5. Is it OK to change the spacing of the tick marks on your axes as you go across the page? a. Yes b. No - that screws up the analysis of the data.

Size: px
Start display at page:

Download "5. Is it OK to change the spacing of the tick marks on your axes as you go across the page? a. Yes b. No - that screws up the analysis of the data."

Transcription

1 Name: Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements =========================================================== Choose the best answer. (30 pts total) Significant Digits, and Converting Units 1. A student did the calculation, = x, in their calculator and read the result x = , from the calculator screen. How should the student record the result, x, to have the correct number of significant digits? a b. 113 c d. 110 e Express 3300 g/cm 3 in kg/m 3. (Note that the trailing zeros in 3300 are merely place holders and are not significant digits. For the zeros to be significant, the number would have to be written as 3.300x10 3.) a. 3.3 x 10 2 kg/m 3 b. 3.3 x 10 9 kg/m 3 c. 3.3 x 10 3 kg/m 3 d. 3.3 x 10 6 kg/m 3 3. Why do we keep 1-2 extra (non-significant) digits in the middle steps of our calculations and only round to the correct number of significant digits in the final step of our calculation? a. to reduce rounding error b. because we like hitting lots of buttons on our calculator c. We don t keep extra (non-significant) digits (or units) because we like to have errors in our results. Graphing 4. When drawing a graph, it is best to draw it small, so it takes only a small part of the graph paper and the data points are crammed together. In physics, we like to maximize the error in our graphs and measurements and make things hard to read. a. True b. False 5. Is it OK to change the spacing of the tick marks on your axes as you go across the page? a. Yes b. No - that screws up the analysis of the data. 6. Which of the following should you include in the axes labels of your graphs? a. units d. Answers a & b b. symbol/variable for what is being plotted e. Answers a, b & c c. word description of what is being plotted 7. Do not mix units in a graph or they won t cancel properly in the slope (Δy/Δx). Use the same type of units for the same type of number on both axes. Which of the following sets of units is NOT ok to use? [Remember: N = kg m/s 2 ] a. y-axis = N and x-axis = m/s 2 b. y-axis = g cm/s 2 and x-axis = cm/s 2 c. y-axis = N and and x-axis = cm/s 2

2 8. Titles for your graphs a. are not always necessary. b. can be written with symbols/variables only. c. are a word description that describes what is in your graph and are always required. 9. Assuming all data points are of equal quality, which of the following is the best fit line? a. b. c. d. 10. When it is acceptable to use a data point as a slope point? a. if the data point appears to fall upon the line b. if the data point appears to fall upon the line and if it falls at the extreme end of the page c. NEVER, because this tends to influence the positioning of the best fit line. 11. To find the best possible value for the slope of a graph (while minimizing uncertainty), the two slope points should NOT be data points, lie at the intersection ( corner ) of the gridlines, and, as much as reasonably possible, lie at the extreme ends of the paper. If you can t have it all, which is the first thing you give up? a. slope points at extreme ends of the page of paper b. slope points at the intersection ( corner ) of the grid lines c. ensuring that the slope point is not a data point

3 12. Which is the incorrect formula for calculating the slope (Δy/Δx) with the slope points (x 1, y 1 ) and (x 2, y 2 )? a. (y 1 y 2 ) / (x 1 x 2 ) b. (y 2 y 1 ) / (x 2 x 1 ) c. (y 1 y 2 ) / (x 2 x 1 ) 13. How do you find the y-intercept of your graph if your graph does not include the origin (0,0)? a. See where your best fit line crosses the vertical axis. b. See where your best fit line crosses the horizontal axis. c. Use the equation of a line to solve for the y-intercept algebraically. Questions 14-15: The data in your experiment is governed by the formula: A = (BC/D) E You graph A on the y (vertical) axis and C on the x (horizontal) axis. 14. What is the slope theoretically equal to? a. B/D b. A/E c. E d. C/A e. C/D 15. What is the y-intercept theoretically equal to? a. B/D b. E c. E d. C/A e. C/D Uncertainty in Measurements Questions 16-17: You are using a ruler to measure lengths. Assume that you can reasonably measure to one-half of the smallest division. This means you can see if the length of the object is closer to one of the tick marks, half-way between two tick marks, or closer to the following tick mark. (If you can t tell if a measurement is closer to a tick mark or half-way in between, then you can only reasonably measure to the nearest whole of the smallest division). This is your instrumental precision (instrumental uncertainty). 16. If the smallest division on your ruler is 1 mm (= 0.1 cm), what is the numerical value of your instrumental precision (instrumental uncertainty)? a. 1 mm b. 0.1 cm c cm d mm 17. If a rod is exactly three centimeters long, how would you record the length to reflect the precision of the instrument (and therefore, how well you can measure the length)? a. 30 mm b. 3.0 cm c cm d cm Note: Most analog instruments can be reasonably read to the nearest ½ of the smallest spacing on the instrument (e.g., ½ mm on a standard metric ruler). If the tick marks are widely spaced, you may estimate to the nearest 1/3 of the smallest spacing. Measuring to ¼ or 1/10 of the smallest spacing would be unreasonable. Questions 18-19: A student made the following six measurements of the mass of an object: m = 56.6 g, 56.6 g, 56.6 g, 56.6 g, 56.6g, 56.6 g. The instrumental uncertainty is δ inst = 0.1 g. 18. What is a reasonable estimate of the sample uncertainty, δ samp? a. 0.0 g b. 0.1 g c. 0.6 g d g 19. What is a reasonable estimate of the uncertainty of the measurement, δm? a. 0.0 g b. 0.1 g c. 0.6 g d g

