SlideShare a Scribd company logo
 
Graphing
[object Object],[object Object],[object Object]
Starting level Add a mass
Starting level Add a mass Stretch is now here
Starting level Stretch is now here Add another mass Add a mass
Starting level We control the mass that is added. It is the independent variable. The stretch depends on the mass added. It is the dependent variable. Stretch is now here Add another mass Stretch is now here Add a mass
[object Object]
A graph of this experimental data is shown on the next slides. Weight  (Newtons) Stretch  (meters) 6.0 0.1240 14.0 0.1475 22.0 0.1775 30.0 0.1950 38.0 0.2195 40.0 0.2300 47.0 0.2525 54.0 0.2675 58.0 0.2875
Each graph should be identified with a title Weight, the independent variable, will be plotted along the horizontal axis (the abscissa). Weight (Newtons) Stretch, the dependent variable, will be plotted along the vertical axis (the ordinate). Stretch (meters) Stretch Versus Weight 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
[object Object],[object Object],[object Object],[object Object],REMEMBER!
Weight (Newtons) Stretch (meters) Stretch Versus Weight Let’s plot the data. (6.0, 0.1240) (14.0, 0.1475) (22.0, 0.1775) (38.0, 0.2195) (40.0, 0.2300) (47.0, 0.2525) (54.0, 0.2675) (58.0, 0.2875) Each data point should be circled, so that it can be easily found and distinguished from other dots on the paper. (30.0, 0.1950) 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight This is not a connect-the-dot exercise. The data appear to fit a straight line similar to this one. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight If there is a general trend to the data, then a best-fit curve describing this trend can be drawn. In this example the data points approximately fall along a straight line. This implies a  linear relationship  between the stretch and the weight. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight Important information can be obtained if we know the equation that describes the data. With an equation we are able to predict the values of the variables beyond the boundaries of the graph. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight If data points follow a linear relationship (straight line), the equation describing this line is of the form y = mx + b where y represents the dependent variable  (in this case, stretch), and  x represents the independent variable (weight). 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight The value of the dependent variable when x = 0 is given by b and is known as the y-intercept.  The y-intercept is found graphically by finding the intersection of the y-axis (x = 0) and the line through the data points.  (From the equation  y = mx + b , if we set x = 0  then y = b.)  In this case b = 0.11 meters. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight m is the  slope  of the best-fit line.  It is found by taking any two points, for instance (x 2 , y 2 ) and (x 1 , y 1 ), on the straight line and subtracting their respective x and y values. Note  y 2  = mx 2  + b y 1  = mx 1  + b Subtracting one equation from the other gives y 2  - y 1  = mx 2  - mx 1  = m(x 2  – x 1 ) Therefore We’ll call this 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) y-intercept = 0.11 meters Stretch Versus Weight run = (34.0 – 17.0) Newtons = 17.0 Newtons rise = (0.21 – 0.16) meters = 0.05 meters To find the slope of this line take two separate points on the line. 17.0 0.16 34.0 0.21 Y 1  = Y 2  = X 2  = X 1  = Point 2 Point 1 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) y-intercept = 0.11 meters Stretch Versus Weight run = (34.0 – 17.0) Newtons = 17.0 Newtons rise = (0.21 – 0.16) meters = 0.05 meters 17.0 0.16 34.0 0.21 Y 1  = Y 2  = X 2  = X 1  = Point 2 Point 1 To find the slope of this line take two separate points on the line. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight At this point everything needed to write the equation that describes the data has been found.  Recall that this equation has the form y y-intercept = 0.11 meters m x + b • = 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight Here are two ways we can get useful information  How much weight will produce a 0.14 m stretch?  From the graph:  we could read it from the plot like this. This would be about 10.2 Newtons 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
Weight (Newtons) Stretch (meters) Stretch Versus Weight Here are two ways we can gain useful information  How much weight will produce a 0.14 m stretch?  Solving the equation gives x (Weight)=10.2 Newtons. Stretch = 0.00294 · Weight + 0.11 for x (Weight) when y (Stretch)=0.14 m 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
A curve through this data is not straight and x and y are not linearly related.  Their relationship could be complicated. y x 0 1 2 3 4 5 6 Suppose you have some x and y data related to each other in the following way. 0 10 20 30 40 50 60
y 2 y x 0 1 2 3 4 5 6 A replot of this data might straighten this line to give a linear relationship. Let’s try y 2  versus x. This relationship would be 0 10 20 30 40 50 60

