Measurements and their errors
3.1.1 Use of SI units and their prefixes
Fundamental base units
Mass - kilogram
length - metre
time - second
current - ampere
temperature - kelvin
prefixes
giga - x10^9
mega - x10^6
kilo - x10^3
centi - x10^-2
milli - x10^-3
micro - x10^-6
nano - x10^-9
3.1.2 Limitations of physical measurements
random and systematic errors
random errors
random errors affect precision. They arise from fluctuations in the measurement, which can make the value higher or lower than the true value
they can be addressed by taking multiple readings, removing anomalies and taking a mean. The more readings taken, the more accurate the value
plotting a graph and using a line of best fit can also reduce random errors
systematic errors
errors that effect the data in the same way, so won't be reduced by repeats
zero error is an example of a systematic error which occurs when the instrument does not read zero when expected
3.1.2 Continued (uncertainties)
definitions
precision - precise measurements are consistent, they fluctuate slightly about the true value
repeatability - if the original experimenter can redo the experiment with the same equipment and method and get the same results it is repeatable
reproducible - if an experiment is redone by a different person or using a different technique and equipment and the same results are found then it is reproducible
resolution - the smallest change in the quantity being measured that gives a recognizable change in reading
accuracy - a measurement close to the true value is accurate
the uncertainty in a measurement is at least +- 1 smallest division
digital readings and given values will either have the uncertainty quoted or assumed to be +- the last significant digit, the resolution of an instrument affects its uncertainty
the uncertainty in a reading is ± half the smallest division
uncertainties should be given to the same number of significant figures as the data
combining uncertainties
Adding / subtracting data - ADD ABSOLUTE UNCERTAINTIES
Multiplying / dividing data - ADD PERCENTAGE UNCERTAINTIES
Raising to a power - MULTIPLY PERCENTAGE UNCERTAINTY BY POWER
definitions
percentage uncertainty - uncertainty as a percentage of the measurement
fractional uncertainty - uncertainty as a fraction of the measurement
absolute uncertainty - uncertainty given as a fixed quantity
graphs
uncertainties are shown as error bars on graphs
the uncertainty in a gradient can be found by lines of best and worst fit
% uncertainty = (best gradient - worse gradient)/worse gradient x 100
using data loggers to reduce human error can also reduce random errors
use appropriuate equipment with adequate resolution
to reduces errors
calibrate apparatus
correct for background radiation in radiation experiments
For repeated data the uncertainty is half the range (largest - smallest value), show as
mean ± range/2
Draw a steepest and shallowest line of worst fit, it must go through all the error bars.
Calculate the gradient of the line of best and worst fit, the uncertainty is the difference between the best and worst gradients
3.1.3 Estimation of physical quantities
orders of magnitude
Powers of ten which describe the size of an object, and which can also be used to compare the sizes of objects.
Estimation is a skill physicists must use in order to approximate the values of physical quantities,
in order to make comparisons, or to check if a value they’ve calculated is reasonable.