Develop a 4 page-500 word précis on Chapter 7 “How to Monitor & Control a TPM Project” of the Wysocki 7th Ed. text.”

Develop a 4 page-500 word précis on Chapter 7 “How to Monitor & Control a TPM Project” of the Wysocki 7th Ed. text.”

Summary of ‘How to Monitor and Control a TPM Project’ … Read More...
Lab Description: Follow the instructions in the lab tasks below to behaviorially create and simulate a flip-flop. Afterwards, you will create a register and Arithmetic Logic Unit (ALU). Refer to Module 7 from the Digilent Real Digital website for more information about ALUs. These two components are the main components required to create an accumulator datapath. This accumulator datapath will act like a simple processor; the ALU will execute simple arithmetic/logic operations and each result will be stored in the register. In an accumulator, the value of the register will be upedated with each operation; the register is used as an input to the ALU and the newly computed result of the operation will be stored back into the register. You will create and implement this accumulator datapath in the last task of this lab. However, you will need to add an additional component to enable it to clearly operate on the FPGA board. You will create and use a clock divider to create a slower version of the FPGA board’s clock when you implement the accumulator datapath on the FPGA board. Refer to Module 10 from the Digilent Real Digital website for more information about clock dividers. Lab Tasks: 1. Create a behavioral VHDL module for a Rising-Edge Triggered (RET) D-Flip-Flop (DFF): a. In your design, use inputs “D” (data), “CLK” (the clock), “RST” (an asynchronous reset), “SET” (a synchronous set or preset signal), “CE” (clock enable), and output “Q” b. Create a VHDL test bench and simulate the flip-flop. Be sure to show the following behaviors with your simulation: i. The output “Q” sampling a ‘0’ from the input “D” ii. The output “Q” sampling a ‘1’ from the input “D” iii. The correct operation of the asynchronous reset iv. The correct operation of the synchronous preset v. The correct operation of the clock enable c. Include a screenshot of your simulation on the lab’s cover sheet. Label each of these behaviors on the waveform (it is ok to print out your cover sheet and write each behavior on the waveform). 2. Create a behavioral VHDL module for a 4-bit Arithmetic Logic Unit (ALU): a. I suggest you refer to Module 7 from the Digilent Real Digital website (in particular, the sections about ALU circuits and behavioral VHDL ALU descriptions). This 4-bit ALU will calculate arithmetic and logical expressions on two 4-bit numbers. Use behavioral expressions for the arithmetic and logic expressions (do not use port map statements to create a structural design using your ripple-carry adder from lab 3). Assume that the select input (or opcode) is 2-bits and is defined as shown in the table below: Opcode Function 00 A 01 A plus 1 10 A plus B 11 A and B b. Create a VHDL test bench to test your ALU. Use two input signal (the 4-bit values for A and B) combinations to test each operation of the ALU. Simulate your design and verify your output. Include a screenshot of your simulation on the lab’s cover sheet. 3. Create an accumulator datapath: a. First, create a 4-bit register. This is very similar to your flip-flop design from lab task 1. Ensure that your 4-bit register has inputs “D” (data), “CLK” (the clock), and “RST” (an asynchronous reset), and an output “Q”. Create a test bench and ensure that your 4-bit register operates correctly. b. Next, create a design module for the accumulator datapath and import your 4-bit register, 4-bit ALU, and seven-sgement display decoder (from lab 2) as components to this system. Connect your register, ALU, and seven-segment display decoder as follows: i. Connect the output of your ALU to the “D” input of your register ii. Connect the “Q” output of your register to both the “A” input of your ALU and the input of your seven-segement display iii. You should be left with four overall inputs: the “B” input of your ALU, the opcode input of your ALU, the CLK, and RST iv. You should be left with one overall output: the seven-segment display output c. Create a test bench to simulate the behavior of your accumulator datapath. In your test bench, simulate a few clock cycles to verify the correct operation of your system. d. Before implementing this system on the FPGA board, create and add one additional component to your system. Create and add a clock divider to this system; the input will be the board’s clock and the output will be a slower version of the clock to use for the register. Design your clock divider to slow the clock frequency to 1 Hz (1 clock cycle per second). Note that the clock on the lab FPGA board (Spartan 3) has a frequency of 50 MHz. If you purchased your board, the FPGA Basys 3 or Nexys 4 DDR FPGA board has a frequency of 100 MHz. I highly recommend taking a look at “Binary counters in VHDL” from Module 10 from the Digilent Real Digital website for information about clock dividers. e. Now, implement this system on the FPGA board. Connect the data input to four switches, connect the ALU opcode inputs to two buttons, the RST signal to one button, the CLK signal to the board’s clock, and the seven-segment display output to the seven-segment display. f. Ask the instructor to check your design, simulation waveforms, and FPGA board implementation of your circuit

Lab Description: Follow the instructions in the lab tasks below to behaviorially create and simulate a flip-flop. Afterwards, you will create a register and Arithmetic Logic Unit (ALU). Refer to Module 7 from the Digilent Real Digital website for more information about ALUs. These two components are the main components required to create an accumulator datapath. This accumulator datapath will act like a simple processor; the ALU will execute simple arithmetic/logic operations and each result will be stored in the register. In an accumulator, the value of the register will be upedated with each operation; the register is used as an input to the ALU and the newly computed result of the operation will be stored back into the register. You will create and implement this accumulator datapath in the last task of this lab. However, you will need to add an additional component to enable it to clearly operate on the FPGA board. You will create and use a clock divider to create a slower version of the FPGA board’s clock when you implement the accumulator datapath on the FPGA board. Refer to Module 10 from the Digilent Real Digital website for more information about clock dividers. Lab Tasks: 1. Create a behavioral VHDL module for a Rising-Edge Triggered (RET) D-Flip-Flop (DFF): a. In your design, use inputs “D” (data), “CLK” (the clock), “RST” (an asynchronous reset), “SET” (a synchronous set or preset signal), “CE” (clock enable), and output “Q” b. Create a VHDL test bench and simulate the flip-flop. Be sure to show the following behaviors with your simulation: i. The output “Q” sampling a ‘0’ from the input “D” ii. The output “Q” sampling a ‘1’ from the input “D” iii. The correct operation of the asynchronous reset iv. The correct operation of the synchronous preset v. The correct operation of the clock enable c. Include a screenshot of your simulation on the lab’s cover sheet. Label each of these behaviors on the waveform (it is ok to print out your cover sheet and write each behavior on the waveform). 2. Create a behavioral VHDL module for a 4-bit Arithmetic Logic Unit (ALU): a. I suggest you refer to Module 7 from the Digilent Real Digital website (in particular, the sections about ALU circuits and behavioral VHDL ALU descriptions). This 4-bit ALU will calculate arithmetic and logical expressions on two 4-bit numbers. Use behavioral expressions for the arithmetic and logic expressions (do not use port map statements to create a structural design using your ripple-carry adder from lab 3). Assume that the select input (or opcode) is 2-bits and is defined as shown in the table below: Opcode Function 00 A 01 A plus 1 10 A plus B 11 A and B b. Create a VHDL test bench to test your ALU. Use two input signal (the 4-bit values for A and B) combinations to test each operation of the ALU. Simulate your design and verify your output. Include a screenshot of your simulation on the lab’s cover sheet. 3. Create an accumulator datapath: a. First, create a 4-bit register. This is very similar to your flip-flop design from lab task 1. Ensure that your 4-bit register has inputs “D” (data), “CLK” (the clock), and “RST” (an asynchronous reset), and an output “Q”. Create a test bench and ensure that your 4-bit register operates correctly. b. Next, create a design module for the accumulator datapath and import your 4-bit register, 4-bit ALU, and seven-sgement display decoder (from lab 2) as components to this system. Connect your register, ALU, and seven-segment display decoder as follows: i. Connect the output of your ALU to the “D” input of your register ii. Connect the “Q” output of your register to both the “A” input of your ALU and the input of your seven-segement display iii. You should be left with four overall inputs: the “B” input of your ALU, the opcode input of your ALU, the CLK, and RST iv. You should be left with one overall output: the seven-segment display output c. Create a test bench to simulate the behavior of your accumulator datapath. In your test bench, simulate a few clock cycles to verify the correct operation of your system. d. Before implementing this system on the FPGA board, create and add one additional component to your system. Create and add a clock divider to this system; the input will be the board’s clock and the output will be a slower version of the clock to use for the register. Design your clock divider to slow the clock frequency to 1 Hz (1 clock cycle per second). Note that the clock on the lab FPGA board (Spartan 3) has a frequency of 50 MHz. If you purchased your board, the FPGA Basys 3 or Nexys 4 DDR FPGA board has a frequency of 100 MHz. I highly recommend taking a look at “Binary counters in VHDL” from Module 10 from the Digilent Real Digital website for information about clock dividers. e. Now, implement this system on the FPGA board. Connect the data input to four switches, connect the ALU opcode inputs to two buttons, the RST signal to one button, the CLK signal to the board’s clock, and the seven-segment display output to the seven-segment display. f. Ask the instructor to check your design, simulation waveforms, and FPGA board implementation of your circuit