4 20. A student made the following nine measurements of the wavelength of a standing wave: l = 14.4 cm, 15.1 cm, 14.2 cm, 14.6 cm, 14.4 cm, 14.8 cm, 13.7 cm, 13.9 cm, 14.9 cm. Assume the instrumental uncertainty is 0.1 cm. The best estimate of the wavelength of the standing wave is approximately 14.4 cm. This means that the difference between the individual measurements and the best estimate are approximately (same order as above): 0.0 cm, +0.7 cm, -0.2 cm, +0.2 cm, 0.0 cm, +0.4 cm, -0.7 cm, -0.5 cm, and +0.5 cm. One reasonable estimate of the sample uncertainty is ± 0.7 cm (Covers all of the samples). Are there any other reasonable estimates of the sample uncertainty? (Choose the best answer.) a. Yes: ±0.1 cm is also reasonable. b. Yes: ±1 cm is also reasonable. c. Yes: ±0.5 cm is also reasonable. d. Yes: ±0.4 cm is also reasonable. e. No: ±0.7 cm is the only reasonable sample uncertainty. Questions 21-23: The following questions test your knowledge of some of the terminology used with the identification and propagation of uncertainty. Use the following x = (10.8 ± 0.4) cm 21. What is the best estimate of x? a cm b. 0.4 cm c. 0.4/10.8 = = 3.85% d to 11.2 cm 22. What is the absolute uncertainty of x? a cm b. 0.4 cm c. 0.4/10.8 = = 3.85% d to 11.2 cm 23. What is the relative uncertainty of x? a cm b. 0.4 cm c. 0.4/10.8 = = 3.85% d to 11.2 cm 24. A student measures a coefficient of linear expansion of (14.2 ± 0.8)x10-6 C -1 for a steel tube and the accepted value for commercially available steel ranges from 11.3 x10-6 C -1 to 13.5x10-6 C -1. How does the measured value compare to the accepted value? (Consider whether the ranges overlap. Is there any agreement at all, no matter how small?) a. They do not agree. b. They are close but do not quite agree. c. They agree within uncertainty. Questions 25-30: Propagating Uncertainty through a calculation Use the Rules for Propagating uncertainty (step-by-step method) to solve the following calculations including uncertainty. You will need to do similar calculations to some of those below in the analysis for several labs this quarter. Pay attention to units! It is usually better to convert units before you do the calculation. Remember to convert the uncertainty if you convert the best estimate. The final answer should be rounded properly following the Rules for reporting experimental values (Appendix C of the Phy 121L/131L lab manual OR see Do s and Don ts of Physics Lab Reports #26). Reduce rounding error by keeping at least two extra nonsignificant digits in intermediate calculations, and only round severely in the last step. A = (10.0 ± 0.1) mm; B = (5.00 ± 0.10) cm; C = (8.0 ± 0.1) mm; D = (4.2 ± 0.2) cm 25. Convert C to cm. a. (0.8 ± 0.1) cm b. (8.0 ± 1.0) cm c. (0.80 ± 0.01) cm

5 26. B + C =? a. (13.0 ± 0.2) cm b. (5.80 ±.11) cm c. (58.0 ± 0.2) mm 27. B D =? a. (0.8 ± 0.3) cm b. (0.80 ±.21) cm c. (0.8 ± 0.1) cm 28. ½D =? a. (4.2 ± 0.1) cm b. (2.10 ± 0.05) cm c. (2.04 ±.10) cm d. (2.1 ± 0.1) cm 29. AC =? a. (80.0 ± 0.02) mm 2 b. (80.0 ± 1.8) mm 2 c. (80.0 ±.2) mm B 2 =? a. (25.0 ± 1.0) cm 2 b. (10.0 ± 4.0) cm 2 c. (25.0 ± 0.2) cm 2 d. (25.0 ± 0.01) cm 2

6 Extra Credit: Propagating Uncertainty through a multistep calculation with hints *** Up to 10 points EC but a maximum score of 35 out of 30 on Review Assignment *** Do following multistep calculations including uncertainty. Write out your final answer (value with its associated uncertainty) following the Rules for reporting experimental values (see Appendix C of the Phy 121L/131L lab manual or Do s and Don ts #26). Reduce rounding error by keeping at least two extra non-significant digits in intermediate calculations. Show all work to receive credit, including converting absolute to relative uncertainties (%) or relative uncertainties to absolute uncertainties, where needed. 1EC. [(34.35 ± 0.05) g (30.35 ± 0.05) g] (9.80 m/s 2 ) =??? Answer = 2EC. [(7.73 ± 0.01) cm] [(19.0 ± 0.1)mm] 2 =??? Give final answer in cm 3. Hint: first step is to make both length measurements have the same units (mm cm). Answer =

3. What is the decimal place of the least significant figure (LSF) in the number 0.152? a. tenths place b. hundredths place c.

