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Chapter 1: A Physics Toolkit Physics Ms. Pollock 2015 - 2016
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Chapter 1 A Physics Toolkit
Physics
Ms Pollock
2015 - 2016
11 Mathematics and Physics
bull Branch of science that involves study of the physical world energy matter and their relationships
bull Many related careers astronomy engineering computer science education medicine
bull httpblogsdiscovermagazinecomcruxfiles201502planets_iau_2jpg
11 Mathematics and Physics
bull Mathematics powerful language of physics
bull Equations important for modeling observations and making predictions
bull Numerical results used to support conclusions
bull httpizquotescomquotes-picturesquote-the-miracle-of-the-appropriateness-of-the-language-of-mathematics-for-the-formulation-of-the-laws-e-p-wigner-278064jpg
Example Problem 1
bull The potential difference (V) or voltage across a circuit equals the current (I) multiplied by the resistance (R) in the circuit That is V (volts) = I (amperes) X R (ohms) What is the resistance of a lightbulb that has a 075 amperes current when plugged into a 120-volt outlet
bull I = 075 amperes V = 120 volts R =
bull V = IR R = V I
bull R = (120 V) 075 A
bull R = 160
Practice Problem 1
bull A lightbulb with a resistance of 500 ohms is used in a circuit with a 90-volt battery What is the current through the bulb
I = VR
I = 9 V 50
I = 018 A
Practice Problem 2
bull An object with uniform acceleration a starting from rest will reach a speed of v in time t according to the formula v = at What is the acceleration of a bicyclist who accelerates from rest to 700 ms in 400 s
A = vt
A = (700 ms)
(400 s)
A = 175 ms2
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
11 Mathematics and Physics
bull Branch of science that involves study of the physical world energy matter and their relationships
bull Many related careers astronomy engineering computer science education medicine
bull httpblogsdiscovermagazinecomcruxfiles201502planets_iau_2jpg
11 Mathematics and Physics
bull Mathematics powerful language of physics
bull Equations important for modeling observations and making predictions
bull Numerical results used to support conclusions
bull httpizquotescomquotes-picturesquote-the-miracle-of-the-appropriateness-of-the-language-of-mathematics-for-the-formulation-of-the-laws-e-p-wigner-278064jpg
Example Problem 1
bull The potential difference (V) or voltage across a circuit equals the current (I) multiplied by the resistance (R) in the circuit That is V (volts) = I (amperes) X R (ohms) What is the resistance of a lightbulb that has a 075 amperes current when plugged into a 120-volt outlet
bull I = 075 amperes V = 120 volts R =
bull V = IR R = V I
bull R = (120 V) 075 A
bull R = 160
Practice Problem 1
bull A lightbulb with a resistance of 500 ohms is used in a circuit with a 90-volt battery What is the current through the bulb
I = VR
I = 9 V 50
I = 018 A
Practice Problem 2
bull An object with uniform acceleration a starting from rest will reach a speed of v in time t according to the formula v = at What is the acceleration of a bicyclist who accelerates from rest to 700 ms in 400 s
A = vt
A = (700 ms)
(400 s)
A = 175 ms2
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
11 Mathematics and Physics
bull Mathematics powerful language of physics
bull Equations important for modeling observations and making predictions
bull Numerical results used to support conclusions
bull httpizquotescomquotes-picturesquote-the-miracle-of-the-appropriateness-of-the-language-of-mathematics-for-the-formulation-of-the-laws-e-p-wigner-278064jpg
Example Problem 1
bull The potential difference (V) or voltage across a circuit equals the current (I) multiplied by the resistance (R) in the circuit That is V (volts) = I (amperes) X R (ohms) What is the resistance of a lightbulb that has a 075 amperes current when plugged into a 120-volt outlet
bull I = 075 amperes V = 120 volts R =
bull V = IR R = V I
bull R = (120 V) 075 A
bull R = 160
Practice Problem 1
bull A lightbulb with a resistance of 500 ohms is used in a circuit with a 90-volt battery What is the current through the bulb
I = VR
I = 9 V 50
I = 018 A
Practice Problem 2
bull An object with uniform acceleration a starting from rest will reach a speed of v in time t according to the formula v = at What is the acceleration of a bicyclist who accelerates from rest to 700 ms in 400 s
A = vt
A = (700 ms)
(400 s)
A = 175 ms2
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Example Problem 1
bull The potential difference (V) or voltage across a circuit equals the current (I) multiplied by the resistance (R) in the circuit That is V (volts) = I (amperes) X R (ohms) What is the resistance of a lightbulb that has a 075 amperes current when plugged into a 120-volt outlet
bull I = 075 amperes V = 120 volts R =
bull V = IR R = V I