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Assignment 2 – Summary/Response – 150 points For your second essay assignment, you will summarize and then respond/react to an article from the book They Say I Say. Choose either Don’t Blame the Eater (462), Should Everyone go to College? (208), I Had A Nice Time With You Tonight. On The App (393) or What Are You Buying When You Buy Organic? (428). Steps in writing this essay: 1. Give the essay a title that lets the reader know a little about the essay. Think about what your main point is and try to show that idea in your title. Center the title. Make it the same size and font as the rest of your essay. 2. For your first paragraph, write a summary of the article. This will be your introduction. The first sentence of your essay should include the author’s name, the title of the article, and the main point of the article. 3. At the end of the summary, add a thesis stating your overall reaction to the article. 4. For the body, each paragraph needs a topic sentence stating one of your main points that support your thesis. Your supporting sentences in each paragraph should provide specific reasons and examples of why you agree or disagree with the author. Occasionally refer to the author’s ideas since your essay is a response to his or her ideas. When referring to the author’s ideas, use both paraphrases and quotes. 5. For your conclusion, restate your position and your reasons for taking that position. The following sentences should become more general so that the reader can see the “bigger picture” of why taking your position is important. 6. Add a Reference page with the article cited in APA format. Formatting: • use APA formatting for in-text citations and the Reference page • double space • one-inch margins • use Times New Roman, Cambria, or Calibri • use 12-point font • the essay needs to be between 1,000 to 1,500 words, not including the Reference page Tentative schedule: • Thursday, Sept. 24 – Writing Workshop • Tuesday, Sept. 29 – Autobiography Review/ Peer Review (Bring TWO copies of your essay to class) • Thursday, Oct. 1 – Timed Autobiography • Tuesday, Oct. 6 – Conferences with Joshua • Sunday, Oct. 11 – Instructor draft due at 11:59 p.m. on Bb under Assignments   Scoring Rubric for Assignment 2: Summary/Response Essay Name:____________________________ Summary of article _____ /15 – Is the summary objective and comprehensive? – Does it include the main points and leave out minor details? – Does it include the author and title of article? Thesis statement _____ /10 – Does the thesis capture the main point/purpose of the entire paper? Response _____ /40 – Does the student take a clear position regarding the article? – Is the argument logical, well developed, and convincing? – Is there a personal anecdote that supports the student’s thesis? – Does the student explain how the anecdote relates to the article and to the thesis? – Is the anecdote developed? References to article _____ /35 – Is the article referenced multiple times to link the student’s argument and anecdote to the article? – Do the references to the article support the student’s argument or are they random? Organization _____ /15 – Does each paragraph flow well to the next? – Are transitional phrases used? – Does the organization of the paragraphs make sense? – Does the organization of sentences within each paragraph make sense? – Do paragraphs have a topic sentence? Presentation _____ /25 – Is the essay free of grammatical, mechanical, and spelling errors? – Is the idea in each sentence clear? – Are there a variety of sentence structures and varied, sophisticated vocabulary? – Does the student follow formatting guidelines? Citations _____ /10 – Are in-text citations used for paraphrases and quotes? – Are quotes used properly? – Is there a Reference page that is formatted correctly? Total points: _____ /150

Assignment 2 – Summary/Response – 150 points For your second essay assignment, you will summarize and then respond/react to an article from the book They Say I Say. Choose either Don’t Blame the Eater (462), Should Everyone go to College? (208), I Had A Nice Time With You Tonight. On The App (393) or What Are You Buying When You Buy Organic? (428). Steps in writing this essay: 1. Give the essay a title that lets the reader know a little about the essay. Think about what your main point is and try to show that idea in your title. Center the title. Make it the same size and font as the rest of your essay. 2. For your first paragraph, write a summary of the article. This will be your introduction. The first sentence of your essay should include the author’s name, the title of the article, and the main point of the article. 3. At the end of the summary, add a thesis stating your overall reaction to the article. 4. For the body, each paragraph needs a topic sentence stating one of your main points that support your thesis. Your supporting sentences in each paragraph should provide specific reasons and examples of why you agree or disagree with the author. Occasionally refer to the author’s ideas since your essay is a response to his or her ideas. When referring to the author’s ideas, use both paraphrases and quotes. 5. For your conclusion, restate your position and your reasons for taking that position. The following sentences should become more general so that the reader can see the “bigger picture” of why taking your position is important. 6. Add a Reference page with the article cited in APA format. Formatting: • use APA formatting for in-text citations and the Reference page • double space • one-inch margins • use Times New Roman, Cambria, or Calibri • use 12-point font • the essay needs to be between 1,000 to 1,500 words, not including the Reference page Tentative schedule: • Thursday, Sept. 24 – Writing Workshop • Tuesday, Sept. 29 – Autobiography Review/ Peer Review (Bring TWO copies of your essay to class) • Thursday, Oct. 1 – Timed Autobiography • Tuesday, Oct. 6 – Conferences with Joshua • Sunday, Oct. 11 – Instructor draft due at 11:59 p.m. on Bb under Assignments   Scoring Rubric for Assignment 2: Summary/Response Essay Name:____________________________ Summary of article _____ /15 – Is the summary objective and comprehensive? – Does it include the main points and leave out minor details? – Does it include the author and title of article? Thesis statement _____ /10 – Does the thesis capture the main point/purpose of the entire paper? Response _____ /40 – Does the student take a clear position regarding the article? – Is the argument logical, well developed, and convincing? – Is there a personal anecdote that supports the student’s thesis? – Does the student explain how the anecdote relates to the article and to the thesis? – Is the anecdote developed? References to article _____ /35 – Is the article referenced multiple times to link the student’s argument and anecdote to the article? – Do the references to the article support the student’s argument or are they random? Organization _____ /15 – Does each paragraph flow well to the next? – Are transitional phrases used? – Does the organization of the paragraphs make sense? – Does the organization of sentences within each paragraph make sense? – Do paragraphs have a topic sentence? Presentation _____ /25 – Is the essay free of grammatical, mechanical, and spelling errors? – Is the idea in each sentence clear? – Are there a variety of sentence structures and varied, sophisticated vocabulary? – Does the student follow formatting guidelines? Citations _____ /10 – Are in-text citations used for paraphrases and quotes? – Are quotes used properly? – Is there a Reference page that is formatted correctly? Total points: _____ /150

. Name a big idea (major concept) in your subject area and write a one paragraph rationale for why students should learn it.

. Name a big idea (major concept) in your subject area and write a one paragraph rationale for why students should learn it.

