Measurements and their errors Flashcards
absolute uncertainty
uncertainty given as a fixed quantity
combing uncertainties: multiplying/dividing data
ADD PERCENTAGE uncertainties
combing uncertainties: adding/subtracting data
ADD ABSOLUTE uncertainties
combing uncertainties: raising to a power
MULTIPLY PERCENTAGE uncertainty by the power
define precision
Precise measurements are consistent, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate
define accuracy
A measurement close to the true value is accurate
define repeatability
If the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable
define reproducability
If the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is reproducible
define resolution
The smallest change in the quantity being measured that gives a recognisable change in reading
Fento
10^-15
fractional uncertainty
uncertainty as a fraction of the measurement
Giga
10^9
how are uncertainties shown on a graph
error bars
e.g. if uncertainty is 5mm, then 5 squares of error bars on either side of the point
line of best fit should go thru all error bars
how can SI units of quantities be derived
using their equations
e.g. F = ma ———–> kgms-2 which is N
how many sig figs to give uncertainty to
same number of sig figs as the data
how to find uncertainty in y intercepts
best y-intercept - worst y-intercept (using libnes of best and worst fit)
how to find uncertainty of a gradient
by lines of worst and best fit
draw steepest and shallowest lines of best fit - both must go through ALL error bars
the uncertainty is the difference between gradients
how to reduce random errors
take at least 3 repeats and calculate a mean - allows you to identify anomalies
use computers/data loggers to reduce human error
use appropriate equipment e.g. higher resolution
how to reduce systematic error
calibrate apparatus by measuring a known value - can identify innacuraccies
if radiation experiement - correct for background radiation
read at eye level to reduce parallax error
use controls in experiments
how to reduce uncertainty
reduce no. readings in a measurement e.g. fixing one end of a ruler
measuring multiple instances, e.g. taking 10 and dividing by 10 to find 1 (uncertainty is also divided by 10)
mega
M 10^6
micro
mu 10^-6
Nano
n 10^-9
percentage uncertainty
uncertainty as a percentage of the measurement
Pico
p 10^-12
Tera
T 10^12
uncertainty
0.5 * range
% uncertainty = uncertainty / mean * 100
if all data is the same the uncertainty is the resolution
uncertainty for digital readings
+ or - the last significant digit
what are systematic errors
cause all results to be too high/low by the same maount each time e.g. zero error or parallax error
usually occur due to apparatus or faults in method
what are the SI units
fundamental units:
Mass (m): kg (kilograms)
Length (I): m (metres)
Time (t): s (seconds)
Amount of substance (n): mol (moles)
Temperature (t): K (kelvin)
Electric current (I): A (amperes)
what do random errors effect
precision - cause difference in measurements which cause a spread about the mean
what do systematic errors effect
accuracy
what is uncertainty
bounds in which the accurate value can be expected to lie
