Finding the overall uncertainty

[Ch3m_]

Homework Statement

How do I find the overall uncertainty of R when R = (h²+l²)/2h

Homework Equations

uncertainty in h = ±0.57%
uncertainty in h²=±1.14%
uncertainty in l²=±7%

The Attempt at a Solution

√1.14²+7²+0.57²

 

[HallsofIvy]

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.

 

[Ch3m_]

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.

<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 h² you multiply the %uncertainty of h by 2 yeah?

 

[HallsofIvy]

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?

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.

There is an engineer's "rule of thumb" that "when quantities are added their errors add and when quantities multiply their relative errors add".