Mathematics: mathematics is interesting and enjoyable. People like its test, … Read More...
Morgan Extra Pages Graphing with Excel to be carried out in a computer lab, 3rd floor Calloway Hall or elsewhere The Excel spreadsheet consists of vertical columns and horizontal rows; a column and row intersect at a cell. A cell can contain data for use in calculations of all sorts. The Name Box shows the currently selected cell (Fig. 1). In the Excel 2007 and 2010 versions the drop-down menus familiar in most software screens have been replaced by tabs with horizontally-arranged command buttons of various categories (Fig. 2) ___________________________________________________________________ Open Excel, click on the Microsoft circle, upper left, and Save As your surname. xlsx on the desktop. Before leaving the lab e-mail the file to yourself and/or save to a flash drive. Also e-mail it to your instructor. Figure 1. Parts of an Excel spreadsheet. Name Box Figure 2. Tabs. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 1: BASIC OPERATIONS Click Save often as you work. 1. Type the heading “Edge Length” in Cell A1 and double click the crack between the A and B column heading for automatic widening of column A. Similarly, write headings for columns B and C and enter numbers in Cells A2 and A3 as in Fig. 3. Highlight Cells A2 and A3 by dragging the cursor (chunky plus-shape) over the two of them and letting go. 2. Note that there are three types of cursor crosses: chunky for selecting, barbed for moving entries or blocks of entries from cell to cell, and tiny (appearing only at the little square in the lower-right corner of a cell). Obtain a tiny arrow for Cell A3 and perform a plus-drag down Column A until the cells are filled up to 40 (in Cell A8). Note that the two highlighted cells set both the starting value of the fill and the intervals. 3. Click on Cell B2 and enter a formula for face area of a cube as follows: type =, click on Cell A2, type ^2, and press Enter (note the formula bar in Fig. 4). 4. Enter the formula for cube volume in Cell C2 (same procedure, but “=, click on A2, ^3, Enter”). 5. Highlight Cells B2 and C2; plus-drag down to Row 8 (Fig. 5). Do the numbers look correct? Click on some cells in the newly filled area and notice how Excel steps the row designations as it moves down the column (it can do it for horizontal plusdrags along rows also). This is the major programming development that has led to the popularity of spreadsheets. Figure 3. Entries. Figure 4. A formula. Figure 5. Plus-dragging formulas. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 6. Now let’s graph the Face Area versus Edge Length: select Cells A1 through B8, choose the Insert tab, and click the Scatter drop-down menu and select “Scatter with only Markers” (Fig. 6). 7. Move the graph (Excel calls it a “chart”) that appears up alongside your number table and dress it up as follows: a. Note that some Chart Layouts have appeared above. Click Layout 1 and alter each title to read Face Area for the vertical axis, Edge Length for the horizontal and Face Area vs. Edge Length for the Graph Title. b. Activate the Excel Least squares routine, called “fitting a trendline” in the program: right click any of the data markers and click Add Trendline. Choose Power and also check “Display equation on chart” and “Display R-squared value on chart.” Fig. 7 shows what the graph will look like at this point. c. The titles are explicit, so the legend is unnecessary. Click on it and press the delete button to remove it. Figure 6. Creating a scatter graph. Figure 7. A graph with a fitted curve. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 8. Now let’s overlay the Volume vs. Edge Length curve onto the same graph (optional for 203L/205L): Make a copy of your graph by clicking on the outer white area, clicking ctrl-c (or right click, copy), and pasting the copy somewhere else (ctrl-v). If you wish, delete the trendline as in Fig. 8. a. Right click on the outer white space, choose Select Data and click the Add button. b. You can type in the cell ranges by hand in the dialog box that comes up, but it is easier to click the red, white, and blue button on the right of each space and highlight what you want to go in. Click the red, white, and blue of the bar that has appeared, and you will bounce back to the Add dialog box. Use the Edge Length column for the x’s and Volume for the y’s. c. Right-click on any volume data point and choose Format Data Series. Clicking Secondary Axis will place its scale on the right of the graph as in Fig. 8. d. Dress up your graph with two axis titles (Layout-Labels-Axis Titles), etc. Figure 8. Adding a second curve and y-axis to the graph Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2: INTERPRETING A LINEAR GRAPH Introduction: Many experiments are repeated a number of times with one of the parameters involved varied from run to run. Often the goal is to measure the rate of change of a dependent variable, rather than a particular value. If the dependent variable can be expressed as a linear function of the independent parameter, then the slope and yintercept of an appropriate graph will give the rate of change and a particular value, respectively. An example of such an experiment in PHYS.203L/205L is the first part of Lab 20, in which weights are added to the bottom of a suspended spring (Figure 9). This experiment shows that a spring exerts a force Fs proportional to the distance stretched y = (y-yo), a relationship known as Hooke’s Law: Fs = – k(y – yo) (Eq. 1) where k is called the Hooke’s Law constant. The minus sign shows that the spring opposes any push or pull on it. In Lab 20 Fs is equal to (- Mg) and y is given by the reading on a meter stick. Masses were added to the bottom of the spring in 50-g increments giving weights in newtons of 0.49, 0.98, etc. The weight pan was used as the pointer for reading y and had a mass of 50 g, so yo could not be directly measured. For convenient graphing Equation 1 can be rewritten: -(Mg) = – ky + kyo Or (Mg) = ky – kyo (Eq. 1′) Procedure 1. On your spreadsheet note the tabs at the bottom left and double-click Sheet1. Type in “Basics,” and then click the Sheet2 tab to bring up a fresh worksheet. Change the sheet name to “Linear Fit” and fill in data as in this table. Hooke’s Law Experiment y (m) -Fs = Mg (N) 0.337 0.49 0.388 0.98 0.446 1.47 0.498 1.96 0.550 2.45 2. Highlight the cells with the numbers, and graph (Mg) versus y as in Steps 6 and 7 of the Basics section. Your Trendline this time will be Linear of course. If you are having trouble remembering what’s versus what, “y” looks like “v”, so what comes before the “v” of “versus” goes on the y (vertical) axis. Yes, this graph is confusing: the horizontal (“x”) axis is distance y, and the “y” axis is something else. 3. Click on the Equation/R2 box on the graph and highlight just the slope, that is, only the number that comes before the “x.” Copy it (control-c is a fast way to Figure 9. A spring with a weight stretching it Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com do it) and paste it (control-v) into an empty cell. Do likewise for the intercept (including the minus sign). SAVE YOUR FILE! 5. The next steps use the standard procedure for obtaining information from linear data. Write the general equation for a straight line immediately below a hand-written copy of Equation 1′ then circle matching items: (Mg) = k y + (- k yo) (Eq. 1′) y = m x + b Note the parentheses around the intercept term of Equation 1′ to emphasize that the minus sign is part of it. Equating above and below, you can create two useful new equations: slope m = k (Eq. 2) y-intercept b = -kyo (Eq. 3) 6. Solve Equation 2 for k, that is, rewrite left to right. Then substitute the value for slope m from your graph, and you have an experimental value for the Hooke’s Law constant k. Next solve Equation 3 for yo, substitute the value for intercept b from your graph and the value of k that you just found, and calculate yo. 7. Examine your linear graph for clues to finding the units of the slope and the yintercept. Use these units to find the units of k and yo. 8. Present your values of k and yo with their units neatly at the bottom of your spreadsheet. 9. R2 in Excel, like r in our lab manual and Corr. in the LoggerPro software, is a measure of how well the calculated line matches the data points. 1.00 would indicate a perfect match. State how good a match you think was made in this case? 10. Do the Homework, Further Exercises on Interpreting Linear Graphs, on the following pages. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com Eq.1 M m f M a g               , (Eq.2) M slope m g       (Eq.3) M b f        Morgan Extra Pages Homework: Graph Interpretation Exercises EXAMPLE WITH COMPLETE SOLUTION In PHYS.203L and 205L we do Lab 9 Newton’s Second Law on Atwood’s Machine using a photogate sensor (Fig. 1). The Atwood’s apparatus can slow the rate of fall enough to be measured even with primitive timing devices. In our experiment LoggerPro software automatically collects and analyzes the data giving reliable measurements of g, the acceleration of gravity. The equation governing motion for Atwood’s Machine can be written: where a is the acceleration of the masses and string, g is the acceleration of gravity, M is the total mass at both ends of the string, m is the difference between the masses, and f is the frictional force at the hub of the pulley wheel. In this exercise you are given a graph of a vs. m obtained in this experiment with the values of M and the slope and intercept (Fig. 2). The goal is to extract values for acceleration of gravity g and frictional force f from this information. To analyze the graph we write y = mx + b, the general equation for a straight line, directly under Equation 1 and match up the various parameters: Equating above and below, you can create two new equations: and y m x b M m f M a g                Figure 1. The Atwood’s Machine setup (from the LoggerPro handout). Figure 2. Graph of acceleration versus mass difference; data from a Physics I experiment. Atwood’s Machine M = 0.400 kg a = 24.4 m – 0.018 R2 = 0.998 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.000 0.010 0.020 0.030 0.040 0.050 0.060  m (kg) a (m/s2) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 2 2 9.76 / 0.400 24.4 /( ) m s kg m kg s g Mm      To handle Equation 2 it pays to consider what the units of the slope are. A slope is “the rise over the run,“ so its units must be the units of the vertical axis divided by those of the horizontal axis. In this case: Now let’s solve Equation 2 for g and substitute the values of total mass M and of the slope m from the graph: Using 9.80 m/s2 as the Baltimore accepted value for g, we can calculate the percent error: A similar process with Equation 3 leads to a value for f, the frictional force at the hub of the pulley wheel. Note that the units of intercept b are simply whatever the vertical axis units are, m/s2 in this case. Solving Equation 3 for f: EXERCISE 1 The Picket Fence experiment makes use of LoggerPro software to calculate velocities at regular time intervals as the striped plate passes through the photogate (Fig. 3). The theoretical equation is v = vi + at (Eq. 4) where vi = 0 (the fence is dropped from rest) and a = g. a. Write Equation 4 with y = mx + b under it and circle matching factors as in the Example. b. What is the experimental value of the acceleration of gravity? What is its percent error from the accepted value for Baltimore, 9.80 m/s2? c. Does the value of the y-intercept make sense? d. How well did the straight Trendline match the data? 2 / 2 kg s m kg m s   0.4% 100 9.80 9.76 9.80 100 . . . %        Acc Exp Acc Error kg m s mN kg m s f Mb 7.2 10 / 7.2 0.400 ( 0.018 / ) 3 2 2           Figure 3. Graph of speed versus time as calculated by LoggerPro as a picket fence falls freely through a photogate. Picket Fence Drop y = 9.8224x + 0.0007 R2 = 0.9997 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 t (s) v (m/s) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2 This is an electrical example from PHYS.204L/206L, potential difference, V, versus current, I (Fig. 4). The theoretical equation is V = IR (Eq. 5) and is known as “Ohm’s Law.” The unit symbols stand for volts, V, and Amperes, A. The factor R stands for resistance and is measured in units of ohms, symbol  (capital omega). The definition of the ohm is: V (Eq. 6) By coincidence the letter symbols for potential (a quantity ) and volts (its unit) are identical. Thus “voltage” has become the laboratory slang name for potential. a. Rearrange the Ohm’s Law equation to match y = mx + b.. b. What is the experimental resistance? c. Comment on the experimental intercept: is its value reasonable? EXERCISE 3 This graph (Fig. 5) also follows Ohm’s Law, but solved for current I. For this graph the experimenter held potential difference V constant at 15.0V and measured the current for resistances of 100, 50, 40, and 30  Solve Ohm’s Law for I and you will see that 1/R is the logical variable to use on the x axis. For units, someone once jokingly referred to a “reciprocal ohm” as a “mho,” and the name stuck. a. Rearrange Equation 5 solved for I to match y = mx + b. b. What is the experimental potential difference? c. Calculate the percent difference from the 15.0 V that the experimenter set on the power supply (the instrument used for such experiments). d. Comment on the experimental intercept: is its value reasonable? Figure 4. Graph of potential difference versus current; data from a Physics II experiment. The theoretical equation, V = IR, is known as “Ohm’s Law.” Ohm’s Law y = 0.628x – 0.0275 R2 = 0.9933 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Current, I (A) Potential difference, V (V) Figure 5. Another application of Ohm’s Law: a graph of current versus the inverse of resistance, from a different electric circuit experiment. Current versus (1/Resistance) y = 14.727x – 0.2214 R2 = 0.9938 0 100 200 300 400 500 600 5 10 15 20 25 30 35 R-1 (millimhos) I (milliamperes) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 4 The Atwood’s Machine experiment (see the solved example above) can be done in another way: keep mass difference m the same and vary the total mass M (Fig. 6). a. Rewrite Equation 1 and factor out (1/M). b. Equate the coefficient of (1/M) with the experimental slope and solve for acceleration of gravity g. c. Substitute the values for slope, mass difference, and frictional force and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? EXERCISE 5 In the previous two exercises the reciprocal of a variable was used to make the graph come out linear. In this one the trick will be to use the square root of a variable (Fig. 7). In PHYS.203L and 205L Lab 19 The Pendulum the theoretical equation is where the period T is the time per cycle, L is the length of the string, and g is the acceleration of gravity. a. Rewrite Equation 7 with the square root of L factored out and placed at the end. b. Equate the coefficient of √L with the experimental slope and solve for acceleration of gravity g. c. Substitute the value for slope and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? 2 (Eq . 7) g T   L Figure 6. Graph of acceleration versus the reciprocal of total mass; data from a another Physics I experiment. Atwood’s Machine m = 0.020 kg f = 7.2 mN y = 0.1964x – 0.0735 R2 = 0.995 0.400 0.600 0.800 1.000 2.000 2.500 3.000 3.500 4.000 4.500 5.000 1/M (1/kg) a (m/s2) Effect of Pendulum Length on Period y = 2.0523x – 0.0331 R2 = 0.999 0.400 0.800 1.200 1.600 2.000 2.400 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 L1/2 (m1/2) T (s) Figure 7. Graph of period T versus the square root of pendulum length; data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 6 In Exercise 5 another approach would have been to square both sides of Equation 7 and plot T2 versus L. Lab 20 directs us to use that alternative. It involves another case of periodic or harmonic motion with a similar, but more complicated, equation for the period: where T is the period of the bobbing (Fig. 8), M is the suspended mass, ms is the mass of the spring, k is a measure of stiffness called the spring constant, and C is a dimensionless factor showing how much of the spring mass is effectively bobbing. a. Square both sides of Equation 8 and rearrange it to match y = mx + b. b. Write y = mx + b under your rearranged equation and circle matching factors as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating k and the second for finding C from the data of Fig. 9. d. A theoretical analysis has shown that for most springs C = 1/3. Find the percent error from that value. e. Derive the units of the slope and intercept; show that the units of k come out as N/m and that C is dimensionless. 2 (Eq . 8) k T M Cm s    Figure 8. In Lab 20 mass M is suspended from a spring which is set to bobbing up and down, a good approximation to simple harmonic motion (SHM), described by Equation 8. Lab 20: SHM of a Spring Mass of the spring, ms = 25.1 g y = 3.0185x + 0.0197 R2 = 0.9965 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 0 0.05 0.1 0.15 0.2 0.25 0.3 M (kg) T 2 2 Figure 9. Graph of the square of the period T2 versus suspended mass M data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 7 This last exercise deals with an exponential equation, and the trick is to take the logarithm of both sides. In PHYS.204L/206L we do Lab 33 The RC Time Constant with theoretical equation: where V is the potential difference at time t across a circuit element called a capacitor (the  is dropped for simplicity), Vo is V at t = 0 (try it), and  (tau) is a characteristic of the circuit called the time constant. a. Take the natural log of both sides and apply the addition rule for logarithms of a product on the right-hand side. b. Noting that the graph (Fig. 10) plots lnV versus t, arrange your equation in y = mx + b order, write y = mx + b under it, and circle the parts as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating  and the second for finding lnVo and then Vo. d. Note that the units of lnV are the natural log of volts, lnV. As usual derive the units of the slope and interecept and use them to obtain the units of your experimental V and t. V V e (Eq. 9) t o    Figure 10. Graph of a logarithm versus time; data from Lab 33, a Physics II experiment. Discharge of a Capacitor y = -9.17E-03x + 2.00E+00 R2 = 9.98E-01 0.00 0.50 1.00 1.50 2.00 2.50

