1 Physics First! Observations, Tools, Units, and Measurements.

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Physics First!Physics First!Observations, Tools, Units, Observations, Tools, Units,

and Measurements.and Measurements.

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Physics First!Physics First!ObjectivesObjectives

Work effectively with SI Units of Work effectively with SI Units of length and time.length and time.Convert among SI prefixes and Convert among SI prefixes and between SI and English units of between SI and English units of length.length.Explain accuracy and precision in Explain accuracy and precision in the context of measurement the context of measurement uncertainty.uncertainty.Accurately measure time and Accurately measure time and distance.distance.

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ObservationsObservations An observation is information that An observation is information that

you obtain through your you obtain through your sensessenses.. sight, hearing, touch, and smellsight, hearing, touch, and smell..

ToolsTools increase the power of senses increase the power of senses or make observations more or make observations more preciseprecise. .

Tools may help you eliminate Tools may help you eliminate personal personal opinionsopinions or or preferencespreferences. .

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ToolsTools

Some of the common tools we will use in Some of the common tools we will use in Physics:Physics:

RulerRuler to measure length in centimeters to measure length in centimeters StopwatchStopwatch to measure time in seconds to measure time in seconds CPO Timer & PhotogatesCPO Timer & Photogates to measure to measure

time in seconds.time in seconds. Triple-beam balanceTriple-beam balance to measure mass to measure mass

in gramsin grams

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SI units of MeasurementSI units of Measurement For a measurement to make sense, it For a measurement to make sense, it

needs to have both a needs to have both a numbernumber and a and a unitunit. .

Example: 5 meters Example: 5 meters

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Units of MeasurementUnits of Measurement Scientists use a set of measuring Scientists use a set of measuring

units called the International System units called the International System of Units, or of Units, or SISI..

SI is a revised version of the SI is a revised version of the metricmetric system, which was originally system, which was originally developed in France in 1791.developed in France in 1791.

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Base Units and Derived UnitsBase Units and Derived Units SI is based on seven metric units SI is based on seven metric units

known as known as basebase units. units. These units are independent of each other.These units are independent of each other.

LengthLength is the straight-line distance is the straight-line distance between two points. The base unit is between two points. The base unit is the meter (m)the meter (m)

MassMass is the quantity of matter in an is the quantity of matter in an object. The base unit is the kilogram object. The base unit is the kilogram (kg)(kg)

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SI Base UnitsSI Base UnitsQuantityQuantity UnitUnit SymboSymbo

llLengthLength metermeter mmMassMass kilogramkilogram kgkgTemperatureTemperature kelvinkelvin KKTimeTime secondsecond ssAmount of a Amount of a substancesubstance

molemole molmol

Electric Electric CurrentCurrent

ampereampere AA

Luminous Luminous IntensityIntensity

candelacandela cdcd

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SI Derived UnitsSI Derived Units Additional SI units, called Additional SI units, called derivedderived units, can units, can

be made from combinations of the base units. be made from combinations of the base units. For example For example volumevolume is the amount of space is the amount of space

an object occupies. The volume of a an object occupies. The volume of a rectangular box equals its length x width x rectangular box equals its length x width x height. Each of these dimensions can be height. Each of these dimensions can be measured in meters, so then you can derive measured in meters, so then you can derive the metric unit for volume by multiplying the metric unit for volume by multiplying meters by meters by meters which gives you meters by meters by meters which gives you cubic meters (mcubic meters (m33))

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SI PrefixesSI Prefixes What is a prefix?What is a prefix?

Something that comes before a Something that comes before a word that changes its meaning.word that changes its meaning.

An SI prefix comes before a An SI prefix comes before a unitunit and and changes its meaning.changes its meaning. An SI prefix indicates how many times a An SI prefix indicates how many times a

unit should be unit should be multipliedmultiplied or or divideddivided by by 10. 10.

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SI PrefixesSI PrefixesPrefixPrefix SymboSymbo

llMeaningMeaning Multiply Unit Multiply Unit

bybygiga-giga- GG billion (10 billion (10 99)) 1,000,000,0001,000,000,000mega-mega- MM million ( 10 million ( 10 66)) 1,000,0001,000,000kilokilo kk thousand (10thousand (1033)) 1,0001,000hectohecto hh hundred (10hundred (1022)) 100100decadeca dada ten (10ten (1011)) 1010(base)(base)decideci dd tenth (10 tenth (10 –1–1)) 0.10.1centicenti cc hundredth(10hundredth(10-2-2)) 0.010.01millimilli mm thousandth (10thousandth (10-3-3)) 0.0010.001micro micro millionth ( 10 millionth ( 10 –6–6)) 0.0000010.000001nanonano nn billionth (10 billionth (10 –9–9)) 0.0000000010.000000001

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Unit ConversionsUnit Conversions The easiest way to convert from one The easiest way to convert from one

unit to the other is to use unit to the other is to use conversion factorsconversion factors..

