university physics young and freedman 13th edition-Chapter Summary Chapter 9

university physics young and freedman 13th edition-Chapter Summary Chapter 9

Section 9.1 “Angular velocity,” of an object is its instantaneous … Read More...
Watch the video, and then answer the questions below. http://www.youtube.com/watch?v=XUF-T5JubDg#t=49 According to the video, which of the three scholars accepted the invasion of Iraq? A. Realists and liberals tended to reject it, but the constructivists thought it was a good idea. B. Realists tended to reject it, but the constructivists and liberals thought it was a good idea. C. Liberals tended to reject it, but the realists and constructivists thought it was a good idea. D. All of the scholars rejected it. E. None of the scholars rejected it. Which of the following was NOT given as a reason to be concerned about the war in Iraq? A. First and foremost, peace needed to prevail. B. The invasion was form of moralizing or crusading. C. The invasion undermined respect for International law. D. The invasion didn’t serve clear U.S. interests. E. The situation had the potential to become a quagmire. In the video, one of the topics under discussion concerns democratic governance. How much do their views conflict? A. Caleb Gallemore and J.D. Bowen disagree, because democracy is a social construct. B. Randall Schweller and J.D. Bowen disagree, because one side believes that democracy is impossible to spread while the other thinks it may be possible. C. Randall Schweller and Caleb Gallemore disagree with J.D. Bowen, because the first two view the attempt to spread democracy as a moralizing crusade. D. J.D. Bowen and Randall Schweller disagree with Caleb Gallemore, who doesn’t think that democracy can be spread successfully. E. All of the authors agree on the possibility of establishing democracy in Iraq. What sorts of things were on the minds of constructivists considering the war in Iraq? A. the history of colonialism, tensions between Islam and the West, and the United States’ perceived role as a world leader B. whether the war served U.S. interests C. whether the Coalition of the Willing would have forces sufficient to topple Saddam Hussein D. the likelihood that the war would result in a quagmire E. the importance of promoting human rights Professor Bowen says that liberals disagreed about invading Iraq but agreed on the form of government to be established there. What was that form of government? A. a loose confederacy of tribes B. a constitutional monarchy with negotiated rights for minorities C. a communist dictatorship with religious tolerance D. a democracy with respect for human rights E. a long-term military installation with UN forces overseeing government functions

Watch the video, and then answer the questions below. http://www.youtube.com/watch?v=XUF-T5JubDg#t=49 According to the video, which of the three scholars accepted the invasion of Iraq? A. Realists and liberals tended to reject it, but the constructivists thought it was a good idea. B. Realists tended to reject it, but the constructivists and liberals thought it was a good idea. C. Liberals tended to reject it, but the realists and constructivists thought it was a good idea. D. All of the scholars rejected it. E. None of the scholars rejected it. Which of the following was NOT given as a reason to be concerned about the war in Iraq? A. First and foremost, peace needed to prevail. B. The invasion was form of moralizing or crusading. C. The invasion undermined respect for International law. D. The invasion didn’t serve clear U.S. interests. E. The situation had the potential to become a quagmire. In the video, one of the topics under discussion concerns democratic governance. How much do their views conflict? A. Caleb Gallemore and J.D. Bowen disagree, because democracy is a social construct. B. Randall Schweller and J.D. Bowen disagree, because one side believes that democracy is impossible to spread while the other thinks it may be possible. C. Randall Schweller and Caleb Gallemore disagree with J.D. Bowen, because the first two view the attempt to spread democracy as a moralizing crusade. D. J.D. Bowen and Randall Schweller disagree with Caleb Gallemore, who doesn’t think that democracy can be spread successfully. E. All of the authors agree on the possibility of establishing democracy in Iraq. What sorts of things were on the minds of constructivists considering the war in Iraq? A. the history of colonialism, tensions between Islam and the West, and the United States’ perceived role as a world leader B. whether the war served U.S. interests C. whether the Coalition of the Willing would have forces sufficient to topple Saddam Hussein D. the likelihood that the war would result in a quagmire E. the importance of promoting human rights Professor Bowen says that liberals disagreed about invading Iraq but agreed on the form of government to be established there. What was that form of government? A. a loose confederacy of tribes B. a constitutional monarchy with negotiated rights for minorities C. a communist dictatorship with religious tolerance D. a democracy with respect for human rights E. a long-term military installation with UN forces overseeing government functions

