1 UNITS OF MEASUREMENTS 1. A quantity is something that has magnitude, size, or amount. 2. In 1960 the General Conference on Weights and Measurements decided all countries would use the International System of Units (Metric) system as the standard units of measurements. 3. Almost every country uses the metric system for daily calculations except the United States and Great Britain. 4.When using the metric system commas are not used with numbers because other countries use commas to represent a decimal point. Ex. 75, 000 is written is written The metric system (SI system) is based on powers of 10.

2 5. There are seven fundamental units in the metric system. All other units are derived from these units.

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4 6. A derived unit is a combination of fundamental units. Example: The unit for energy is the Joule = force x length = Nm = kg x m 2 / s 2 Example: The unit for force is the Newton = N= kg x m / s 2 Example: Area is calculated L x W = m x m = m 2 7. If a unit is not a fundamental unit, it is a derived unit.

5 8.What about volume? Notice that liter ( the unit for volume) is not a fundamental unit. To determine the volume of an object a length must be measured. So, volume is derived from length. Volume = l x w x h = m x m x m = m 3

ml = 1 Liter 1000cm 3 = 1 L ml = 1 cm 3 A 1 cm x 1 cm x 1cm cube will hold 1 ml of liquid. 1 ml = 1cm 3 = 1 cc (cubic centimeter)

cm 3 = 1000 ml 1000 ml = 1 Liter 1000cm 3 = 1 L

8 Why Metric?

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Scientists Measure Physical Quantities 1.3 Scientists Measure Physical Quantities

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12 A physical quantity must include: A NUMBER + A UNIT A NUMBER + A UNIT

The metric system provides a standard unit of measurements used by all countries. Is the man 92.5 m, 92.5 cm, 92.5 in, or 92.5 ft?

14 How many centimeters are in an inch?

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17 UNCERNTAINTY IN MEASUREMENTS AND SIGNIFICANT FIGURES 1. Whenever a measurement is taken, the last digit is uncertain and estimated.

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19 Which clock would be the most accurate?

20 RULES FOR COUNTING SIGNIFICANT FIGURES 1.All nonzero digits are significant. Ex. 123 g 3 significant figures. 25 g 2 significant figures g 4 significant figures 2.All zeros between non zero digits are significant. Ex. 506 L 3 significant figures L 5 significant figures 3.Decimal numbers that begin with zero. The zeros to the left of the first nonzero number are not significant. Ex L 3 significant figures L 2 significant figures

21 4.Decimal numbers that end in zero. The last zero is significant. Ex g 3 significant figures g 5 significant figures 8.0 g 2 significant figures 5.Non decimal numbers that end in zero. The zero is significant only when a written decimal is shown. Ex. 480 g 2 significant figures 900 g 1 significant figure 90. g 2 significant figure

22 PRACTICE g _____ L _____ ml _____ m _____ kg _____ dm _____ mm _____ cg _____ km _____ cm _____ g _____ kg _____ L _____ cm _____ Determine the number of significant figures.

23 Rounding Significant Figures Sample: round to 3 significant figures (sf) _______ round to 1 sf ______ round to 3 sf ______ round to 4 sf ______ round to 2 sf ______ Practice Round to the indicated number of significant figures km to 2 sf _____ L to 2 sf _____ g to 2 sf _____ L to 3 sf _____ g to 2 sf _____ ml to ml 2 sf _____ 7.12 ml to 1 sf _____ to 2 sf _____

24 MULTIPLYING AND DIVIDING SIGNIFICANT FIGURES 1.The arithmetic product or quotient should be rounded off to the same number of significant figures as in the measurement with the fewest significant figures. ??????????????????????? Keep the smallest number of significant figures. Examples: 2.86 g x 2.0 g = 5.72 g the answer is 5.7 g 38 ml / 1.25 ml = 30.4 ml the answer is 30. ml g x g = g the answer is g

25 Adding and Subtracting Significant Figures 1. The arithmetic result should be rounded off so that the final digit is in the same place as the leftmost uncertain digit. Ex g - 98 g = g the answer is 116 g g – g = g the answer is g

26 PRACTICE cm x 2.6 cm = ____________ dm x dm = ____________ g g = ____________ m m m ____________ g / 2 cm 3 = ____________ g / ml = ____________ g / 4.06 cm x 1.8 cm x cm = ____________

27 Scientific Notation 1.Convert to scientific notation 2.13 x Convert to scientific notation 2.0 x Practice: Convert to scientific notation

28 CALCULATOR PRACTICE 1. 3 x x 7.56 x =2 x x x 4.00 x = 1.48 x Practice: Don’t forget to keep the correct number of significant figures x x 10 2 = x x = x x 10 4 = 4.(3 x 10 5 )( 2 x 10 7 ) = 5.(7.5 x 10 6 )/(4 x ) =

29 BACK TO ROUNDING SIGNIFICANT FIGURES INVOLVING SCIENTIFIC NOTATION 1. Round 400 g to 3 significant figures x Round to 2 significant figures 3.0 x Simply change the number to scientific notation when going from a smaller number of significant figures to a larger.

