Definitions Flashcards
Error
The difference between the measured value and the true value
Uncertainty
The range/interval within which the true value lies
Independent variable
The variable for which values are changed by the experimenter
Dependent variable
The variable for which values are measured for each and every change of the independent variable
Control variable
May affect the outcome of the investigation
Must be kept constant or at least monitored
Random error
Present due to the way an instrument works, the surrounding environment changing or the way it is used
How is random error reduced
By taking repeated values and then averaging them
Systematic errors
Measurements that are consistently too large or too small by the same amount each time
Why might we have systematic errors
Not measuring zero error
Not calibrating equipment
Poor technique ( causing parallax error)
Recording the wrong unit
What is zero error
When the measuring equipment is not set on zero accurately
Should be added or subtracted from recorded values
How to take zero error into consideration
Minus or add onto recorded values
How can systematic error be seen on a graph
The line of best fit doesn’t go through zero
Doesn’t effect gradient of line of best fit but simply alters y intercept
Accuracy
A measurement close to the true value
Precision
The consistency between values obtained by repeated values
Seen to be precise if they cluster together
Really precise if all lie on line of best fit
Uncertainty for a single reading is at least
Half the resolution of the equipment
Uncertainty for repeated readings that are different can be taken as
Half the range of the readings
A reading is
A value found from a single judgement
A measurement
Requires the value to be taken from two readings or judgments
E.g.
Stopwatch
A non zero ended ruler
Extension of spring (original and extension)
Uncertainty of a reading
+/- 0.5 resolution
Uncertainty of a measurement
+/- 1 of the resolution
The uncertainty should be quoted to the same decimal places as…
The reading
Resolution
The smallest change in value that can be measured using the instrument
Resolution allows us to assess the
Minimum possible uncertainty
Tolerance
A percentage uncertainty quoted by the manufacturer
With a digital measuring machine what is the uncertainty
Will be +/- the smallest division shown on the meter
Percentage uncertainty eq
Uncertainty/ value x100%
Combining uncertainties by adding them or subtracting them
Add the absolute uncertainties of each quantity
Combining the uncertainties by multiplying or dividing
Add the percentage uncertainties of each quantity
Combining uncertainties of a quantity is raised to a power
Multiply the percentage uncertainty by the power
Table heading should include
Quantity/ units
In this format
In a table the number of significant figures/decimal places should be….
Consistent down the column
How to write logarithmic headings for tables
Ln (quantity/ unit)
As ln/logs don’t have units of their own
Significant figures should always be the same as
The smallest number of significant figures
Good experimental design
Design to limit uncertainty number (have as few as possible)
Parallax
A type of error that is created when looking at the scale from an angle
Makes measurement larger or smaller than true value
What to remember not to do w a micrometer
Use The ratchet
Not to over tighten
Percentage uncertainty of repeat measurements
1/2 range / mean value x100%
What can you do to decrease random error
Repeat
What does random error mean for precision
They reduce precision
How precise an experiment is from the graph
How much the points scatter from the line of best fit
Percentage difference between two values
Difference between two values / the average of the two values
x100%
Percentage difference between an experimental value and a stated value
Difference between values/ stated value
x100%
The use of multiple readings reduce the
Uncertainty
In general the percentage uncertainty of each measurement will be
The same percentage uncertainty for the whole experiment
The overall uncertainty will be reduced significantly by measuring multiple measurements
What can be used to reduce uncertainty and help determine precise measurements with rulers
A set square
What piece of equipment can be used to help keep eye level on oscillating things
A plumbline
To measure small angles what can we use
Trigonometry
Why is trigonometry used to measure small angles
Because protractor would give rise to uncertainty of 10% if angle was 5* and it measured to nearest 0.5*
If you measure opposite and adjacent distances then can use tan angle
Techniques for timing oscillations
Use a pointer to show when it passes a certain point
Don’t miscount oscillations
Don’t start timing initially
Try to time at least 20 oscillations
Fiducial mark
A pointer
Techniques for timing oscillations
Use a pointer to show when it passes a certain point
Don’t miscount oscillations
Don’t start timing initially
Try to time at least 20 oscillations
Fiducial mark
A pointer
3 reasons to use data loggers
Record data automatically
Can record data with v small intervals
Over long periods of time
Sample rate
Number of readings taken per second
Data logger can record several…
Variables simultaneously
Graph goes through origin it is called
Directly proportional
If graph doesn’t quite go through origin then…
It is still a linear relationship
A result that doesn’t fit the general pattern and lies a long way from the line of best fit
An anomaly
An anomalous result
Gradient how to calculate
Rise over run
BIG triangle!!!
What can the uncertainty in a measurement on a graph be shown as
Error bars
If there is uncertainty on both the x and y components then you need to draw an…
Error rectangle
If you are plotting a log graph then what happens w error bars
Calculate logs of maximum and minimum values
Determine the error bars using these values
To determine the uncertainty in a gradient
Three lines should be drawn on the graph
Line of best fit and…
The steepest line and shallowest gradient line that can be drawn using the bottoms of the error bars
Then find percentage uncertainty in gradient
(Highest grad-lowest grad)/gradient of line of best fit
X100%
How to make an exponential graph linear
Take natural logs of all components
Ln
Name as many of the 6 standard SI base quantities and units
Length - meter (m) Mass - kilogram (kg) Time - seconds (s) Electric current - amperes (A) Temperature - Kelvin (K) Amount of substance - mole (mol)
Centi
c
X10 -2
Milli m
X10 -3
Micro m
‘. (Has a flick)
X10 -6
Nano
n
X10 -9
Pico
p
X10 -12
Fento
f
X10 -15
Kilo K
X10 3
Mega M
X10 6
Giga G
X10 9
Tera T
X10 12
How to exchange indices when they are made to a power
You times the indices as if they were in a bracket
Significant figure number
The same as the smallest number that you are working with
Linear relationship equation
y= mx+c
Gradient is also known as
Rate of change
What size triangle for a gradient
LARGE triangle
BIG triangle
To calculate an instantaneous gradient
Draw a tangent at the point
Make big triangle
Calculate gradient from the triangle
Mathematically how can gradient be found
Differentiation
What kind of scale to use when you want a linear graph with an exponential relationship
Logarithmic scale
Small angle approximation sin
Sin ° = °
Small angle approximation cos °
Cos ° = 1 for small values of °
Small angle approximation for tan °
Tan ° = °
Converting from degrees to radians
Pie/ 180 x degrees
Converting from radians to degrees
180/ pie x radians
Avogadro number
6.02 x10 23
Method for turning up a dial in an experiment to increase accuracy
Turn it up till result is found.
Then go over value and then come back down to find value again
Record and average
Surface area of a sphere
4 pie r^2
Surface area of a cylinder
2 pie r^2 + 2 pie r h
An angle in radians equation
• = arc length/ radius
Random error examples
Human reaction time
Changes in room temperature
Contact resistance of crocodile clips
Too quick changing readings- hard to read off quickly
Vernier calliper measures to nearest
0.1 mm
Micrometer measures to nearest
0.01 mm