Watch the video, and then answer the questions below. According … Read More...
Project 1: Particle Trajectory in Pleated Filters Due: 12:30 pm, Dec. 1, 2015, submission through blackboard Course: Numerical Methods Instructor: Dr. Hooman V. Tafreshi Most aerosol filters are made of pleated fibrous media. This is to accommodate as much filtration media as possible in a limited space available to an air filtration unit (e.g., the engine of a car). A variety of parameters contribute to the performance of a pleated filter. These parameters include, but are not limited to, geometry of the pleat (e.g., pleat height, width, and count), microscale properties of the fibrous media (e.g., fiber diameters, fiber orientation, and solid volume fraction), aerodynamic and thermal conditions of the flow (e.g., flow velocity, temperature, and operating pressure), and particle properties (e.g., diameter, density, and shape). Figure 1: Examples of pleated air filters [1‐2]. In this project you are asked to calculate the trajectory of aerosol particles as they travel inside a rectangular pleat channel. Due to the symmetry of the pleat geometry, you only need to simulate one half of the channel (see Figure 2). Figure 2: The simulation domain and boundary conditions (the figure’s aspect ratio is altered for illustration purposes). Trajectory of the aerosol particles can be calculated in a 2‐D domain by solving the Newton’s 2nd law written for the particles in the x‐ and y‐directions, v(h) inlet velocity fibrous media v(y) y tm l h x Ui u(l) u(x) 2 2 p 1 p 1 ( , ) d x dx u x y dt  dt    2 2 p 1 p 1 ( , ) d y dy v x y dt  dt    where 2 1/18 p p   d    is the particle relaxation time, 10 μm p d  is the particle diameter, 1000 kg/m3 p   is the particle density, and   1.85105 Pa.s is the air viscosity. Also, u(x, y) and v(x, y) represent the components of the air velocity in the x and y directions inside the pleat channel, respectively. The x and y positions of the particles are denoted by xp and yp, respectively. You may use the following expressions for u(x, y) and v(x, y) .     2 3 1 2 u x, y u x y h                  sin 2 v x,y v h π y h        where   i 1 u x U x l h          is the average air velocity inside the pleat channel in the x‐direction and Ui is the velocity at the pleat entrance (assume 1 m/s for this project). l = 0.0275 m and h =0.0011 m are the pleat length and height, respectively. Writing the conservation of mass for the air flowing into the channel, you can also obtain that   i v h U h l h         . These 2nd order ODEs can easily be solved using a 4th order Rung‐Kutta method. In order to obtain realistic particle trajectories, you also need to consider proper initial conditions for the velocity of the particles: x(t  0)  0 , ( 0) i p p y t   y , p ( 0) cos i i dx t U dt    , p ( 0) sin i i dy t U dt     . where i  is the angle with respect to the axial direction by which a particle enters the pleat channel (see Figure 3). The inlet angle can be obtained from the following equation: 2 75 0.78 +0.16 1.61St i i p p i y y e h h                    where   2 St 18 2 ρPdPUi μ h  is the particles Stokes number. Figure 3: An illustration of the required particle trajectory calculation inside a rectangular pleated filter. You are asked to calculate and plot the trajectories of particles released from the vertical positions of ?? ? ? 0.05?, ?? ? ? 0.25?, ?? ? ? 0.5?, ?? ? ? 0.75? , and ?? ? ? 0.95? in one single figure. To do so, you need to track the trajectories until they reach one of the channel walls (i.e., stop when xp  l or p y  h ). Use a time step of 0.00001 sec. For more information see Ref. [3]. For additional background information see Ref. [4] and references there. In submitting your project please stick to following guidelines: 1‐ In blackboard, submit all the Matlab files and report in one single zip file. For naming your zip file, adhere to the format as: Lastname_firstname_project1.zip For instance: Einstein_albert_project1.zip 2‐ The report should be in pdf format only with the name as Project1.pdf (NO word documents .docx or .doc will be graded). 3‐ Your zip file can contain as many Matlab files as you want to submit. Also please submit the main code which TA’s should run with the name as: Project1.m (You can name the function files as you desire). Summary of what you should submit: 1‐ Runge–Kutta 4th order implementation in MATLAB. 2‐ Plot 5 particle trajectories in one graph. 3‐ Report your output (the x‐y positions of the five particles at each time step) in the form of a table with 11 columns (one for time and two for the x and y of each particle). Make sure the units are second for time and meter for the x and y. 4‐ Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit. Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not have unnecessary frames around them or are not plotted on a grey background (default setting of some software programs!). inlet angle Particle trajectory i p y i 0 p x  Important Note: It is possible to solve the above ODEs using built‐in solvers such as ode45 in MATLAB, and you are encouraged to consider that for validating your MATLAB program. However, the results that you submit for this project MUST be obtained from your own implementation of the 4th order Runge‐Kutta method. You will not receive full credit if your MATALB program does not work, even if your results are absolutely correct! References: 1. http://www.airexco.net/custom‐manufacturedbr12‐inch‐pleated‐filter‐c‐108_113_114/custommadebr12‐ inch‐pleated‐filter‐p‐786.html 2. http://www.ebay.com/itm/Air‐Compressor‐Air‐Filter‐Element‐CFE‐275‐Round‐Pleated‐Filter‐ /251081172328 3. A.M. Saleh and H.V. Tafreshi, A Simple Semi‐Analytical Model for Designing Pleated Air Filters under Loading, Separation and Purification Technology 137, 94 (2014) 4. A.M. Saleh, S. Fotovati, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Service Life of Pleated Filters Exposed to Poly‐Dispersed Aerosols, Powder Technology 266, 79 (2014)