3. What is the decimal place of the least significant figure (LSF) in the number 0.152? a. tenths place b. hundredths place c. Name: Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements =========================================================== Choose the best answer. (30 pts total) Significant Digits,

More information

Mostly Review. Phy 123L

Mostly Review. Phy 123L Name: Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements =========================================================== Choose the best answer. (30 pts total) 1. Do the following

More information

Experimental Uncertainty (Error) and Data Analysis

Experimental Uncertainty (Error) and Data Analysis Experimental Uncertainty (Error) and Data Analysis Advance Study Assignment Please contact Dr. Reuven at yreuven@mhrd.org if you have any questions Read the Theory part of the experiment (pages 2-14) and

More information

Experimental Uncertainty (Error) and Data Analysis

Experimental Uncertainty (Error) and Data Analysis E X P E R I M E N T 1 Experimental Uncertainty (Error) and Data Analysis INTRODUCTION AND OBJECTIVES Laboratory investigations involve taking measurements of physical quantities, and the process of taking

More information

Dr. Julie J. Nazareth

Dr. Julie J. Nazareth Name: Dr. Julie J. Nazareth Lab Partner(s): Physics: 133L Date lab performed: Section: Capacitors Parts A & B: Measurement of capacitance single, series, and parallel combinations Table 1: Voltage and

More information

ERROR AND GRAPHICAL ANALYSIS WORKSHEET

ERROR AND GRAPHICAL ANALYSIS WORKSHEET Student Names: Course: Section: Instructor: ERROR AND GRAPHICAL ANALYSIS WORKSHEET Instructions: For each section of this assignment, first read the relevant section in the Yellow Pages of your Lab Manual.

More information

Graphical Data Analysis Minneapolis Community and Tech. College v Experimental Measurements. Graphical Analysis and Straight lines

Graphical Data Analysis Minneapolis Community and Tech. College v Experimental Measurements. Graphical Analysis and Straight lines Graphical Data Analysis Minneapolis Community and Tech. College v.8.08 Experimental Measurements All experimentally measured numbers consist of one or more exact numbers that contain no uncertainty and

More information

Measurement: The Basics

Measurement: The Basics I. Introduction Measurement: The Basics Physics is first and foremost an experimental science, meaning that its accumulated body of knowledge is due to the meticulous experiments performed by teams of

More information

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield LECSS Physics 11 Introduction to Physics and Math Methods 1 Physics 11 Introduction to Physics and Math Methods In this introduction, you will get a more in-depth overview of what Physics is, as well as

More information

These variables have specific names and I will be using these names. You need to do this as well.

These variables have specific names and I will be using these names. You need to do this as well. Greek Letters In Physics, we use variables to denote a variety of unknowns and concepts. Many of these variables are letters of the Greek alphabet. If you are not familiar with these letters, you should

More information

PHY 123 Lab 1 - Error and Uncertainty and the Simple Pendulum

PHY 123 Lab 1 - Error and Uncertainty and the Simple Pendulum To print higher-resolution math symbols, click the Hi-Res Fonts for Printing button on the jsmath control panel. PHY 13 Lab 1 - Error and Uncertainty and the Simple Pendulum Important: You need to print

More information

Appendix B: Skills Handbook

Appendix B: Skills Handbook Appendix B: Skills Handbook Effective communication is an important part of science. To avoid confusion when measuring and doing mathematical calculations, there are accepted conventions and practices

More information

Notes: Unit 1: Math and Measurement

Notes: Unit 1: Math and Measurement Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)

More information

Notes: Unit 1: Math and Measurement

Notes: Unit 1: Math and Measurement Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)

More information

PHYSICS LAB: CONSTANT MOTION

PHYSICS LAB: CONSTANT MOTION PHYSICS LAB: CONSTANT MOTION Introduction Experimentation is fundamental to physics (and all science, for that matter) because it allows us to prove or disprove our hypotheses about how the physical world

More information

The slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.

The slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope. LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find

More information

5-Sep-15 PHYS101-2 GRAPHING

5-Sep-15 PHYS101-2 GRAPHING GRAPHING Objectives 1- To plot and analyze a graph manually and using Microsoft Excel. 2- To find constants from a nonlinear relation. Exercise 1 - Using Excel to plot a graph Suppose you have measured

More information

Intermediate Algebra Chapter 12 Review

Intermediate Algebra Chapter 12 Review Intermediate Algebra Chapter 1 Review Set up a Table of Coordinates and graph the given functions. Find the y-intercept. Label at least three points on the graph. Your graph must have the correct shape.

More information

Kinematics Unit. Measurement

Kinematics Unit. Measurement Kinematics Unit Measurement The Nature of Science Observation: important first step toward scientific theory; requires imagination to tell what is important. Theories: created to explain observations;

More information

Experiment 1 Simple Measurements and Error Estimation

Experiment 1 Simple Measurements and Error Estimation Experiment 1 Simple Measurements and Error Estimation Reading and problems (1 point for each problem): Read Taylor sections 3.6-3.10 Do problems 3.18, 3.22, 3.23, 3.28 Experiment 1 Goals 1. To perform

More information

Uncertainty and Graphical Analysis

Uncertainty and Graphical Analysis Uncertainty and Graphical Analysis Introduction Two measures of the quality of an experimental result are its accuracy and its precision. An accurate result is consistent with some ideal, true value, perhaps

More information

Math 112 Group Activity: The Vertical Speed of a Shell

Math 112 Group Activity: The Vertical Speed of a Shell Name: Section: Math 112 Group Activity: The Vertical Speed of a Shell A shell is fired straight up by a mortar. The graph below shows its altitude as a function of time. 400 300 altitude (in feet) 200

More information

Experiment 4 Free Fall

Experiment 4 Free Fall PHY9 Experiment 4: Free Fall 8/0/007 Page Experiment 4 Free Fall Suggested Reading for this Lab Bauer&Westfall Ch (as needed) Taylor, Section.6, and standard deviation rule ( t < ) rule in the uncertainty

More information

INTRODUCTION TO LABORATORY EXPERIMENT AND MEASUREMENT

INTRODUCTION TO LABORATORY EXPERIMENT AND MEASUREMENT INTRODUCTION TO LABORATORY EXPERIMENT AND MEASUREMENT Purpose Theory a. To take some simple measurements to use for statistical analysis b. To learn how to use a Vernier caliper and a micrometer screw

More information

Significant Digits What digits are important when recording a measurement?

Significant Digits What digits are important when recording a measurement? Significant Digits What digits are important when recording a measurement? Why? Scientists do a lot of measuring. When scientists use an instrument (ruler, graduated cylinder, spectrophotometer, balance

More information

1 Measurement Uncertainties

1 Measurement Uncertainties 1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.

More information

PSC 1121 Celebration of Knowledge 1 Fall 2002

PSC 1121 Celebration of Knowledge 1 Fall 2002 Fall 2002 Problem 1. (15 points) To help his teammates finish up an activity after class, Jorge agrees to find the mass (in grams) of the last four objects himself. The fours sets of measurements are shown

More information

Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12

Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12 Equation A mathematical sentence formed by setting two expressions equal to each other Example 1: 3 6 = 18 Example 2: 7 + x = 12 Variable A symbol, usually a letter, that is used to represent one or more

More information

Introduction to Uncertainty and Treatment of Data

Introduction to Uncertainty and Treatment of Data Introduction to Uncertainty and Treatment of Data Introduction The purpose of this experiment is to familiarize the student with some of the instruments used in making measurements in the physics laboratory,

More information

Graphs. 1. Graph paper 2. Ruler

Graphs. 1. Graph paper 2. Ruler Graphs Objective The purpose of this activity is to learn and develop some of the necessary techniques to graphically analyze data and extract relevant relationships between independent and dependent phenomena,

More information

Uncertainty, Error, and Precision in Quantitative Measurements an Introduction 4.4 cm Experimental error

Uncertainty, Error, and Precision in Quantitative Measurements an Introduction 4.4 cm Experimental error Uncertainty, Error, and Precision in Quantitative Measurements an Introduction Much of the work in any chemistry laboratory involves the measurement of numerical quantities. A quantitative measurement

More information

The data in this answer key is sample data only. Student answers will vary based on personal data.

The data in this answer key is sample data only. Student answers will vary based on personal data. Answer Key Road Rage The data in this answer key is sample data only. Student answers will vary based on personal data. This activity will explore how to predict where and when two cars will crash into

More information

Math Refresher Answer Sheet (NOTE: Only this answer sheet and the following graph will be evaluated)

Math Refresher Answer Sheet (NOTE: Only this answer sheet and the following graph will be evaluated) Name: Score: / 50 Math Refresher Answer Sheet (NOTE: Only this answer sheet and the following graph will be evaluated) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. MAKE SURE CALCULATOR

More information

Introduction to Physics Physics 114 Eyres

Introduction to Physics Physics 114 Eyres What is Physics? Introduction to Physics Collecting and analyzing experimental data Making explanations and experimentally testing them Creating different representations of physical processes Finding

More information

Unit 9: Quadratics Intercept Form

Unit 9: Quadratics Intercept Form For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic

More information

EXPERIMENT MEASUREMENT

EXPERIMENT MEASUREMENT PHYS 1401 General Physics I EXPERIMENT 1 MEASUREMENT and UNITS I. OBJECTIVE The objective of this experiment is to become familiar with the measurement of the basic quantities of mechanics and to become

More information

MATH EVALUATION. What will you learn in this Lab?