A conversion factor is a A conversion factor is a ratioratio of of equivalent measurements that is equivalent measurements that is used to convert a quantity of one used to convert a quantity of one unit to another. unit to another.

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Unit ConversionsUnit Conversions Nutrition labels often have some Nutrition labels often have some

measurements listed in grams and measurements listed in grams and milligrams. milligrams.

Suppose you want to know the number of Suppose you want to know the number of grams in 160 milligrams? grams in 160 milligrams?

Based on the prefix milli- you know that 1 Based on the prefix milli- you know that 1 gram is gram is 10001000 milligrams. This gives two milligrams. This gives two ratios or possible conversion factors:ratios or possible conversion factors:1 g/1000 mg and 1000 mg/1 g1 g/1000 mg and 1000 mg/1 g

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Unit ConversionsUnit Conversions Since you are converting from Since you are converting from

milligrams to grams, the number should milligrams to grams, the number should get smaller. Multiplying by the ratio on get smaller. Multiplying by the ratio on the left yields a smaller number.the left yields a smaller number.

160 mg x 1g/1000mg = 0.160 g160 mg x 1g/1000mg = 0.160 g Notice that the mg units cancel leaving Notice that the mg units cancel leaving

you with grams, the larger unit.you with grams, the larger unit.

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Unit ConversionsUnit Conversions Another way to convert units is by moving Another way to convert units is by moving

the decimal to the left or right.the decimal to the left or right. Remember the prefixes? Use a word play.Remember the prefixes? Use a word play.Kyle Hates Dates because Dates Cost MoneyKyle Hates Dates because Dates Cost MoneyKilo Hecto Deca (base) Deci Centi MilliKilo Hecto Deca (base) Deci Centi Milli Then move the decimal the same direction Then move the decimal the same direction

and same number of spaces it takes to go and same number of spaces it takes to go between prefixes.between prefixes.

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Unit ConversionsUnit Conversions

Kyle Hates Dates because Dates Cost Kyle Hates Dates because Dates Cost MoneyMoney

Kilo Hecto Deca (base) Deci Centi MilliKilo Hecto Deca (base) Deci Centi Milli Example:Example:

To convert 568. mm to meters, starting at To convert 568. mm to meters, starting at millimilli, move three places to the , move three places to the leftleft to get to to get to ((basebase). Move the decimal three places to the ). Move the decimal three places to the left to get 0.568 m.left to get 0.568 m.

To convert 67 m to hm (hectometers), start at To convert 67 m to hm (hectometers), start at ((basebase) and move the decimal two places to ) and move the decimal two places to the the leftleft to get 0.67 hm. to get 0.67 hm.

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Unit ConversionsUnit Conversions

Convert the Convert the following to following to meters:meters:

1.1. 0.54 km0.54 km2.2. 894 cm894 cm3.3. 27 dm27 dm4.4. 45 mm45 mm5.5. 0.0098 dam0.0098 dam6.6. 73 hm73 hm

540 m540 m 8.94 m8.94 m 2.7 m2.7 m 0.045 m0.045 m 0.098 m0.098 m 7300 m7300 m

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Limits of Measurement - AccuracyLimits of Measurement - Accuracy When we make a measurement, we are When we make a measurement, we are

comparing what’s being measured to a comparing what’s being measured to a standard unitstandard unit, such as the meter., such as the meter.

Accuracy is how Accuracy is how closeclose a measurement is to a measurement is to the the actual valueactual value of what’s being measured. of what’s being measured.

For example: Suppose the length of a piece of For example: Suppose the length of a piece of train track is exactly 21.37642 cm. If we train track is exactly 21.37642 cm. If we measured it with a classroom ruler and got measured it with a classroom ruler and got 21.38 cm, we’ve made an accurate 21.38 cm, we’ve made an accurate measurement. If we got 22.76 cm, we’re not measurement. If we got 22.76 cm, we’re not as accurate because we’re off by about 1.38 as accurate because we’re off by about 1.38 cm.cm.

