Identify legislative and regulative requirements relative to information security for a bank

Identify legislative and regulative requirements relative to information security for a bank

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

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

Computer education improves students’ investigation skill by encouraging them to … Read More...
In the context of self-knowledge, what is the take home message of the Socrates quote, “know thyself”? The most important aspect of self-knowledge is whether your opinion is good or bad. The most salient of all goals is obtaining high self-esteem. The most salient of all goals is personality continuity. The most important aspect of self-knowledge is the degree to which it is accurate.

In the context of self-knowledge, what is the take home message of the Socrates quote, “know thyself”? The most important aspect of self-knowledge is whether your opinion is good or bad. The most salient of all goals is obtaining high self-esteem. The most salient of all goals is personality continuity. The most important aspect of self-knowledge is the degree to which it is accurate.

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ENGR 2010 (Section 02) – Assignment 7 Due: Wednesday November 25th, 11:59 pm Points: 20 Prof. Lei Reading: Sections 6.2-6.3 of Nilsson and Riedel, Electric Circuits, 9th Edition Submit electronic solutions (i.e. using Microsoft Word or a scanned copy of your written work) to the following problems on Blackboard. To receive credit, you must show work indicating how you arrived at each final answer. Problem 1 Consider the RC circuit on the right. and suppose that Vs(t) is a time-varying voltage input shown at the bottom. a) Suppose VC(0) = 0V. Plot VR(t) and VC(t) from 0ms to 300ms. Show your work in obtaining VR(t) and VC(t). b) Suppose the capacitance value is changed to 2μF, and VC(0) = 0V. Plot VR(t) and VC(t) from 0ms to 300ms. Show your work in obtaining VR(t) and VC(t). c) Explain how VC(t) qualitatively compares with Vs(t), and how VR(t) qualitatively compares with Vs(t). d) Explain how the capacitance value affects VC(t). t Vs(t) 1V -1V 50ms 100ms 150ms 200ms 250ms + – Vs(t) 100000 Ohms 1 uF + – VC(t) + – VR(t) 0ms 300ms Note: Capacitors are often used to protect against sudden changes in a voltage value, which could damage electronic components. Here, Vs(t) undergoes many sudden changes, but VC(t) undergoes less change. Problem 2 Using PSpice, perform two transient analysis simulations – one for the circuit in part (a), and one for the circuit in part(b) of problem 1 – to verify that your plots in problem 1 are correct. For each simulation, plot the traces for VR(t) and VC(t). Hint: You may need to perform arithmetic operations between simulation traces. Take a screenshot of your constructed circuits and the simulation traces for VR(t) and VC(t), which you will submit onto Blackboard. t Vs(t) 1V -1V 50ms 100ms 150ms 200ms 250ms + – Vs(t) 100000 Ohms 1 uF + – VC(t) + – VR(t) 0ms 300ms 1 uF or 2 uF Problem 3 Consider the Resistor-Diode circuit on the right, and suppose that Vs(t) is a time-varying voltage input shown at the bottom. Suppose that for the diode to turn on, it needs 0.7V between the positive and negative terminals. a) Plot VR(t) and VD(t) from 0ms to 300ms b) Explain how VD(t) qualitatively compares with Vs(t), and how VR(t) qualitatively compares with Vs(t). t Vs(t) 1V -1V 50ms 100ms 0ms 150ms 200ms 250ms 300ms + – Vs(t) 100000 Ohms + – VD(t) + – VR(t) Problem 4 Using PSpice, perform a transient analysis simulation for the circuit in problem 3 – to verify that your plots in problem 3 are correct. For the simulation, plot the traces for VR(t) and VD(t). To create the diode in PSpice, use the Dbreak component. After placing the component on the page, highlight the component, and edit the Pspice model (Edit -> PSpice Model) and set Rs to 0. Hint: You may need to perform arithmetic operations between simulation traces. Take a screenshot of your constructed circuit and the simulation traces for VR(t) and VD(t), which you will submit onto Blackboard. Note that your simulation trace plots may not be exactly the same as those from Problem 3, since the PSpice diode model has a turn-on voltage that’s not exactly 0.7V. t Vs(t) 1V -1V 50ms 100ms 0ms 150ms 200ms 250ms 300ms + – Vs(t) 100000 Ohms + – VD(t) + – VR(t) Problem 5 (Bonus: 5 points) In the circuit from problem 1 (shown on the right), write several sentences to explain why VC(t) is often referred to as the “low-pass filtered” output, and VR(t) is often referred to as the “high-pass filtered” output. You will need to look up the definitions for “low-pass” and “high-pass” filters. Examining your plots for VC(t) and VR(t) will help. t Vs(t) 1V -1V 50ms 100ms 150ms 200ms 250ms + – Vs(t) 100000 Ohms 1 uF + – VC(t) + – VR(t) 0ms 300ms

