Uncertainties Definition and 152 Threads

Homework Statement A nominally linear electrical output force measuring device has the following manufacturer specifications: Input range : 0-100 lbf Full Scale output : 30mV Temperature effect on: Zero 0.002 % full scale/degrees Fahrenheit Span 0.002 % of reading/degrees Fahrenheit The...

Homework Statement My teacher made up this question, but I think there's something wrong. Consider the wave packet in momentum representation defined by Φ(p)=N if -P/2<p<P/2 and Φ(p)=0 at any other point. Determine Ψ(x) and uncertainties Δp and Δx. Homework Equations Fourier trick and...

Homework Statement Suppose you measure three numbers as follows: Homework Equations x= 200. +-2. y= 50. +-2. z= 40. +-2. where the three uncertainties are independent and random. Use step-by-step propagation to find the quantity q= x/(y-z) with its uncertainty. The Attempt at a...

Why is it that only one significant figure for any uncertainty is taught? It seems like a nice general rule, but isn't it an unnecessary constraint and ultimately a poor rule in many cases? For example ## 5 \pm 1 ## could mean an error of either 0.5 or 1.5, which is a very large range. Wouldn't...

I'm doing an analysis where I have a set of random variables with some known uncertainties (the uncertainties are different for each random variable). The random variable is roughly Gaussian distributed. I'd like to get a meaningful characteristic value and uncertainty for the whole set. I can...

Homework Statement I am given a frequency value of 95 GHz (9.5x10^10 Hz), C= 25 F, L=1.12x10^(-25) H. The question is to find the uncertainties in frequency by taking account of inductor being 5% accurate & capacitor being 8% accurate. Homework Equations I believe this is the correct formula...

What limits the precision with which you can describe the uncertainty of a measurement? I will describe two examples that feel qualitatively different, but I am not sure if they are quantitatively different in how you would deal with the uncertainty. 1) Measuring the length of a pencil with a...

Hey could someone help me grasp the seemingly impossible concept of uncertainties? I'm having a lot of trouble understanding how to estimate, calculate and pretty much anything else to do with uncertainties. Muchly appreciated

Homework Statement Remember: all answers (including uncertainties) must have three significant digits. For all problems: use the value of g given: g = 9.802 m/s2 0.0005 m/s2. Look at the diagram in the above image. Suppose the total mass of hook 2 is m2 = 951.0 g 2.3 g, and θ = 31.90o...

There is a quantity (W) that I would like to calculate that is, ultimately, a function of parameters that I can measure directly (a and b), W = W(a, b) But I cannot measure a and b perfectly, there will be some uncertainty in these measurements. This uncertainty will propagate into my...

In an attempt to determine how the temperature varies over a distance of 100m I have taken five temperature measurements for every 10 meters, for a total of 55 measurements. I have then, for each dataset of N=5, calculated the mean value, standard deviation and standard error. Finally, I've...

Hello, I have some questions on uncertainties in measurement: Say you have a ruler with 1mm graduations, and you are trying to measure the length of a metal rod. One end of the metal rod is at the 120.0mm graduation, and the other is in between the 19 and 20mm graduation, and you approximate...

I got a table for a simple pendulum. I have 8 lengths, from 0.20m going up by 0.01 to 0.27. For each length, I have time for 10 oscillations (10T) that I've measured, and I have repeated the measurement twice for each length. Then I got the average time for 10T. I divided this average to give me...

I'm having a tough time understanding uncertainties and the concept of how to find the absolute and relative uncertainties of functions. I understand how to find the relative and absolute uncertainties in problems like 40±2 m (The absolute uncertainty is 2m and the relative is 0.05 if I'm not...

Homework Statement what is the uncertainty of \frac{a+b}{c+d} if a=b=c=d and σ_a = σ_b =σ_c=_d Homework Equations σ_{a+b}=√(σ_a^2+σ_b^2) σ_{\frac{a}{b}}=√((\frac{σ_a}{a})^2+(\frac{σ_b}{b}^2)) The Attempt at a Solution since a=b=c=d σ_{a+b}=√2 σ_a σ_{\frac{a}{b}}=√2...