More Related Content

What's hot

6161103 10.9 mass moment of inertia
6161103 10.9 mass moment of inertia6161103 10.9 mass moment of inertia
6161103 10.9 mass moment of inertiaetcenterrbru
 
Free Ebooks Download ! Edhole.com
Free Ebooks Download ! Edhole.comFree Ebooks Download ! Edhole.com
Free Ebooks Download ! Edhole.com
Edhole.com
 
7. centroid and centre of gravity
7. centroid and centre of gravity7. centroid and centre of gravity
7. centroid and centre of gravity
Ekeeda
 
Mm210(4)
Mm210(4)Mm210(4)
Mm210(4)
Osman Atalay
 
Deflection of simply supported beam and cantilever
Deflection of simply supported beam and cantileverDeflection of simply supported beam and cantilever
Deflection of simply supported beam and cantilever
yashdeep nimje
 
Linear Dynamics and Non-Linear Finite Element Analysis using ANSYS Workbench
Linear Dynamics and Non-Linear Finite Element Analysis using ANSYS WorkbenchLinear Dynamics and Non-Linear Finite Element Analysis using ANSYS Workbench
Linear Dynamics and Non-Linear Finite Element Analysis using ANSYS Workbench
Ravishankar Venkatasubramanian
 
Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...
Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...
Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...
JudithLandrys
 
How to Calculate Normal Stress 2
How to Calculate Normal Stress 2How to Calculate Normal Stress 2
How to Calculate Normal Stress 2
NinetyEast
 
Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...
Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...
Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...Mehmet Bariskan
 
Moment of inertia of plane figures
Moment of inertia of plane figuresMoment of inertia of plane figures
Moment of inertia of plane figures
AurobindaSthitapragn
 
centroid & moment of inertia
centroid & moment of inertiacentroid & moment of inertia
centroid & moment of inertia
sachin chaurasia
 
lab report structure continuous beam
lab report structure continuous beamlab report structure continuous beam
lab report structure continuous beam
YASMINE HASLAN
 
Phys111 lecture02
Phys111 lecture02Phys111 lecture02
Phys111 lecture02
labaikmurtaza
 
Experiment 6 MOS LAB
Experiment 6 MOS LABExperiment 6 MOS LAB
Experiment 6 MOS LAB
Rajat Katiyar
 
Vectors and Kinematics
Vectors and KinematicsVectors and Kinematics
Vectors and Kinematics
Dr. Virendra Kumar Verma
 
Practicas de fisica 1
Practicas de fisica 1Practicas de fisica 1
Practicas de fisica 1
Victor Hombrados Balza
 

What's hot (18)

6161103 10.9 mass moment of inertia
6161103 10.9 mass moment of inertia6161103 10.9 mass moment of inertia
6161103 10.9 mass moment of inertia
 
Free Ebooks Download ! Edhole.com
Free Ebooks Download ! Edhole.comFree Ebooks Download ! Edhole.com
Free Ebooks Download ! Edhole.com
 
7. centroid and centre of gravity
7. centroid and centre of gravity7. centroid and centre of gravity
7. centroid and centre of gravity
 
Mm210(4)
Mm210(4)Mm210(4)
Mm210(4)
 
FEA_project1
FEA_project1FEA_project1
FEA_project1
 
Deflection of simply supported beam and cantilever
Deflection of simply supported beam and cantileverDeflection of simply supported beam and cantilever
Deflection of simply supported beam and cantilever
 
Staircase Design Report
Staircase Design ReportStaircase Design Report
Staircase Design Report
 
Linear Dynamics and Non-Linear Finite Element Analysis using ANSYS Workbench
Linear Dynamics and Non-Linear Finite Element Analysis using ANSYS WorkbenchLinear Dynamics and Non-Linear Finite Element Analysis using ANSYS Workbench
Linear Dynamics and Non-Linear Finite Element Analysis using ANSYS Workbench
 
Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...
Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...
Mathematics for the Trades A Guided Approach Canadian 2nd Edition Carman Test...
 