ENGR 2010 (Section 02) – Assignment 7 Due: Wednesday November 25th, 11:59 pm Points: 20 Prof. Lei Reading: Sections 6.2-6.3 of Nilsson and Riedel, Electric Circuits, 9th Edition Submit electronic solutions (i.e. using Microsoft Word or a scanned copy of your written work) to the following problems on Blackboard. To receive credit, you must show work indicating how you arrived at each final answer. Problem 1 Consider the RC circuit on the right. and suppose that Vs(t) is a time-varying voltage input shown at the bottom. a) Suppose VC(0) = 0V. Plot VR(t) and VC(t) from 0ms to 300ms. Show your work in obtaining VR(t) and VC(t). b) Suppose the capacitance value is changed to 2μF, and VC(0) = 0V. Plot VR(t) and VC(t) from 0ms to 300ms. Show your work in obtaining VR(t) and VC(t). c) Explain how VC(t) qualitatively compares with Vs(t), and how VR(t) qualitatively compares with Vs(t). d) Explain how the capacitance value affects VC(t). t Vs(t) 1V -1V 50ms 100ms 150ms 200ms 250ms + – Vs(t) 100000 Ohms 1 uF + – VC(t) + – VR(t) 0ms 300ms Note: Capacitors are often used to protect against sudden changes in a voltage value, which could damage electronic components. Here, Vs(t) undergoes many sudden changes, but VC(t) undergoes less change. Problem 2 Using PSpice, perform two transient analysis simulations – one for the circuit in part (a), and one for the circuit in part(b) of problem 1 – to verify that your plots in problem 1 are correct. For each simulation, plot the traces for VR(t) and VC(t). Hint: You may need to perform arithmetic operations between simulation traces. Take a screenshot of your constructed circuits and the simulation traces for VR(t) and VC(t), which you will submit onto Blackboard. t Vs(t) 1V -1V 50ms 100ms 150ms 200ms 250ms + – Vs(t) 100000 Ohms 1 uF + – VC(t) + – VR(t) 0ms 300ms 1 uF or 2 uF Problem 3 Consider the Resistor-Diode circuit on the right, and suppose that Vs(t) is a time-varying voltage input shown at the bottom. Suppose that for the diode to turn on, it needs 0.7V between the positive and negative terminals. a) Plot VR(t) and VD(t) from 0ms to 300ms b) Explain how VD(t) qualitatively compares with Vs(t), and how VR(t) qualitatively compares with Vs(t). t Vs(t) 1V -1V 50ms 100ms 0ms 150ms 200ms 250ms 300ms + – Vs(t) 100000 Ohms + – VD(t) + – VR(t) Problem 4 Using PSpice, perform a transient analysis simulation for the circuit in problem 3 – to verify that your plots in problem 3 are correct. For the simulation, plot the traces for VR(t) and VD(t). To create the diode in PSpice, use the Dbreak component. After placing the component on the page, highlight the component, and edit the Pspice model (Edit -> PSpice Model) and set Rs to 0. Hint: You may need to perform arithmetic operations between simulation traces. Take a screenshot of your constructed circuit and the simulation traces for VR(t) and VD(t), which you will submit onto Blackboard. Note that your simulation trace plots may not be exactly the same as those from Problem 3, since the PSpice diode model has a turn-on voltage that’s not exactly 0.7V. t Vs(t) 1V -1V 50ms 100ms 0ms 150ms 200ms 250ms 300ms + – Vs(t) 100000 Ohms + – VD(t) + – VR(t) Problem 5 (Bonus: 5 points) In the circuit from problem 1 (shown on the right), write several sentences to explain why VC(t) is often referred to as the “low-pass filtered” output, and VR(t) is often referred to as the “high-pass filtered” output. You will need to look up the definitions for “low-pass” and “high-pass” filters. Examining your plots for VC(t) and VR(t) will help. t Vs(t) 1V -1V 50ms 100ms 150ms 200ms 250ms + – Vs(t) 100000 Ohms 1 uF + – VC(t) + – VR(t) 0ms 300ms

