Lab 1a: Experimental Uncertainties

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Physics 144 Chowdary How Things Work Spring 2006 Name: Partners Name(s): Lab 1a: Experimental Uncertainties Introduction Our first exploration today is intended to introduce you to the true nature of experimentation: no measurement is complete without some comment on the confidence with which it was measured. The key to doing experiments in any scientific field is making measurements. But when you make a measurement, there is always some uncertainty associated with it. Many times, these uncertainties are called experimental errors, but to me, that has always implied sloppiness. Of course, a good experimentalist will always seek to minimize the uncertainties in an experiment. But it is impossible ever to make a perfect measurement. In addition to minimizing errors, an experimentalist has to know how to determine the magnitude of the uncertainty. As we will see in this lab, knowing how large the uncertainty is in a measurement can be critical to making conclusions based on the data. In most of our everyday experience, the confidence that we have in our information is never explicitly stated. For instance, when asking someone what the temperature is outside, the response is always nearly a single number: It s 65 o today. This usually means that the true temperature outside is somewhere near 65 o, within a few degrees or so. The amount from which our measured value may be off from the actual value is called the experimental uncertainty or confidence limit of our measurement. When we hear that the temperature is 65o, we assume an uncertainty of a few degrees, and dress appropriately. Experience tells us that most times the temperature difference is rarely outside that range. You do often hear the confidence level given for polls. You probably expect to hear it. In fact, you should demand to hear it. And whenever you hear an experimental result obtained by measurement, you should demand to know the experimental uncertainty. The concepts and numerical tools illustrated in this lab have many applications in business (e.g., quality control and marketing surveys), politics (opinion polls), law (questions of evidence and proof), medicine (significance of changes in a patient's lab results), economics (measures of economic indicators), sociology (measurements of societal trends), etc. There are several goals of this lab: in particular, after finishing this lab, you should understand a) how measurement uncertainty can be reduced with the use of repeated measurements; b) how to characterize the magnitude of the uncertainty for a measured quantity; and c) how to make appropriate conclusions from your data, based on the uncertainty. Specifically, we ll develop the tools needed to answer the following question: How many brown M&M s would you expect to find in a typical bag? Later, you ll apply these tools to answer the following questions: Does the acceleration of an object sliding down a ramp depend on the mass of the object? Does the acceleration of an object sliding down a ramp depend on the angle of the ramp?

3 Table 1: Class Results Name Total # # Brown It probably isn t surprising that both the Total # and # Brown might be different for each person. However, you should notice that the numbers are only slightly different. The real questions now are What is the best estimate for the number of Brown M&M s? How big is slightly? 3) There are lots of ways to present this information. One way is as in Table 1. Let s try a graphical way next. First, let s see how much variation there is in the individual measurements of the Brown M&M s: # Brown M&M's Student Number Graph 1: Variation in # Brown M&M s

4 4) Hopefully, from Graph 1 you notice that the # Brown seems to fluctuate about some value. It seems likely that that value would be a good estimate for the number of Brown M&M s in a typical bag. Question #3: What does that value seem to be, according to Graph 1? How could you calculate that value? What other common name would we give to that kind of calculation? Calculate this value using your calculator, and draw a dashed horizontal line representing this value on Graph 1. Please talk to your instructor. 5) So it seems to make sense that averaging together the number of Brown M&M s found in a number of different bags will give a good estimate for the number of Brown M&M s in a typical bag. However, to really know this number, we d need to measure the number of Brown M&M s in every bag ever created! Then, we could obtain the true mean. Of course, this is not practical (but it sure would be tasty), so we settle for looking at a sub-set of the overall number of bags. Obviously, the larger our subs et, the closer our experimental mean will be to the true mean. So we have our experimental average. However, we still haven t determined our confidence level: we don t know how much variation to expect in a single bag. Also, we don t know have a good estimate for how close our experimental mean is to the true mean. Luckily, these two estimates are closely linked. WARNING: Lots of people are confused by the distinction in the previous paragraph. We re actually trying to answer two questions, both related to the experimental mean: 1) In any given bag, by how many Brown M&M s do you expect to be off from the experimental mean? (i.e., for any single measurement, how far off do you expect that experimental result to be from the experimental mean). 2) How far away do you expect the experimental mean is from the true mean? Please ask your instructor if you don t understand these two questions. 6) From Graph 1, we get a sense of the variation in individual measurements from the experimental mean (which itself is our best estimate of the true mean). Now, we ll make another plot that shows this variation in a different way. We ll plot the number of times a particular number of Brown M&M s was found vs. that particular number. The number of times a particular number is found is called the frequency of that number. So for example, if there were 5 bags that had 16 Brown M&M s, the frequency of 16 would be 5. Here s an example: let s say we found 3 bags with 12 M&M s; 4 bags with 15 M&M s; 5 bags with 16 M&M s; and 3 bags with 17 M&M s. I d make a table with two columns: the first column would be a particular measurement (here the number of M&M s in a bag) and the second column would be the frequency of that measurement (here the number of bags with that number of M&M s). Then I d plot the first column on the horizontal axis and the second column on the vertical axis. I find it easy to use X s. This kind of a plot is called a frequency distribution plot or a histogram. You have almost certainly seen this when teachers report how students did on an exam.