MATH EVALUATION. What will you learn in this Lab? MATH EVALUATION What will you learn in this Lab? This exercise is designed to assess whether you have been exposed to the mathematical methods and skills necessary to complete the lab exercises you will

More information

Newton's 2 nd Law. . Your end results should only be interms of m

Newton's 2 nd Law. . Your end results should only be interms of m Newton's nd Law Introduction: In today's lab you will demonstrate the validity of Newton's Laws in predicting the motion of a simple mechanical system. The system that you will investigate consists of

More information

PHY2048 Physics with Calculus I

PHY2048 Physics with Calculus I PHY2048 Physics with Calculus I Section 584761 Prof. Douglas H. Laurence Exam 1 (Chapters 2 6) February 14, 2018 Name: Solutions 1 Instructions: This exam is composed of 10 multiple choice questions and

More information

MAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.

MAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution. MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the

More information

161 Sp18 T1 grades (out of 40, max 100)

161 Sp18 T1 grades (out of 40, max 100) Grades for test Graded out of 40 (scores over 00% not possible) o Three perfect scores based on this grading scale!!! o Avg = 57 o Stdev = 3 Scores below 40% are in trouble. Scores 40-60% are on the bubble

More information

In chemistry we use metric units (called SI units after the French term for Systeme internationale.

In chemistry we use metric units (called SI units after the French term for Systeme internationale. Metric system / SI units: In chemistry we use metric units (called SI units after the French term for Systeme internationale. SI units: The SI units we ll be primarily concerned with are shown here: Base

More information

Methods and Tools of Physics

Methods and Tools of Physics Methods and Tools of Physics Order of Magnitude Estimation: Essential idea: Scientists aim towards designing experiments that can give a true value from their measurements, but due to the limited precision

More information

Physics 10 Scientific Measurement Workbook Mr. Proctor

Physics 10 Scientific Measurement Workbook Mr. Proctor Physics 10 Scientific Measurement Workbook Mr. Proctor Name: MEASUREMENT OF MATTER - Science 10 textbook reference pages 344-351 The Seven Fundamental Measurements (with units) in Physics are: meter (m)

More information

Physics I (Navitas) EXAM #1 Fall 2015

Physics I (Navitas) EXAM #1 Fall 2015 95.141 Physics I (Navitas) EXAM #1 Fall 2015 Name, Last Name First Name Student Identification Number: Write your name at the top of each page in the space provided. Answer all questions, beginning each

More information

LAB 2 - ONE DIMENSIONAL MOTION

LAB 2 - ONE DIMENSIONAL MOTION Name Date Partners L02-1 LAB 2 - ONE DIMENSIONAL MOTION OBJECTIVES Slow and steady wins the race. Aesop s fable: The Hare and the Tortoise To learn how to use a motion detector and gain more familiarity

More information

Computer simulation of radioactive decay

Computer simulation of radioactive decay Computer simulation of radioactive decay y now you should have worked your way through the introduction to Maple, as well as the introduction to data analysis using Excel Now we will explore radioactive

More information

Physics 115 Experiment 1. Introduction to Measurement and Error Analysis (PHY 115 and 117)

Physics 115 Experiment 1. Introduction to Measurement and Error Analysis (PHY 115 and 117) Physics 115 Experiment 1 Introduction to Measurement and Error Analysis (PHY 115 and 117) Introduction In the sciences, measurement plays an important role. The accuracy of the measurement, as well as

More information

Quarter 2 400, , , , , , ,000 50,000

Quarter 2 400, , , , , , ,000 50,000 Algebra 2 Quarter 2 Quadratic Functions Introduction to Polynomial Functions Hybrid Electric Vehicles Since 1999, there has been a growing trend in the sales of hybrid electric vehicles. These data show

More information

ALGEBRA 2 Summer Review Assignments Graphing

ALGEBRA 2 Summer Review Assignments Graphing ALGEBRA 2 Summer Review Assignments Graphing To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately and efficiently find the slope of any line, be able to write

More information

Multiple Representations: Equations to Tables and Graphs Transcript

Multiple Representations: Equations to Tables and Graphs Transcript Algebra l Teacher: It s good to see you again. Last time we talked about multiple representations. If we could, I would like to continue and discuss the subtle differences of multiple representations between

More information

MATH REFRESHER ANSWER SHEET (Note: Only this answer sheet and the following graph page will be evaluated)

MATH REFRESHER ANSWER SHEET (Note: Only this answer sheet and the following graph page will be evaluated) NAME: SCORE: /50 MATH REFRESHER ANSWER SHEET (Note: Only this answer sheet and the following graph page will be evaluated) 1. 23. 2. 24. 3. 25. 4. 26. 5. 27. 6. 28. 7. 29. 8. 30. 9. 31. 10. 32. 11. 33.