bull R = (120 V) 075 A
bull R = 160
Practice Problem 1
bull A lightbulb with a resistance of 500 ohms is used in a circuit with a 90-volt battery What is the current through the bulb
I = VR
I = 9 V 50
I = 018 A
Practice Problem 2
bull An object with uniform acceleration a starting from rest will reach a speed of v in time t according to the formula v = at What is the acceleration of a bicyclist who accelerates from rest to 700 ms in 400 s
A = vt
A = (700 ms)
(400 s)
A = 175 ms2
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 1
bull A lightbulb with a resistance of 500 ohms is used in a circuit with a 90-volt battery What is the current through the bulb
I = VR
I = 9 V 50
I = 018 A
Practice Problem 2
bull An object with uniform acceleration a starting from rest will reach a speed of v in time t according to the formula v = at What is the acceleration of a bicyclist who accelerates from rest to 700 ms in 400 s
A = vt
A = (700 ms)
(400 s)
A = 175 ms2
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 2
bull An object with uniform acceleration a starting from rest will reach a speed of v in time t according to the formula v = at What is the acceleration of a bicyclist who accelerates from rest to 700 ms in 400 s
A = vt
A = (700 ms)
(400 s)
A = 175 ms2
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 3
bull How long will it take a scooter accelerating at 0400 ms2 to go from rest to a speed of 400 ms2
T = va
T = (400 ms2)
(0400 ms2)
T = 10 s
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 4
bull The pressure on a surface is equal to the force divided by the area P = FA A 53-kg woman exerts a force (weight) of 520 newtons If the pressure exerted on the floor is 32500 Nm2 what is the area of the soles of her shoes
A = FP
A = 520 N
32500 Nm2
A = 0016 m2
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
SI Units
bull Internationally recognized system of measurement
bull 7 base units combinations of base units for derived units
bull Real-life use GPS 3-dimensional location
Base Quantity
Base Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Temperature
Kelvin K
Amount of substance
Mole Mol
Electric current
Ampere A
Luminous intensity
Candela cd
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
SI Units
bull Regulated by International Bureau of Weights and Measures (France)
bull Standard for US kept at National Institute of Science and Technology (Maryland)
bull Conversions of size with prefixes
httpswwwgooglecomurlsa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCLyg3rjD-cYCFcuSDQodUM4HVgampurl=http3A2F2Fwwwradiolaborg2Fstory2Fkg2Fampei=azS1Vfy-B8ulNtCcn7AFamppsig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJgampust=1438025164890918
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
SI Prefixes
bull Chart with SI conversions on page 6 of the textbook
bull httpsfiguresboundlesscom9232largeprefix2png
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Dimensional Analysis
bull Solving physics problems often involves unit conversion
bull Dimensional analysis ndash treating units as algebraic quantities
bull Used to select conversion factors ndash allows units to cancel
bull May require series of conversions
bull httpwwwchemistrylandcomCHM151S01-FoundationDimensionalAnalysisNewApproachgif
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 5
bull How many megahertz is 750 kilohertz
750 kHz X 1 MHz = 075 MHz
1000 kHz
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 6
bull Convert 5021 centimeters to kilometers
5021 cm X 1 km = 00521 km
10000 cm
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 7
bull How many seconds are in a leap year
1 leap year X 366 days X 24 h X 60 min X 60 s = 31622400 s
1 leap year 1 day 1 h 1 min
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 8
bull Convert the speed 5300 ms to kmh
5300 m X 1 km = 53 km
1000 m
1s X 1 min X 1 h = 0000278 h
60 s 60 min
53 km = 1906475 kmh
0000278 h
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Significant Digits
bull Valid digits in a measurement
bull Last digit given in measurement ALWAYS uncertain
bull Based on limitations of measurement device and limitations of person doing measuring
bull httpmathsfirstmasseyacnzAlgebraDecimalsimageszeros1gif
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Rules for Significant Digits
bull All non-zero numbers significant
bull Lead zeros not significant
bull Ending zeros not significant unless decimal present
bull Place-holding zeros not significant
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Arithmetic with Significant Digits
bull Result of calculation never more precise than least-precise
bull For addition and subtraction round to least precise value involved
bull For multiplication and division round to least precise value involved
bull No uncertainty involved with counting (exact numbers) or conversion factors
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 9