How to Calculate Normal Stress 2
How to Calculate Normal Stress 2How to Calculate Normal Stress 2
How to Calculate Normal Stress 2
 
Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...
Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...
Vibration Midterm-THEORETICAL SOLUTION AND STATIC ANALYSES STUDY OF VIBRATION...
 
Moment of inertia of plane figures
Moment of inertia of plane figuresMoment of inertia of plane figures
Moment of inertia of plane figures
 
centroid & moment of inertia
centroid & moment of inertiacentroid & moment of inertia
centroid & moment of inertia
 
lab report structure continuous beam
lab report structure continuous beamlab report structure continuous beam
lab report structure continuous beam
 
Phys111 lecture02
Phys111 lecture02Phys111 lecture02
Phys111 lecture02
 
Experiment 6 MOS LAB
Experiment 6 MOS LABExperiment 6 MOS LAB
Experiment 6 MOS LAB
 
Vectors and Kinematics
Vectors and KinematicsVectors and Kinematics
Vectors and Kinematics
 
Practicas de fisica 1
Practicas de fisica 1Practicas de fisica 1
Practicas de fisica 1
 

Viewers also liked

Googleplaces_Computer Explorers
Googleplaces_Computer ExplorersGoogleplaces_Computer Explorers
Googleplaces_Computer Explorers
Brand Journalists
 
REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE
REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE
REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE
LennisEsteban2
 
Cent os 安装 subversion
Cent os 安装 subversionCent os 安装 subversion
Cent os 安装 subversionYUCHENG HU
 
Direct Marketing Software
Direct Marketing SoftwareDirect Marketing Software
Direct Marketing SoftwareNextBee Media
 
Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...
Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...
Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...
Realty411 Magazine for Real Estate Investors
 
Git
GitGit
Confluencewiki 使用空间
Confluencewiki 使用空间Confluencewiki 使用空间
Confluencewiki 使用空间
YUCHENG HU
 

Viewers also liked (7)

Googleplaces_Computer Explorers
Googleplaces_Computer ExplorersGoogleplaces_Computer Explorers
Googleplaces_Computer Explorers
 
REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE
REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE
REGLAMENTO DE NORMAS DE SEGURIDAD E HIGIENE
 
Cent os 安装 subversion
Cent os 安装 subversionCent os 安装 subversion
Cent os 安装 subversion
 
Direct Marketing Software
Direct Marketing SoftwareDirect Marketing Software
Direct Marketing Software
 
Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...
Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...
Give Thanks, Give Back - Our Los Angeles Real Estate Expo Benefits the Los An...
 
Git
GitGit
Git
 
Confluencewiki 使用空间
Confluencewiki 使用空间Confluencewiki 使用空间
Confluencewiki 使用空间
 

Similar to Springpractice

Statics week01
Statics week01Statics week01
Statics week01
JM Ajeb
 
ejercicio viga con dos rótulas
ejercicio viga con dos rótulasejercicio viga con dos rótulas
ejercicio viga con dos rótulas
Mario García
 
Damped and undamped motion differential equations.pptx
Damped and undamped motion differential equations.pptxDamped and undamped motion differential equations.pptx
Damped and undamped motion differential equations.pptx
BrijeshMishra525980
 
Newton’s Divided Difference Formula
Newton’s Divided Difference FormulaNewton’s Divided Difference Formula
Newton’s Divided Difference Formula
Jas Singh Bhasin
 
1VectorAdditionofForcesObjectivesTousethe.docx
 1VectorAdditionofForcesObjectivesTousethe.docx 1VectorAdditionofForcesObjectivesTousethe.docx
1VectorAdditionofForcesObjectivesTousethe.docx
ShiraPrater50
 