6 Column 1 Column 2 Column 3 Column 4 # Brown # Brown Average (# Brown Average) Average Table 3: Calculating the Uncertainty. 10) The square root of the number in the shaded box is known as the standard deviation. This is the best estimate of the spread in the class results, and tells you the confidence level that you have: for any single bag, there is a 68% chance that the number of Brown M&M s will fall within the range between the experimental mean the standard deviation and the experimental mean + the standard deviation. (Actually, this 68% is only true if the histogram is a bell-shaped curve, known more formally as a Gaussian. Our calculation of the standard deviation is still correct, and it is still a good indicator of the confidence level; it s just that we might not be able to say 68%.) On Graph 3, draw a dashed vertical line representing the experimental mean the standard deviation and the experimental mean + the standard deviation. Note that some of our measurements fall outside this range. As mentioned above, this range tells us where to expect to find 68% of all M&M bags. If we wanted to know the range in which 95% of the measurements would fall, we d double the standard deviation. And if we wanted to be even more certain, a range of 3 standard deviations to either side of the experimental mean would include 99.7% of all possible results! 11) However, this only answers half our questions. We ve identified the experimental mean along with the standard deviation. This answers the first question: In any given bag, by how many Brown M&M s do you expect to be off from the experimental mean? (i.e., for any single measurement, how far off do you expect that experimental result to be from the experimental mean). What about the second question: How far away do you expect the experimental mean is from the true mean? Well, it turns out to be fairly straightforward, given that we ve already calculated the standard deviation. The quantity of interest that we want is called the standard deviation of the mean, and is given by the standard deviation divided by the square root of the number of measurements that were made. This makes some sense: the more measurements you make, the closer your experimental mean should be to the true mean. So the standard deviation of the mean = standard deviation number of measurements And you expect the true mean to be within one standard deviation of the mean of the experimental average.

7 12) Determine the standard deviation of the mean. Conclusions We ve learned that making multiple measurements of the same quantity gives a better estimate than a single measurement. Averaging together multiple measurements to get the experimental mean gives an estimate of the true mean. We ve seen several ways to represent the spread in measurements, via graphs and calculation. We re confident that any single measurement lies in the range: experiment al mean ± standard deviation. We re confident that the true mean lies in the range: experiment al mean ± standard deviation of the mean Questions a) Your instructor is about to open up a bag of M&M s. Write down your best estimate for the number of Brown M&M s your instructor will find. b) The other lab section does the same lab as your half, and determines that their true mean lies in the range 9 ± 3. Might it reasonable to conclude that their bags came from a different case than your lab section s bags?

8 Lab 1b: Graphing Motion Introduction Our second activity today will give you practice with the connection between position, velocity, and acceleration. You ll get exposure to graphing motion curves (position vs. time, velocity vs. time, and acceleration vs. time). You ll use a computer and an ultrasonic motion detector to generate motion curves. You ll use the techniques you develop here in the next section of today s lab activities. All the motion in this section is one-dimensional. We ve seen one-dimensional motion in the path of a ball as it travels up and down when thrown straight up. Here, we ll look at it for a cart on a low friction track as it moves back and forth. Position vs. Time At your lab station is a cart on a low friction track. You can see that you can roll the cart back and forth along the track. The track is marked with a ruler, so you can measure the position of the cart. Below is a proposed position vs. time graph for the cart moving back and forth. position time 1) With your partner(s), determine how you would have to move the cart along the track in order to get this position vs. time graph. When/where would you not be moving? When would you be moving fast or slow? When would you be moving to the left or to the right? Briefly describe how you would move the cart to get the position vs. time graph shown.