30 IMPORTANT REMINDER: Your calculator does not know how to do significant figures. YOU must report numbers using the correct number of significant figures. If you trust the number your calculator gives you, you might get the answer wrong!!!! TI or Casio don’t care what grade you get on the test.

31 ACCURACY AND PRECISION 1.Accuracy is the closeness of the measurements to the true or accepted value. 2.The accuracy of an instrument can only be determined if the true or or accepted value for the measured item is known. 3. Precision refers to the agreement among the numerical values of a set of numbers.

32 Picture 1 is accurate and precise Picture 2 is precise but not accurate. Picture 3 is neither accurate or precise.

33 4. Scientific instruments should be accurate. If instruments are accurate, they are also precise. 5. If an instrument is precise, it may not be accurate.

34 Dimensional Analysis (Factor Label) 1. Dimensional Analysis (factor label) is a problem solving technique. 2. This method of problem solving uses conversion factors. 3. A conversion factor is a ratio that is equal to one. Example: 4 quarters = $1 24 hours = 1 day 185 days = 1 student school year

35 Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors”

36 Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors” 3 feet 3 feet 12 inches 12 inches 1 foot 1 foot = 36 inches ( ( ) ) ( ( ) )

37 Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1 12 inches 1 foot = 1

38 Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1

39 Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot = 12 inches

40 Fahrenheit Celsius 32°F 0°C

41 Fahrenheit Celsius Kelvin 32°F 0°C 273K 0 K -273 °C -273 °C -459 °F -459 °F

42 32°F 0°C 273K

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44 Fahrenheit Celsius Kelvin 32°F 0°C 273K 0 K

45 Fahrenheit Celsius Kelvin 32°F 0°C 273K 0 K 212 °F 212 °F 100 °C 100 °C 373K

46 32°F 0°C 273K

47 Temperature measures the average kinetic energy of the molecules. Heat measures the average kinetic energy And incorporates mass.

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49 Heat versus temperature Temperature  A measure of hotness or coldness of an object  Based on average molecular kinetic energy Heat  Based on total internal energy of molecules  Doubling amount at same temperature doubles heat

50 How do we measure temperature?  Think about using a thermometer…..  How does the thermometer know how hot the substance is?  The molecules of the substance bump into the thermometer and transfer energy. How often and how hard they bump into the thermometer are directly related to their speed. Temperature turns out to be related to the average speed of the molecules in a substance  Temperature is not a measure of the total amount of energy in an object.

51 SI joule USCS Units of Energy calorie J = 1 cal

52 Units of Energy (heat energy) 1000 calories = 1 kilocalorie 1000 calories = 1 Calorie

Thermal Energy Temperature & Heat Temperature is related to the average kinetic energy of the particles in a substance.

SI unit for temp. is the Kelvin a. K = C (10C = 283K) b. C = K – 273 (10K = -263C) Thermal Energy – the total of all the kinetic and potential energy of all the particles in a substance.

Thermal energy relationships As temperature increases, so does thermal energy (because the kinetic energy of the particles increased). Even if the temperature doesn’t change, the thermal energy in a more massive substance is higher (because it is a total measure of energy).

Heat The flow of thermal energy from one object to another. Heat always flows from warmer to cooler objects. Ice gets warmer while hand gets cooler Cup gets cooler while hand gets warmer

Why does water have such a high specific heat? Water molecules form strong bonds with each other; therefore it takes more heat energy to break them. Metals have weak bonds and do not need as much energy to break them. water metal

Specific Heat a. Some things heat up or cool down faster than others. Land heats up and cools down faster than water

How to calculate changes in thermal energy Q = m x  T x Cp Q = change in thermal energy – must be in joules – can be positive (+) or negative (-) m = mass of substance – must be in grams (g)  T = change in temperature (Tf – Ti) - (Kelvin) or (Celsius) Cp = specific heat of substance (J/g ˚C) or (J/g K)

b. Specific heat is the amount of heat required to raise the temperature of 1 kg of a material by one degree (C or K). 1) C water = 4184 J / kg C 2) C sand = 664 J / kg C This is why land heats up quickly during the day and cools quickly at night and why water takes longer.

61 HEAT FLOW PROBLEMS A 4.0 g sample of glass was heated from 274 to 314 K. And was found to have absorbed 32 J of energy as heat. What is the specific heat of glass?

62 HEAT FLOW PROBLEMS If a 5.00 g sample of lead releases -25Kj of heat and the temperature of the sample decreased from determine the temperature change.

63 HEAT FLOW PROBLEMS If 980 Kg of energy are added to 6.2 L of water at 291 K, what will be the final temperature of the water be?

