Assignment One Suggested Due Date: July 17th In this assignment you will read three articles You will answer questions about Hayek, Lucas, and Mankiw et. al. which consider just those particular articles. Then at the end of the assignment there is a cluster of questions that deal with both Lucas and Mankiw et al where you will have an opportunity to compare and contrast those two articles. When you have completed the assignment, place it in the appropriate drop box in WTClass. Hayek: The Use of Knowledge in Society http://www.econlib.org/library/Essays/hykKnw1.html Adapted from Michael K. Salemi “The Use of Knowledge in Society” F. A. Hayek Discussion Questions 1.1. “The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form, but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess (H.3)” a. What does Hayek mean by a “rational economic order”? b. What does Hayek mean by “dispersed bits of incomplete and frequently contradictory knowledge”? c. Why is Hayek critical of the common assumptions in economic analysis that buyers, sellers, producers and the economist all know every relevant thing about the economy? d. What, in summary, does Hayek mean by the quoted statement? 1.2. What, according to Hayek, is the information needed to operate effectively in a complex market economy? a. What does Hayek mean by “planning”? b. What is the minimum information needed by economic planners and individuals? c. Does the minimum differ for planners and for individuals? How? Why? d. What happens when some individuals possess more information than other individuals? e. What does Hayek mean when he says (H.16) “…the sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form”? f. Why, according to Hayek, can the “information problem” be solved by “the price system”? 1.3. Why, according to Hayek, is the true function of the price system the communication of information? a. Why does Hayek use the term ‘marvel’ in his discussion of the economy of knowledge? b. What does Hayek mean when he says (H.26) “…man has been able to develop that division of labor on which our civilization is based because he happened to stumble upon a method which made it possible”? Read Robert Lucas’ “Some Macroeconomics for the 21st Century” in the Journal of Economic Perspectives. (Skip the appendix.) All four of these links go to the same article. Some of the links might not be accessible to you, but I think that at least one of them should work for all of you. https://www.aeaweb.org/articles.php?doi=10.1257/jep.14.1.159 http://www.jstor.org/stable/2647059 http://www.econ.psu.edu/~aur10/Econ%20570%20Fall%202009/Lucas%20JEP%202000.pdf http://faculty.georgetown.edu/mh5/class/econ102/readings/Macro_21st_Century.pdf 1. According to Lucas, why has the world’s economy grown so much since 1960? 2. According to Lucas, why do some nations grow faster than others? 3. According to Lucas, why will growth and inequality decrease in the next 100 years? 4. Is Lucas’ model in this paper “economics?” Read Greg Mankiw, Romer and Wiel’s article in The Quarterly Journal of Economics. http://www.econ.nyu.edu/user/debraj/Courses/Readings/MankiwRomerWeil.pdf 1. Many economists think the Solow Growth Model is of limited use. (One of my professors at OU stated that it took economists 50 years to figure out that their growth model has nothing to do with growth.) But does the Solow model give “…the right answer to the questions it is designed to address?” 2. Why is human capital important when testing the Solow model against the data? 3. Explain how the authors conclude that the incomes of the world’s nations are converging? Now that you’ve answered questions about Lucas and Mankiw et al separately, consider this question: Both of these papers develop the notion that the economies of the world’s nations will tend to “converge” over time. Compare and contrast the way(s) in which the papers advance the idea of convergence. Assignment Two Due Date July 24th This assignment is very straight forward. You’ll read two papers and answer questions about each of them. Read Krugman’s paper on unemployment http://www.kc.frb.org/PUBLICAT/ECONREV/EconRevArchive/1994/4Q94KRUG.pdf 1. What is the difference between structural and cyclical unemployment? In this context, what is the difference between Europe and the US? What is the evidence that Krugman uses to back his opinion? 2. What is the natural rate of unemployment? Why is it higher/rising in Europe? Again, what is the evidence? 3. What is the relationship between the rising unemployment in Europe and the rise in inequality in the US. (What does Krugman mean by inequality?) 4. What is NOT to blame for either the rise in unemployment or inequality? 5. What policies, if any, can be put into place to combat rising inequality/unemployment? 6. Are you convinced by Krugman’s argument which rules out globalization as the likely cause for high European unemployment and high US wage inequality? 7. Consider Table 2 in Krugman. Why does Krugman include Table 2 in his paper? In other words, what point is strengthened by the data in Table 2 and why is it crucial to Krugman’s larger thesis? NOW, recreate the data for Table 2 for either the UK or US for the latest year possible. Has anything changed as a result of the Great Recession? Read Thomas Sargent’s paper about the credibility of “Reaganonomics.” http://minneapolisfed.contentdm.oclc.org/cdm/ref/collection/p15334coll1/id/366 http://minneapolisfed.contentdm.oclc.org/cdm/singleitem/collection/p15334coll1/id/366/rec/1 You might like this: http://www.ispot.tv/ad/7Lj9/ally-bank-predictions-featuring-thomas-sargent 1. What is a dynamic game? 2. Why should we think of monetary and fiscal policy as dynamic game? Who are the players and what are the strategies? 3. When are government budgets inflationary? (Again, think in terms of a game.) 4. What are the consequences if the monetary authority does not coordinate with fiscal policy agents? 