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AQA A-Level Physics Topic 1 - Measurements and Their Errors; made directly in accordance with the AQA 7408 specification
SI units
mass (m) |
kilograms (kg) |
length (l) |
metres (m) |
time (t) |
seconds (s) |
amount of substance (n) |
moles (mol) |
temperature (t) |
kelvin (K) |
electric current (I) |
amperes (A) |
Derivation of SI Units
A derived unit is comprised of a combination of SI units. |
These can be derived by using the definition of the unit, or their equations eg. F=ma |
eg. to find the SI units of force (F), multiply the units of mass and acceleration to give kgms^-2 (or N) |
This means that every unit can be broken down into its SI base units. |
Prefixes
Tera (T) |
10^12 |
Giga (G) |
10^9 |
Mega (M) |
10^6 |
Kilo (K) |
10^3 |
Centi (c) |
10^-2 |
Milli (m) |
10^-3 |
Micro (µ) |
10^-6 |
Nano (n) |
10^-9 |
Pico (p) |
10^-12 |
Femto (f) |
10^-15 |
These prefixes could be added before any SI units
Conversions between units
It is possible to convert between different units of the same quantity. Here are some examples listed below: |
1 eV = 1.6 × 10^–19 J |
1 kW h = 3 600 000 J or 3.6 MJ (×10^6) |
Types of Errors
Random error |
Cause variations in both directions and are usually uncontrollable |
Systematic error |
Caused by faults in the experimental method or apparatus |
Zero error |
A type of systematic error caused by uncalibrated equipment |
Parallax error |
A type of systematic error caused by the apparent position of an object due to the viewing angle |
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Reviewing measurements
Precise |
Consistent and fluctuate around a mean value |
Accuracy |
A measurement that is close to the true value |
Repeatability |
The original person can redo the experiement and get the same results |
Reproducibility |
A different person does an experiment differently and gets the same results |
Resolution |
The smallest change in the quantity being measured that gives a recognisable change in reading |
Uncertainty
The bounds in which the accurate value can be expected to lie |
They should be given to the same number of significant figures as the data. |
Types of Uncertainity
Absolute |
Uncertainty given as a fixed quantity |
Fractional |
Uncertainty as a fraction of the measurement |
Percentage |
Uncertainty as a percentage of the measurement |
Resolution and Uncertainity
Readings are when one value is found |
Measurements are when the difference between 2 readings is found |
The uncertainty in a reading is +/- half the smallest division |
The uncertainty in a measurement is at least +/- 1 smallest division |
The resolution of an instrument will affect its uncertainty |
Digital readings and given values will either have the uncertainty quoted, or assumed to be +/- the last significant digit |
For repeated data, the uncertainty is half the range |
Reducing Uncertainity
You can reduce uncertainty in the following ways: |
• fixing one end of a ruler so there is only uncertainty in on reading |
• measuring multiple times |
• (for fractional and percentage) measure larger quantities |
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Combining Uncertainties
Adding/subtracting data - ADD ABSOLUTE UNCERTAINTIES |
Multiplying/diving data - ADD PERCENTAGE UNCERTAINTIES |
Raising to a power - MULTIPLY PERCENTAGE UNCERTAINITY BY POWER |
Uncertainties in graphs
Uncertainties are shown as error bars on graphs |
A line fo best fit on a graph should go through all error bars (excluding anomalies) |
The uncertainity in a gradient can be found by lines of best and worst fit |
This can be done using the gradients of the steepest and shallowest lines of best fits |
You can also use these two lines to find the uncertainty in the y-intercept |
Estimation of physical quantities
Orders of magnitude are powers of ten which describe the size of an object |
These can be used to compare the sizes of objects |
Estimation is a skill used to approximate the values of physical quantities, in order to make comparisons, or to check if a value calculated is reasonable. |
Variables
Dependant |
The variable that is being measured |
Independent |
The variable that is being changed |
Control |
Other variables that stay the same |
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