bull A 6201 cm + 74 cm + 068 cm + 120 cm = 26281 263 cm
bull B 16 km + 162 m + 1200 cm =
bull 160000 cm + 162 cm + 1200 cm = 161362 cm 160000 cm or 1600 m or 16 km
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 10
bull A 108 g ndash 8264 g = 2536 g 25 g
bull B 475 m ndash 04168 m = 43332 433 m
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 11
bull A 139 cm X 23 cm = 3197 cm2 320 cm2
bull B 32145 km X 423 km = 13597335 km2 136 km2
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problem 12
bull A 1378 g 113 mL = 121946903 gmL 122 gmL
bull B 1821 g 44 cm3 = 413863636 gcm3 41 gcm3
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Scientific Methods
bull Making observations doing experiments creating models or theories
bull Used by all scientists to describe phenomena
bull Must be reproducible
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Scientific Methods
bull Not set steps
bull Can be completed in different order and repeated as needed
bull httpwwwgooglecomimgresimgurl=httpscienceinvestigatorswikispacescomfileviewscientif_method_OKpng442326542scientif_method_OKpngampimgrefurl=httpscienceinvestigatorswikispacescomThe2BScientific2BMethodamph=642ampw=710amptbnid=VEYOMoLZSVmQ9Mampdocid=dQk6MaTZ70IFoMamphl=enampei=WkG1VcX6CIemNtOUg6gDamptbm=ischampved=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
11 Section Review
bull 13 Why are concepts in physics described with formulas
bull Formulas concise and used to predict new data
bull 14 The fore of a magnetic field on a charged moving particle is given by F = Bqv where F is the force in kgms2 q is the charge in As and v is the speed in ms B is the strength of the magnetic field measured in teslas T What is 1 tesla described in base units
bull 1 kgAs2
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
11 Section Review
bull 15 A proton with charge 160 X 10-19 As is moving at 24 X 105 ms through a magnetic field of 45 T You want to find the force on the proton
bull A Substitute the values into the equation you will use Are the units correct
bull F = Bqv = (45 kgAs2)(160 X 10-19 As)(24 X 105 ms) force measured in kgms2 which is correct
bull B The values are written in scientific notation m X 10n Calculate the 10n part of the equation to estimate the size of the answer
bull 10-14 answer 20 X 10-14 or 2 X 10-13
bull C Calculate your answer Check it against your estimate from part b
bull 1728 X 10-13 kgms2 very close to estimate
bull D Justify the number of significant digits in your answer
bull The least precise value is 45 so the answer can have two significant figures The rounded answer is 17 X 10-13 kgms2
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
11 Section Review
bull 16 Rewrite F = Bqv to find v in terms of F q and B
bull V = FBq
bull 17 An accepted value for the acceleration due to gravity is 9801 ms2 In the experiment with pendulums you calculate that the value is 94 ms2 Should the accepted value be tossed out to accommodate your new findings Explain
bull The value 9801 has been established by repeated experiments To reject the value would require an explanation of why it is wrong Physical factors could explain the variation in the result
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Measurement
bull Comparison between an unknown quantity and a standard
bull Measurements reported with uncertainty to confirm or refute results
bull httpwwwuncertainnumberscomnotes_imageserror_and_uncertainty_intervalpng
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Precision Versus Accuracy
bull Both characteristics of measured values
bull Precision ndash how close measurements are to each other shown by significant figures
bull Accuracy ndash how close measurements are to accepted value shown by comparison to standard
bull httpwpsprenhallcomwpsmediaobjects165169061SW-comartfig1_2_5gif
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Techniques of Good Measurement
bull Important to use instruments correctly
bull Common source of error angle of measurement (parallax)
bull Variation in accuracy of GPSbull httpswwwgooglecomurl
sa=iamprct=jampq=ampesrc=sampsource=imagesampcd=ampcad=rjaampuact=8ampved=0CAcQjRxqFQoTCKiz0-Td-cYCFUifgAodwmAJagampurl=https3A2F2Fgcpsdesire2learncom2Fd2l2Flor2Fviewer2FviewFiled2lfile2F66052F78132FScale_Drawings_printhtmlampei=ClC1VaiGIci-ggTCwaXQBgamppsig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBAampust=1438032216140797
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
12 Section Review
bull 18 Some wooden rulers do not start with 0 at the edge but have it set in a few millimeters How could this improve the accuracy of the ruler
bull The edge of the ruler can be worn over time changing the accuracy of the ruler
bull 19 You find a micrometer that has been badly bent How would it compare to a new high-quality meterstick in terms of its precision Its accuracy