More information

Experiment 1 - Mass, Volume and Graphing

Experiment 1 - Mass, Volume and Graphing Experiment 1 - Mass, Volume and Graphing In chemistry, as in many other sciences, a major part of the laboratory experience involves taking measurements and then calculating quantities from the results

More information

Student Instruction Sheet: Unit 3, Lesson 3. Solving Quadratic Relations

Student Instruction Sheet: Unit 3, Lesson 3. Solving Quadratic Relations Student Instruction Sheet: Unit 3, Lesson 3 Solving Quadratic Relations Suggested Time: 75 minutes What s important in this lesson: In this lesson, you will learn how to solve a variety of quadratic relations.

More information

Appendix A: Significant Figures and Error Analysis

Appendix A: Significant Figures and Error Analysis 1 Appendix A: Significant Figures and Error Analysis Every measurement of a physical quantity contains some amount of uncertainty or error. We often speak of a certain number or measurement as being precise

More information

Partner s Name: EXPERIMENT MOTION PLOTS & FREE FALL ACCELERATION

Partner s Name: EXPERIMENT MOTION PLOTS & FREE FALL ACCELERATION Name: Partner s Name: EXPERIMENT 500-2 MOTION PLOTS & FREE FALL ACCELERATION APPARATUS Track and cart, pole and crossbar, large ball, motion detector, LabPro interface. Software: Logger Pro 3.4 INTRODUCTION

More information

Reference Guide. Science Reference 9/25/ Copyright 1996 Gary Lewis Revisions 2007 by John Pratte

Reference Guide. Science Reference 9/25/ Copyright 1996 Gary Lewis Revisions 2007 by John Pratte Reference Guide Contents...1 1. General Scientific Terminology...2 2. Types of Errors...3 3. Scientific Notation...4 4. Significant Figures...6 5. Graphs...7 6. Making Measurements...8 7. Units...9 8.

More information

Herndon High School Geometry Honors Summer Assignment

Herndon High School Geometry Honors Summer Assignment Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in

More information

How to Write a Good Lab Report

How to Write a Good Lab Report How to Write a Good Lab Report Sample Lab Instruction Experimental Investigation of C/D Introduction: How is the circumference of a circle related to its diameter? In this lab, you design an experiment

More information

Experiment 2: Projectile Motion

Experiment 2: Projectile Motion Experiment 2: Projectile Motion You will verify that a projectile s velocity and acceleration components behave as described in class. A ball bearing rolls off of a ramp, becoming a projectile. It flies

More information

Physics 2020 Laboratory Manual

Physics 2020 Laboratory Manual Physics 00 Laboratory Manual Department of Physics University of Colorado at Boulder Spring, 000 This manual is available for FREE online at: http://www.colorado.edu/physics/phys00/ This manual supercedes

More information

Lab 7 Energy. What You Need To Know: Physics 225 Lab

Lab 7 Energy. What You Need To Know: Physics 225 Lab b Lab 7 Energy What You Need To Know: The Physics This lab is going to cover all of the different types of energy that you should be discussing in your lecture. Those energy types are kinetic energy, gravitational

More information

Simple Harmonic Motion

Simple Harmonic Motion Introduction Simple Harmonic Motion The simple harmonic oscillator (a mass oscillating on a spring) is the most important system in physics. There are several reasons behind this remarkable claim: Any

More information

The measurements you make in the science laboratory, whether for time,

The measurements you make in the science laboratory, whether for time, Measuring Up Middle Grades Science Middle Grades Measuring Science Up Exploring Experimental Error through Measurement MATERIALS balance beaker, 250 ml copy of Nick and Nack template graduated cylinder,

More information

Principles and Problems. Chapter 1: A Physics Toolkit

Principles and Problems. Chapter 1: A Physics Toolkit PHYSICS Principles and Problems Chapter 1: A Physics Toolkit CHAPTER 1 A Physics Toolkit BIG IDEA Physicists use scientific methods to investigate energy and matter. CHAPTER 1 Table Of Contents Section

More information

Conceptual Explanations: Simultaneous Equations Distance, rate, and time

Conceptual Explanations: Simultaneous Equations Distance, rate, and time Conceptual Explanations: Simultaneous Equations Distance, rate, and time If you travel 30 miles per hour for 4 hours, how far do you go? A little common sense will tell you that the answer is 120 miles.