Morgan Extra Pages Graphing with Excel to be carried out in a computer lab, 3rd floor Calloway Hall or elsewhere The Excel spreadsheet consists of vertical columns and horizontal rows; a column and row intersect at a cell. A cell can contain data for use in calculations of all sorts. The Name Box shows the currently selected cell (Fig. 1). In the Excel 2007 and 2010 versions the drop-down menus familiar in most software screens have been replaced by tabs with horizontally-arranged command buttons of various categories (Fig. 2) ___________________________________________________________________ Open Excel, click on the Microsoft circle, upper left, and Save As your surname. xlsx on the desktop. Before leaving the lab e-mail the file to yourself and/or save to a flash drive. Also e-mail it to your instructor. Figure 1. Parts of an Excel spreadsheet. Name Box Figure 2. Tabs. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 1: BASIC OPERATIONS Click Save often as you work. 1. Type the heading “Edge Length” in Cell A1 and double click the crack between the A and B column heading for automatic widening of column A. Similarly, write headings for columns B and C and enter numbers in Cells A2 and A3 as in Fig. 3. Highlight Cells A2 and A3 by dragging the cursor (chunky plus-shape) over the two of them and letting go. 2. Note that there are three types of cursor crosses: chunky for selecting, barbed for moving entries or blocks of entries from cell to cell, and tiny (appearing only at the little square in the lower-right corner of a cell). Obtain a tiny arrow for Cell A3 and perform a plus-drag down Column A until the cells are filled up to 40 (in Cell A8). Note that the two highlighted cells set both the starting value of the fill and the intervals. 3. Click on Cell B2 and enter a formula for face area of a cube as follows: type =, click on Cell A2, type ^2, and press Enter (note the formula bar in Fig. 4). 4. Enter the formula for cube volume in Cell C2 (same procedure, but “=, click on A2, ^3, Enter”). 5. Highlight Cells B2 and C2; plus-drag down to Row 8 (Fig. 5). Do the numbers look correct? Click on some cells in the newly filled area and notice how Excel steps the row designations as it moves down the column (it can do it for horizontal plusdrags along rows also). This is the major programming development that has led to the popularity of spreadsheets. Figure 3. Entries. Figure 4. A formula. Figure 5. Plus-dragging formulas. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 6. Now let’s graph the Face Area versus Edge Length: select Cells A1 through B8, choose the Insert tab, and click the Scatter drop-down menu and select “Scatter with only Markers” (Fig. 6). 7. Move the graph (Excel calls it a “chart”) that appears up alongside your number table and dress it up as follows: a. Note that some Chart Layouts have appeared above. Click Layout 1 and alter each title to read Face Area for the vertical axis, Edge Length for the horizontal and Face Area vs. Edge Length for the Graph Title. b. Activate the Excel Least squares routine, called “fitting a trendline” in the program: right click any of the data markers and click Add Trendline. Choose Power and also check “Display equation on chart” and “Display R-squared value on chart.” Fig. 7 shows what the graph will look like at this point. c. The titles are explicit, so the legend is unnecessary. Click on it and press the delete button to remove it. Figure 6. Creating a scatter graph. Figure 7. A graph with a fitted curve. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 8. Now let’s overlay the Volume vs. Edge Length curve onto the same graph (optional for 203L/205L): Make a copy of your graph by clicking on the outer white area, clicking ctrl-c (or right click, copy), and pasting the copy somewhere else (ctrl-v). If you wish, delete the trendline as in Fig. 8. a. Right click on the outer white space, choose Select Data and click the Add button. b. You can type in the cell ranges by hand in the dialog box that comes up, but it is easier to click the red, white, and blue button on the right of each space and highlight what you want to go in. Click the red, white, and blue of the bar that has appeared, and you will bounce back to the Add dialog box. Use the Edge Length column for the x’s and Volume for the y’s. c. Right-click on any volume data point and choose Format Data Series. Clicking Secondary Axis will place its scale on the right of the graph as in Fig. 8. d. Dress up your graph with two axis titles (Layout-Labels-Axis Titles), etc. Figure 8. Adding a second curve and y-axis to the graph Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2: INTERPRETING A LINEAR GRAPH Introduction: Many experiments are repeated a number of times with one of the parameters involved varied from run to run. Often the goal is to measure the rate of change of a dependent variable, rather than a particular value. If the dependent variable can be expressed as a linear function of the independent parameter, then the slope and yintercept of an appropriate graph will give the rate of change and a particular value, respectively. An example of such an experiment in PHYS.203L/205L is the first part of Lab 20, in which weights are added to the bottom of a suspended spring (Figure 9). This experiment shows that a spring exerts a force Fs proportional to the distance stretched y = (y-yo), a relationship known as Hooke’s Law: Fs = – k(y – yo) (Eq. 1) where k is called the Hooke’s Law constant. The minus sign shows that the spring opposes any push or pull on it. In Lab 20 Fs is equal to (- Mg) and y is given by the reading on a meter stick. Masses were added to the bottom of the spring in 50-g increments giving weights in newtons of 0.49, 0.98, etc. The weight pan was used as the pointer for reading y and had a mass of 50 g, so yo could not be directly measured. For convenient graphing Equation 1 can be rewritten: -(Mg) = – ky + kyo Or (Mg) = ky – kyo (Eq. 1′) Procedure 1. On your spreadsheet note the tabs at the bottom left and double-click Sheet1. Type in “Basics,” and then click the Sheet2 tab to bring up a fresh worksheet. Change the sheet name to “Linear Fit” and fill in data as in this table. Hooke’s Law Experiment y (m) -Fs = Mg (N) 0.337 0.49 0.388 0.98 0.446 1.47 0.498 1.96 0.550 2.45 2. Highlight the cells with the numbers, and graph (Mg) versus y as in Steps 6 and 7 of the Basics section. Your Trendline this time will be Linear of course. If you are having trouble remembering what’s versus what, “y” looks like “v”, so what comes before the “v” of “versus” goes on the y (vertical) axis. Yes, this graph is confusing: the horizontal (“x”) axis is distance y, and the “y” axis is something else. 3. Click on the Equation/R2 box on the graph and highlight just the slope, that is, only the number that comes before the “x.” Copy it (control-c is a fast way to Figure 9. A spring with a weight stretching it Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com do it) and paste it (control-v) into an empty cell. Do likewise for the intercept (including the minus sign). SAVE YOUR FILE! 5. The next steps use the standard procedure for obtaining information from linear data. Write the general equation for a straight line immediately below a hand-written copy of Equation 1′ then circle matching items: (Mg) = k y + (- k yo) (Eq. 1′) y = m x + b Note the parentheses around the intercept term of Equation 1′ to emphasize that the minus sign is part of it. Equating above and below, you can create two useful new equations: slope m = k (Eq. 2) y-intercept b = -kyo (Eq. 3) 6. Solve Equation 2 for k, that is, rewrite left to right. Then substitute the value for slope m from your graph, and you have an experimental value for the Hooke’s Law constant k. Next solve Equation 3 for yo, substitute the value for intercept b from your graph and the value of k that you just found, and calculate yo. 7. Examine your linear graph for clues to finding the units of the slope and the yintercept. Use these units to find the units of k and yo. 8. Present your values of k and yo with their units neatly at the bottom of your spreadsheet. 9. R2 in Excel, like r in our lab manual and Corr. in the LoggerPro software, is a measure of how well the calculated line matches the data points. 1.00 would indicate a perfect match. State how good a match you think was made in this case? 10. Do the Homework, Further Exercises on Interpreting Linear Graphs, on the following pages. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com Eq.1 M m f M a g               , (Eq.2) M slope m g       (Eq.3) M b f        Morgan Extra Pages Homework: Graph Interpretation Exercises EXAMPLE WITH COMPLETE SOLUTION In PHYS.203L and 205L we do Lab 9 Newton’s Second Law on Atwood’s Machine using a photogate sensor (Fig. 1). The Atwood’s apparatus can slow the rate of fall enough to be measured even with primitive timing devices. In our experiment LoggerPro software automatically collects and analyzes the data giving reliable measurements of g, the acceleration of gravity. The equation governing motion for Atwood’s Machine can be written: where a is the acceleration of the masses and string, g is the acceleration of gravity, M is the total mass at both ends of the string, m is the difference between the masses, and f is the frictional force at the hub of the pulley wheel. In this exercise you are given a graph of a vs. m obtained in this experiment with the values of M and the slope and intercept (Fig. 2). The goal is to extract values for acceleration of gravity g and frictional force f from this information. To analyze the graph we write y = mx + b, the general equation for a straight line, directly under Equation 1 and match up the various parameters: Equating above and below, you can create two new equations: and y m x b M m f M a g                Figure 1. The Atwood’s Machine setup (from the LoggerPro handout). Figure 2. Graph of acceleration versus mass difference; data from a Physics I experiment. Atwood’s Machine M = 0.400 kg a = 24.4 m – 0.018 R2 = 0.998 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.000 0.010 0.020 0.030 0.040 0.050 0.060  m (kg) a (m/s2) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 2 2 9.76 / 0.400 24.4 /( ) m s kg m kg s g Mm      To handle Equation 2 it pays to consider what the units of the slope are. A slope is “the rise over the run,“ so its units must be the units of the vertical axis divided by those of the horizontal axis. In this case: Now let’s solve Equation 2 for g and substitute the values of total mass M and of the slope m from the graph: Using 9.80 m/s2 as the Baltimore accepted value for g, we can calculate the percent error: A similar process with Equation 3 leads to a value for f, the frictional force at the hub of the pulley wheel. Note that the units of intercept b are simply whatever the vertical axis units are, m/s2 in this case. Solving Equation 3 for f: EXERCISE 1 The Picket Fence experiment makes use of LoggerPro software to calculate velocities at regular time intervals as the striped plate passes through the photogate (Fig. 3). The theoretical equation is v = vi + at (Eq. 4) where vi = 0 (the fence is dropped from rest) and a = g. a. Write Equation 4 with y = mx + b under it and circle matching factors as in the Example. b. What is the experimental value of the acceleration of gravity? What is its percent error from the accepted value for Baltimore, 9.80 m/s2? c. Does the value of the y-intercept make sense? d. How well did the straight Trendline match the data? 2 / 2 kg s m kg m s   0.4% 100 9.80 9.76 9.80 100 . . . %        Acc Exp Acc Error kg m s mN kg m s f Mb 7.2 10 / 7.2 0.400 ( 0.018 / ) 3 2 2           Figure 3. Graph of speed versus time as calculated by LoggerPro as a picket fence falls freely through a photogate. Picket Fence Drop y = 9.8224x + 0.0007 R2 = 0.9997 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 t (s) v (m/s) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2 This is an electrical example from PHYS.204L/206L, potential difference, V, versus current, I (Fig. 4). The theoretical equation is V = IR (Eq. 5) and is known as “Ohm’s Law.” The unit symbols stand for volts, V, and Amperes, A. The factor R stands for resistance and is measured in units of ohms, symbol  (capital omega). The definition of the ohm is: V (Eq. 6) By coincidence the letter symbols for potential (a quantity ) and volts (its unit) are identical. Thus “voltage” has become the laboratory slang name for potential. a. Rearrange the Ohm’s Law equation to match y = mx + b.. b. What is the experimental resistance? c. Comment on the experimental intercept: is its value reasonable? EXERCISE 3 This graph (Fig. 5) also follows Ohm’s Law, but solved for current I. For this graph the experimenter held potential difference V constant at 15.0V and measured the current for resistances of 100, 50, 40, and 30  Solve Ohm’s Law for I and you will see that 1/R is the logical variable to use on the x axis. For units, someone once jokingly referred to a “reciprocal ohm” as a “mho,” and the name stuck. a. Rearrange Equation 5 solved for I to match y = mx + b. b. What is the experimental potential difference? c. Calculate the percent difference from the 15.0 V that the experimenter set on the power supply (the instrument used for such experiments). d. Comment on the experimental intercept: is its value reasonable? Figure 4. Graph of potential difference versus current; data from a Physics II experiment. The theoretical equation, V = IR, is known as “Ohm’s Law.” Ohm’s Law y = 0.628x – 0.0275 R2 = 0.9933 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Current, I (A) Potential difference, V (V) Figure 5. Another application of Ohm’s Law: a graph of current versus the inverse of resistance, from a different electric circuit experiment. Current versus (1/Resistance) y = 14.727x – 0.2214 R2 = 0.9938 0 100 200 300 400 500 600 5 10 15 20 25 30 35 R-1 (millimhos) I (milliamperes) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 4 The Atwood’s Machine experiment (see the solved example above) can be done in another way: keep mass difference m the same and vary the total mass M (Fig. 6). a. Rewrite Equation 1 and factor out (1/M). b. Equate the coefficient of (1/M) with the experimental slope and solve for acceleration of gravity g. c. Substitute the values for slope, mass difference, and frictional force and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? EXERCISE 5 In the previous two exercises the reciprocal of a variable was used to make the graph come out linear. In this one the trick will be to use the square root of a variable (Fig. 7). In PHYS.203L and 205L Lab 19 The Pendulum the theoretical equation is where the period T is the time per cycle, L is the length of the string, and g is the acceleration of gravity. a. Rewrite Equation 7 with the square root of L factored out and placed at the end. b. Equate the coefficient of √L with the experimental slope and solve for acceleration of gravity g. c. Substitute the value for slope and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? 2 (Eq . 7) g T   L Figure 6. Graph of acceleration versus the reciprocal of total mass; data from a another Physics I experiment. Atwood’s Machine m = 0.020 kg f = 7.2 mN y = 0.1964x – 0.0735 R2 = 0.995 0.400 0.600 0.800 1.000 2.000 2.500 3.000 3.500 4.000 4.500 5.000 1/M (1/kg) a (m/s2) Effect of Pendulum Length on Period y = 2.0523x – 0.0331 R2 = 0.999 0.400 0.800 1.200 1.600 2.000 2.400 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 L1/2 (m1/2) T (s) Figure 7. Graph of period T versus the square root of pendulum length; data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 6 In Exercise 5 another approach would have been to square both sides of Equation 7 and plot T2 versus L. Lab 20 directs us to use that alternative. It involves another case of periodic or harmonic motion with a similar, but more complicated, equation for the period: where T is the period of the bobbing (Fig. 8), M is the suspended mass, ms is the mass of the spring, k is a measure of stiffness called the spring constant, and C is a dimensionless factor showing how much of the spring mass is effectively bobbing. a. Square both sides of Equation 8 and rearrange it to match y = mx + b. b. Write y = mx + b under your rearranged equation and circle matching factors as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating k and the second for finding C from the data of Fig. 9. d. A theoretical analysis has shown that for most springs C = 1/3. Find the percent error from that value. e. Derive the units of the slope and intercept; show that the units of k come out as N/m and that C is dimensionless. 2 (Eq . 8) k T M Cm s    Figure 8. In Lab 20 mass M is suspended from a spring which is set to bobbing up and down, a good approximation to simple harmonic motion (SHM), described by Equation 8. Lab 20: SHM of a Spring Mass of the spring, ms = 25.1 g y = 3.0185x + 0.0197 R2 = 0.9965 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 0 0.05 0.1 0.15 0.2 0.25 0.3 M (kg) T 2 2 Figure 9. Graph of the square of the period T2 versus suspended mass M data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 7 This last exercise deals with an exponential equation, and the trick is to take the logarithm of both sides. In PHYS.204L/206L we do Lab 33 The RC Time Constant with theoretical equation: where V is the potential difference at time t across a circuit element called a capacitor (the  is dropped for simplicity), Vo is V at t = 0 (try it), and  (tau) is a characteristic of the circuit called the time constant. a. Take the natural log of both sides and apply the addition rule for logarithms of a product on the right-hand side. b. Noting that the graph (Fig. 10) plots lnV versus t, arrange your equation in y = mx + b order, write y = mx + b under it, and circle the parts as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating  and the second for finding lnVo and then Vo. d. Note that the units of lnV are the natural log of volts, lnV. As usual derive the units of the slope and interecept and use them to obtain the units of your experimental V and t. V V e (Eq. 9) t o    Figure 10. Graph of a logarithm versus time; data from Lab 33, a Physics II experiment. Discharge of a Capacitor y = -9.17E-03x + 2.00E+00 R2 = 9.98E-01 0.00 0.50 1.00 1.50 2.00 2.50