5. Has Sargent done of good job characterizing the interplay between policymakers in the government, the central bank, and the public? 6. What is the connection between policy coordination and credibility? 7. Why, according to Sargent, were Reagan’s fiscal and monetary policy regimes “incredible?” Explain carefully. Assignment Three Due Date July 31 Read Taylor, Miskin, Obstfeld and Rogoff. Answer the questions for each article, then answer the final cluster that requires you to consider Miskin, Obstfeld and Rogoff. Suggested due date: January 2nd. Read John Taylor’s article about monetary transmission mechanisms. http://web.econ.unito.it/bagliano/ecmon_readings/taylor_jep95.pdf Also, to understand traditional monetary policy, listen to this: http://www.econtalk.org/archives/2008/08/john_taylor_on.html These questions refer to the article, not the podcast. 1. How does monetary policy (or changes in monetary policy) affect output and inflation? In other words, what is the monetary policy transmission mechanism? 2. What is the importance of financial market prices in Taylor’s view? 3. What is the importance of rational expectations and rigidities in the prices of labor and goods? 4. What is a reaction function? Why is a reaction function important? 5. What is an “optimal monetary policy rule?” 6. Has the monetary transmission mechanism changed? How? 7. What are the criticisms of Taylor’s views? How does he respond? What do you think? Read Mishkin’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.3 1. What is a financial crisis? 2. How did adverse selection and moral hazard contribute to the financial crisis in Mexico and East Asia in the 1990s? What are adverse selection and moral hazard? 3. Did irresponsible monetary and fiscal policy contribute to the crisis in the 90s? Why or why not? 4. How is it possible for the IMF to help in a crisis when a domestic central bank might not be able to help. 5. What should the US learn (or have learned??) from the crisis in the 90s? Read Rogoff’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 Answer the questions and place the answers in the appropriate drop box in WTClass. 1. According to Rogoff, is the status quo in international lending viable or not? Explain. 2. Can the IMF handle international financial crises? Why or why not? 3. Rogoff gives six solutions to save the global financial system (deep pockets lender of last resort, an international financial crisis manager, an international bankruptcy court, an international regulator, international deposit insurance corporation, and a world monetary authority.) What is wrong with all of these? 4. Can developing economies cope with speculative capital flows without help? Explain. 5. What will be (should be) the role that equity financing play in developing country projects? Read Obstfeld on Global Capital Markets: http://www.nber.org/papers/w6559.pdf 1. Look at table 1 and figure 1. How does Obstfeld use the data in that table to suggest that 1) markets became less open then more open in the 20th century. 2. What is the “openness trilemma?” What are the economic and/or policy trade-offs with having a global, open and integrated financial system? 3. How does economic integration impact a nation’s ability to tax capital? Can you think of some high profile cases in the news lately that illustrate this fact? (Hint: you should be able to.) 4. What is the international diversification puzzle? What market failures have arisen (if any) have arisen due to more integration and openness? Comparing Obstfeld, Miskin, and Rogoff 1. Would the authors’ advice about policies to reduce the costs of financial integration be the same? Why or why not? 2. Would the authors’ agree that we need an international regulatory body to stave off international financial crises? Why or why not? 3. What is your opinion? Is it good to have a global financial market? Why or why not? Assignment Four Due Date August 7 Straight forward assignment: Read and answer the questions. Read Arnold Kling’s history of the policies that created the great recession http://mercatus.org/publication/not-what-they-had-mind-history-policies-produced-financial-crisis-2008 1. Using only the executive summary, what does Kling think caused the Financial Crisis of 2008? (Use only one sentence.) 2. One page 5, what is “the fact?” and what does this “fact” mean to you? 3. Briefly summarize the four components of the Financial Crisis? 4. On page 10, Kling states, “These property bubbles (in the U.K. and Spain) cannot be blamed on U.S. policy.” How confident are you on that point? Is Kling wrong? 5. Kling’s matrix of causes, gives almost all weight to what two factors? What three factors are almost completely not responsible? 6. Many have blamed designer financial (my term) like CDS and CDO and the shadow banking system for the collapse. How do these fit into Kling’s narrative? 7. Outline the progression of policy that caused/responded to economic conditions in the 30s, 70s and 80s and 00s. 8. What role did the mortgage interest deduction have on housing market? 9. What institution invented and allowed the expansion of mortgage-backed securities? 10. What is regulatory arbitrage? 11. Why did the Basel agreement create an advantage for mortgage securitization? 12. Did the Federal Reserve (and presumably other regulatory agencies know and even encourage regulatory capital arbitrage? What author does Kling cite to establish this? 13. What did the 2002 modification of the Basel Rules do to capital requirements? (See figure 4) 14. Summarize the Shadow Regulatory Committee’s statement 160. 15. Did non market institutions, such as the IMF and Bernanke, think, in 2006, that financial innovation had make the banking sector more or less fragile? 16. What is time inconsistency? (You can look this up elsewhere.) 17. How might “barriers to entry” by related to “safety and soundness?” 18. A Curmudgeon is an old man who is easily annoyed and angered. He also complains a lot. (I had to look it up.) I think I’ll change my xbox gamertag to this word, but I’ll bet it is taken. 