9 2) On the axes below, sketch the velocity vs. time curve that corresponds to the position vs. time curve above. Some things to consider: a) On the position vs. time graph, were there any times when the velocity was zero? How did you know? Draw those first. b) On the position vs. time graph, weere there any times when the velocity was constant? Here s how you could check: for constant velocity, the acceleration is zero. Zero acceleration is constant acceleration, so we 1 2 can use eq. (1.2.3): x = x0 + v0 t + 2 a t. What does this become for a = 0? That should look like the equation of a straight line. So a straight line on a position vs. time graph means constant velocity. The steeper the slope, the faster it moves. That makes sense, since a steep slope means a larger change in position. We can go one step further: if part of a position vs. time graph is curved, the velocity isn t constant; in other words there s an acceleration! c) How about positive velocity vs. negative velocity? Well, positive velocity means that the cart is moving in the positive direction, and negative velocity means that the cart is moving in the negative direction. d) Put that together and draw the sketch below. There aren t any numbers, but it should show zero, positive, negative; large vs. small, constant vs. non -constant. velocity time 3) Are there any times when the acceleration is NOT zero? Mark those points on the curve above with arrows. If the acceleration is positive (here that means the cart is speeding up), mark it with a plus sign. If the acceleration is negative, mark it with a minus sign. Note that you can t really have abrupt changes like we re showing here. Some things to note: Velocity is the slope of a position vs. time graph Acceleration is the slope of a velocity vs. time graph

10 Graphing Motion with LabPro At your lab bench, you should see a green box labeled LabPro. This is an interface that uses various sensors to collect data and sends the data directly to the computer, where it can be analyzed in a variety of ways. You should see that the LabPro unit is connected to a rectangular blue box with a gold screen on it (the Motion Detector). The Motion Detector is mounted on a stand at one end of the ramp. The Motion Detector works on the same principle as the echolocation used by bats to hunt insects and avoid midair collisions, except the Motion Detector use sound waves, while bats likely use some complicated combination of senses. Basically, the Motion Detector sends out a sound wave, and the sound wave bounces off nearby objects, returning to the Motion Detector. The time between the sound wave being emitted and then being detected can be used to determine the position of the nearby object. In this way, the Motion Detector can create a position vs. time graph. Then, by using the slope argument we talked about earlier, the computer can create velocity vs. time and acceleration vs. time graphs as well. Procedure 1) Turn on the power to the LabPro unit by turning on the power to the power strip on the table. Log onto the computer. On the desktop is a folder called PHYS141. Open that folder, and then open the folder named Phys144. You should see an icon named Lab #1.MBL; double-click that icon to launch a data collection program called LoggerPro. You might get some initialization messages; just click Scan, then OK. 2) You should see a graph open up, with Distance on the vertical axis and Time on the horizontal axis, just like the position vs. time graphs we worked with earlier. You ll notice that the Distance axis goes from 1.5 to 1.5, but we can t actually get to less than zero since that would be the other side of the Motion Detector, which only works in one direction! Also, due to limitations on the machine, it doesn t work well for distances less than 50 cm from the detector. So make sure you limit the motion of the cart to between 50 cm from the detector and 1.5 m from the detector. 3) Position the cart approximately 70 cm from the detector. Note that the detector isn t set all the way at one end, so you need to be careful using the ruler on the track. Hold the cart fixed, and hit Enter on the keyboard. You should here the Motion Detector emitting a rapid clicking noise. The program collects data for 10 seconds; move the cart back and forth and you should see the position vs. time graph appear on the screen. 4) Now, as best you can, follow your description of how to move the cart to get the position vs. time graph you worked with earlier. It doesn t have to be perfect, but I would like to see a flat line, a steep positive-slope line, a shallow negative-slope line, and another flat line. Play around until you get something you like, and then call me over to look at it. 5) Looking at your position vs. time graph, what do you think the velocity vs. time graph will look like? You can make the computer plot velocity vs. time for you. Go to View, then Graph Options, then Axis Options, and on Vertical axis, click Velocity and hit OK. Does the velocity vs. time graph look like you d expect? Note that there may be some funny points. There are two reasons: the Motion Detector isn t perfect, and you might have noticed some funny bumps and wiggles in the position vs. time curve. So that will give some problems. Also, the slope calculation can t be perfect either. However, most of the results should seem quite reasonable to you. 6) Now, looking at your velocity vs. time graph, what do you think acceleration vs. time will look like? Again, you can make the computer plot this for you as well, following the same procedure as above. What does this graph look like? 7) Go back and remove the velocity and acceleration parts from the graph, leaving just distance vs. time.

AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

ISA HELP BOOKLET AQA SCIENCE NAME: Class:

ISA HELP BOOKLET AQA SCIENCE NAME: Class: Controlled Assessments: The ISA This assessment is worth 34 marks in total and consists of three parts: A practical investigation and 2 written test papers. It

Motion Graphs. It is said that a picture is worth a thousand words. The same can be said for a graph.

Motion Graphs It is said that a picture is worth a thousand words. The same can be said for a graph. Once you learn to read the graphs of the motion of objects, you can tell at a glance if the object in

EXPERIMENTAL ERROR AND DATA ANALYSIS

EXPERIMENTAL ERROR AND DATA ANALYSIS 1. INTRODUCTION: Laboratory experiments involve taking measurements of physical quantities. No measurement of any physical quantity is ever perfectly accurate, except

Microsoft Excel Tutorial

Microsoft Excel Tutorial by Dr. James E. Parks Department of Physics and Astronomy 401 Nielsen Physics Building The University of Tennessee Knoxville, Tennessee 37996-1200 Copyright August, 2000 by James

A Guide to Using Excel in Physics Lab

A Guide to Using Excel in Physics Lab Excel has the potential to be a very useful program that will save you lots of time. Excel is especially useful for making repetitious calculations on large data sets.

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable

0 Introduction to Data Analysis Using an Excel Spreadsheet

Experiment 0 Introduction to Data Analysis Using an Excel Spreadsheet I. Purpose The purpose of this introductory lab is to teach you a few basic things about how to use an EXCEL 2010 spreadsheet to do

2After completing this chapter you should be able to

After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time

How To Run Statistical Tests in Excel

How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting

State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

ART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D

ART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D Components Tracks An animation track is a recording of a particular type of animation; for example, rotation. Some tracks

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

At the skate park on the ramp

At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises

STB- 2. Installation and Operation Manual

STB- 2 Installation and Operation Manual Index 1 Unpacking your STB- 2 2 Installation 3 WIFI connectivity 4 Remote Control 5 Selecting Video Mode 6 Start Page 7 Watching TV / TV Guide 8 Recording & Playing

Data Acquisition And Analysis

Data Acquisition And Analysis Objective: To gain familiarity with some of the measurement tools you will use in lab this semester. To learn how to measure distance with a motion sensor and force with a

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

2-1 Position, Displacement, and Distance

2-1 Position, Displacement, and Distance In describing an object s motion, we should first talk about position where is the object? A position is a vector because it has both a magnitude and a direction:

Data representation and analysis in Excel

Page 1 Data representation and analysis in Excel Let s Get Started! This course will teach you how to analyze data and make charts in Excel so that the data may be represented in a visual way that reflects

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

1.3.1 Position, Distance and Displacement

In the previous section, you have come across many examples of motion. You have learnt that to describe the motion of an object we must know its position at different points of time. The position of an

1.2 Investigations and Experiments

Science is about figuring out cause and effect relationships. If we do something, what happens? If we make a ramp steeper, how much faster will a car roll down? This is an easy question. However, the process

Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)

Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure

AP * Statistics Review. Descriptive Statistics

AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

Augmented reality enhances learning at Manchester School of Medicine

Augmented reality enhances learning at Manchester School of Medicine Welcome to the Jisc podcast. The University of Manchester is taking a unique approach to prescription training for its medical students

13 Managing Your Class Now that we ve covered all the learning tools in Moodle, we ll look at some of the administrative functions that are necessary to keep your course and students organized. This chapter

INTRODUCTION TO ERRORS AND ERROR ANALYSIS

INTRODUCTION TO ERRORS AND ERROR ANALYSIS To many students and to the public in general, an error is something they have done wrong. However, in science, the word error means the uncertainty which accompanies

Lab 11. Simulations. The Concept

Lab 11 Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that

8. THE NORMAL DISTRIBUTION

8. THE NORMAL DISTRIBUTION The normal distribution with mean μ and variance σ 2 has the following density function: The normal distribution is sometimes called a Gaussian Distribution, after its inventor,

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Lecture - 41 Value of Information In this lecture, we look at the Value