64 HEAT FLOW PROBLEMS Determine the energy change when 3.00 g of copper changes from a temperature of 450 K to 275 K.

lecturePLUS Timberlake 65 Density Density compares the mass of an object to its volume D = mass = g or g volume mL cm 3 Note: 1 mL = 1 cm 3

Gold is very dense - it feels very heavy for its size. D = 19.3g/cm 3

Each substance has its own density. A larger amount will still have the same density because it will be an equivalent fraction. MetalDensity Gold19.3 Silver10.5 Platinum21.4 Palladium12.0 Copper9.0 9ct10.9 to ct12.9 to ct Yellow15.2 to ct White14.7 to ct17.7 to 17.8 Sterling Silver10.2 to Platinum20.1

 If you pack more mass into the same volume, it is more dense.  Draw a picture on your handout that represents this principle.

 If you pack the SAME mass into a SMALLER volume, it is MORE dense  Draw a picture on your handout that represents this principle.

 Just because something has more mass DOES NOT mean it is more DENSE.

You can make something have less dense by increasing the volume until it is more than the mass.

RULE OF JAMIE (a former student):  Anything with a density less than one will float in water. If there are numbers to the left of the decimal it will sink!

So why do ships float ? The density of steel is 7.8 g/cm 3 The density of waters 1 g/cm 3 Think of a steel ship as a can that is empty and watertight. The majority of its space is taken up by nothing more than air which has a specific gravity of about So if a make a ship that is like a can, empty inside and watertight it floats. Its volume sufficient that it causes its specific gravity to remain below 1.0 even after adding the weight of its contents. The steel ship will remain afloat as long as its density remains below that of water. The problem is that if water is allowed to enter the ship it would sink. Ships made of steel have to be sealed so water can not get in and increase its density. Steel can float only because of the way it is shaped, the space it takes up, and the seal that keeps its watertight. The ability of steel to float is the ability of people to shape metal and solve problems by examining outcomes.

lecturePLUS Timberlake 74 Learning Check D1 Osmium is a very dense metal. What is its density in g/cm 3 if g of the metal occupies a volume of 2.22cm 3 ?

lecturePLUS Timberlake 75 Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL

lecturePLUS Timberlake 76 Learning Check What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm 3 2) 6 g/m 3 3) 252 g/cm 3 33 mL 25 mL

lecturePLUS Timberlake 77 Learning Check3 Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) 2) 3) K K W W W V V V K

lecturePLUS Timberlake 78 Solution 2) 6 g/cm 3 Volume (mL) of water displaced = 33 mL - 25 mL= 8 mL Volume of metal (cm 3 ) = 8 mL x 1 cm 3 = 8 cm 3 1 mL Density of metal = mass = 48 g = 6 g/cm 3 volume 8 cm 3

lecturePLUS Timberlake 79 Solution (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) K W V

lecturePLUS Timberlake 80 Density as Conversion Factors A substance has a density of 3.8 g/mL. Density = 3.8 g/mL Equality 3.8 g = 1 mL Conversion factors. 3.8 g and 1 mL 1 mL 3.8 g

lecturePLUS Timberlake 81 Learning Check The density of octane, a component of gasoline, is g/ml. What is the mass, in kg, of 875 ml of octane?

lecturePLUS Timberlake 82 Learning Check  If 36.0 g sample occupies a volume of 50.0 ml, determine the density in g/L.

lecturePLUS Timberlake 83 Learning Check If an object has a density of 1.35 g/ml and a mass of kg, determine the volume in liters.

lecturePLUS Timberlake 84 Learning Check Determine the mass in grams if a sample with a volume of liters has a density of g/ml.

lecturePLUS Timberlake 85 THINGS TO REMEMBER The density of water is 1.00 g/ml at 0˚ C Has an object heats up it becomes less dense.

86 GRAPHS 1.When two quantities are directly proportional to each other, if dividing by the other gives a constant value. Example K = Y / X 2.Students will graph speed vs distance. The time is constant.

87 10 mi/hr 20 mi/hr 30 mi/hr 40 mi/hr 50mi/hr 60 mi/hr 70 mi/hr Speed Distance Calculate the distance if the time remains constant at ( 2 hours) Speed = Distance / Time

88 Graph speed verses time. The distance will remain constant at 200 miles. speed = distance / time 10 mi/hr 20 mi/ hr 30 mi/hr 40 mi/hr 50 mi/hr 60/ mi/hr 70 mi/hr speed time

89 Mass and volume are related directly.

90 Volume and pressure are related indirectly. Graph of an indirect relationship

91 Pie Graph

92 Bar Graph

93 Exponential Relationships One variable goes up slowly and the other very quickly.

94 Which swimmer is faster (red, green or blue)? What happened to the green swimmer between 10 and 20 seconds?