Measurements in Physics PDF

9t int Knowledge Learnin9 Objectives Measurement ofquantities/materials in SI units of measurement daily life Measurement oflength, area and mass Need ofmeasurement in d£tÏly life Measurement oftime and...

9t int Knowledge Learnin9 Objectives Measurement ofquantities/materials in SI units of measurement daily life Measurement oflength, area and mass Need ofmeasurement in d£tÏly life Measurement oftime and temperature Accurate and approximate measurements Measurement is the act of determining the size (length, area, volume, etc.), mass, degree of hotness or coldness of an object or time o1 an activity using specific devices.A quantig that can be measured is calleda physical quantity. Look attheactivities shown in the following pictures. Identify the physical quantity being measured in each activity. Write your answers in the space provided. The value ofa measuredphysical quantity is expressed in two parts:a numericalvalueanda rd unit.Thenume%ca1vMueisthemagnitudeo!themeasuredquanlily The unit is the standa amount o1a physical quantity. For exampls, when we measure length, thestandard unitÎS metre. Similarly, kilogram is the standard unit of mass and second is the standard 1#/ NEED FOR STANDARD UNITS OF MEASUREMENT Inancient times, people used their body parts for measuring length. For example, the handspan, the length ofa forearm and the length ofa foot (Fig. 2.1) were accepted as the units of measurement. They relied on natural phenomena such as sunrise and sunset, phases ofthe moon andseasons tomeasure time. Handspan Cubit Foot Fig. 2.I Ancient methods ofmeasuring length and width using body parts These ancient methods were notaccurate and reliable. For example, if people across the world use their handspans formeasuring length, it would notgenerate the same result. Let us understand this bya simple activity. , Aim: To show that measurements using body parts are not standard , Materials required: Table and ruler “ , Procedure: ” 1. Measure the length of the table using your handspan. ‹ 2. Ask your friends to measure thesame using their handspans. , 3. Compare thevalues obtained by each person. , 4. ”Now, measure thelength of the table using the ruler. Ask your friends also to measure thesame using the ruler. Compare thevalues. Length ofthe table i Person Using ruler Me Friend 1 ,.. Friend2 Observation: Length ofthe table measured using handspan is different in each case. Length ofthe table measured usinga ruler is same in all the cases. COnclusion: Measurements using body parts are not standard. ' tittntiii- iiiititi.ti1it.ini1"iiitii"iiidtJ\tiii.i"iiJ1tiittsi1ittiitit St£tridard measuring units that would remain constant across the globe. *;.17  /çyTg\y SYST5w OF UNITS OF M*'*' y äS ufe a physicãlqUã/1tiÇ.This ¢ çş ã orld, jO.uS£? divÏ3rs£ł U+ÍtS tO £ł and conv ni øt ş Ø. th. All over the p Ø P meaSure/yjeNtS.Thus, foruniformi W Ø €ł confusion in comITIU nicating iehi:, tș a sta nda rcl Sgt OÎ**! ’ts for measurement calledthe metr¡y worldwide haveaccep ted GIS(in French the ¥ctêm£? lyt * ij known as theI nter natio RãlS Stem «! is commonly are the mo s t wi dely u ed y tełTl //!Uni! !*d * n i Ofã et qț d'Unités or SI. stunits Eł O hysícalq uantities. Well-defineduFłits forthe measufEł/// /1! *P pe nd Upon otherquan tities are called funÖãl The physical quantities tha t do not de țjer/tt g fundame ntal physicalq uant ities, !heiry physical quäntities. Table2.1shoV¥S the SeV’» units and symbols. Table 2.1SIunits __ -- - ”--” ” t Besides these seven S. No. F»däme R tä j gu ä ntity , si Uni y , ,__] fundamental quantiti£?S,ãț¡Ot§ęt 1. ! Length ITletf9 *** physical quantities are caii d 2. Mass ” kilogram kg derived quantities. 