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Limits of Measurement - AccuracyLimits of Measurement - Accuracy Accuracy is important so that we can Accuracy is important so that we can

report report correctcorrect measurements. measurements. Other scientists might want to Other scientists might want to repeatrepeat

our work. How would it work out if our our work. How would it work out if our measurements were not accurate?measurements were not accurate?

Suppose you were building a roof. Suppose you were building a roof. How important would accurate How important would accurate measurements be?measurements be? If you cut a board a few inches too long If you cut a board a few inches too long

or too short, it might not fit right.or too short, it might not fit right.

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Limits of Measurement - AccuracyLimits of Measurement - Accuracy

Accuracy is important in cooking. How Accuracy is important in cooking. How would your cookies taste if the recipe would your cookies taste if the recipe called for 1 tsp of salt and you put in 1 ½ called for 1 tsp of salt and you put in 1 ½ tsp?tsp? Too salty!Too salty!

Accuracy is important with most Accuracy is important with most measurements. What would you be doing measurements. What would you be doing if your car’s gas gauge read ½ full when if your car’s gas gauge read ½ full when you only had ¼ of a tank of gas?you only had ¼ of a tank of gas? You’d be walking to a gas station!You’d be walking to a gas station!

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Limits of Measurement - PrecisionLimits of Measurement - Precision Suppose you wanted to time a race between Suppose you wanted to time a race between

your friends. You could use one of the your friends. You could use one of the following wristwatches:following wristwatches: One that reads only in minutes (no second hand).One that reads only in minutes (no second hand). One that reads in minutes and seconds.One that reads in minutes and seconds. One with a stopwatch that reads to hundredths of One with a stopwatch that reads to hundredths of

a second.a second. Which would give you a better Which would give you a better

measurement? Why?measurement? Why? The stopwatch that reads to hundredths of a The stopwatch that reads to hundredths of a

second gives a more precise measurement.second gives a more precise measurement.

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Limits of Measurement - PrecisionLimits of Measurement - Precision PrecisionPrecision shows how shows how exactexact a a

measurement is. measurement is. The stopwatch might show that your The stopwatch might show that your

friend ran one mile in 6 minutes, friend ran one mile in 6 minutes, 19.44 seconds. What would the 19.44 seconds. What would the other watches have said?other watches have said? The watch with only a minute hand The watch with only a minute hand

would say would say 6 minutes6 minutes.. The watch with a second hand would The watch with a second hand would

say say 6 minutes, 19 seconds6 minutes, 19 seconds..

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Limits of Measurement - PrecisionLimits of Measurement - Precision Ever watch running or swimming races in the Ever watch running or swimming races in the

Olympics? How much time separates the Olympics? How much time separates the Gold and Silver medalists?Gold and Silver medalists? Often just a few hundredths of a second.Often just a few hundredths of a second.

If another friend ran the same mile the next If another friend ran the same mile the next day in 6 minutes, 19.24 seconds. With which day in 6 minutes, 19.24 seconds. With which watch would you know who was faster?watch would you know who was faster? The stopwatch is the only one precise The stopwatch is the only one precise

enough.enough. Precision is important because it allows us to Precision is important because it allows us to

tell the difference between close tell the difference between close measurements, and to exactly repeat measurements, and to exactly repeat measurements.measurements.

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Appropriate PrecisionAppropriate Precision How precisely can you measure with How precisely can you measure with

a given tool?a given tool? Think about a classroom ruler. The Think about a classroom ruler. The

smallest markings are smallest markings are 0.1 cm0.1 cm (1 (1 mm) apart. mm) apart. We can measure with certainty to We can measure with certainty to 0.1 0.1

cmcm.. We then estimate to We then estimate to 0.01 cm0.01 cm (1/10 (1/10thth of of

the smallest gradations).the smallest gradations).

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Appropriate PrecisionAppropriate Precision With your ruler, measure the height and With your ruler, measure the height and

width of the box below (in your notes).width of the box below (in your notes).

2.58 cm

5.34 cm For height, I measure For height, I measure 2.58 cm2.58 cm. Notice that the . Notice that the 2.52.5

is certain (we should all agree), and the is certain (we should all agree), and the 88 is is estimated (we should be close, but may differ +/- estimated (we should be close, but may differ +/- 1). It would not make sense to estimate to another 1). It would not make sense to estimate to another decimal place. decimal place. 2.58 cm2.58 cm is at the appropriate level is at the appropriate level of precision for this ruler.of precision for this ruler.