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1- Which of the following is not a basic role of managers? Interpersonal Entrepreneurial Informational Decisional 2- A company’s IT architecture includes all of the following except: Hardware and software Networks Database management systems The members of the IT staff How IT decisions will be made 3- Which of the following is NOT one of the three objectives that the IT strategic plan must meet to allow an organization to achieve its goals? Alignment with the strategic plan Clearly defined IT steering committee IS development resources allocated Seamless IT architecture 4- In the _____ phase of the decision-making process, managers examine a situation and identify and define the problem. implementation choice design intelligence consideration 5- Which of the following systems acquisition methods can result in a company’s acquiring software that is controlled by another company, may be difficult to enhance or modify, and may not support the desired business processes? Systems development life cycle Prototyping End-user development Buy option Component-based development 6- Which of the following systems acquisition methods requires staff to systematically go through every step in the development process and has a lower probability of missing important user requirements? Systems development life cycle Prototyping End-user development External acquisition Object-oriented development 7- Which of the following is NOT an advantage of the buy option for acquiring IS applications? Few types of off-the-shelf software are available, thus limiting confusion. The software can be tried out. The buy option saves time. The company will know what it is getting. All of these 8- Evaluating the benefits of IT projects is more complex than evaluating their costs for all of the following reasons except: Benefits are harder than costs to quantify. Benefits tend to be more tangible than costs. IT can be used for several different purposes. The probability of obtaining a return from an IT investment is based on the probability of implementation success. The proposed system may be “cutting edge.” 9- Decisions today are becoming _____ complex due to _____ uncertainty in the decision environment. less, decreased more, decreased less, increased more, increased neither more nor less, decreased 10- Which of the following is/are disadvantages of the buy option for acquiring IS applications? The software may not exactly meet the company’s needs. The software may be impossible to modify. The company will not have control over software improvements. The software may not integrate with existing systems. All of these

1- Which of the following is not a basic role of managers? Interpersonal Entrepreneurial Informational Decisional 2- A company’s IT architecture includes all of the following except: Hardware and software Networks Database management systems The members of the IT staff How IT decisions will be made 3- Which of the following is NOT one of the three objectives that the IT strategic plan must meet to allow an organization to achieve its goals? Alignment with the strategic plan Clearly defined IT steering committee IS development resources allocated Seamless IT architecture 4- In the _____ phase of the decision-making process, managers examine a situation and identify and define the problem. implementation choice design intelligence consideration 5- Which of the following systems acquisition methods can result in a company’s acquiring software that is controlled by another company, may be difficult to enhance or modify, and may not support the desired business processes? Systems development life cycle Prototyping End-user development Buy option Component-based development 6- Which of the following systems acquisition methods requires staff to systematically go through every step in the development process and has a lower probability of missing important user requirements? Systems development life cycle Prototyping End-user development External acquisition Object-oriented development 7- Which of the following is NOT an advantage of the buy option for acquiring IS applications? Few types of off-the-shelf software are available, thus limiting confusion. The software can be tried out. The buy option saves time. The company will know what it is getting. All of these 8- Evaluating the benefits of IT projects is more complex than evaluating their costs for all of the following reasons except: Benefits are harder than costs to quantify. Benefits tend to be more tangible than costs. IT can be used for several different purposes. The probability of obtaining a return from an IT investment is based on the probability of implementation success. The proposed system may be “cutting edge.” 9- Decisions today are becoming _____ complex due to _____ uncertainty in the decision environment. less, decreased more, decreased less, increased more, increased neither more nor less, decreased 10- Which of the following is/are disadvantages of the buy option for acquiring IS applications? The software may not exactly meet the company’s needs. The software may be impossible to modify. The company will not have control over software improvements. The software may not integrate with existing systems. All of these

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Watch the videos, and then answer the questions below. http://www.youtube.com/watch?v=kt6SYhX_Ymo http://www.youtube.com/watch?v=ka3yTfmyjAw Building Justice Which of the following is true of the International Criminal Court (ICC)? A. It was the first court to try individuals for crimes against humanity. B. It was founded to prosecute Nazi war criminals. C. It is a permanent court with universal jurisdiction. D. It was created by a treaty that has been signed by all of the world’s nations. E. none of these options What distinguishes a “crime against humanity” from other kinds of crimes? A. Crimes against humanity involve government officials as perpetrators. B. Crimes against humanity target particular ethnic groups. C. Crimes against humanity are punishable by the death penalty. D. Crimes against humanity involve attacks on civilians. E. all of these options An important goal of the ICC is to eliminate “impunity” for crimes, which means eliminating which of the following? A. the ability of perpetrators to obtain the weapons they need to commit the crimes B. the expectation of perpetrators that they can commit crimes without being punished C. the expectation of perpetrators that they can evade arrest by national authorities D. the ability of perpetrators to get a court-appointed lawyer if they are arrested and tried E. the ability of perpetrators to cross national boundaries and escape extradition Supporting a Strong International Justice System Which of the following is NOT a part of the emerging international justice system? A. local courts B. national courts C. regional courts D. international Courts E. United Nations tribunals Which of the following represents one of the major challenges faced by the ICC? A. increasing awareness of its cause B. obtaining more funding from the United Nations C. securing greater state cooperation with its activities D. apprehending and prosecuting Germain Katanga E. getting the United States to join

Watch the videos, and then answer the questions below. http://www.youtube.com/watch?v=kt6SYhX_Ymo http://www.youtube.com/watch?v=ka3yTfmyjAw Building Justice Which of the following is true of the International Criminal Court (ICC)? A. It was the first court to try individuals for crimes against humanity. B. It was founded to prosecute Nazi war criminals. C. It is a permanent court with universal jurisdiction. D. It was created by a treaty that has been signed by all of the world’s nations. E. none of these options What distinguishes a “crime against humanity” from other kinds of crimes? A. Crimes against humanity involve government officials as perpetrators. B. Crimes against humanity target particular ethnic groups. C. Crimes against humanity are punishable by the death penalty. D. Crimes against humanity involve attacks on civilians. E. all of these options An important goal of the ICC is to eliminate “impunity” for crimes, which means eliminating which of the following? A. the ability of perpetrators to obtain the weapons they need to commit the crimes B. the expectation of perpetrators that they can commit crimes without being punished C. the expectation of perpetrators that they can evade arrest by national authorities D. the ability of perpetrators to get a court-appointed lawyer if they are arrested and tried E. the ability of perpetrators to cross national boundaries and escape extradition Supporting a Strong International Justice System Which of the following is NOT a part of the emerging international justice system? A. local courts B. national courts C. regional courts D. international Courts E. United Nations tribunals Which of the following represents one of the major challenges faced by the ICC? A. increasing awareness of its cause B. obtaining more funding from the United Nations C. securing greater state cooperation with its activities D. apprehending and prosecuting Germain Katanga E. getting the United States to join