3. Time seCond s They arecalled so ãSth£łïÇ„¡t, are obtainedby combín‹»g unity , 4. Electric current ampere  of two or more fundamentai ‹ 5. Temperature kelvin K physical quantities. Forł3xãmp;Ï? 6. ’ Amount ofsubstance mole mol the unit of area íž m2, the unit ofvolume ïsm* and the unit of 7. Luminous intensity candela cd velocity is m/s. There are more systems ofunits of measurement that are used by people io different parts of the world. For example, FPS system, MKS system and CGS system. Table 2.2 shows the units of length, mass and time in diXerent systems ofunits. Tahle 2.2 OiRerent systems ofunits for measurement SI fOOt metre “”* ğfafTl kilogram pound kilogram second second second second Rules to Represent Values inSIunits Units ofphysical quantities were named indi0efent Way. S Some oftheunit nalTłł3S *f* derived from Latin, Grsek or French words. Examplesi nclude metre, litreandgrarñ,TO*” units are named ańer scientists. Examples ‹hCIUd6 newton, kelvin and ampere. While writing the SI unit ofa physical quantity, certain rules have tobe followed. If the unit is named ačer the scientist, then the symbol should be the first alphabet written in upper case (capital 0BI1IN 0F N4d¢Es letter). However, the unit name should be in lower caše OF VNIYS (small letters). 1. ‘Metre’ came from the Examples: The SI unit of power is W or watt, the SI unit of Greek word metron, which means ‘measure. force isN or newton and the SI unit of terl1perature isK or kelvin. 2. ‘Gram’ came from the Latin root word gramma, If the unit is not named añer the scientist, then the symbol which means ‘asmall and the unit name arewritten in lower case. weight’. Examples: metre or m, kilogram or kg and second or s. 3.‘Litre’came from the French word litron (an An exception is litre because its symbol can be written in old measure ofcapacity), both lower and upper case asy or L. which was derived from Plural form of the symbols should not be used. the Greek word litra, which was a currency unit. Examples: 10 centimetres is written as 10 cm, 5 kilograms as5 kg and 10 seconds as 10 s. Mu/tipfes and 5ubmUftim3) 7 ‹ 2.1 pound = 3. Unit of mass is * 3.1 ton = - -------- MEASUREMENT OF TIME A particular moment ina day is called an instance of time. Time period is the duration between two events. In ancient times, The time interval between there was no time-measuring device. Our ancestors depended one sunrise and the next was considered a day. on many natural events to measure time. The tlme interval between The need tomeasure time even forshorter intervals paved thEi one new moon andthenext was considered a month. way for the invention of clocks. Many devices have been invent€id The time taken forthe to measure time. The study of these devic€iS IS Called halo! g¥ progression of all seasons Some ofthedevices used lormeasuring time are aS fOllOWS. was considered a year.  Sundial l äf metallic plate called St ia ngu A sundial has a circular plate with t r po inte d at an a ng le. The dexice is gnomon fixed at itscentre, gnomon t ins uch a Wä that the placed in the open in su nligh dir ecl ion. The s h adow ofgnomon on the points in the north—South usinga indicate s the time. The majordrawbEtCk Of circular plate during NÏght time and sundial is that the devicecannot beused thedevice. cloudy days when there is no sunlight Calling on Water clock time at night. The Greeks invented water clocks to measure It was based on the rising and falling ofa liquid column. Time was measured by theregulated flow of liquid into or out ofa vessel. The drawback with water clocks WztS that they required regular monitoring as the rate of flow of water would Vary’ WÏth temperature. Waterclock Sand clock A sand clock is also known as an hourglass.A sand clock measures thepassage ofa few minutes or an hour oftime. It has two vertical glass bulbs allowinga regulated trickle of sand from top to bo2om. Once thetopbulb is emptied, it can be inverted to begin measuring time again. These days hourglasses are used as ornamental pieces, Sand clock egg timers for cooking and clocks in board games. Quartz clock With theinvention of the quartz crystal in 1921, timekeeping accuracy was highlyimproved. The quartz clock was invented in 1927. It is an analogue clock in which the hours, minutes and sometimes seconds are indicated by hands ona dial. Quartz CIOC/ Digital clock A digital clock isa ’device thatdisplays the time digitally. It uses numbers and other symbols tO ShOW time. Digital CIOC* Units of Time With new inventions and developments in tllTlg-measuring devices, it became possibl ’0 measure time in terms ofhOUr, minute and SecoFÏd. The Sl unit of time issecond {S) A day is divided into 24 equaldUrations and each duration is called an hour (h). SfÊÏa** durations are measured in minutes(min) weeks, months and years. EtFld Second s (s). Larger durations are me£tS‘f’d i^ 26 Different units of time are used based on therequirement. For example, it is appropriate to mention the age ofa person in years, the time fortravelling short distances in hours and the running time of an athlete in minutes or seconds. Relationships between various short time- measuring units are: 60 seconds 1 minute 60 minutes 1 hour 24 hours 1 day Relationships between various long time-measuring units are: 7 days 1 week 30or31 days 1 month 12 months 1 year 10 years 1 decade 100 years 10 decades =1 century 1000 years 100 decades = 10 centuries =1 millennium Clocks are used to measure time withina day. Clocks read time intwo formats: 12-hour format and 24-hour format. 