Project 1: Particle Trajectory in Pleated Filters Due: 12:30 pm, Dec. 1, 2015, submission through blackboard Course: Numerical Methods Instructor: Dr. Hooman V. Tafreshi Most aerosol filters are made of pleated fibrous media. This is to accommodate as much filtration media as possible in a limited space available to an air filtration unit (e.g., the engine of a car). A variety of parameters contribute to the performance of a pleated filter. These parameters include, but are not limited to, geometry of the pleat (e.g., pleat height, width, and count), microscale properties of the fibrous media (e.g., fiber diameters, fiber orientation, and solid volume fraction), aerodynamic and thermal conditions of the flow (e.g., flow velocity, temperature, and operating pressure), and particle properties (e.g., diameter, density, and shape). Figure 1: Examples of pleated air filters [1‐2]. In this project you are asked to calculate the trajectory of aerosol particles as they travel inside a rectangular pleat channel. Due to the symmetry of the pleat geometry, you only need to simulate one half of the channel (see Figure 2). Figure 2: The simulation domain and boundary conditions (the figure’s aspect ratio is altered for illustration purposes). Trajectory of the aerosol particles can be calculated in a 2‐D domain by solving the Newton’s 2nd law written for the particles in the x‐ and y‐directions, v(h) inlet velocity fibrous media v(y) y tm l h x Ui u(l) u(x) 2 2 p 1 p 1 ( , ) d x dx u x y dt  dt    2 2 p 1 p 1 ( , ) d y dy v x y dt  dt    where 2 1/18 p p   d    is the particle relaxation time, 10 μm p d  is the particle diameter, 1000 kg/m3 p   is the particle density, and   1.85105 Pa.s is the air viscosity. Also, u(x, y) and v(x, y) represent the components of the air velocity in the x and y directions inside the pleat channel, respectively. The x and y positions of the particles are denoted by xp and yp, respectively. You may use the following expressions for u(x, y) and v(x, y) .     2 3 1 2 u x, y u x y h                  sin 2 v x,y v h π y h        where   i 1 u x U x l h          is the average air velocity inside the pleat channel in the x‐direction and Ui is the velocity at the pleat entrance (assume 1 m/s for this project). l = 0.0275 m and h =0.0011 m are the pleat length and height, respectively. Writing the conservation of mass for the air flowing into the channel, you can also obtain that   i v h U h l h         . These 2nd order ODEs can easily be solved using a 4th order Rung‐Kutta method. In order to obtain realistic particle trajectories, you also need to consider proper initial conditions for the velocity of the particles: x(t  0)  0 , ( 0) i p p y t   y , p ( 0) cos i i dx t U dt    , p ( 0) sin i i dy t U dt     . where i  is the angle with respect to the axial direction by which a particle enters the pleat channel (see Figure 3). The inlet angle can be obtained from the following equation: 2 75 0.78 +0.16 1.61St i i p p i y y e h h                    where   2 St 18 2 ρPdPUi μ h  is the particles Stokes number. Figure 3: An illustration of the required particle trajectory calculation inside a rectangular pleated filter. You are asked to calculate and plot the trajectories of particles released from the vertical positions of ?? ? ? 0.05?, ?? ? ? 0.25?, ?? ? ? 0.5?, ?? ? ? 0.75? , and ?? ? ? 0.95? in one single figure. To do so, you need to track the trajectories until they reach one of the channel walls (i.e., stop when xp  l or p y  h ). Use a time step of 0.00001 sec. For more information see Ref. [3]. For additional background information see Ref. [4] and references there. In submitting your project please stick to following guidelines: 1‐ In blackboard, submit all the Matlab files and report in one single zip file. For naming your zip file, adhere to the format as: Lastname_firstname_project1.zip For instance: Einstein_albert_project1.zip 2‐ The report should be in pdf format only with the name as Project1.pdf (NO word documents .docx or .doc will be graded). 3‐ Your zip file can contain as many Matlab files as you want to submit. Also please submit the main code which TA’s should run with the name as: Project1.m (You can name the function files as you desire). Summary of what you should submit: 1‐ Runge–Kutta 4th order implementation in MATLAB. 2‐ Plot 5 particle trajectories in one graph. 3‐ Report your output (the x‐y positions of the five particles at each time step) in the form of a table with 11 columns (one for time and two for the x and y of each particle). Make sure the units are second for time and meter for the x and y. 4‐ Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit. Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not have unnecessary frames around them or are not plotted on a grey background (default setting of some software programs!). inlet angle Particle trajectory i p y i 0 p x  Important Note: It is possible to solve the above ODEs using built‐in solvers such as ode45 in MATLAB, and you are encouraged to consider that for validating your MATLAB program. However, the results that you submit for this project MUST be obtained from your own implementation of the 4th order Runge‐Kutta method. You will not receive full credit if your MATALB program does not work, even if your results are absolutely correct! References: 1. http://www.airexco.net/custom‐manufacturedbr12‐inch‐pleated‐filter‐c‐108_113_114/custommadebr12‐ inch‐pleated‐filter‐p‐786.html 2. http://www.ebay.com/itm/Air‐Compressor‐Air‐Filter‐Element‐CFE‐275‐Round‐Pleated‐Filter‐ /251081172328 3. A.M. Saleh and H.V. Tafreshi, A Simple Semi‐Analytical Model for Designing Pleated Air Filters under Loading, Separation and Purification Technology 137, 94 (2014) 4. A.M. Saleh, S. Fotovati, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Service Life of Pleated Filters Exposed to Poly‐Dispersed Aerosols, Powder Technology 266, 79 (2014)

