What is Uncertainties: Definition and 167 Discussions
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter.The measurement uncertainty is often taken as the standard deviation of a state-of-knowledge probability distribution over the possible values that could be attributed to a measured quantity. Relative uncertainty is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean, median, or mode). Thus, the relative measurement uncertainty is the measurement uncertainty divided by the absolute value of the measured value, when the measured value is not zero.
Please, I need practical instruction/calculation to find the uncertainty associated with the use of opacity meters (smoke meters). I cannot even start to calculate; I cannot find anything on this topic.
Thx a lot.
Hey, this is my first post ever on PF, and I have done my best to follow the guidelines on posts asking for help with homework. Please know that I am not after the answer just to cheat and get the questions right, I am after the method so that I could do a similar question myself in the future...
Hey, I'm being asked to find the experimental limit of angular resolution.
The equation is as follows: theta = d / D
where d = 0.75 \pm 0.003 mm
and, D = 10.3 \pm 0.2 m
The angular limit of resolution will be given in radians. How do I work out the resultant uncertainty?
Any help would be great! I'm just starting off with Quantum and am having trouble with this problem.
Homework Statement
Angular momentum eigenstates |l,m> satisfy the equality in the Heisenberg uncertainty relationship.
Calculate the uncertainties of Delta Lz and Delta Ly in an...
I am finished collecting data for my experiment and now I am processing it.
I have a graph of temperature against time from which I will determine, after processing, whether or not rate of cooling is proportional to the (excess temperature)5/4
I've produced my tables, calculated uncertainties...
Homework Statement
Dear All,
Suppose I had to values: A (±a) and B (±b) where A not equal to a and B not equal to b. I have to find the product of A and B taking into consideration uncertainties.
Homework Equations
A (±a) * B (±b) = C (±c) where c = (a/A+b/B)
The Attempt at a...
I am processing the data in my pulley experiment and I have a doubt.
I am measuring the efficiency, thus, I measured the work I inputed in the system. For when the mass being lifted by me was moved by 0.05m, I exerted a 1.4 N force and I had to exert that force for 0.275, 0.28, 0.285. (Those...
Hi,
This problem has been bugging me for while. I hope someone can explain it.
1) If I measure something with a digital device and I know that the reading is correct, my only uncertainty is the limited significant figures displayed by the device. So if it read 24.6 the actual value...
Homework Statement
The graph below shows the potential (V) applied to, and the current I(mA) drawn by, an electrical circuit. Use the max and min slope method to determine the:
a) equation of line of best fit of the graph below (answer must be and equation relating to V and I). Your answers...
Homework Statement
Consider the continuous time state space model governed by:
A = [-1 0;1 0]
B = [1; 0]
C = [1 -1]
D = 0
a) suppose we are using the following state feedback and observer gains
K = [k1 k2]
L = [l1;l2]
find the loop gain symbolically using MATLAB (aka find...
Homework Statement
I am having trouble determining the error for a set of linear equations that represent a simple circuit with two voltage sources. I have found two possible uncertainties by solving using substitution, detailed below.
The circuit is shown below...
Homework Statement
Is it true that if a particle has lower energy than another particle, then it also has smaller uncertainties in momentum and position?
Homework Equations
Uncertainty principle
The Attempt at a Solution
If you consider the Bohr model, lower energy states mean...
I'm beginning to study control theory, and I keep reading about matched and unmatched uncertainties in the literature, but I have yet to find the definitions of matched and unmatched. Could someone explain it to me? Thanks.
I am confused over how to work with errors and uncertainties.
So far when dealing with a small number of measurements I have used the partial derivative method to calculate the final error in my result e.g. if my result is
E=mgh \text{ then assuming no error in g my uncertainty is }...
Homework Statement
Find the number of moles:
v = 10.00 +/- 0.03 cm3
c = 1.00 mol dm-3
Homework Equations
n = cv
The Attempt at a Solution
When you are converted cm3 to dm3, do you need to also convert the uncertainty?
When you finding n, and you are not given an uncertainty for...
Hi
Ok, we all know that if a quantity T is measured N times, then all measurements have the same standard deviation (SD). Now, with this assumption one can derive the width of the average to get SD/sqrt(N).