19. How did credit scoring and credit default swaps enlarge the mortgage securities market? 20. Why, up until 2007, did we think that monetary expansion was all that was needed to mitigate the impact of financial crises? 21. Suppose that financial markets are inherently unstable. What does this mean are two goals of regulation and regulators? 22. Why are type two errors so problematic? (Two reasons.) 23. How could we make the banking sector easy to fix? Assignment Five Due August 13 Read the linked lectures and answer the questions. Lecture 1 http://econlog.econlib.org/archives/2008/11/lectures_in_mac.html 1.1 Why do you think macroeconomic realities must be reconciled with microeconomic analysis? (This is not a rhetorical question, but it will be hard for you to answer. There is no “wrong” answer you could give. Just think about it for a few minutes.) Lecture 2 http://econlog.econlib.org/archives/2008/11/lectures_in_mac_1.html 2.1 Consider this article after you have read Hayek. How do prices and wages perform the function of “central planning?” 2.2 Kling makes that claim that, because most workers do not do manual labor anymore, the economy is different that it was in 1930. Assuming he is correct, do you think central planning would be harder today or easier? Why? Lecture 3 http://econlog.econlib.org/archives/2008/11/lectures_on_mac.html 3.1 Give a one sentence definition of structural unemployment, of frictional unemployment and of cyclical unemployment. Lecture 4 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_1.html 4.1 So, why does the economy adjust employment rather than wages? Lecture 5 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_2.html 5.1 Kling gives 5 reasons the DotCom recession was worse than the previous two recessions (at least in duration). Which reason do you think is the most compelling? Lecture 6 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_3.html 6.1 Why are Keynesian remedies (blunt fiscal and monetary policy measures) less appropriate in a post industrial economy, according to Kling? Lecture 7 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_4.html 7.1 Why is it so hard to separate finance and government, according to Kling? Lecture 8 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_5.html 8.1 Why is American Express Travelers Checks so interesting? Do credit cards work in a similar way? (I really don’t know the answer to this one. I just know that credit cards have made travelers checks obsolete.) Lecture 9. http://econlog.econlib.org/archives/2008/12/lectures_on_mac_6.html 9.1 According to this article, why do we have banks (financial sector or financial intermediation?) Lecture 10 http://econlog.econlib.org/archives/2008/12/lectures_on_mac_7.html 10.1 Why are banks better than barter, according to this leture? 10.2 Politics tends to favor bailouts of failed firms. Why is this exactly wrong?

Assignment One Suggested Due Date: July 17th In this assignment you will read three articles You will answer questions about Hayek, Lucas, and Mankiw et. al. which consider just those particular articles. Then at the end of the assignment there is a cluster of questions that deal with both Lucas and Mankiw et al where you will have an opportunity to compare and contrast those two articles. When you have completed the assignment, place it in the appropriate drop box in WTClass. Hayek: The Use of Knowledge in Society http://www.econlib.org/library/Essays/hykKnw1.html Adapted from Michael K. Salemi “The Use of Knowledge in Society” F. A. Hayek Discussion Questions 1.1. “The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form, but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess (H.3)” a. What does Hayek mean by a “rational economic order”? b. What does Hayek mean by “dispersed bits of incomplete and frequently contradictory knowledge”? c. Why is Hayek critical of the common assumptions in economic analysis that buyers, sellers, producers and the economist all know every relevant thing about the economy? d. What, in summary, does Hayek mean by the quoted statement? 1.2. What, according to Hayek, is the information needed to operate effectively in a complex market economy? a. What does Hayek mean by “planning”? b. What is the minimum information needed by economic planners and individuals? c. Does the minimum differ for planners and for individuals? How? Why? d. What happens when some individuals possess more information than other individuals? e. What does Hayek mean when he says (H.16) “…the sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form”? f. Why, according to Hayek, can the “information problem” be solved by “the price system”? 1.3. Why, according to Hayek, is the true function of the price system the communication of information? a. Why does Hayek use the term ‘marvel’ in his discussion of the economy of knowledge? b. What does Hayek mean when he says (H.26) “…man has been able to develop that division of labor on which our civilization is based because he happened to stumble upon a method which made it possible”? Read Robert Lucas’ “Some Macroeconomics for the 21st Century” in the Journal of Economic Perspectives. (Skip the appendix.) All four of these links go to the same article. Some of the links might not be accessible to you, but I think that at least one of them should work for all of you. https://www.aeaweb.org/articles.php?doi=10.1257/jep.14.1.159 http://www.jstor.org/stable/2647059 http://www.econ.psu.edu/~aur10/Econ%20570%20Fall%202009/Lucas%20JEP%202000.pdf http://faculty.georgetown.edu/mh5/class/econ102/readings/Macro_21st_Century.pdf 1. According to Lucas, why has the world’s economy grown so much since 1960? 2. According to Lucas, why do some nations grow faster than others? 3. According to Lucas, why will growth and inequality decrease in the next 100 years? 4. Is Lucas’ model in this paper “economics?” Read Greg Mankiw, Romer and Wiel’s article in The Quarterly Journal of Economics. http://www.econ.nyu.edu/user/debraj/Courses/Readings/MankiwRomerWeil.pdf 1. Many economists think the Solow Growth Model is of limited use. (One of my professors at OU stated that it took economists 50 years to figure out that their growth model has nothing to do with growth.) But does the Solow model give “…the right answer to the questions it is designed to address?” 2. Why is human capital important when testing the Solow model against the data? 3. Explain how the authors conclude that the incomes of the world’s nations are converging? Now that you’ve answered questions about Lucas and Mankiw et al separately, consider this question: Both of these papers develop the notion that the economies of the world’s nations will tend to “converge” over time. Compare and contrast the way(s) in which the papers advance the idea of convergence. Assignment Two Due Date July 24th This assignment is very straight forward. You’ll read two papers and answer questions about each of them. Read Krugman’s paper on unemployment http://www.kc.frb.org/PUBLICAT/ECONREV/EconRevArchive/1994/4Q94KRUG.pdf 1. What is the difference between structural and cyclical unemployment? In this context, what is the difference between Europe and the US? What is the evidence that Krugman uses to back his opinion? 2. What is the natural rate of unemployment? Why is it higher/rising in Europe? Again, what is the evidence? 3. What is the relationship between the rising unemployment in Europe and the rise in inequality in the US. (What does Krugman mean by inequality?) 4. What is NOT to blame for either the rise in unemployment or inequality? 5. What policies, if any, can be put into place to combat rising inequality/unemployment? 6. Are you convinced by Krugman’s argument which rules out globalization as the likely cause for high European unemployment and high US wage inequality? 7. Consider Table 2 in Krugman. Why does Krugman include Table 2 in his paper? In other words, what point is strengthened by the data in Table 2 and why is it crucial to Krugman’s larger thesis? NOW, recreate the data for Table 2 for either the UK or US for the latest year possible. Has anything changed as a result of the Great Recession? Read Thomas Sargent’s paper about the credibility of “Reaganonomics.” http://minneapolisfed.contentdm.oclc.org/cdm/ref/collection/p15334coll1/id/366 http://minneapolisfed.contentdm.oclc.org/cdm/singleitem/collection/p15334coll1/id/366/rec/1 You might like this: http://www.ispot.tv/ad/7Lj9/ally-bank-predictions-featuring-thomas-sargent 1. What is a dynamic game? 2. Why should we think of monetary and fiscal policy as dynamic game? Who are the players and what are the strategies? 3. When are government budgets inflationary? (Again, think in terms of a game.) 4. What are the consequences if the monetary authority does not coordinate with fiscal policy agents? 5. Has Sargent done of good job characterizing the interplay between policymakers in the government, the central bank, and the public? 6. What is the connection between policy coordination and credibility? 7. Why, according to Sargent, were Reagan’s fiscal and monetary policy regimes “incredible?” Explain carefully. Assignment Three Due Date July 31 Read Taylor, Miskin, Obstfeld and Rogoff. Answer the questions for each article, then answer the final cluster that requires you to consider Miskin, Obstfeld and Rogoff. Suggested due date: January 2nd. Read John Taylor’s article about monetary transmission mechanisms. http://web.econ.unito.it/bagliano/ecmon_readings/taylor_jep95.pdf Also, to understand traditional monetary policy, listen to this: http://www.econtalk.org/archives/2008/08/john_taylor_on.html These questions refer to the article, not the podcast. 1. How does monetary policy (or changes in monetary policy) affect output and inflation? In other words, what is the monetary policy transmission mechanism? 2. What is the importance of financial market prices in Taylor’s view? 3. What is the importance of rational expectations and rigidities in the prices of labor and goods? 4. What is a reaction function? Why is a reaction function important? 5. What is an “optimal monetary policy rule?” 6. Has the monetary transmission mechanism changed? How? 7. What are the criticisms of Taylor’s views? How does he respond? What do you think? Read Mishkin’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.3 1. What is a financial crisis? 2. How did adverse selection and moral hazard contribute to the financial crisis in Mexico and East Asia in the 1990s? What are adverse selection and moral hazard? 3. Did irresponsible monetary and fiscal policy contribute to the crisis in the 90s? Why or why not? 4. How is it possible for the IMF to help in a crisis when a domestic central bank might not be able to help. 5. What should the US learn (or have learned??) from the crisis in the 90s? Read Rogoff’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 Answer the questions and place the answers in the appropriate drop box in WTClass. 1. According to Rogoff, is the status quo in international lending viable or not? Explain. 2. Can the IMF handle international financial crises? Why or why not? 3. Rogoff gives six solutions to save the global financial system (deep pockets lender of last resort, an international financial crisis manager, an international bankruptcy court, an international regulator, international deposit insurance corporation, and a world monetary authority.) What is wrong with all of these? 4. Can developing economies cope with speculative capital flows without help? Explain. 5. What will be (should be) the role that equity financing play in developing country projects? Read Obstfeld on Global Capital Markets: http://www.nber.org/papers/w6559.pdf 1. Look at table 1 and figure 1. How does Obstfeld use the data in that table to suggest that 1) markets became less open then more open in the 20th century. 2. What is the “openness trilemma?” What are the economic and/or policy trade-offs with having a global, open and integrated financial system? 3. How does economic integration impact a nation’s ability to tax capital? Can you think of some high profile cases in the news lately that illustrate this fact? (Hint: you should be able to.) 4. What is the international diversification puzzle? What market failures have arisen (if any) have arisen due to more integration and openness? Comparing Obstfeld, Miskin, and Rogoff 1. Would the authors’ advice about policies to reduce the costs of financial integration be the same? Why or why not? 2. Would the authors’ agree that we need an international regulatory body to stave off international financial crises? Why or why not? 3. What is your opinion? Is it good to have a global financial market? Why or why not? Assignment Four Due Date August 7 Straight forward assignment: Read and answer the questions. Read Arnold Kling’s history of the policies that created the great recession http://mercatus.org/publication/not-what-they-had-mind-history-policies-produced-financial-crisis-2008 1. Using only the executive summary, what does Kling think caused the Financial Crisis of 2008? (Use only one sentence.) 2. One page 5, what is “the fact?” and what does this “fact” mean to you? 3. Briefly summarize the four components of the Financial Crisis? 4. On page 10, Kling states, “These property bubbles (in the U.K. and Spain) cannot be blamed on U.S. policy.” How confident are you on that point? Is Kling wrong? 5. Kling’s matrix of causes, gives almost all weight to what two factors? What three factors are almost completely not responsible? 6. Many have blamed designer financial (my term) like CDS and CDO and the shadow banking system for the collapse. How do these fit into Kling’s narrative? 7. Outline the progression of policy that caused/responded to economic conditions in the 30s, 70s and 80s and 00s. 8. What role did the mortgage interest deduction have on housing market? 9. What institution invented and allowed the expansion of mortgage-backed securities? 10. What is regulatory arbitrage? 11. Why did the Basel agreement create an advantage for mortgage securitization? 12. Did the Federal Reserve (and presumably other regulatory agencies know and even encourage regulatory capital arbitrage? What author does Kling cite to establish this? 13. What did the 2002 modification of the Basel Rules do to capital requirements? (See figure 4) 14. Summarize the Shadow Regulatory Committee’s statement 160. 15. Did non market institutions, such as the IMF and Bernanke, think, in 2006, that financial innovation had make the banking sector more or less fragile? 16. What is time inconsistency? (You can look this up elsewhere.) 17. How might “barriers to entry” by related to “safety and soundness?” 18. A Curmudgeon is an old man who is easily annoyed and angered. He also complains a lot. (I had to look it up.) I think I’ll change my xbox gamertag to this word, but I’ll bet it is taken. 19. How did credit scoring and credit default swaps enlarge the mortgage securities market? 20. Why, up until 2007, did we think that monetary expansion was all that was needed to mitigate the impact of financial crises? 21. Suppose that financial markets are inherently unstable. What does this mean are two goals of regulation and regulators? 22. Why are type two errors so problematic? (Two reasons.) 23. How could we make the banking sector easy to fix? Assignment Five Due August 13 Read the linked lectures and answer the questions. Lecture 1 http://econlog.econlib.org/archives/2008/11/lectures_in_mac.html 1.1 Why do you think macroeconomic realities must be reconciled with microeconomic analysis? (This is not a rhetorical question, but it will be hard for you to answer. There is no “wrong” answer you could give. Just think about it for a few minutes.) Lecture 2 http://econlog.econlib.org/archives/2008/11/lectures_in_mac_1.html 2.1 Consider this article after you have read Hayek. How do prices and wages perform the function of “central planning?” 2.2 Kling makes that claim that, because most workers do not do manual labor anymore, the economy is different that it was in 1930. Assuming he is correct, do you think central planning would be harder today or easier? Why? Lecture 3 http://econlog.econlib.org/archives/2008/11/lectures_on_mac.html 3.1 Give a one sentence definition of structural unemployment, of frictional unemployment and of cyclical unemployment. Lecture 4 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_1.html 4.1 So, why does the economy adjust employment rather than wages? Lecture 5 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_2.html 5.1 Kling gives 5 reasons the DotCom recession was worse than the previous two recessions (at least in duration). Which reason do you think is the most compelling? Lecture 6 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_3.html 6.1 Why are Keynesian remedies (blunt fiscal and monetary policy measures) less appropriate in a post industrial economy, according to Kling? Lecture 7 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_4.html 7.1 Why is it so hard to separate finance and government, according to Kling? Lecture 8 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_5.html 8.1 Why is American Express Travelers Checks so interesting? Do credit cards work in a similar way? (I really don’t know the answer to this one. I just know that credit cards have made travelers checks obsolete.) Lecture 9. http://econlog.econlib.org/archives/2008/12/lectures_on_mac_6.html 9.1 According to this article, why do we have banks (financial sector or financial intermediation?) Lecture 10 http://econlog.econlib.org/archives/2008/12/lectures_on_mac_7.html 10.1 Why are banks better than barter, according to this leture? 10.2 Politics tends to favor bailouts of failed firms. Why is this exactly wrong?

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Phys4A: Practice problems for the 1st midterm test Fall 2015 1 If K has dimensions ML2/T 2, the k in K = kmv 2 must be: Answer: dimensionless 2. A 8.7 hour trip is made at an average speed of 73.0 km/h. If the first third of the trip (chronologically) was driven at 96.5 km/h, what was the average speed for the rest of the journey? Answer: 61 km/h 3. A car travels 95 km to the north at 70.0 km/h, then turns around and travels 21.9 km at 80.0 km/h. What is the difference between the average speed and the average velocity on this trip? Answer: 27 km/h 4. A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval? Answer: 0.32 m/s2 5. A package is dropped from a helicopter moving upward at 15 m/s. If it takes 16.0 s before the package strikes the ground, how high above the ground was the package when it was released? (Disregard air resistance.) Answer: 1000m 6. If vector B is added to vector A, the result is 6i + j. If B is subtracted from A, the result is –4i + 7j. What is the magnitude of A? Answer: 4.1 7. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis? Answer: 51° W of N 8 A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A man can row a boat at 2.00 mi/h. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is, Answer: 1.15 h 9 An airplane is heading due east. The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air. If the wind is blowing from the south at 92.5 km/h, the velocity of the airplane relative to the ground is: Answer: 381 km/h at 76o east of north 10. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building? Answer: 23.6m 11. A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory? Answer: 0.160 s 12. A helicopter is traveling at 54 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground? Note: air resistance negligible. Answer: 70 m/s 13 A rescue airplane is diving at an angle of 37º below the horizontal with a speed of 250 m/s. It releases a survival package when it is at an altitude of 600 m. If air resistance is ignored, the horizontal distance of the point of impact from the plane at the moment of the package’s release is, Answer: 720 m 14. A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point. What was the angle of launch? Answer: 69.0° 15. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time? Answer: 2.2 m/s2 16 A ball is whirled in a horizontal circle of radius r and speed v. The radius is increased to 2r keeping the speed of the ball constant. The period of the ball changes by a factor of Answer: two

Phys4A: Practice problems for the 1st midterm test Fall 2015 1 If K has dimensions ML2/T 2, the k in K = kmv 2 must be: Answer: dimensionless 2. A 8.7 hour trip is made at an average speed of 73.0 km/h. If the first third of the trip (chronologically) was driven at 96.5 km/h, what was the average speed for the rest of the journey? Answer: 61 km/h 3. A car travels 95 km to the north at 70.0 km/h, then turns around and travels 21.9 km at 80.0 km/h. What is the difference between the average speed and the average velocity on this trip? Answer: 27 km/h 4. A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval? Answer: 0.32 m/s2 5. A package is dropped from a helicopter moving upward at 15 m/s. If it takes 16.0 s before the package strikes the ground, how high above the ground was the package when it was released? (Disregard air resistance.) Answer: 1000m 6. If vector B is added to vector A, the result is 6i + j. If B is subtracted from A, the result is –4i + 7j. What is the magnitude of A? Answer: 4.1 7. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis? Answer: 51° W of N 8 A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A man can row a boat at 2.00 mi/h. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is, Answer: 1.15 h 9 An airplane is heading due east. The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air. If the wind is blowing from the south at 92.5 km/h, the velocity of the airplane relative to the ground is: Answer: 381 km/h at 76o east of north 10. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building? Answer: 23.6m 11. A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory? Answer: 0.160 s 12. A helicopter is traveling at 54 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground? Note: air resistance negligible. Answer: 70 m/s 13 A rescue airplane is diving at an angle of 37º below the horizontal with a speed of 250 m/s. It releases a survival package when it is at an altitude of 600 m. If air resistance is ignored, the horizontal distance of the point of impact from the plane at the moment of the package’s release is, Answer: 720 m 14. A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point. What was the angle of launch? Answer: 69.0° 15. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time? Answer: 2.2 m/s2 16 A ball is whirled in a horizontal circle of radius r and speed v. The radius is increased to 2r keeping the speed of the ball constant. The period of the ball changes by a factor of Answer: two

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ENGR 3300: Fluid Mechanics, Fall 2015 Assignment 3 Due: Friday, Oct. 2, 2015 Topics: Chapter 3 & 4 Solutions must be neatly written and must include the following steps (if applicable) to receive full credit. 1. Given: List all known parameters in the problem. 2. Find: List what parameters the problem is asking you to find. 3. Solution: List all equations needed to solve the problem, and show all your work. Draw any necessary sketches or free body diagrams. Circle or box your final answer, and make sure to include appropriate units in your final answer. Grading: 15 total points (10 points for completeness + 5 points for one randomly chosen problem graded for correctness) 1. Water flows at a steady rate up a vertical pipe and out a nozzle into open air. The pipe diameter is 1 inch and the nozzle diameter is 0.5 inches. (a) Determine the minimum pressure that would be required at section 1 (shown in the figure below) to produce a fluid velocity of 30 ft/s at the nozzle (section 2). (b) If the pipe was inverted, determine the minimum pressure that would be required at section 1 to maintain the 30 ft/s velocity at the nozzle. 2. Water flows from a large tank through a small pipe with a diameter of 5 cm. A mercury manometer is placed along the pipe. Assuming the flow is frictionless, (a) estimate the velocity of the water in the pipe and (b) determine the rate of discharge (i.e. volumetric flow rate) from the tank. 3. An engineer is designing a suit for a race car driver and wants to supply cooling air to the suit from an air inlet on the body of the race car. The air speed at the inlet location must be 65 mph when the race car is traveling at 230 mph. Under these conditions, what would be the static pressure at the proposed inlet location? 4. Air flows downward toward a horizontal flat plate. The velocity field is given by ? = (??! − ??!)(2 + cos ??) where a = 5 s-1, ω = 2π s-1, and x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in seconds. (a) Obtain an algebraic equation for a streamline at t = 0. (b) Plot the streamline that passes through point (x,y) = (3,3) at this instant.

ENGR 3300: Fluid Mechanics, Fall 2015 Assignment 3 Due: Friday, Oct. 2, 2015 Topics: Chapter 3 & 4 Solutions must be neatly written and must include the following steps (if applicable) to receive full credit. 1. Given: List all known parameters in the problem. 2. Find: List what parameters the problem is asking you to find. 3. Solution: List all equations needed to solve the problem, and show all your work. Draw any necessary sketches or free body diagrams. Circle or box your final answer, and make sure to include appropriate units in your final answer. Grading: 15 total points (10 points for completeness + 5 points for one randomly chosen problem graded for correctness) 1. Water flows at a steady rate up a vertical pipe and out a nozzle into open air. The pipe diameter is 1 inch and the nozzle diameter is 0.5 inches. (a) Determine the minimum pressure that would be required at section 1 (shown in the figure below) to produce a fluid velocity of 30 ft/s at the nozzle (section 2). (b) If the pipe was inverted, determine the minimum pressure that would be required at section 1 to maintain the 30 ft/s velocity at the nozzle. 2. Water flows from a large tank through a small pipe with a diameter of 5 cm. A mercury manometer is placed along the pipe. Assuming the flow is frictionless, (a) estimate the velocity of the water in the pipe and (b) determine the rate of discharge (i.e. volumetric flow rate) from the tank. 3. An engineer is designing a suit for a race car driver and wants to supply cooling air to the suit from an air inlet on the body of the race car. The air speed at the inlet location must be 65 mph when the race car is traveling at 230 mph. Under these conditions, what would be the static pressure at the proposed inlet location? 4. Air flows downward toward a horizontal flat plate. The velocity field is given by ? = (??! − ??!)(2 + cos ??) where a = 5 s-1, ω = 2π s-1, and x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in seconds. (a) Obtain an algebraic equation for a streamline at t = 0. (b) Plot the streamline that passes through point (x,y) = (3,3) at this instant.

Name: Lab Time: BIO 218 Experiment Paper Rubric (20 points) General Formatting: (2 pts.) • Margins should be 1 inch top, bottom, left, and right. • Font should be 12 point Times New Roman or similar font. • Double-spaced. • Pages numbered. Title page is unnumbered. Next page is numbered at the bottom right corner with a 2 followed by pages 3, 4, and 5. • All sections must be included: Abstract, Introduction, Methods, Results, Discussion, and Literature Cited. • At least 3 pages (double spaced) but no more than five pages long. • All scientific names should be formatted correctly by italicizing and capitalizing the genus name and having the species name in lowercase (Bufo americanus). • Title page should have a specific title, student name, course, lab section time, and date. Project elements (18 pts. Total) • Abstract (2 points) o Summarize most important points using past tense. Use present tense to suggest a general conclusion which supports or refutes the hypothesis. • Introduction (3 points) o General background on topic and species (state scientific name!) o Discuss the possible tests of the hypothesis. o Reads from general to specific. o States hypothesis/hypotheses to be addressed. May discuss null and all alternative hypotheses. • Methods (2 points) o Reports how experiment was conducted and all materials used. Use enough detail so others could repeat the study. o Discuss the type(s) of data collected. o Discuss how data was to be analyzed/compared/used to test hypothesis. • Results (3 points) o Reports what happened in the experiment. o If comparisons made, discuss how they were made. o Report statistical and other data. Use “significant” only for statistical significance. o NO interpretation of data (no data analysis). o At least one original figure present and formatted correctly. Figures such as pictures and graphs are numbered and have captions underneath. o At least one table present and formatted correctly. Tables such as charts are numbered and have captions above them. • Discussion: (3 points) o Discusses the results of the experiment and ties in how the results fit with the literature. o Use past tense to discuss your results and shift to present tense to discuss previously published information. o States how results supported or refuted the original hypothesis. Hypotheses are never proven! o Ties in results with big picture within topic of biology. • Literature Cited: (2 points: .5 per citation) o At least 2 peer-reviewed journal articles (provided) + 2 peer-reviewed journal articles (found on your own). o References used in text properly. o References all listed in this section are alphabetized by author’s last name and formatted correctly. o All references listed in the Literature Cited section are cited in text. Writing Elements (3 pts.) • Grammar or spelling is error-free and excellent print quality. (1 pt) • Writing is clear and flows logically throughout paper. (1 pt) • Appropriate content in each section? (1 pt) Additional Comments:

Name: Lab Time: BIO 218 Experiment Paper Rubric (20 points) General Formatting: (2 pts.) • Margins should be 1 inch top, bottom, left, and right. • Font should be 12 point Times New Roman or similar font. • Double-spaced. • Pages numbered. Title page is unnumbered. Next page is numbered at the bottom right corner with a 2 followed by pages 3, 4, and 5. • All sections must be included: Abstract, Introduction, Methods, Results, Discussion, and Literature Cited. • At least 3 pages (double spaced) but no more than five pages long. • All scientific names should be formatted correctly by italicizing and capitalizing the genus name and having the species name in lowercase (Bufo americanus). • Title page should have a specific title, student name, course, lab section time, and date. Project elements (18 pts. Total) • Abstract (2 points) o Summarize most important points using past tense. Use present tense to suggest a general conclusion which supports or refutes the hypothesis. • Introduction (3 points) o General background on topic and species (state scientific name!) o Discuss the possible tests of the hypothesis. o Reads from general to specific. o States hypothesis/hypotheses to be addressed. May discuss null and all alternative hypotheses. • Methods (2 points) o Reports how experiment was conducted and all materials used. Use enough detail so others could repeat the study. o Discuss the type(s) of data collected. o Discuss how data was to be analyzed/compared/used to test hypothesis. • Results (3 points) o Reports what happened in the experiment. o If comparisons made, discuss how they were made. o Report statistical and other data. Use “significant” only for statistical significance. o NO interpretation of data (no data analysis). o At least one original figure present and formatted correctly. Figures such as pictures and graphs are numbered and have captions underneath. o At least one table present and formatted correctly. Tables such as charts are numbered and have captions above them. • Discussion: (3 points) o Discusses the results of the experiment and ties in how the results fit with the literature. o Use past tense to discuss your results and shift to present tense to discuss previously published information. o States how results supported or refuted the original hypothesis. Hypotheses are never proven! o Ties in results with big picture within topic of biology. • Literature Cited: (2 points: .5 per citation) o At least 2 peer-reviewed journal articles (provided) + 2 peer-reviewed journal articles (found on your own). o References used in text properly. o References all listed in this section are alphabetized by author’s last name and formatted correctly. o All references listed in the Literature Cited section are cited in text. Writing Elements (3 pts.) • Grammar or spelling is error-free and excellent print quality. (1 pt) • Writing is clear and flows logically throughout paper. (1 pt) • Appropriate content in each section? (1 pt) Additional Comments:

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Task 5 – Learning Outcomes 2.3 Determine heat transfer coefficient using experimental and tabulated data a. In an experimental result showed that air at 300 K and bulk velocity 10 m/s flows over a flat horizontal plate with a temperature of 1000 K at all points on its surface. Given that Nu=0.32Pr1/3 Re½ (Ta/Ts)0.117 Calculate the heat transfer rate from one side over the first 100 mm and the first 200 mm. Ta is the bulk air temperature and Ts is the surface temperature. Given that:

Task 5 – Learning Outcomes 2.3 Determine heat transfer coefficient using experimental and tabulated data a. In an experimental result showed that air at 300 K and bulk velocity 10 m/s flows over a flat horizontal plate with a temperature of 1000 K at all points on its surface. Given that Nu=0.32Pr1/3 Re½ (Ta/Ts)0.117 Calculate the heat transfer rate from one side over the first 100 mm and the first 200 mm. Ta is the bulk air temperature and Ts is the surface temperature. Given that:

Solution   a)   Nu=0.32Pr1/3 Re½ (Ta/Ts)0.117 Pr=0.69 Re1=10/.1*1.788*10e-5 Ta=1000, … Read More...
Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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b. The figure below shows a cross section through an insulated heated pipe which is made of steel (thermal conductivity, k = 45 W/m K) with an inner radius (r1) of 800 mm and an outer radius (r2) of 1300 mm. The pipe is coated with two layers of insulating materials, the first layer has a thickness of 200 mm and thermal conductivity, k =25.9 W/m K, the second layer has a thickness of 400 mm and the thermal conductivity, k = 35 W/m K. Air at Tf1 = 310 oC flows through the pipe and the convective heat transfer coefficient from the air to the outside has a value of h1 = 120 W/m2 K, The outside surface of the pipe is surrounded by air which is at 50 oC (Tf2) and the convective heat transfer coefficient on this surface has a value of h2 = 90 W/m2 K. Calculate, (a) the thermal resistance (b) the heat transferred (c) temperature T1, T2, T3 and T4 (d) comment on your results.

b. The figure below shows a cross section through an insulated heated pipe which is made of steel (thermal conductivity, k = 45 W/m K) with an inner radius (r1) of 800 mm and an outer radius (r2) of 1300 mm. The pipe is coated with two layers of insulating materials, the first layer has a thickness of 200 mm and thermal conductivity, k =25.9 W/m K, the second layer has a thickness of 400 mm and the thermal conductivity, k = 35 W/m K. Air at Tf1 = 310 oC flows through the pipe and the convective heat transfer coefficient from the air to the outside has a value of h1 = 120 W/m2 K, The outside surface of the pipe is surrounded by air which is at 50 oC (Tf2) and the convective heat transfer coefficient on this surface has a value of h2 = 90 W/m2 K. Calculate, (a) the thermal resistance (b) the heat transferred (c) temperature T1, T2, T3 and T4 (d) comment on your results.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

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