7he 7we/ve-hour C/ock Ina 12-hour clock, the hour hand goes around the clock twicea day (Fig. 2.10). The clock shows thesame time twice ina day. For example, you wake up in the morning at6:00 and go out to play inthe evening at 6:00. 11 12 1 11 12 1 0 ! 2 10 23. hands Wr aria merldlem. 8 8 S pm. for postmgrtdlem. 6 7 6 5 6:00 inthe morning 6:00 inthe evening Fig. 2. 10A 12-hour clock shows thesauce tingeh i‹ea d‹t\. a.m. is used toshow thetime after midnight and before noon. So, 6:00 inthe morning is Written as 6:00 a.m. p.m. is used to show thetime after noon and before midnight. So, 6:00 in the evening is Written as 6:00 p.m. The abbreviations a.m. and p.m. are not written with 12:OO; instead, we say noon and Midnight. 27  Q Ck The Tvventy-(our-hourC! at A 24.h UtCjOCkii a digitalC!OCk th {"Ićtrł3 ćłdded to 12 torepresent the time. Ełr OO Inthis formćtt ofClOCk, the hoUrS ćt!* ”.ćts 13 :00,5:00 p.m. as17:0o, ›:3g C) O k W !! read 1:o0 p.m |^Ot eXampIe,a digi al24-hou r p.m. as 19:30and soon. For examp]e,a digital24-hour clock willreaą Ch. The hourS before lflC*On ćtre Writt£łl’1 ćts SU „,. ćłs 11:30 and so on. 6:00 a.m. ćłs 6:00,1 :20 a.m. as1 :20, 11 :30 żt 12-hour clock time Solution: From 2:30 p.m. to 3:50 p.m., the duration = 20 minutes Therefore, the duration of this show Was 20 minutes. 2. In the next show, they saw a woman performing tightrope walking, followed bya man walking with many cups and saucers on his head. Thisshow (asted for 25 minutes. AIwhat tlme dldthis show get over? Solution: This show staled at 3:50 p,m. The duration of the show was 25 minutes. So, 25 minutes after3:50 p.m. - 4:15 p.rr\, Therefore, the show gotover at4:15 p,m.  3. The last show was bythetrapeze artists. It started at 5:30 p.m. and got over at6:00 p.m. For how long did the trapeze artists perform? Solution: From 5:30 p.m. to 6:00 p.m., the duration = 30 minutes Therefore, the trapeze artists performed for 30 minutes. Nowadays, special clocks can measure 1. A matinee show started at 2:00 p.m. and got time periods that are less than evena over at4:30 p.m. The duration of the movie was second. These clocks are used in scientific research. Time periods as small as 2. The sports day celebration ina school began at 1 microsecondt 10^ ofa seconds and 8:30 a.m. and got over at 4:30 p.m. The duration of the celebration was j 1 1 nanosecond} t ofasecond 3. The train to Mumbai was scheduled to depart the station at 6:00 p.m. But, it was delayed by2 hours canalso be measured and 20 minutes. The train then started to Mumbai accuratdly. ” at Calendars Calendars measure time in days, weeks and months. There are 12 months ina year, and each month hasa fixed number ofdays. Let us find outa trick to remember thenumber of days ina month through the following activity. Makea fist with your left hand and learn the shortcut to remember thenumber ofd.ays in every month. Starting with your Returning to your forefinger's knuckle forefinger's knuckle 1stknuckle: January -31“days Grooye: February — 28 or 29 days 1st knuckle: August — 31 days F bruary 2nd knuckle: March — 31 days Groove: September — 30 days January Gfoove: April — 30 days 2nd knuckle: October — 31 days 3rdknuckle: May — 31 days Groove: November — 30 days Gfoove: June — 30 days 3rd knuckle: December — 31 days 4thknuckle: July — 31 days ',. 29  lth 366 days arecalled le or 366 days in an year. The years W ap There area total Of 365 years. Leap years have 29 days inFebruary ,'1 Alfred's family went for a 27 February to4 March in2010. How man , days ofvacation didAlfred's family have? Earth revolves around the sun in36s 2. Dan's pet catdisappeared on 21 December anda quarter days.A normai year h» 2011 and returned home on 13April, 2012. only 365 days. The quarter da 1 Forhow many days was the pet cat missing? 