Formulas, Functions and Charts

Formulas, Functions and Charts :: 167 8 Formulas, Functions and Charts 8.1 INTRODUCTION In this leson you can enter formula and functions and perform mathematical calcualtions. You will also be able to

LESSON 7: IMPORTING AND VECTORIZING A BITMAP IMAGE

LESSON 7: IMPORTING AND VECTORIZING A BITMAP IMAGE In this lesson we ll learn how to import a bitmap logo, transform it into a vector and perform some editing on the vector to clean it up. The concepts

1 of 7 9/5/2009 6:12 PM

1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

Hello Purr. What You ll Learn

Chapter 1 Hello Purr This chapter gets you started building apps. It presents the key elements of App Inventor the Component Designer and the Blocks Editor and leads you through the basic steps of creating

Simple Linear Regression

STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze

INTRUSION PREVENTION AND EXPERT SYSTEMS

INTRUSION PREVENTION AND EXPERT SYSTEMS By Avi Chesla avic@v-secure.com Introduction Over the past few years, the market has developed new expectations from the security industry, especially from the intrusion

Getting Started in Tinkercad By Bonnie Roskes, 3DVinci Tinkercad is a fun, easy to use, web-based 3D design application. You don t need any design experience - Tinkercad can be used by anyone. In fact,

MATH 140 Lab 4: Probability and the Standard Normal Distribution

MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes

Spreadsheets and Laboratory Data Analysis: Excel 2003 Version (Excel 2007 is only slightly different)

Spreadsheets and Laboratory Data Analysis: Excel 2003 Version (Excel 2007 is only slightly different) Spreadsheets are computer programs that allow the user to enter and manipulate numbers. They are capable

A Sales Strategy to Increase Function Bookings

A Sales Strategy to Increase Function Bookings It s Time to Start Selling Again! It s time to take on a sales oriented focus for the bowling business. Why? Most bowling centres have lost the art and the

Plots, Curve-Fitting, and Data Modeling in Microsoft Excel

Plots, Curve-Fitting, and Data Modeling in Microsoft Excel This handout offers some tips on making nice plots of data collected in your lab experiments, as well as instruction on how to use the built-in

A Quick Algebra Review

1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals

ITS Training Class Charts and PivotTables Using Excel 2007

When you have a large amount of data and you need to get summary information and graph it, the PivotTable and PivotChart tools in Microsoft Excel will be the answer. The data does not need to be in one

USER MANUAL (PRO-CURO LITE, PRO & ENT) [SUPPLIED FOR VERSION 3]

Pro-curo Software Ltd USER MANUAL (PRO-CURO LITE, PRO & ENT) [SUPPLIED FOR VERSION 3] CONTENTS Everyday use... 3 Logging on... 4 Main Screen... 5 Adding locations... 6 Working with locations... 7 Duplicate...

T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these

REPORT WRITING GUIDE

Report Writing Guide F2009 1 REPORT WRITING GUIDE Introduction The importance of good report writing and data presentation cannot be overemphasized. No matter how good an experiment, or how brilliant a

Gas Dynamics Prof. T. M. Muruganandam Department of Aerospace Engineering Indian Institute of Technology, Madras. Module No - 12 Lecture No - 25

(Refer Slide Time: 00:22) Gas Dynamics Prof. T. M. Muruganandam Department of Aerospace Engineering Indian Institute of Technology, Madras Module No - 12 Lecture No - 25 Prandtl-Meyer Function, Numerical

Herzog Keyboarding Grades 3 through 5. Overarching Essential Questions

Herzog Keyboarding Grades 3 through 5 Overarching Essential Questions How will learning to keyboard help me with my academics today and my career tomorrow? Introduction The lessons in the Herzog Keyboarding

Chapter 7: Momentum and Impulse

Chapter 7: Momentum and Impulse 1. When a baseball bat hits the ball, the impulse delivered to the ball is increased by A. follow through on the swing. B. rapidly stopping the bat after impact. C. letting

THE STATISTICAL TREATMENT OF EXPERIMENTAL DATA 1

THE STATISTICAL TREATMET OF EXPERIMETAL DATA Introduction The subject of statistical data analysis is regarded as crucial by most scientists, since error-free measurement is impossible in virtually all

Linear Equations. 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber

Linear Equations 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI- 83

Tutorial 1: The Freehand Tools

UNC Charlotte Tutorial 1: The Freehand Tools In this tutorial you ll learn how to draw and construct geometric figures using Sketchpad s freehand construction tools. You ll also learn how to undo your

Assignment 2: Animated Transitions Due: Oct 12 Mon, 11:59pm, 2015 (midnight)

1 Assignment 2: Animated Transitions Due: Oct 12 Mon, 11:59pm, 2015 (midnight) Overview One of the things that make a visualization look polished is to add animation (animated transition) between each

8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight

1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled

If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?

Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question

CSC 120: Computer Science for the Sciences (R section)

CSC 120: Computer Science for the Sciences (R section) Radford M. Neal, University of Toronto, 2015 http://www.cs.utoronto.ca/ radford/csc120/ Week 2 Typing Stuff into R Can be Good... You can learn a

DVR GUIDE Using your DVR/Multi-Room DVR 1-866-WAVE-123 wavebroadband.com Table of Contents Control Live TV... 4 Playback Controls... 5 Remote Control Arrow Buttons... 5 Status Bar... 5 Pause... 6 Rewind...

The Bullet-Block Mystery

LivePhoto IVV Physics Activity 1 Name: Date: 1. Introduction The Bullet-Block Mystery Suppose a vertically mounted 22 Gauge rifle fires a bullet upwards into a block of wood (shown in Fig. 1a). If the

Correcting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners

Correcting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners Background The lateral response artifact (LRA) in radiochromic film images from flatbed scanners was first pointed

EDUH 1017 - SPORTS MECHANICS

4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH 1017 - SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use

PERSONAL LEARNING PLAN- STUDENT GUIDE

PERSONAL LEARNING PLAN- STUDENT GUIDE TABLE OF CONTENTS SECTION 1: GETTING STARTED WITH PERSONAL LEARNING STEP 1: REGISTERING FOR CONNECT P.2 STEP 2: LOCATING AND ACCESSING YOUR PERSONAL LEARNING ASSIGNMENT

(I) s(t) = s 0 v 0 (t t 0 ) + 1 2 a (t t 0) 2 (II). t 2 = t 0 + 2 v 0. At the time. E kin = 1 2 m v2 = 1 2 m (a (t t 0) v 0 ) 2

Mechanics Translational motions of a mass point One-dimensional motions on the linear air track LD Physics Leaflets P1.3.3.8 Uniformly accelerated motion with reversal of direction Recording and evaluating

Drawing a histogram using Excel

Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

6th Grade Lesson Plan: Probably Probability

6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use

Exercise 1: How to Record and Present Your Data Graphically Using Excel Dr. Chris Paradise, edited by Steven J. Price

Biology 1 Exercise 1: How to Record and Present Your Data Graphically Using Excel Dr. Chris Paradise, edited by Steven J. Price Introduction In this world of high technology and information overload scientists

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

Mailing lists process, creation and approval. Mailing lists process, creation and approval

Mailing lists process, creation and approval Steps to creating your mailing list 1. Establish whether there is a generic mailing list that can be used (i.e. a list a sector or team use for every mailing)

CREATIVE S SKETCHBOOK

Session Plan for Creative Directors CREATIVE S SKETCHBOOK THIS SKETCHBOOK BELONGS TO: @OfficialSYP 1 WELCOME YOUNG CREATIVE If you re reading this, it means you ve accepted the We-CTV challenge and are

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

Encoded Phased Array Bridge Pin Inspection

Encoded Phased Array Bridge Pin Inspection James S. Doyle Baker Testing Services, Inc. 22 Reservoir Park Dr. Rockland, MA 02370 (781) 871-4458; fax (781) 871-0123; e-mail jdoyle@bakertesting.com Product

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

Microsoft Word defaults to left justified (aligned) paragraphs. This means that new lines automatically line up with the left margin.

Microsoft Word Part 2 Office 2007 Microsoft Word 2007 Part 2 Alignment Microsoft Word defaults to left justified (aligned) paragraphs. This means that new lines automatically line up with the left margin.

