Question

Im doing a lab report on measurements and the uncertainty in measurement.

We took measurements and are asked to calculate the volume

V=lwh

im good up until here .. where we are asked to apply the equation involving the uncertainties .

V= lwh + lw(∆h) + wh(∆l) + lh(∆w)

what is the point of this equation ? and how do i properly apply it ?

relative uncertainty (using a ruler accurate to the 0.1cm ) is ±.05 .. which im assuming is equal to 0.1

Answer 1

It comes from statistics, when you have uncertainties you can't just add them, you use specific formulas for each operation. (you can look this up online i dont remember the exact reason)

if you have multiplication you use:

\(\large \dfrac{\Delta V }{V}=\sqrt{(\dfrac{\Delta l }{l})^2+(\dfrac{\Delta w }{w})^2+(\dfrac{\Delta h}{h})^2}\)

\(\Delta x\) is the uncertainty in the measurement \(x\)

so now you want to the uncertainty in the volume, you plug everything you know and solve

Answer 2

thanks for responding.. i appreciate it.. but im not understanding this .. the equation you used looks nothing like the one i was talking about.. Is your equation derived from the one i posted up here?

Answer 3

is the point of this equation to solve for ∆V ?

Answer 4

yeah, that's the point, solving for the uncertainty in the volume.

I havent come across the equation you posted, if they're asking you to use that then i would use it, but the equation i wrote is what i've always used in any of the classes that have required error propagation.

Answer 5

oh ok ... well ill try out both and see what happens. thanks

Answer 6

no problem, good luck !