Hello everyone, I have a large number of measurements with associated uncertainties, and I know that the real values are bounded above by some constant. How can I estimate the value of that constant, and the uncertainty on the estimate? Thanks

Hi, I have been given a random set of data. 10 numbers. 121 123 125 100 123 123 101 146 122 140 The question says. 1. Calculate the average of the data... No problem I can do that, my answer is 122.4 2. Determine the uncertainty for the average value. < This is the part that blows...

Homework Statement d1 = 2.53 cm +/- .05 cm d2 = 1.753 m +/- .001 m 0 = 23.5 degrees +/- .5 degrees v1 = 1.55 m/s +/- .15 m/s Using the measured quantities above, calculate the following. Express the uncertainty calculated value. Homework Equations d3 = 4 ( d1 + d2) The...

d1 = 2.53 cm +/- .05 cm d2 = 1.753 m +/- .001 m 0 = 23.5 degrees +/- .5 degrees v1 = 1.55 m/s +/- .15 m/s Using the measured quantities above, calculate the following. Express the uncertainty calculated value. a = 4 v1^2 / d2 a = 4 (1.55 m/s +/-.15 m/s)^2 / 1.753 m +/- .001 m a = 6.8 m/s...

Hi there, I'm trying to compare two hypotheses, each with a mean and an error (in this case Gaussian as well), to tell the probability of one being correct given the other. Currently, the only thing I know how to do is calculate the Gaussian probability of the second hypothesis being correct...

Hi, I hope I'm asking this in the right place. I need to understand this in order to complete a project, but it's not exactly a 'homework question'. I have some data which has a linear trend. The x values all have the same (random) uncertainty of ≈5cm and the y values all have the same random...

Just a quick question, would propagation of uncertainties with the partial derivatives still give the right answer when you only have one variable?

Lets say a sensor measures within accuracy of +/- 0.05N And you take multiple measurements and graph it out. (I.e., 5.12N, 5.15N, 5.05N...). What is the uncertainty of the final average? One way I read is: Sx = s/√N where s = std. dev. N = number of data points But...

My textbook isn't very clear on this. Let's say i find the mass of an object to be 24.5kg +-.2kg. Then i want to use that answer to calculate F (F=ma) when acceleration is equal to -9.81m/s2. What would the final answer look like. Also what about addition and subtraction. For sake of simplicity...

There are two kinds of uncertainty in QM: one of operators (Uncertainty Principles), and one of states (superposition). Is there any direct connection between them?

How do people generally determine uncertainties on results that are based on Monte Carlo simulations? Take this fictive example, just so we have something specific to talk about: I look at 106 particles, confined to a box. There is a small hole in one of the walls, and at some time t0 I am...

Homework Statement You are going to examine the viscosity of a fluid by dropping a ball bearing into a cylinder of fluid and measuring the fall time. You will use a ruler to measure the height, h, of the fluid column, and a stop watch to measure the fall time, t. The ruler and stop watch...

Hey, My question is on determining an 'uncertainty' quantity using total angular momentum operators in the x,y and z directions where we know the commutation relations between the x,y and z directions of the total angular momentum operators. I'm not really sure where to go with this at...

1. After I calculated from my original data with lowest significant figure of 3, I got 0.3765 and uncertainty of 0.1274 2.original data with lowest significant figure of 2 .calculated value of 0.69897 and uncertainty of 0.0789 The Attempt at a Solution This is how I answered...

I have a set of data points \{\{x_1, y_1\}, \{x_2, y_2\} ... \} each with an uncertainty \{\{dx_1, dy_1,\}, \{dx_2, dy_2\} ...\}. Is there any way of fitting a nonlinear model to the data that incorporates the uncertainties on both x and y? I know that you can use the Weights command to...

