# Understanding uncertainties

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1. Feb 22, 2015

### xyz_a

1. The problem statement, all variables and given/known data

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 0.07o, and the system is in equilibrium. Find the following quantities, with uncertainties:

- the total weight on hook 2. w2 = ___ N +/- ___ N

- the magnitude of the force on hook 1. F1 = ___ N +/- ___ N

- The magnitude of the total force on hook 3. F3 = ___ N +/- ___ N

2. Relevant equations

F = m * a

3. The attempt at a solution

w2 = m * g = 0.9510 * 9.802 = 9.32N

F1 = 9.32 * cos(31.90) = 7.91N

F3 = 9.32 * sin(31.90) = 4.93N

I am just unable to solve the uncertainties. Someone else suggested that I use this equation Δf = df/dx*Δx + df/dy*Δy but I don't know how to use it or which values I have to use with it. Can someone please explain how I can do this? I'm really bad at solving uncertainties since I never really understood how to do it. Thank you.

2. Feb 22, 2015

### haruspex

There are two essentially different appeoaches to dealing with error ranges. One engineering approach is to consider, literally, the range of possible values consistent with the given information. This is used where e.g. machine tolerances are critical in manufacturing. More common in scientific circles is to treat the ranges as representing some (unstated) number of standard deviations of a normally distributed error. In this approach one adds up variances. See http://en.m.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification

3. Feb 22, 2015

### xyz_a

Honestly I don't understand how to use it. That was my main issue since I did state in the first post that I did not knew how to use the formula I had been given or which values I had to use, especially since it involves uncertainties of sin and cos.
Can someone please try to explain this step by step or even with a similar example? I don't want anyone to do this for me, I just want to be able to understand properly so that I can do it myself.

4. Feb 22, 2015

### haruspex

There are lots of useful references online. Rather than rewriting it in my own words, I've looked around for an easier text than the one I linked before. Try this one: http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm.