Phy 211 General Physics I Chapter 1 Measurement Lecture Notes Observations The sciences are ultimately based on observations of the natural unnatural world There are 2 types of observations Qualitative Subjective touchy feely Example the outside temperature is hot today Quantitative Objective based on a number and a reference scale Quantitative observations are referred to as measurements Example the outside temperature is 80oF today Notes Quantitative observations are only as reliable as the measurement device and the individual s performing the measurement The accuracy associated with a measurement or set of measurements is the often specified as the Error Error accepted value measured value accepted value 100 The precision associated with a set of measurements is the often specified as the Range highest value lowest value Range Range average value 100 average value 100 The standard deviation is similar to the range value for a set of measurements Errors in Measurement The error associated with calculated physical quantities such as the area of a circle can be estimated by the application of a little calculus For a quantity f dependent on measured variables x y i e f x y f df dx dy Error or uncertainty x y where dx is the range of x dy is the range of y etc Example 1 Consider a circle with a measured radius r of 0 10 m 0 01m Acircle 0 10 m 2 0 031 m2 Error dA A 2 dr p r dr 2p rdr 0 0063 m2 r r Relative Error dA 2prdr 2 0 01 m 0 20 or 20 A pr 2 0 10 m Example 2 Consider a sphere with a measured radius r of 0 10 m 0 01m 34 2 V Vsphere 4 3 0 10 Error dV dr m p0 0043 r 3 dr m 4pr 2dr 0 0013 m3 r r 3 dV 4p r 2dr 3 0 01 m Relative Error 0 30 or 30 4 3 V 0 10 m pr 3 Systems of Measurement There are several units systems for measurement of physical quantities The most common unit systems are the metric and the USCS systems For consistency the l Systeme Internationale or SI was adopted The SI system is a special set of metric units International System SI base units Mass Kilogram kg Length meter m Time second s Temperature Kelvin K Current Ampere A Luminous Intensity candela cd Amount of substance mole mol All of the other SI units are derived from these base units Examples of derived units 1 Newton 1 N 1 kg m s2 1 Joule 1 J 1 kg m2 s2 1 Coulomb 1 C 1 A s Common Metric Prefixes Prefix Symbol Meaning Power of 10 Giga G 1 000 000 000 109 Mega M 1 000 000 106 kilo k 1 000 103 centi c 0 01 10 2 milli m 0 001 10 3 micro 0 000 001 10 6 nano n 0 000 000 001 10 9 Using Metric prefixes 1 mm 1x10 3 m 35 mm 35 x 10 3 m or 3 5 x 10 2 m 1 kg 1x103 g 12 kg 12 x 103 g or 1 2 x 104 g Unit Conversion In physics converting units from one unit system to another especially within the Metric system can appear daunting at first glance However with a little guidance and a lot of practice you can develop the necessary skill set to master this process Example How is 25 2 miles hour expressed in m s 1 Eliminate assign mi units to the denominator and hr units to the numerator of the conversion factor 25 2 2 Replace assign m units to the numerator and s units to the denominator of the conversion factor 25 2 3 mi 25 2 mi m hr hr 1 hr s mi mi 25 2 mi m m hr hr 1 hr mi s s Relate assign the corresponding value to its unit 1 mi 1609 m 1 hr 3600 s 25 2 mi 25 2 mi m 1609 m 1 hr 11 3 hr 1 hr s 1 mi 3600 s Length Time Mass Length is the 1 D measure of distance Quantities such as area and volume and their associated units are ultimately derived from measures of length Definition of SI Unit The meter is the length of the path traveled by light in vacuum during a time interval of 1 299 792 458 s or roughly 3 33564 ns Examples of units derived from length in this case radius r 1 Area of a circle Acircle r2 units are m2 4 3 p r 3 2 Volume of a sphere Vsphere units 3 are m Time is the physical quantity that measures either 1 when did an event take place 2 the duration of the event Definition of the SI Unit The second is the time taken by 9 192 631 770 oscillations of the light emitted by a cesium 133 atom Mass is the measure of inertia for a body or loosely speaking the amount of matter present Definition of the SI Unit The kilogram is the amount of mass in a platinum iridium cylinder of 3 9 cm height and diameter
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