I have often encountered a dataset D, where each measurement has been assigned no...
Hi
In http://sl-proj-bi-specification.web.cern.ch/sl-proj-bi-specification/Activities/Glossary/techglos.pdf it says that: ... if the sources of uncertainties are numerous, the Gaussian distribution is generally a good approximation.
I don't quite understand why. The Central Limit Theorem (CLT)...
Homework Statement
I'm writing up a prac, which involves calculating the uncertainty for 1/(xy)^0.5.
There are two formulas that I think apply:
Homework Equations
For R = xy, u(R)/R = u(x)/x + u(y)/y
and
using differentials in calculus
dR = (dR/dx)dx + (dR/dy)dy [note...
Homework Statement
"From your graph, calculate the EMF and internal resistance of your cells. Include uncertainties in your calculations"
Now I know how to work out the emf and int. resistance, but I am just not sure about how to incorporate uncertainties.
Homework Equations
y = mx +...
Hello, I am a newbie to these forums, so please be patient with me! OK, my first (but not only) problem is getting to understand Black Hole physics... I understand they (BHs) arise as solutions to the EFE's, and there are currently many efforts to tie in Quantum Theory in a consistent way which...
I have this question for homework and I'm well stuck! The specific heat capacity of a liquid was found by heating a measures quantity of the liquid for a certain length of time. The following results were obtained.
Power of heater: ( 50.0 ± 0.5)W
Mass of liquid: (200 ± 10)g
Time of heating...
I have this question for homework and I'm well stuck!
The specific heat capacity of a liquid was found by heating a measures quantity of the liquid for a certain length of time. The following results were obtained.
Power of heater: ( 50.0 ± 0.5)W
Mass of liquid: (200 ± 10)g
Time of...
Homework Statement
A proton in a tin nucleus is known to lie within a sphere whose diameter is about 2.2 multiplied by 10E-14 m. What are the uncertainties in the momentum and kinetic energy of the proton?
Homework Equations
delta(x)*delta(p) >= hbar
delta(E)*delta(t) >= hbar
The...
Greetings,
In trying to even ask this question it’s obvious I don’t understand enough about the topic of QM and light.
Here is my attempt at my question:
If I shine a laser beam at a target or sensor – the electronics every time detects the beam. How do the Schrodinger wave equation...
Homework Statement
Determine the relationship between ^m/m and ^g/g from the relationship, m= 4pi^2/g
^= uncertainty
Homework Equations
m= 4pi^2/gThe Attempt at a Solution
^m/m = 4^g/g?
Hey :-)
I want to establish the uncertainty in my fitted model to my data
I can evaluate the variance for the predicted model, but I'm getting very confused as to how the variance can then give me the uncertainty in my model :S
I know that the standard error of the mean may be taken as the...
erm, ok let's say i have a value, with uncertainty, like y = 10 ± 3
so let's say i multiply y by 2, then it becomes 20
but does the uncertainty becomes 3 x 2 = 6? , hence y = 20±6 ?
what about divide? does it becomes 1.5?
i roughly understand fractional uncertainty and propagation...
Homework Statement
Calculate the density p and its uncertainty \Deltap showing all working
Mass M (kg)
0.0163
\Delta{M} (kg)
?
Diameter D (m)
0.014
\Delta{D} (m)
?
Homework Equations
\rho=MV
p= \frac{6M}{\Pi{D}^3}
Z=\frac{A^2B}{3C^{0.5}}...
Hi,
I don´t know how this standard type uncertainty calculation can be solved. The situation is as follows: on a graph are three curves with different values, their slope is the speed of each car. The uncertainty of the y-axis (time) is 5%. Now the problem is that i want to display the values...
Why is it that if you have two data points a \pm b and c \pm d whose uncertainties are symmetrically distributed, the sum of the points is
a+c \pm \sqrt{b^2+d^2}
Can someone please help me with this derivation.
Also, another separate question, suppose I have many uncertain data...
Homework Statement
I'm doing a physics lab and need to do the uncertainties, and the method I'm using is the natural log method, hich goes like this:
(equation used was k*(x^a)*(y^b)*(z^c) )
http://img297.imageshack.us/img297/3663/lnform.jpg
The equation I'm doing...