4 + 4— 4 to1 day in four years (— 1 3. Lekha came toDelhi on 12 January 2014 This one day is added toFebrua‹y where she stayed for45 days. On which theleap year making ita total of date did she start the return journey g)$ 366 days. from Delhi? IVIEASUREMENT OF TEMPERATURE Thedegree ofhotness or coldness of any object is called its temperature. “ Scale Temperature is commonly represented using the units degree Celsius ° Stem (°C) and degree Fahrenheit (°F). The SI unit of temperature is kelvin (K). § The instrument used to measure temperature is calleda thermometer , (Fig. 2.11).A thermometer consists of the following parts: Bulb: This is the part that actually touches the object whose. Liquid co|umn temperature is to be measured. It consists ofa liquid that is either «° mercury or alcohol. Stem: It isa glass capillary tube through which the mercury or alcohol rises. Bulb Scale: lt is the marking on the stern which indicates the temperature of the substance. Fig. 2. 11 Pads of a the!+‹””'”‘”-” Temperature Scales Temperature is measured using diñerenttemperature scales. Ina temperature scale. **^ reference temperatures are chosen(most commonly, thefreezing and boiling pointsOf water) and the difference between thèse two is divided intoa ceÛain number ofdivisions Each division is taken as one unit of the scale. The commonly-used scales are the Celsius scale, theFahrenheit scale and the KelvinS^*! Ce/sïus Scafe This scale was developed byAnders Celsius. The unit of this scale is Celsius WÏth themat«r (a)], the freezing point O 0* symbol °C (read as degree Celsius). On thÏS SCaIe [Fig. 2.12 is taken as0 °C and the boiling point as 100 °C.0 °C iS also poi^ called thelowerfixed ice point, whereas 100 °C is also called the uppertlxed point or steam point.Ther 100 divisions between these two points. 50  Fahrenheit Scale This scale was developed by Daniel GabrielFahrenheit. The unit of this scale isFahrenheit with the symbol °F (read as degree Fahrenheit). On this scale [Fig. 2.12 (b)], the freezing point of water is taken as 32 °F and the boiling point as 212 °F. That is, the lower fixed point is 32 °F, and the upper fixed point is 212 °F. There are 180 divisions between these two points. 100 ”C 212 ”F 100 Celsius 180 Fahrenheit degrees degrees 0’C 32 ”F (a) Celsius scale (b) Fahrenheit scale Fig. 2. 12 Temperature scales This scale was invented by Lord Kelvin. The unit of this scale is Kelvin with the symbol K. On this scale, the freezing point of water is taken as 273 K and the boiling point as 373 K. It is also called the absolute scale of temperature since0 K is the absolute zero, that is, the lowest attainable temperature inthe universe. Table 2.8 gives ice points and steam points in the three temperature scales. Table 2.8 Ice points and steam points in different scales RelationshipS b£'.tWÏgÏ2FÏ diffeFf2Flt UFlitS Of mÏ3fitSUremeFÏt OftO.mpf '.FfittUrP.CtrO.: ’C (°F— 32) 9 "F ( t”C+ 32 K = “C+ 273 Types of Thermometer There arevarious thermometers used fordifferent types of temperat‹ir‘e measurements. The !TlOStCOMmonly used thermometers aro clinical thermon›ater, digital thermometer, laboratory thermigmeter and maximum—mÏFlimUm thElrmCÏmf ter. ci:nİcaI Thermometer re the temperature of humanbody. (Fig. 2.13) İSUSed to measu A clinical thermometer 37 °C or 98.6 °F,bUt İt Amies tem pera ture ofh uma n bodyiS approximately Thenormal ac tivity , time of the day,e nvironmental conditions, etc. It rises orfEt||S depending on age, °F ÌSa medicai temperature beyond 40 °C or 104 during a state ofillness. Rise of body nt. emergency and requires immediate treatme Aim:"To read"a"clini at thermometer ”““”"“ “”””""""”"“"”"""”“"““ “""”"“ “" " "”” Materials required: Clinical thermometer and antiseptic solution Procedure: 1. \lash the thermometer before using, preferably with an antiseptic solution. 2. Ensure that the mercury level is below 36.9 °C or 98.4 °F. 3. Place the thermometer under the tongue ofthe person whose temperature is to be measured. 4. Wait fora minute. 