Chapter5
Chapter5Chapter5
OConnor_SimulationProject
OConnor_SimulationProjectOConnor_SimulationProject
OConnor_SimulationProjectKevin O'Connor
 
Ch 7 PART 1.ppt
Ch 7 PART 1.pptCh 7 PART 1.ppt
Ch 7 PART 1.ppt
taqi27
 
Resolução.física sears zemansky 12ª edição young e freedman (todos os...
Resolução.física   sears   zemansky   12ª edição   young e freedman (todos os...Resolução.física   sears   zemansky   12ª edição   young e freedman (todos os...
Resolução.física sears zemansky 12ª edição young e freedman (todos os...
ASTRIDEDECARVALHOMAG
 
Bending stress
Bending stressBending stress
Bending stress
Taral Soliya
 
PART I.3 - Physical Mathematics
PART I.3 - Physical MathematicsPART I.3 - Physical Mathematics
PART I.3 - Physical Mathematics
Maurice R. TREMBLAY
 
Transverse speed and wave speed
Transverse speed and wave speedTransverse speed and wave speed
Transverse speed and wave speed
Nick Irwin
 
Applied mechanics of solids (a.f
Applied mechanics of solids (a.fApplied mechanics of solids (a.f
Applied mechanics of solids (a.f
Manuel Miranda
 
pdfslide.net_unsymmetrical-bendingppt.pdf
pdfslide.net_unsymmetrical-bendingppt.pdfpdfslide.net_unsymmetrical-bendingppt.pdf
pdfslide.net_unsymmetrical-bendingppt.pdf
AkhileshKumar374947
 
Physics statics
Physics   staticsPhysics   statics
Physics staticsiamkim
 
Tension coefficient method
Tension coefficient methodTension coefficient method
Tension coefficient method
Divya Vishnoi
 
Chapter 9 tutorial exercises with solutions 19 02 2013
Chapter 9    tutorial exercises with solutions 19 02 2013Chapter 9    tutorial exercises with solutions 19 02 2013
Chapter 9 tutorial exercises with solutions 19 02 2013TRL4EVER
 
Math Project !.docx What is the effect of changing the transformations on a s...
Math Project !.docx What is the effect of changing the transformations on a s...Math Project !.docx What is the effect of changing the transformations on a s...
Math Project !.docx What is the effect of changing the transformations on a s...
GOOGLE
 

Similar to Springpractice (20)

Statics week01
Statics week01Statics week01
Statics week01
 
ejercicio viga con dos rótulas
ejercicio viga con dos rótulasejercicio viga con dos rótulas
ejercicio viga con dos rótulas
 
Damped and undamped motion differential equations.pptx
Damped and undamped motion differential equations.pptxDamped and undamped motion differential equations.pptx
Damped and undamped motion differential equations.pptx
 
Chapter 14 Statics
Chapter 14 StaticsChapter 14 Statics
Chapter 14 Statics
 
Chapter 14 Statics
Chapter 14 StaticsChapter 14 Statics
Chapter 14 Statics
 
Newton’s Divided Difference Formula
Newton’s Divided Difference FormulaNewton’s Divided Difference Formula
Newton’s Divided Difference Formula
 
1VectorAdditionofForcesObjectivesTousethe.docx
 1VectorAdditionofForcesObjectivesTousethe.docx 1VectorAdditionofForcesObjectivesTousethe.docx
1VectorAdditionofForcesObjectivesTousethe.docx
 
Chapter5
Chapter5Chapter5
Chapter5
 
OConnor_SimulationProject
OConnor_SimulationProjectOConnor_SimulationProject
OConnor_SimulationProject
 
Ch 7 PART 1.ppt
Ch 7 PART 1.pptCh 7 PART 1.ppt
Ch 7 PART 1.ppt
 
Resolução.física sears zemansky 12ª edição young e freedman (todos os...
Resolução.física   sears   zemansky   12ª edição   young e freedman (todos os...Resolução.física   sears   zemansky   12ª edição   young e freedman (todos os...
Resolução.física sears zemansky 12ª edição young e freedman (todos os...
 