Protocol for Leaf Image Analysis Surface Area

Protocol for Leaf Image Analysis Surface Area By Kitren Glozer Associate Project Scientist Dept. of Plant Sciences, University of California, Davis Contact information: Dept. of Plant Sciences, University

FREQUENCY RESPONSE OF AN AUDIO AMPLIFIER

2014 Amplifier - 1 FREQUENCY RESPONSE OF AN AUDIO AMPLIFIER The objectives of this experiment are: To understand the concept of HI-FI audio equipment To generate a frequency response curve for an audio

Using Excel for descriptive statistics

FACT SHEET Using Excel for descriptive statistics Introduction Biologists no longer routinely plot graphs by hand or rely on calculators to carry out difficult and tedious statistical calculations. These

Waveforms and the Speed of Sound

Laboratory 3 Seth M. Foreman February 24, 2015 Waveforms and the Speed of Sound 1 Objectives The objectives of this excercise are: to measure the speed of sound in air to record and analyze waveforms of

Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas:

Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas: Developing strategies for determining the zeroes of quadratic functions Making connections between the meaning

Physics 40 Lab 1: Tests of Newton s Second Law

Physics 40 Lab 1: Tests of Newton s Second Law January 28 th, 2008, Section 2 Lynda Williams Lab Partners: Madonna, Hilary Clinton & Angie Jolie Abstract Our primary objective was to test the validity

Analytical Test Method Validation Report Template

Analytical Test Method Validation Report Template 1. Purpose The purpose of this Validation Summary Report is to summarize the finding of the validation of test method Determination of, following Validation

Understanding barcodes. www.brightpearl.com. White paper

White paper Understanding barcodes. Barcodes turn manual product look-ups into an automated process that s efficient and virtually errorfree. In this white paper, you ll learn what they are, when to use

Science Notebooks in the Classroom. Notebook Criteria

presentapresents Presents Science Notebooks in the Classroom kdkrifr Notebook Criteria This document was developed by Bay Area Schools for Excellence in Education (BASEE) a local systemic change project

The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

Why are thesis proposals necessary? The Purpose of having thesis proposals is threefold. First, it is to ensure that you are prepared to undertake the

Guidelines for writing a successful MSc Thesis Proposal Prof. Dr. Afaf El-Ansary Biochemistry department King Saud University Why are thesis proposals necessary? The Purpose of having thesis proposals

Building Qualtrics Surveys for EFS & ALC Course Evaluations: Step by Step Instructions

Building Qualtrics Surveys for EFS & ALC Course Evaluations: Step by Step Instructions Jennifer DeSantis August 28, 2013 A relatively quick guide with detailed explanations of each step. It s recommended

Polynomial Degree and Finite Differences

CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

MAIL MERGE MADE EASY A STEP-BY-STEP GUIDE FOR LABELS OR EMAIL MERGES

MAIL MERGE MADE EASY A STEP-BY-STEP GUIDE FOR LABELS OR EMAIL MERGES WHY MAIL MERGE? Labels: Mail merge in Office lets you convert your contact list data into a sheet of mailing labels, with complete control

Using Microsoft Access

Using Microsoft Access Relational Queries Creating a query can be a little different when there is more than one table involved. First of all, if you want to create a query that makes use of more than

Interactive Logging with FlukeView Forms

FlukeView Forms Technical Note Fluke developed an Event Logging function allowing the Fluke 89-IV and the Fluke 189 models to profile the behavior of a signal over time without requiring a great deal of

Review Assessment: Lec 02 Quiz

COURSES > PHYSICS GUEST SITE > CONTROL PANEL > 1ST SEM. QUIZZES > REVIEW ASSESSMENT: LEC 02 QUIZ Review Assessment: Lec 02 Quiz Name: Status : Score: Instructions: Lec 02 Quiz Completed 20 out of 100 points

Lecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.8-4.12, second half of section 4.7

Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.8-4.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal

MSc in Autonomous Robotics Engineering University of York

MSc in Autonomous Robotics Engineering University of York Practical Robotics Module 2015 A Mobile Robot Navigation System: Labs 1a, 1b, 2a, 2b. Associated lectures: Lecture 1 and lecture 2, given by Nick

The electrical field produces a force that acts

Physics Equipotential Lines and Electric Fields Plotting the Electric Field MATERIALS AND RESOURCES ABOUT THIS LESSON EACH GROUP 5 alligator clip leads 2 batteries, 9 V 2 binder clips, large computer LabQuest

Appendix C. Vernier Tutorial

C-1. Vernier Tutorial Introduction: In this lab course, you will collect, analyze and interpret data. The purpose of this tutorial is to teach you how to use the Vernier System to collect and transfer

2013 MBA Jump Start Program

2013 MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Algebra Review Calculus Permutations and Combinations [Online Appendix: Basic Mathematical Concepts] 2 1 Equation of