More information

Proton. Size of cell. 100 = 10 2, so the logarithm of 100 is 2, written Log 100= 2

Proton. Size of cell. 100 = 10 2, so the logarithm of 100 is 2, written Log 100= 2 Homework 1 Date Due Name You will be making a chart of the sizes of things in the Universe. It should come out similar to Figure., but more precise. The plot you will be working on is at the end of this

More information

2018 Arizona State University Page 1 of 16

2018 Arizona State University Page 1 of 16 NAME: MATH REFRESHER ANSWER SHEET (Note: Write all answers on this sheet and the following graph page.) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

More information

Using Scientific Measurements

Using Scientific Measurements Section 3 Main Ideas Accuracy is different from precision. Significant figures are those measured precisely, plus one estimated digit. Scientific notation is used to express very large or very small numbers.

More information

WISE Regression/Correlation Interactive Lab. Introduction to the WISE Correlation/Regression Applet

WISE Regression/Correlation Interactive Lab. Introduction to the WISE Correlation/Regression Applet WISE Regression/Correlation Interactive Lab Introduction to the WISE Correlation/Regression Applet This tutorial focuses on the logic of regression analysis with special attention given to variance components.

More information

1010 REAL Review for Final Exam

1010 REAL Review for Final Exam 1010 REAL Review for Final Exam Chapter 1: Function Sense 1) The notation T(c) represents the amount of tuition paid depending on the number of credit hours for which a student is registered. Interpret

More information

Chapter 6. Systems of Equations and Inequalities

Chapter 6. Systems of Equations and Inequalities Chapter 6 Systems of Equations and Inequalities 6.1 Solve Linear Systems by Graphing I can graph and solve systems of linear equations. CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.6 What is a system

More information

Simple Harmonic Motion

Simple Harmonic Motion Physics Topics Simple Harmonic Motion If necessary, review the following topics and relevant textbook sections from Serway / Jewett Physics for Scientists and Engineers, 9th Ed. Hooke s Law (Serway, Sec.

More information

Chapter 8B - Trigonometric Functions (the first part)

Chapter 8B - Trigonometric Functions (the first part) Fry Texas A&M University! Spring 2016! Math 150 Notes! Section 8B-I! Page 79 Chapter 8B - Trigonometric Functions (the first part) Recall from geometry that if 2 corresponding triangles have 2 angles of

More information

Chapter 1 Review of Equations and Inequalities

Chapter 1 Review of Equations and Inequalities Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve

More information

LHS Algebra Pre-Test

LHS Algebra Pre-Test Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well

More information

STEP Support Programme. Hints and Partial Solutions for Assignment 17

STEP Support Programme. Hints and Partial Solutions for Assignment 17 STEP Support Programme Hints and Partial Solutions for Assignment 7 Warm-up You need to be quite careful with these proofs to ensure that you are not assuming something that should not be assumed. For

More information

Experiment 3 Simple Measurements and Error Estimation

Experiment 3 Simple Measurements and Error Estimation PHY191 Experiment 3: Simple Measurements and Error Estimation 8/20/2007 Page 1 Experiment 3 Simple Measurements and Error Estimation Reading and problems: Homework 3: turn in as part of your preparation

More information

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives: Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations

More information

Lesson 5b Solving Quadratic Equations

Lesson 5b Solving Quadratic Equations Lesson 5b Solving Quadratic Equations In this lesson, we will continue our work with Quadratics in this lesson and will learn several methods for solving quadratic equations. The first section will introduce

More information

Lab 1: Introduction to Measurement

Lab 1: Introduction to Measurement Lab 1: Introduction to Measurement Instructor: Professor Dr. K. H. Chu Measurement is the foundation of gathering data in science. In order to perform successful experiments, it is vitally important to

More information

Measurement. Scientific Notation. Measurements and Problem Solving. Writing Numbers in Scientific Notation

Measurement. Scientific Notation. Measurements and Problem Solving. Writing Numbers in Scientific Notation Measurement Chapter 2 Measurements and Problem Solving Quantitative observation Comparison based on an accepted scale e.g. Meter stick Has 2 parts number and unit Number tells comparison Unit tells scale

More information

LESSON 2 ALGEBRA & FUNCTIONS

LESSON 2 ALGEBRA & FUNCTIONS LESSON ALGEBRA & FUNCTIONS A) SIMPLIFYING EXPRESSIONS An expression does not have an equal sign with a left side and a right side. In an expression we can only simplify rather than solve. Simplify each

More information

Chapter 2 Measurements and Solving Problems

Chapter 2 Measurements and Solving Problems History of Measurement Chapter 2 Measurements and Solving Problems Humans once used handy items as standards or reference tools for measurement. Ex: foot, cubit, hand, yard. English System the one we use.

