainties accurately.
PREREQUISITESStudents in physics or engineering, researchers conducting experiments, and professionals involved in measurements and data analysis will benefit from this discussion.
<br /> <br /> Yeah those are the actual uncertainties in the values<br /> h = ±0.57% is the % uncertainty, where h is a measurement of length in m<br /> To get the uncertainty in h<sup>2</sup> you multiply the %uncertainty of h by 2 yeah?HallsofIvy said:Use the "differential"- R = (h2+l2)/2h dR= [(1- 2(h^2+ l^2))/h^2]dh+ (l/h)dl. Set dh and dl equal to the uncertainties in h and l respectively. You will need "current" values for h and l as well as for dh and dl. I do not understand you last values. Where you have "h = ±0.57%" do you mean the uncertainty in h (my "dh") rather than h itself? Also you have "h2=±1.14%" which is 2 times your h, not h squared.
You are confusing me by saying "actual uncertainty" at one point and "% uncertainty" at another- those are NOT the same thing. If h= 10, say, and the "actual uncertainty" (I would say "relative error") is 0.5 then the "percentage uncertainty" is (0.5)/(10)= 0.05= 5%. If f(x)= x2 then df= 2x(dx) The "actual uncertainty in f is 2 times the value of f time the "actual uncertainty" in x. The "percent uncertainty" in f is df/f. Dividing both sides of the previous equation by f, df/f= 2x(dx)/f= 2x(dx)/x2= 2(dx/x) so the percent uncertainty in x2 is 2 times the percent uncertainty in x.Ch3m_ said:Yeah those are the actual uncertainties in the values
h = ±0.57% is the % uncertainty, where h is a measurement of length in m
To get the uncertainty in h2 you multiply the %uncertainty of h by 2 yeah?