Bending stress
Bending stressBending stress
Bending stress
 
PART I.3 - Physical Mathematics
PART I.3 - Physical MathematicsPART I.3 - Physical Mathematics
PART I.3 - Physical Mathematics
 
Transverse speed and wave speed
Transverse speed and wave speedTransverse speed and wave speed
Transverse speed and wave speed
 
Applied mechanics of solids (a.f
Applied mechanics of solids (a.fApplied mechanics of solids (a.f
Applied mechanics of solids (a.f
 
pdfslide.net_unsymmetrical-bendingppt.pdf
pdfslide.net_unsymmetrical-bendingppt.pdfpdfslide.net_unsymmetrical-bendingppt.pdf
pdfslide.net_unsymmetrical-bendingppt.pdf
 
Physics statics
Physics   staticsPhysics   statics
Physics statics
 
Tension coefficient method
Tension coefficient methodTension coefficient method
Tension coefficient method
 
Chapter 9 tutorial exercises with solutions 19 02 2013
Chapter 9    tutorial exercises with solutions 19 02 2013Chapter 9    tutorial exercises with solutions 19 02 2013
Chapter 9 tutorial exercises with solutions 19 02 2013
 
Math Project !.docx What is the effect of changing the transformations on a s...
Math Project !.docx What is the effect of changing the transformations on a s...Math Project !.docx What is the effect of changing the transformations on a s...
Math Project !.docx What is the effect of changing the transformations on a s...
 

Recently uploaded

Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
Vikramjit Singh
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
kaushalkr1407
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
RaedMohamed3
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
Celine George
 
Additional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdfAdditional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdf
joachimlavalley1
 
Honest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptxHonest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptx
timhan337
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Levi Shapiro
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
Celine George
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
Thiyagu K
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
Jean Carlos Nunes Paixão
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
Balvir Singh
 
CACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdfCACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdf
camakaiclarkmusic
 
Phrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXX
Phrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXXPhrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXX
Phrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXX
MIRIAMSALINAS13
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
beazzy04
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
Anna Sz.
 
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup   New Member Orientation and Q&A (May 2024).pdfWelcome to TechSoup   New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
TechSoup
 
Supporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptxSupporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptx
Jisc
 
The approach at University of Liverpool.pptx
The approach at University of Liverpool.pptxThe approach at University of Liverpool.pptx
The approach at University of Liverpool.pptx
Jisc
 

Recently uploaded (20)

Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
 
Additional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdfAdditional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdf
 
Honest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptxHonest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptx
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
 
CACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdfCACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdf
 
Phrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXX
Phrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXXPhrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXX
Phrasal Verbs.XXXXXXXXXXXXXXXXXXXXXXXXXX
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
 
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup   New Member Orientation and Q&A (May 2024).pdfWelcome to TechSoup   New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
 
Supporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptxSupporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptx
 
The approach at University of Liverpool.pptx
The approach at University of Liverpool.pptxThe approach at University of Liverpool.pptx
The approach at University of Liverpool.pptx
 

