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Properties of Matter Measurement “To measure is to know” “If you cannot measure it, you cannot improve it” Lord Kelvin (Sir William Thomson) Scientific Notation • In physics, the numbers we deal with are either very small (size of atoms) or very large (distances in space) • This requires a different method in writing out our numbers • In scientific notation, numbers are represented through the power of ten. 101 = 10 102 = (10x10) = 100 103 = (10x10x10) = 1000 • The distance from the earth to the sun is 149,597,870,600 m. This can be written as 1.496 x 1011 m Number Scientific Notation 1000 1 x 103 1,000,000 1 x 106 0.01 1 x 10 -2 0.000000001 1 x 10-9 Scientific Notation: Quick Tip To write a number in scientific notation: Move the decimal point to create a new number between 1 and 10 Count the number of places the decimal point was moved This is the exponent of 10 The exponent is positive if the original number is greater than one The exponent is negative if the original number is less than one Prefixes for the Power of Ten Power Prefix Abbreviation 103 Kilo k 106 Mega M 109 Giga G 10-3 Milli m 10-6 Micro μ 10-9 Nano n Prefixes Measurements in Physics: SI Units Physical Quantity Name Symbol Length metre m Mass kilogram kg Time second s Electric Current ampere A kelvin K Luminous Intensity candela cd Amount of Substance mole mol Thermodynamic Temperature • All measurements conducted in physics are related to seven chosen fundamental quantities • This is known as the International System of Units or Systeme International (abbreviated to SI). • All other units of physical constants (known as derived units) can be broken down into groups of the seven fundamental units. For example, speed is measured in meters per second (m/s). Deriving Units in Physics from the SI Units Converting to SI Units Miles can be converted to kilometers by multiplying by 1.61 If you were in a situation where you wanted to convert 5 miles to metres you would proceed as follows: 1st change miles to kilometres (1mile = 1.61km) 5mile = 5 x 1.61 = 8.05 km 2nd change kilometres to metres (1km = 1000m) 8.05 km = 8.05 x 1000 = 8050 m • Note: there are 100 centimetres in 1 meter. This makes 5 miles equal to 805,000 cm. Distance, Speed, and Time When discussing speed we normally refer to kilometres per hour (km/hr). In physics, speed is often spoken about in terms of meters per second (m/s). It is therefore necessary to be able to convert from one to the other. Converting from hours to seconds 1hr = 60 min 1 min = 60 sec 1hr or 60 min = (60 x 60) = 3600 sec Speed = Distance/time Speed = 8050 m / 3600 s = 2.2 m/s Measurement in Practice • Is measurement important? • What do we need to be aware of when taking measurements? • Every measurement is inexact • Need a statement of uncertainty to quantify the inexactness • How do we make measurements accurate? • Need to compare with a standard • Traceability – a method of ensuring a measurement is an accurate representation of what it is trying to measure by tracing back to a standard Traceability and Measurement Successful measurements depend on… • Accurate instruments • Traceability to national standards • An understanding of uncertainty • Application of good measurement practice Accurate measurements enable us to… • Maintain quality control during production process • Comply with and enforce laws and regulations • Undertake research and development • Calibrate instruments and achieve traceability to a national measurement standard • Develop, maintain and compare national and international measurement standards Traceability / Calibration • Test against a standard of higher accuracy • NSAI National Standards Authority Ireland • NPL National Physical Laboratory UK Definition of Kilogram • Previously: Defined in terms of a standard kilogram • 2019: The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to 1.356392489652×1050 Hz. Definition of a Second • The value of the second is based on the frequency of light emitted by cesium atoms • Shown is a cesium clock in the National Institute of Standards and Technology • 1𝑠 = 9192631770 ∆ν𝐶𝑠 Definition of the Meter • The original definition of a meter was in terms of the Earth’s circumference • Then changed to be based on this platinum-iridium bar • 2019 – new definition • A metre = length of path travelled by light in vacuum during a time interval of 1s 9192631770 • 1m = 299792458 𝑐 ∆ν𝐶𝑠 Traceability What factors cause inaccuracy? • Environmental effects • Inferior measuring equipment • Poor measuring techniques Method of guaranteeing a measurement’s accuracy: unbroken chain of reference back to national and international standards. The Standards Pyramid • Primary Standards: Highest accuracy available • Secondary Standards: Calibrated against primary standards • Working Standards: Slip Gauges (Length); Certified Weights (Mass); Standard Solutions, etc. • Irish State body Responsible for Standards: National Standards Authority Ireland (NSAI) Working Standards • A gauge block (gage block, Johansson gauge, slip gauge, or Jo block) is a precision ground and lapped length measuring standard. It is used as a reference for the setting of measuring equipment used in machine shops, such as micrometers, sine bars, and dial indicators (when used in an inspection role). • Not always easy or convenient to use physical objects as standards. Problems with absolute or global accuracy and consistency. Ideally one would like to have Reproducible Standards, i.e. standards that, in principle, could be generated anywhere globally, to the required accuracy. Uncertainty What is uncertainty? • Doubt that exists about the results of any measurement • Confidence in a measurement • It does not matter how accurate a measuring instrument is considered to be, the measurement made will always be subject to a certain amount of uncertainty 200 cm ± 1 cm at a level of confidence of 95% Why does uncertainty matter? • Good quality measurements • Pass or failure • Calibration certificate • Calibration of instruments Significant Figures • There is an uncertainty associated with all measurements • Uncertainty is also called experimental error • Values are written using significant figures • A digit is significant if it is meaningful with regard to the accuracy of the value • Zeros may be ambiguous • Scientific notation helps clarify the significance of any zeros Significant Figures, Examples Example: 0.00123 3 significant figures In numbers less than 1, zeros immediately to the right of the decimal point are not significant Can also be clarified by writing in scientific notation: 1.23 x 10-3 Example: 100 May have 1 significant figure Zeros are ambiguous Rewrite in scientific notation 1.00 x 102 shows 3 significant figures Significant Figures in Calculations Multiplication and division • Use the full accuracy of all known quantities when doing the computation • At the end of the calculation, round the answer to the number of significant figures present in the least accurate starting quantity • Example: 976 x 0.000064 m = 0.062464 m ~ 0.062 m (Due to the 2 significant figures in the 0.000064 m) Rounding Error • In multiple step problems, you could round at different steps • Different final values may be obtained • These differences are the rounding error • Carry an extra significant figure through intermediate steps in the computation and perform the final rounding at the very end Significant Figures in Calculations Addition and subtraction • The location of the least significant digit in the answer is determined by the location of the least significant digit in the starting quantity that is known with the least accuracy • Example: 4.52 + 1.2 = 5.72 ~ 5.7 (Due to the location of the significant digit in the 1.2) Exact Numbers • Some values are exact • Not measured but defined • Example, 1 min = 60 sec • Appears to have 1 significant figure, but it is a definition • Can be thought of as 60.00000000… seconds • The number of significant figures in a calculation is determined by the number of significant figures in other quantities involved