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AQA A LEVEL PHYSICS MISCONCEPTIONS 3.1 Measurements and their errors 3.1.1 Use of SI units and their prefixes =} ni QUANTITY S| BASE UNIT SYMB MASS KILOGRAM kg LENGTH METRE m TIME SECOND | s CURRENT AMPERE | A TEMPERATURE KELVIN K AMOUNT OF SUBSTANCE MOLE | mal Prefixes of order of magnitude Common Unit Conversions J&eV * Acommon unit conversion in physics is between Joules (J) and electronvolts (eV) « The electronvolt is derived from the equation work done (or energy transferred) W = qV © 1eV=1.6 «10% Cx 1V=1.6 «1077) © Toconvert fromJ— eV, divide by1.6 x10- © Toconvert fromeV— J, multiply by 1.6 x 10-? QUANTITY SIZE DIAMETER OF AN ATOM 10°? m WAVELENGTH OF UV LIGHT 40 nm HEIGHT OF AN ADULT HUMAN 2m DISTANCE BETWEEN THE EARTH AND THE SUN 4.5 «40% m AU) MASS OF AHYDROGEN ATOM 40°77 kg MASS OF AN ADULT HUMAN 70 kg MASS OF ACAR 4000 kg SECONDS IN ADAY 90000 s SECONDS IN A YEAR 3% 10's SPEED OF SOUND IN AIR 300 ms~1 POWER OF A LIGHTBULB 60W ATMOSPHERIC PRESSURE 41x40" Pa PRECISE, NOT ACCURATE INACCURATE, ACCURATE, IMPRECISE PRECISE y ACCURATE, NOT PRECISE NUMBER OF MEASUREMENTS o| VALUE Zero Error -> This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero. -> To overcome this , this must be accounted for when the results are recorded. Accur: nd Precision ; -> Precise measurements have very little spread about the mean. -> Accuracy : This is a measurement to see how close the measurements are to their close value. -> The accuracy can be increased by repeating measurements and finding a mean of the results. The repetition of reading also allows us to identify anomalies which can be omitted from the final results. ACCURATE ACCURATE | PRECISE BUT NEITHER ACCURATE AND PRECISE NOT PRECISE NOT ACCURATE NOR PRECISE Resolution -> The resolution of a measuring instrument is the smallest change when measuring a quantity that can be detected. Repeatability -> Ameasurement is repeatable if the original experimenter repeats the investigation using the same method and equipment and obtains the same results. Reproducibility : -> Ameasurement is repeatable if repeated by another person or by using different equipment or techniques and the same results are obtained. Uncertainties : This is the possible difference between the measured value and the true value of a quantity. >ummary: Type Uncertainty Reason Typical Value Reading Estimating position of pointer between + half smallest division marks Measurement Difference of two readings or At least + one smallest division calculations -> When we are adding or subtracting we add the absolute uncertainties . -> When we are multiplying or dividing we add the percentage / fractional uncertainties together. -> When we are raising to a power , we multiply the percentage uncertainty by the power. Uncertainties in graphs: -> Error bars can be used to represent the absolute uncertainties of graphs. -> To find the uncertainty in the gradient , two worst fit lines can be drawn through the error bars. ( shallowest and steepest) AIUANTEDY, LINE OF THE as BEST FIT 40- SHALLOWEST (WORST GRADIENT) 37 30-5 40 QUANTITY B The line of best fit passes as close as possible to all the points. The steepest and shallowest lines are known as the worst fit « The percentage uncertainty inthe gradient can be found using: best gradient — worst gradient i x 9, Percentage uncertainty Best OradiGnt 100% « The percentage uncertainty inthe y-intercept can be found using: best y intercept — worst y interce| Percentage uncertainty = ul ey rare bt * 100% 