5. Remove thethermometer and check the reading by keeping it at eye level. The capillary tube ofa clinical thermometer has aj¿ÿ¡¿k or bend that does notallow the mercury to flow back into the bulb before the temperature has been read. The mercury breaks atthe kink when it contracts due toa decrease in temperature. It prevents the mercury from falling beyond this point. This is the reason we have tojerk the thermometer before takinga new reading. The jerk pushes the mercury back into the bulb. laboratory 7hermometer , Laboratory thermometers (Fig. 2.14) are used in laboratories during experiments. The range oftemperature thata laboratory thermometer can measure is between -10 °C and 110 °C. Oigital Thermometer ›’ - --'“‘‘' ““ NOWEtduys, electronic thermometers called digitalthermome ters (Fig. 2,15) sure widely used formeasuringtemperatu ,g re. These do not contain mercury. Hence, there is no risk of mercury spilling ot1 breakage. The temperature is e-asier îoread in this type than in conventionalthermcmu\ers as Ïtappears una d igitaldi»çIay. The thermometer used tomeasure the maximum and minimum called the maximum—minimum thermometer. temperatures during a daÿ ItS range is -30 °c to 50 °C. Thisthermomł?t is also known as six’s thermometer. 32  MEASUREMENTS ACCURATE AND APPROXIMATE measurements, whereas in others we do not. Insomesituations we require accurate Whena room has to be laid with carpet,a shirt has to be stitched ora child has to be given theo ther hand, if you want toknow the medicines, we require accurate measurements. On from your place, you do not need accuracy in terms distance of the nearest railway station of the distance is sufficient. This way of of metres or millimetres. An approximate value called estimation. Measuring considering the approximate value ofa measurement is also one cup ofsugar fora cake batter is an accurate measurement, whereas pouring one cup of milk to drink at night is an approximate measurement. Averages When we perform experiments that involve measurements ofquantities, we need tomeasure a quantity multiple times and note down thevalues. This is because every time we measure, thevalue can change slightly. So, taking the average of measurements gives usa more appropriate result. Average value can be calculated using the formula: Sum of all observations Average value = Number ofobservations Aim: To find out the average pulse rate of the students ina class Materials required: Stopwatch Procedure: t 1. Press your forefinger and middle finger on your left wrist and find your pulse. t 2. Start the stopwatch and count your pulse. 3. Stop the stopwatch after 60 seconds. Note down thepulse count. This is your pulse rate. 4. Note the pulse rate for three students. 5. Find the average pulse rate using thefOl'muIa (sum of the pulse rates of all studentst Ob number ofstudents servation: Name ofthestudents t TOta|plJlse rate of all three students = Result: Average pulse rate Total " 3 "  t (a measured physical quantity is expressed witha numerical value anda unit) SI units are the standard units of measurement. Length " Area Mass SI unit: metre or m SI unit: square metre or m* SIunit: kilogram or kg Some other units of Some other units of Some other units of measurement aremillimetre measurement aresquare measurement aregrams (mm), centimetre (cm) millimetre (mm*), square (g) and milligrams (mg). and (kilometre) km. centimetre (cm*) and square Rulers, measuring tapes, kilometre km*. Beam balance and digital Vemier callipers and balance are used to Graph sheets can be used to screw gauges areused to measure mass. measure areas. measure length. Time Temperature SIunit: second ors SI unit: Kelvin orK Some other units of measurement are Some other units of measurement are milliseconds (ms), minutes (min) and hour (hr). Celsius (°C) and Fahrenheit (°F). Sundials, quartz clocks, water clocks and Clinical and laboratory thermometers are sand clocks are used tomeašure time. used tomeasure temperature. >'G*ù?fśé4 g.« Physical quantity:a quantity that can be measured Fundamental physical quantity:a physical quantity that does notdepend upon other quantities Derived physical quantity:a physical quantity whose units can be obtained by combining units Oł or more fundamental physical quantities Measurement: theactofdetermining the amount ofa physical quantity Longth: the distance between two points Parallax error: the error produced when readings of scales are taken from an angle from the Iir\0 f SİX Area: the amount ofsurface covered by an object Maec: theamount ofmatter preeent in an object Leap year: the year that has 366 daye Temperature: the degree of hotnese or coldness of an obțect