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Appropriate PrecisionAppropriate Precision Choose the appropriately precise Choose the appropriately precise

measurement for each tool.measurement for each tool.ToolTool GradatioGradatio

nnCircle the appropriate Circle the appropriate MeasurementMeasurement

RulerRuler 0.1 cm0.1 cm 12 cm12 cm 12.2 cm12.2 cm 12.23 cm12.23 cmScaleScale 0.1 g0.1 g 45 g45 g 44.9 g44.9 g 44.88 g44.88 gGraduateGraduated d CylinderCylinder

1 ml1 ml 22 ml22 ml 22.3 ml22.3 ml 22.38 ml22.38 ml

Thermo-Thermo-metermeter

2 2 ooCC 4444ooCC 44.244.2ooCC 44.1844.18ooCC

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The following is planned only for The following is planned only for Honors Physics First.Honors Physics First.

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Reporting MeasurementsReporting Measurements It is important to report measurements It is important to report measurements

with the correct level of precision.with the correct level of precision. We use the term We use the term significant digitssignificant digits to to

describe the appropriate precision of describe the appropriate precision of measured and calculated quantities.measured and calculated quantities.

When we report with the correct number When we report with the correct number of significant digits, we of significant digits, we truthfullytruthfully show show the the limitationslimitations of our measurements. of our measurements.

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Reporting MeasurementsReporting Measurements Significant digits are all the digits that are Significant digits are all the digits that are

certaincertain in a measurement plus the last digit in a measurement plus the last digit that is that is estimatedestimated. .

For example, when we measured the box For example, when we measured the box above and got above and got 2.58 cm2.58 cm we showed the we showed the appropriate precision for the tool that we appropriate precision for the tool that we used.used. Reporting fewer digits (e.g. Reporting fewer digits (e.g. 2.6 cm2.6 cm) would suggest ) would suggest

that we used a that we used a lessless precise tool. precise tool. Reporting more digits (e.g. Reporting more digits (e.g. 2.584 cm2.584 cm) would ) would

suggest that we used a suggest that we used a moremore precise tool. precise tool. Truth in reporting is very important in Truth in reporting is very important in

science!science!

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Reporting MeasurementsReporting Measurements How many Significant Digits does a How many Significant Digits does a

particular measurement have?particular measurement have? Rules for significant digitsRules for significant digits

All All nonzerononzero numbers are significant numbers are significant Zeros between nonzero digits Zeros between nonzero digits areare

significantsignificant Zeros Zeros beyondbeyond the decimal point at the the decimal point at the

end of a number are significantend of a number are significant Zeros before the first nonzero digit Zeros before the first nonzero digit are are

notnot significant significant

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Reporting MeasurementsReporting Measurements ExamplesExamples

1.021.02 has has threethree significant figures significant figures 123.0123.0 has has fourfour significant figures significant figures 0.00540.0054 has has twotwo significant figures significant figures 9.005619.00561 has has sixsix significant figures significant figures

How many significant digits?How many significant digits?2.54 2.54 4.0024.002 5280.05280.00.004050.00405 0.2300.230 121212001200 800.2800.2 599.03599.03

3 4 53 3 2

2-4? 4 5

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Calculating with MeasurementsCalculating with Measurements What’s the area of the box above? What’s the area of the box above? Multiply Height x Width, and the calculator Multiply Height x Width, and the calculator

tells you tells you 13.777213.7772. Is this correct?. Is this correct? NO!NO! When you calculate with measurements, When you calculate with measurements,

your final answer must be rounded to the your final answer must be rounded to the appropriate number of significant digits. appropriate number of significant digits. That is, round to the That is, round to the leastleast significant digits of the significant digits of the

numbers with which you calculated.numbers with which you calculated. To avoid rounding errors, only round your To avoid rounding errors, only round your

finalfinal answer. Keep a few extra digits through answer. Keep a few extra digits through your calculations and then round at the end.your calculations and then round at the end.

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Calculating with MeasurementsCalculating with Measurements The area of the box should be rounded The area of the box should be rounded

to to 13.8 cm13.8 cm22, or , or 33 significant digits, significant digits, because the numbers used in the because the numbers used in the calculation had only 3 significant digits.calculation had only 3 significant digits.

Do the following calculations and round Do the following calculations and round to the correct number of significant to the correct number of significant digits.digits. 3.2 x 9.8 = 3.2 x 9.8 = 5.76 x 4.2 = 5.76 x 4.2 = 0.00236 x 1.6 = 0.00236 x 1.6 =

31240.0038