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This assignment challenges you to analyze how two writers present arguments about a significant issue or topic. For this assignment, you will choose two current newspaper or scholarly journal articles that focus on a current issue relevant to the people on the continent of Africa, and/or people of African descent. Your goal is to identify the purposes and claims of each author, locate their arguments in a rhetorical situation, and analyze the appeals each writer makes to support their argument. You will then evaluate the arguments: which author better satisfies their readers? Which author crafts the more fitting response? In sum, then, the main goals are: 1. Identify the purposes and claims that two authors make about a significant issue. 2. Locate the arguments in a rhetorical situation (what exigencies do the authors address? What constraints and resources exist for the authors? To whom are they writing? When and where was each article published? 3. Analyze the appeals (logical, ethical, emotional) put forth by the writers. 4. Evaluate the arguments. Which argument is more fitting? Which author better satisfies readers? (Your evaluation need not be either/or: maybe one author is more effective logically, for instance, while the second author is more effective ethically and emotionally.)

This assignment challenges you to analyze how two writers present arguments about a significant issue or topic. For this assignment, you will choose two current newspaper or scholarly journal articles that focus on a current issue relevant to the people on the continent of Africa, and/or people of African descent. Your goal is to identify the purposes and claims of each author, locate their arguments in a rhetorical situation, and analyze the appeals each writer makes to support their argument. You will then evaluate the arguments: which author better satisfies their readers? Which author crafts the more fitting response? In sum, then, the main goals are: 1. Identify the purposes and claims that two authors make about a significant issue. 2. Locate the arguments in a rhetorical situation (what exigencies do the authors address? What constraints and resources exist for the authors? To whom are they writing? When and where was each article published? 3. Analyze the appeals (logical, ethical, emotional) put forth by the writers. 4. Evaluate the arguments. Which argument is more fitting? Which author better satisfies readers? (Your evaluation need not be either/or: maybe one author is more effective logically, for instance, while the second author is more effective ethically and emotionally.)