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Question 2 (1 point) Which of the following is correct about interpreting the results of statistical tests? Question 2 options: 1) Obtaining a probability value of .05 tells us the difference between groups is definitely not caused by chance fluctuation. 2) If a probability value falls above .05, then the results will have to be replicated before we can have confidence in them. 3) Obtaining a probability value of .05 gives us confidence that the findings are not the result of chance, but does not eliminate this possibility. 4) A .05 probability value means there is a 5 percent chance the finding reflects a real difference. Question 3 (1 point) Which of the following statements is true about theories of personality? Question 3 options: 1) They provide only a part of the picture of human personality. 2) They support the expert’s viewpoint. 3) Theories are predicted from one hypothesis or another. 4) They are directly tested using empirical methods. Question 4 (1 point) Which of the following statements is correct about hypothetical constructs? Question 4 options: 1) They are useful inventions by researchers that have no physical reality. 2) They are easier to measure than personality variables. 3) They cannot be measured with personality tests. 4) They have poor reliability and validity. Question 5 (1 point) According to the “law of parsimony,” Question 5 options: 1) a good theory generates a large number of hypotheses. 2) the best theory is the one that explains a phenomenon with the fewest constructs. 3) hypotheses are generated from theories. 4) theories should require as few studies as possible to support them. ________________________________________ Question 6 (1 point) Which of the following does a correlation coefficient not tell us? Question 6 options: 1) If the difference between two means reflects a real difference or can be attributed tochancefluctuation. 2) The strength of a relationship between two measures. 3) The direction of a relationship between two measures. 4) How well a score on one measure can be predicted by a score on another measure. Question 7 (1 point) A researcher finds that males make fewer errors than females when working in a competitive situation. However, women make fewer errors than men when working in acooperative situation. This is an example of Question 7 options: 1) a confound. 2) two manipulated independent variables. 3) an interaction. 4) a failure to replicate.

Question 2 (1 point) Which of the following is correct about interpreting the results of statistical tests? Question 2 options: 1) Obtaining a probability value of .05 tells us the difference between groups is definitely not caused by chance fluctuation. 2) If a probability value falls above .05, then the results will have to be replicated before we can have confidence in them. 3) Obtaining a probability value of .05 gives us confidence that the findings are not the result of chance, but does not eliminate this possibility. 4) A .05 probability value means there is a 5 percent chance the finding reflects a real difference. Question 3 (1 point) Which of the following statements is true about theories of personality? Question 3 options: 1) They provide only a part of the picture of human personality. 2) They support the expert’s viewpoint. 3) Theories are predicted from one hypothesis or another. 4) They are directly tested using empirical methods. Question 4 (1 point) Which of the following statements is correct about hypothetical constructs? Question 4 options: 1) They are useful inventions by researchers that have no physical reality. 2) They are easier to measure than personality variables. 3) They cannot be measured with personality tests. 4) They have poor reliability and validity. Question 5 (1 point) According to the “law of parsimony,” Question 5 options: 1) a good theory generates a large number of hypotheses. 2) the best theory is the one that explains a phenomenon with the fewest constructs. 3) hypotheses are generated from theories. 4) theories should require as few studies as possible to support them. ________________________________________ Question 6 (1 point) Which of the following does a correlation coefficient not tell us? Question 6 options: 1) If the difference between two means reflects a real difference or can be attributed tochancefluctuation. 2) The strength of a relationship between two measures. 3) The direction of a relationship between two measures. 4) How well a score on one measure can be predicted by a score on another measure. Question 7 (1 point) A researcher finds that males make fewer errors than females when working in a competitive situation. However, women make fewer errors than men when working in acooperative situation. This is an example of Question 7 options: 1) a confound. 2) two manipulated independent variables. 3) an interaction. 4) a failure to replicate.

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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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1. Develop a thought experiment that attempts to uncover hidden assumptions about human freedom. 2. Find a paragraph from a book, magazine, ect. First, tell whether there are claims in the paragraph. If there are, identify the types of claims (descriptive, normative, a priori, a posteriori) in the paragraph

1. Develop a thought experiment that attempts to uncover hidden assumptions about human freedom. 2. Find a paragraph from a book, magazine, ect. First, tell whether there are claims in the paragraph. If there are, identify the types of claims (descriptive, normative, a priori, a posteriori) in the paragraph

Let us think of a thought experiment that wants to … Read More...