More information

C. A laboratory course helps the students realize the distinction.

C. A laboratory course helps the students realize the distinction. lntro-1 NTRODUCTON How To Make A Good Grade n A Lab Course Without Really Trying A laboratory course may seem to involve a lot of work for too few credits. However, remembering the following points may

More information

Linear Motion with Constant Acceleration

Linear Motion with Constant Acceleration Linear Motion 1 Linear Motion with Constant Acceleration Overview: First you will attempt to walk backward with a constant acceleration, monitoring your motion with the ultrasonic motion detector. Then

More information

Introduction to Determining Power Law Relationships

Introduction to Determining Power Law Relationships 1 Goal Introduction to Determining Power Law Relationships Content Discussion and Activities PHYS 104L The goal of this week s activities is to expand on a foundational understanding and comfort in modeling

More information

Summer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages

Summer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages 8 Common Core Mathematics 6 6 Vocabulary absolute value additive inverse property adjacent angles the distance between a number and zero on a number line. Example: the absolute value of negative seven

More information

Honors Chemistry 2016 Summer Assignment

Honors Chemistry 2016 Summer Assignment This Honors Chemistry Summer Assignment will review mathematical concepts necessary when performing mathematical calculation and laboratory experiments and focus on laboratory safety. Measurements are

More information

Fundamentals of data, graphical, and error analysis

Fundamentals of data, graphical, and error analysis Fundamentals of data, graphical, and error analysis. Data measurement and Significant Figures UTC - Physics 030L/040L Whenever we take a measurement, there are limitations to the data and how well we can

More information

Uncertainties in AH Physics

Uncertainties in AH Physics Advanced Higher Physics Contents This booklet is one of a number that have been written to support investigative work in Higher and Advanced Higher Physics. It develops the skills associated with handling

More information

Learning Packet. Lesson 5b Solving Quadratic Equations THIS BOX FOR INSTRUCTOR GRADING USE ONLY

Learning Packet. Lesson 5b Solving Quadratic Equations THIS BOX FOR INSTRUCTOR GRADING USE ONLY Learning Packet Student Name Due Date Class Time/Day Submission Date THIS BOX FOR INSTRUCTOR GRADING USE ONLY Mini-Lesson is complete and information presented is as found on media links (0 5 pts) Comments:

More information

Measurement Error PHYS Introduction

Measurement Error PHYS Introduction PHYS 1301 Measurement Error Introduction We have confidence that a particular physics theory is telling us something interesting about the physical universe because we are able to test quantitatively its

More information

CONTENTS Page Rounding 3 Addition 4 Subtraction 6 Multiplication 7 Division 10 Order of operations (BODMAS)

CONTENTS Page Rounding 3 Addition 4 Subtraction 6 Multiplication 7 Division 10 Order of operations (BODMAS) CONTENTS Page Rounding 3 Addition 4 Subtraction 6 Multiplication 7 Division 10 Order of operations (BODMAS) 12 Formulae 13 Time 14 Fractions 17 Percentages 19 Ratio and Proportion 23 Information Handling

More information

Physics Experiment 1 Measurement, Random Error & Error analysis

Physics Experiment 1 Measurement, Random Error & Error analysis Advanced reading- from Physics by Giancoli, 6 th Edition (Sections 1-4, 1-5 & 1-6) Part A-Measurement of Length and Error Analysis Equipment: 1 Ruler 1 Vernier Caliper 1 Micrometer Caliper Several Coins.

More information

AP PHYSICS 1 SUMMER PREVIEW

AP PHYSICS 1 SUMMER PREVIEW AP PHYSICS 1 SUMMER PREVIEW Name: Your summer homework assignment is to read through this summer preview, completing the practice problems, and completing TASK 1 and Task 2. It is important that you read

More information

Preparation for Physics. Mathematical Graphs Equations of a Line

Preparation for Physics. Mathematical Graphs Equations of a Line III-1 Mathematical Graphs and Scientific Graphs Mathematical Graphs Equations of a Line In mathematics, graphs are made while studying functions to give a feel for the shape of the graph of a function.

More information

Don t forget to turn in all graphs and the objective and conclusion.

Don t forget to turn in all graphs and the objective and conclusion. Mathematics and Problem Solving In this lab, you will be applying your knowledge of mathematics to scientific and astronomical problems. It is NOT a test. DO work with your friends and check your results

More information

Chapter 9: Roots and Irrational Numbers

Chapter 9: Roots and Irrational Numbers Chapter 9: Roots and Irrational Numbers Index: A: Square Roots B: Irrational Numbers C: Square Root Functions & Shifting D: Finding Zeros by Completing the Square E: The Quadratic Formula F: Quadratic

More information

Unit 1 Introduction to Chemistry & Data Analysis Chapters 1 2 of your book.

Unit 1 Introduction to Chemistry & Data Analysis Chapters 1 2 of your book. Unit 1 Introduction to Chemistry & Data Analysis Chapters 1 2 of your book. Early Booklet E.C.: / 2 Unit 1 Hwk. Pts: / 29 Unit 1 Lab Pts: / 56 Late, Incomplete, No Work, No Units Fees? Y / N Learning Targets

More information