bull The micrometer would be precise but less accurate than the new meterstick
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
12 Section Review
bull 20 Does parallax affect the precision of a measurement that you make Explain
bull No precision is based on the closeness of measurements to each other As long as the parallax is maintained the precision is as well
bull 21 Your friend tells you that his height is 182 cm In your own words explain the range of heights implied by this statement
bull His height between 1815 and 1825 cm The uncertainty is 05 cm
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
12 Section Review
bull 22 A box has a length of 181 cm and a width of 192 cm and it is 203 cm tall
bull A What is its volume 7050 cm3
bull B How precise is the measure of length Of volume
bull Length is precise to 01 cm Volume is precise to 10 cm3
bull C How tall is a stack of 12 of these boxes 2436 cm
bull D How precise is the measure of the height of one box Of 12 boxes
bull The height of one box is precise to 01 cm as is the height of 12 boxes
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
12 Section Review
bull 23 Your friend states in a report that the average time required to circle a 15-mi track was 65414 s This was measured by timing 7 laps using a clock with a precision of 01 s How much confidence do you have in the results of the report Explain
bull Result never more precise than least precise measurement calculated average lap time greater than precision possible with clock
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Graphing Data
bull Graphs designed to convey information quickly and simply
bull Patterns more readily evident
bull httpwwwschoolatoznsweduaudetresourcesiStock_000015151608Small_LSvpzPdLDE_lpng
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Identifying Variables
bull Only one factor changed at a time in experiment
bull Variable ndash any factor that might affect the behavior of an experimental setup
bull Independent ndash factor changed or manipulated
bull Dependent ndash factor that depends on independent variable
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Line Graphs
bull Shows how dependent variable changes with independent variable
bull Linear relationship y = mx + b
bull Slope = YX
bull Quadratic relationship y = ax2 + bx + c
bull Inverse relationship y = axbull httpsjrlf8zwikispacescomfileviewgraph_2JPG34302007graph_2JPG
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problems
bull 24 The mass values of specified volumes of pure gold nuggets are given in the table
Volume (cm3) Mass (g)
10 194
20 386
30 581
40 774
50 965
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problems
bull A Plot mass versus volume from the values given in the table and draw the curve that best fits all points
2 3 4 50
20
40
60
80
100
120
Density of Gold
194 Series2 Series3
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problems
bull B Describe the resulting curve
bull Straight line
bull C According to the graph what type of relationship exists between the mass of the pure gold nuggets and their volume
bull Linear relationship
bull D What is the value of the slope of this graph Include the proper units
bull 19gcm3
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Practice Problems
bull E Write the equation showing mass as a function of volume for gold
bull m = (19 gcm3)V
bull F Write a word interpretation for the slope of the line
bull The mass for each cubic centimeter of pure gold is 19 g
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Predicting Values
bull Known values used to make predictions
bull Important to know how to extrapolate from data
bull Models used to predict how systems will behave
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
13 Section Review
bull 25 Graph the following data Time is the independent variable
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Chart Title
Speed (ms) Series2 Series3
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
13 Section Review
bull 26 What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume
bull When the volume of the material is zero there is a nonzero total mass This could happen if the mass of the container were included
bull 27 Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm
bull 16 g
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
13 Section Review
bull 28 Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms
bull 75 A
bull 29 In your own words explain the meaning of a shallower line or a smaller slope than the one in Figure 1-16 in the graph of stretch versus total mass for a different spring
bull Spring with line of smaller slope stiffer so more mass required to stretch to one centimer
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
Chapter 1 Homework
bull Appendix B Additional Problems
bull Page 858
bull 1 ndash 12
bull You DO NOT have to write the question