Springpractice

  • 1.  
  • 3.
  • 5. Starting level Add a mass Stretch is now here
  • 6. Starting level Stretch is now here Add another mass Add a mass
  • 7. Starting level We control the mass that is added. It is the independent variable. The stretch depends on the mass added. It is the dependent variable. Stretch is now here Add another mass Stretch is now here Add a mass
  • 8.
  • 9. A graph of this experimental data is shown on the next slides. Weight (Newtons) Stretch (meters) 6.0 0.1240 14.0 0.1475 22.0 0.1775 30.0 0.1950 38.0 0.2195 40.0 0.2300 47.0 0.2525 54.0 0.2675 58.0 0.2875
  • 10. Each graph should be identified with a title Weight, the independent variable, will be plotted along the horizontal axis (the abscissa). Weight (Newtons) Stretch, the dependent variable, will be plotted along the vertical axis (the ordinate). Stretch (meters) Stretch Versus Weight 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 11.
  • 12. Weight (Newtons) Stretch (meters) Stretch Versus Weight Let’s plot the data. (6.0, 0.1240) (14.0, 0.1475) (22.0, 0.1775) (38.0, 0.2195) (40.0, 0.2300) (47.0, 0.2525) (54.0, 0.2675) (58.0, 0.2875) Each data point should be circled, so that it can be easily found and distinguished from other dots on the paper. (30.0, 0.1950) 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 13. Weight (Newtons) Stretch (meters) Stretch Versus Weight This is not a connect-the-dot exercise. The data appear to fit a straight line similar to this one. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 14. Weight (Newtons) Stretch (meters) Stretch Versus Weight If there is a general trend to the data, then a best-fit curve describing this trend can be drawn. In this example the data points approximately fall along a straight line. This implies a linear relationship between the stretch and the weight. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 15. Weight (Newtons) Stretch (meters) Stretch Versus Weight Important information can be obtained if we know the equation that describes the data. With an equation we are able to predict the values of the variables beyond the boundaries of the graph. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 16. Weight (Newtons) Stretch (meters) Stretch Versus Weight If data points follow a linear relationship (straight line), the equation describing this line is of the form y = mx + b where y represents the dependent variable (in this case, stretch), and x represents the independent variable (weight). 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 17. Weight (Newtons) Stretch (meters) Stretch Versus Weight The value of the dependent variable when x = 0 is given by b and is known as the y-intercept. The y-intercept is found graphically by finding the intersection of the y-axis (x = 0) and the line through the data points. (From the equation y = mx + b , if we set x = 0 then y = b.) In this case b = 0.11 meters. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 18. Weight (Newtons) Stretch (meters) Stretch Versus Weight m is the slope of the best-fit line. It is found by taking any two points, for instance (x 2 , y 2 ) and (x 1 , y 1 ), on the straight line and subtracting their respective x and y values. Note y 2 = mx 2 + b y 1 = mx 1 + b Subtracting one equation from the other gives y 2 - y 1 = mx 2 - mx 1 = m(x 2 – x 1 ) Therefore We’ll call this 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 19. Weight (Newtons) Stretch (meters) y-intercept = 0.11 meters Stretch Versus Weight run = (34.0 – 17.0) Newtons = 17.0 Newtons rise = (0.21 – 0.16) meters = 0.05 meters To find the slope of this line take two separate points on the line. 17.0 0.16 34.0 0.21 Y 1 = Y 2 = X 2 = X 1 = Point 2 Point 1 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 20. Weight (Newtons) Stretch (meters) y-intercept = 0.11 meters Stretch Versus Weight run = (34.0 – 17.0) Newtons = 17.0 Newtons rise = (0.21 – 0.16) meters = 0.05 meters 17.0 0.16 34.0 0.21 Y 1 = Y 2 = X 2 = X 1 = Point 2 Point 1 To find the slope of this line take two separate points on the line. 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 21. Weight (Newtons) Stretch (meters) Stretch Versus Weight At this point everything needed to write the equation that describes the data has been found. Recall that this equation has the form y y-intercept = 0.11 meters m x + b • = 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 22. Weight (Newtons) Stretch (meters) Stretch Versus Weight Here are two ways we can get useful information How much weight will produce a 0.14 m stretch? From the graph: we could read it from the plot like this. This would be about 10.2 Newtons 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 23. Weight (Newtons) Stretch (meters) Stretch Versus Weight Here are two ways we can gain useful information How much weight will produce a 0.14 m stretch? Solving the equation gives x (Weight)=10.2 Newtons. Stretch = 0.00294 · Weight + 0.11 for x (Weight) when y (Stretch)=0.14 m 0 10 20 30 40 50 60 0.10 0.14 0.18 0.22 0.26 0.30
  • 24. A curve through this data is not straight and x and y are not linearly related. Their relationship could be complicated. y x 0 1 2 3 4 5 6 Suppose you have some x and y data related to each other in the following way. 0 10 20 30 40 50 60
  • 25. y 2 y x 0 1 2 3 4 5 6 A replot of this data might straighten this line to give a linear relationship. Let’s try y 2 versus x. This relationship would be 0 10 20 30 40 50 60