Q=mcT, variables with uncertainties are m and T.
If it were only Q=mT, the %uncertainty of Q would be %uncertainty of m + % uncertainty of T.
But c=constant (no uncertainties), so what is the uncertainty of Q when Q=mcT? Do you just multiply the constant to the %uncertainties of m and T...
Hello fellow physicists :)
I have recently done an experiment and am trying to propagate the uncertainty. Unfortuantely, I haven't done that in years, and need to remember how its done.
For example:
When theta= 20 (+-2)
I want to find sin20 and the uncertainty:
sin20=0.34 (+-?)
How can I...
Homework Statement
A glider moves on a level (horizontal) air track. The motion detector records five velocities of the glider: 0.48 m/s, 0.48 m/s, 0.53 m/s, 0.48 m/s, 0.47 m/s. The average velocity, uncertainty in the velocity, and relative uncertainty are
Homework Equations
Avg...
I am a First year Physics Student going into Second Year in a few weeks. I've been coping very well with all the work and theory. However Along with tight and Limited Lab schedule my sessions feel rushed and unfurfilling, particularly the analysis section.
Although we are given a lab manual...
I'm currently writing an extended essay about black holes in binary systems and accretion disks, and I wonder how I should proceed when calculating the size of the accretion disk.
Take, for instance, the binary system A 0620-00 where the mass of the black hole is said to be 5-10 solar masses...
Homework Statement
How do I combine the uncertainties to get a mean value±error?
Okay I know I have huge errors and if anyone could suggest what's wrong (I have huge errors in strain because the changes in length were tiny and the calibration errors were of the same order) that's great but my...
I've been trying to determine the Boltzmann constant by observation of Brownian motion. I undertook four experiments and hence got four different estimated values for kB. To analyse the data, I estimated the mean value and the standard deviation. This is maybe not the best way to analyze the...
Calculating uncertainties, using calculus. What do these letters represent??
Homework Statement
I think I've forgotten some basic calculus. Please help, this is reeally easy and quick answer for someone who know this, but its taking me forever to figure out.
I attached document that I am...
Homework Statement
I am unsure how to do uncertainties for my lab experiment. For example, we are suppose to estimate or guess the uncertainty for like the time and measurements.. Is there any general rule for proper guessing? Then I am unsure on what to do with the uncertainties in math...
Homework Statement
When doing operations with numbers with uncertainties, if the significant figures of the resultant number's uncertainty is lower the significant figures of the resultant number, how should I show the resultant uncertainty. For example,
Homework Equations
if you do the...
1. Homework Statement
For uncorrelated uncertainties LaTeX Code: \\delta x and LaTeX Code: \\delta y give the values and uncertainties for W in standard format.
A.) W=x+y with x=4.2(0.2) and y=0.7(0.1)
2. Homework Equations
[b]3. The Attempt at a Solution
well i think i am...
Homework Statement
For uncorrelated uncertainties \delta x and \delta y give the values and uncertainties for W in standard format.
A.) W=x+y with x=4.2(0.2) and y=0.7(0.1)
Homework Equations
[b]3. The Attempt at a Solution
well i think i am supposed to take the partial...
Hi all!
I'm currently doing an experiment using a compound pendulum trying to determine the value of g.
I have a problem with my uncertainties:
Error in period T:
The period is measured with the use of a photo-gate of accuracy +/- 0.0001s.
For each height i did 20 measurements from which i...
Homework Statement
Hi all.
Lets say i have some data points (x, y) (we will call these data 'D'). There is no uncertainty in x, and the uncertainty in y is 1.
I believe t hat x and y are connected as y = ax2, and I want to find the probability of a having a certain value given the data...
Homework Statement
1. A cylindrical can with radius of 3.1 +/- 0.4 cm and height 4.5 +/- 0.5 cm. What is the uncertainty in volume in cm cubed?
2. If theta= 0.40 +/- 0.02 radians, what is the uncertainty of y = tan (theta)?
Homework Equations
Volume of cylinder = Pie * r^2 * h...