Question

How can I find the uncertainty of experimental data?Let's suppose I have recorded the time of drop of a mass 10 times from 10 different known heights. With this, I use a least squares method to find velocities and accelerations. After finishing this process, how am I supposed to find the uncertainties? What is the formula or process that I have to complete with the available data?

Answer 1

uncertainty in velocity and acceleration is not and independent quantity.

It is the result of uncertainty in measurement of height h and time t.

uncertainty is nothing bu standard deviation of the observations , it is defined as

$\sigma = \sqrt{(\bar{x^2}) - (\bar{x})^2}$

also know as root mean square deviation.

1. square each observation and square it

2. get the mean of the squares

3. get the average and square it.

4. find the square root of the deviation, it is called standard deviation.

SD of each measurement propagates to the computed values

1. when quantities are added or subtracted the uncertainty for each quantity adds up

2. when quantities are multiplied or divided , find the fractional or percentage uncertainty, add up the percentage uncertainty

suppose two quantities a and b are multiplied

a = 100 +/- 5 percentage uc = +/-5 %

b = 80 +/- 20 percentage uncertainty = +/-25%

result of multiplication = 100*80 = 8000

uncertainty = 5% +25% = 30%

result = 8000 +/- 30%

or 8000 +/- 2400