Homework Statement Trial 1: 1.05 ± 0.05 m. Trial 2: 2.0 m. Trial 3: 1.5 m. Trial 4: 1.05 ± 0.05 m. Homework Equations Not sure The Attempt at a Solution So to add them up, I just add the "base" measurements" and then tack on the ± and stick in the "uncertainties" like so: 1.05...

Hi! I'm newbie in Monte Carlo. My question concerns the statistical uncertainties of my simulations. Let's say that the result of my Monte Carlo is a certain distribution A (e.g. number of particles as a function of the depth in a target) and I have run NA events to generate that...

Homework Statement let a=360.9±0.1, let b=180.4±0.1, let c=212.5±0.13 and let d=211.7±0.16 whats f (including uncertainty) where f-1 = ((a/b)-1)/((c/d)-1) Homework Equations add the percentage uncertainties in quadrature if dividing two variables add the absolute uncertainties...

Suppose F = x/y dF= \frac{\partialF}{\partialx}\deltax+\frac{\partialF}{\partialy}\deltay This gives dF=\frac{\deltax}{Y}-\frac{x}{y^2}\deltay That is, the partial derivative of y comes out negative. Should i leave it as a negative? I see no reason to take the absolute value of...

Okay, so I have this equation: F = F1 + F2 - dF1F2 Anyways, I have the uncertainties for F1 and F2, how would I go about getting the uncertainty for F? Do I just simply add the uncertainties or do I use the formula deltaF1/F1 +deltaF2/F2 = deltaF/F? Thanks for your help.

I am trying to plot the flux from an Astrophysical source as a function of time. Due to the nature of the source, I am only receiving a handful of photons in each time bin. So imagine I had 10 observing periods of 10 days each, in which my telescope received the following number of photons...

Rather than arithmetic ("plus or minus") uncertainties, are there classical (not of Heisenberg uncertainty principle) measurements whose uncertainties otherwise appear as geometric ("times or divided by")?

How to round off percentage uncertainties? Here's is an example question: Find the percentage of uncertainty in (225.7+/-0.5)mm. I know that to find out percentage, it's simply 0.5/225.7 x 100 = 0.22153088...% Now, my question is, how much do I round off for this percentage uncertainty...

I have a physics project, but how do I express the uncertainty of a dimensionless quantity? E.g. how do I express the uncertainty of the coefficient of friction? Do I just write 0.403 ±0.02?

Homework Statement For my physics course work i need to work out the uncertainty of stress, is there formula for this or is it just the largest value of uncertainty for example is my area is 7.548E-08 +/- 6.452% and my force 2 +/- 25% Homework Equations stress= Force/area The...

Homework Statement I have conducted a simple experiment about polarized light. The angles were 0, 10, 20, 30 etc. The device used to measure the angles has units of 1 degree. Therefore the uncertainty is +-0.5 for each angle measurement. I was then required to produce a column beside this...

i have a measurement which has random uncertainty of 0.02 and scale reading 0.01. how do i combine these uncertainties - add in quadrature the percentage uncertainty or the absolute uncertainty? and does this give the percentage uncertainty or the absolute uncertainty of my measurement? thanks

Ive to work out the uncertainties for youngs modulus. would i take all 4 measurements and mutliply then divide by 4 ? would 1.788m have an uncertain if +/- 0.01 ? how would i get the uncertainties from 5.73x10-3 im very confused and my tutor isn't helpful at all.

Homework Statement I did a Physics lab in which I measured the height of the first bounce of a ball. I used a motion sensor to calculate it, so the uncertainty was really small: the smallest value it could measure was 0.0001, so the uncertainty would be 0.0001/2 = ±0.00005 (<--that's 5...

In what way can one do a goodness of fit test on a set of data that contains no uncertainties? I am doing a simulated data analysis assignment for a physics lab course and they provided me with data for a supposed xray spectrum for some material. The data consists of energy bins with a count...

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...