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The Classic Five-Part Structure 1. Introduce the topic to be argued. Establish its importance. 2. Provide background information so readers will be able to follow your discussion. 3. State your claim (your argumentative thesis) and develop your argument by making a logical appeal. Support your claims with facts, opinions, and examples. If appropriate, mix an emotional appeal or an appeal to authority with your logical appeals. 4. Acknowledge counterarguments and treat them with respect. Rebut these arguments. Reject their evidence or their logic or concede some validity and modify your claim accordingly. Be flexible; you might split the counterarguments and rebut them one at a time at different locations in the paper, or you might begin the paper with a counterargument, rebut it, and then move on to your own claim. 5. Conclude by summarizing the main points of your argument. Then remind readers of what you want them to believe or do. Give them something to remember. The Problem-Solution Structure I. There is a serious problem. A. The problem exists and is growing. (Provide support for argument.) B. The problem is serious. (Provide support.) C. Current methods cannot cope with the problem. (Provide support.) II. There is a solution to the problem. (Your claim goes here.) A. The solution is practical. (Provide support.) B. The solution is desirable. (Provide support.) C. We can implement the solution. (Provide support.) D. Alternate solutions are not as strong as the proposed solution. (Review – and reject – competing solutions.) In both cases, you know before you begin writing whether you will use an inductive (analytic) or deductive (synthetic) arrangement for your argument. The decision to move inductively or deductively is about strategy. Induction moves from support to a claim. Deduction moves from a claim to support – to particular facts, opinions, and examples. This is the preferred form for most writing in the humanities. You can position your claim at the beginning, middle, or end of your presentation. In the problem/solution structure, the claim is made only after the writer introduces a problem. With the five-part structure, you have more flexibility in positioning your claim. One factor that can help determine placement is the likelihood of your audience agreeing with you. When your audience is likely to be neutral or supportive, making your claim early on will not alienate readers (synthetic presentation). When your audience is likely to disagree, placing your thesis at the end of your presentation allows you time to build a consensus, step by step, until you reach your conclusion (analytical presentation).

The Classic Five-Part Structure 1. Introduce the topic to be argued. Establish its importance. 2. Provide background information so readers will be able to follow your discussion. 3. State your claim (your argumentative thesis) and develop your argument by making a logical appeal. Support your claims with facts, opinions, and examples. If appropriate, mix an emotional appeal or an appeal to authority with your logical appeals. 4. Acknowledge counterarguments and treat them with respect. Rebut these arguments. Reject their evidence or their logic or concede some validity and modify your claim accordingly. Be flexible; you might split the counterarguments and rebut them one at a time at different locations in the paper, or you might begin the paper with a counterargument, rebut it, and then move on to your own claim. 5. Conclude by summarizing the main points of your argument. Then remind readers of what you want them to believe or do. Give them something to remember. The Problem-Solution Structure I. There is a serious problem. A. The problem exists and is growing. (Provide support for argument.) B. The problem is serious. (Provide support.) C. Current methods cannot cope with the problem. (Provide support.) II. There is a solution to the problem. (Your claim goes here.) A. The solution is practical. (Provide support.) B. The solution is desirable. (Provide support.) C. We can implement the solution. (Provide support.) D. Alternate solutions are not as strong as the proposed solution. (Review – and reject – competing solutions.) In both cases, you know before you begin writing whether you will use an inductive (analytic) or deductive (synthetic) arrangement for your argument. The decision to move inductively or deductively is about strategy. Induction moves from support to a claim. Deduction moves from a claim to support – to particular facts, opinions, and examples. This is the preferred form for most writing in the humanities. You can position your claim at the beginning, middle, or end of your presentation. In the problem/solution structure, the claim is made only after the writer introduces a problem. With the five-part structure, you have more flexibility in positioning your claim. One factor that can help determine placement is the likelihood of your audience agreeing with you. When your audience is likely to be neutral or supportive, making your claim early on will not alienate readers (synthetic presentation). When your audience is likely to disagree, placing your thesis at the end of your presentation allows you time to build a consensus, step by step, until you reach your conclusion (analytical presentation).

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CAUSAL ANALYSIS GUIDELINES: According to John J. Ruskiewicz and Jay T. Dolmage, “We all analyze and explain things daily. Someone asks, ‘Why?’ We reply, ‘Because . . .’ and then offer reasons and rationales” (138). This type of thinking is at the core of the causal analysis. You will write a causal analysis which explores, through carefully examined research and logical analysis, certain causes or factors which contribute to an issue or problematic situation, based on the topic you choose to write on. Your causal analysis should explore more than one type of cause, such as necessary causes, sufficient causes, precipitating causes, proximate causes, remote causes, reciprocal causes, contributing factors, and chains of causes, as outlined in our course text in the chapter devoted to Causal Analyses. Your project should also reflect significant critical thinking skills. In addition to the actual causal analysis essay, you will be also create an annotated bibliography. These process elements will help you organize and focus your ideas and research in a beneficial way. The following is an organizational structure that outlines the chronology and content of your Causal Analysis: I. Introduction: In one (or at the most two) paragraph(s) introduce your topic. Give a brief overview of your topic and thesis in a few sentences. your evaluative claim and your causal claim. It should be specific, logical, and clear. II. History/Background to Current Situation: This section should take as much space as needed—a few to several paragraphs. Discuss the significant and relevant history of your topic up to the current situation and how it came to be. Use research as needed to give precise and accurate background for context in making your later causal argument. Comment on your research as well, so that you don’t lose your voice. As you explore other points of view, your own point of view will evolve in significant ways. III. Evaluative Claim: Once you have given a brief history/background of the current situation, evaluate the situation, the topic, as it is at present. Again, use research as appropriate to support your judgments. While this section of your essay could run anywhere from one to three paragraphs, typically one paragraph is the norm, as you are basically passing judgment on the situation, arguing evaluatively. This is an argument of pathos and logos, predominantly. IV. Causal Argument: This is the longest portion of your essay, the “meat,” the heart of your work. Once you have detailed the history/background to current situation and evaluated the current situation, you are ready to present your causal analysis. Demonstrate a link between the current situation and the causes for its negative condition. Of course, you will use current significant and relevant research to support your causal claim, and you will want to find the most dominant and pervasive logical causes, utilizing research, for the current situation as possible. These will connect forward as well to your proposal. Remember to use specific supporting detail/examples, and to analyze all of your research causally, thoroughly, and with clarity. NOTE: SECTIONS THREE AND FOUR ABOVE ARE INTERCHANGEABLE. IN OTHER WORDS, IF YOU FEEL YOU CAN PRESENT A BETTER ARGUMENT BY SHOWING CAUSES FIRST AND THEN EVALUATING THE CURRENT SITUATION, THAT CAN WORK JUST AS WELL AS THE ORDER OUTLINED ABOVE. I WILL LEAVE IT UP TO YOU AS THE WRITER TO ESTABLISH WHICH ORDER WORKS MOST EFFECTIVELY. V. Counterargument/Conditions of Rebuttal and Rebuttal: There will be those who disagree with you so you will want to acknowledge their points of view. What are their assumptions about this topic? What questions do they raise for consideration? Acknowledging other points of view gives your essay credibility and shows that you have been fair and broad in your inquiry and presentation. (You will need at least one credible source to represent at least one counterargument.) Then explain how you have considered this counterargument, but still find your own analysis to be more logical and accurate; this is your rebuttal. VI. Conclusion: Summarize the meaningful conclusions you have drawn clearly and precisely, remembering to resummarize your thesis. Give your specific proposal here as well. This will become your transition paragraph between the causal analysis and the proposal, so you must state your proposal precisely to pave the way for the proposal argument in full to come. Keep in mind these critical thinking outcomes: • Pursue the best information via reliable research (no Internet web sites should be used—Use the library electronic databases, such as ____, for academic research. • Engage in broad and deep inquiry • Analyze different points of view • Examine and challenge your own underlying assumptions as you undergo this exciting journey in scholarship. Please also reflect on these questions as you progress through your research and project work: About yourself: • What assumptions (beliefs) did you have about this topic coming into the project? • Have some of those assumptions been challenged? Have some been validated? • What questions do you still have about your issue? • What questions have you been able to answer through your research? About your audience: • What questions might your audience have about your topic? What points of view do they represent? • What information do you want to provide to help answer those questions? • How can you address a diverse audience so that its members will be moved to see your own point of view as significant and worth consideration? • How has pursuing the best information in a fair and honest, ethical, and logical manner allowed you to show respect for your audience as well as yourself as a thinker? Documentation Style: MLA format for paper format, in-text citations, works cited page, and annotated bibliography format. Paper Length: 6-8 double-spaced pages. Annotated Bibliography: At least 4 sources, formatted in MLA style. List of Sources Page: At least 5-8 sources used; formatted in MLA style. Warning: Plagiarism is punishable with an “F,” so be sure to document your research carefully. Causal Analysis Topics Choose one: • Causes of bullying • Causes of gun violence in schools • Causes of obesity in children • Causes of lying / Reasons why people lie • Causes of the fear of darkness Write in the 3rd-person point of view (using pronouns such as he, she, they, etc.). Do not write in the 1st- person (I, me, etc.) or 2nd-person (you, your) point of view.

CAUSAL ANALYSIS GUIDELINES: According to John J. Ruskiewicz and Jay T. Dolmage, “We all analyze and explain things daily. Someone asks, ‘Why?’ We reply, ‘Because . . .’ and then offer reasons and rationales” (138). This type of thinking is at the core of the causal analysis. You will write a causal analysis which explores, through carefully examined research and logical analysis, certain causes or factors which contribute to an issue or problematic situation, based on the topic you choose to write on. Your causal analysis should explore more than one type of cause, such as necessary causes, sufficient causes, precipitating causes, proximate causes, remote causes, reciprocal causes, contributing factors, and chains of causes, as outlined in our course text in the chapter devoted to Causal Analyses. Your project should also reflect significant critical thinking skills. In addition to the actual causal analysis essay, you will be also create an annotated bibliography. These process elements will help you organize and focus your ideas and research in a beneficial way. The following is an organizational structure that outlines the chronology and content of your Causal Analysis: I. Introduction: In one (or at the most two) paragraph(s) introduce your topic. Give a brief overview of your topic and thesis in a few sentences. your evaluative claim and your causal claim. It should be specific, logical, and clear. II. History/Background to Current Situation: This section should take as much space as needed—a few to several paragraphs. Discuss the significant and relevant history of your topic up to the current situation and how it came to be. Use research as needed to give precise and accurate background for context in making your later causal argument. Comment on your research as well, so that you don’t lose your voice. As you explore other points of view, your own point of view will evolve in significant ways. III. Evaluative Claim: Once you have given a brief history/background of the current situation, evaluate the situation, the topic, as it is at present. Again, use research as appropriate to support your judgments. While this section of your essay could run anywhere from one to three paragraphs, typically one paragraph is the norm, as you are basically passing judgment on the situation, arguing evaluatively. This is an argument of pathos and logos, predominantly. IV. Causal Argument: This is the longest portion of your essay, the “meat,” the heart of your work. Once you have detailed the history/background to current situation and evaluated the current situation, you are ready to present your causal analysis. Demonstrate a link between the current situation and the causes for its negative condition. Of course, you will use current significant and relevant research to support your causal claim, and you will want to find the most dominant and pervasive logical causes, utilizing research, for the current situation as possible. These will connect forward as well to your proposal. Remember to use specific supporting detail/examples, and to analyze all of your research causally, thoroughly, and with clarity. NOTE: SECTIONS THREE AND FOUR ABOVE ARE INTERCHANGEABLE. IN OTHER WORDS, IF YOU FEEL YOU CAN PRESENT A BETTER ARGUMENT BY SHOWING CAUSES FIRST AND THEN EVALUATING THE CURRENT SITUATION, THAT CAN WORK JUST AS WELL AS THE ORDER OUTLINED ABOVE. I WILL LEAVE IT UP TO YOU AS THE WRITER TO ESTABLISH WHICH ORDER WORKS MOST EFFECTIVELY. V. Counterargument/Conditions of Rebuttal and Rebuttal: There will be those who disagree with you so you will want to acknowledge their points of view. What are their assumptions about this topic? What questions do they raise for consideration? Acknowledging other points of view gives your essay credibility and shows that you have been fair and broad in your inquiry and presentation. (You will need at least one credible source to represent at least one counterargument.) Then explain how you have considered this counterargument, but still find your own analysis to be more logical and accurate; this is your rebuttal. VI. Conclusion: Summarize the meaningful conclusions you have drawn clearly and precisely, remembering to resummarize your thesis. Give your specific proposal here as well. This will become your transition paragraph between the causal analysis and the proposal, so you must state your proposal precisely to pave the way for the proposal argument in full to come. Keep in mind these critical thinking outcomes: • Pursue the best information via reliable research (no Internet web sites should be used—Use the library electronic databases, such as ____, for academic research. • Engage in broad and deep inquiry • Analyze different points of view • Examine and challenge your own underlying assumptions as you undergo this exciting journey in scholarship. Please also reflect on these questions as you progress through your research and project work: About yourself: • What assumptions (beliefs) did you have about this topic coming into the project? • Have some of those assumptions been challenged? Have some been validated? • What questions do you still have about your issue? • What questions have you been able to answer through your research? About your audience: • What questions might your audience have about your topic? What points of view do they represent? • What information do you want to provide to help answer those questions? • How can you address a diverse audience so that its members will be moved to see your own point of view as significant and worth consideration? • How has pursuing the best information in a fair and honest, ethical, and logical manner allowed you to show respect for your audience as well as yourself as a thinker? Documentation Style: MLA format for paper format, in-text citations, works cited page, and annotated bibliography format. Paper Length: 6-8 double-spaced pages. Annotated Bibliography: At least 4 sources, formatted in MLA style. List of Sources Page: At least 5-8 sources used; formatted in MLA style. Warning: Plagiarism is punishable with an “F,” so be sure to document your research carefully. Causal Analysis Topics Choose one: • Causes of bullying • Causes of gun violence in schools • Causes of obesity in children • Causes of lying / Reasons why people lie • Causes of the fear of darkness Write in the 3rd-person point of view (using pronouns such as he, she, they, etc.). Do not write in the 1st- person (I, me, etc.) or 2nd-person (you, your) point of view.

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