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Problem 3a: (6pts) As shown below, a two-dimensional vector can be defined by its x and y coordinates in an x-y Cartesian coordinate system. The vector can also be defined by its x ‘ and y ‘ coordinates in an x ‘− y’ Cartesian coordinate system that is rotated by a positive angle θ with respect to the x-y Cartesian coordinate system The relation between the two sets of coordinates, (x, y) and ( x ‘ , y ‘), is defined by the following transformation: A x y ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = x ‘ y ‘ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ where the transformation matrix is given by: A = cosθ sinθ −sinθ cosθ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (i) Determine the inverse of the matrix A. (4 pts) (ii) Show that the inverse determined in Part (a) is the transformation matrix corresponding to rotation by a negative angle (i.e., rotation by –θ). (2 pts) Hint: cos(θ) = cos (−θ) and sin (θ) = −sin (−θ)

Problem 3a: (6pts) As shown below, a two-dimensional vector can be defined by its x and y coordinates in an x-y Cartesian coordinate system. The vector can also be defined by its x ‘ and y ‘ coordinates in an x ‘− y’ Cartesian coordinate system that is rotated by a positive angle θ with respect to the x-y Cartesian coordinate system The relation between the two sets of coordinates, (x, y) and ( x ‘ , y ‘), is defined by the following transformation: A x y ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = x ‘ y ‘ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ where the transformation matrix is given by: A = cosθ sinθ −sinθ cosθ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (i) Determine the inverse of the matrix A. (4 pts) (ii) Show that the inverse determined in Part (a) is the transformation matrix corresponding to rotation by a negative angle (i.e., rotation by –θ). (2 pts) Hint: cos(θ) = cos (−θ) and sin (θ) = −sin (−θ)

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http://www.constitution.org/mac/prince17.htm How does Machiavelli feel about cruelty versus clemency? A. Machiavelli equates clemency with being loved and cruelty with being despised, and suggests that being despised is acceptable. B. Machiavelli suggests that cruelty doesn’t always result in being despised and winning the love of your subjects is the most important thing. C. Machiavelli says that cruelty, when applied in a prudent manner, will be held in more esteem than too much mercy. D. Cruelty and clemency are identical; being merciful to one person means that you must be cruel to another. E. Clemency is equated with happiness, and a happy set of subjects is the ultimate goal of a successful leader. What is the difference between hatred and fear? A. Fear makes people respect you. Hatred makes them work against you. B. Fear and hatred follow one another. If you create fear you will eventually create hatred. All leaders should avoid this. C. Hatred from external powers breeds nationalism within your country, causing people to fear external powers. D. Fear and hatred are opposites. E. Hatred follows love; fear follows clemency. http://www.constitution.org/mac/prince23.htm According to Machiavelli, what is a flatterer? A. Someone who wants to lavish gifts upon you in exchange for power. B. An external power that wants to ally with you. C. Someone who will tell you what you think rather than giving their own opinion. D. Someone who tests your opinions against their own to make a good argument. E. An external power that wants to make strong trade alliances to weaken you over time. According to Machiavelli, what is the best way to seek truth from advisers? A. Advisors should present any complaints to you as a group. B. Advisors should be called upon when the leader has a question, otherwise they are to remain silent. C. An advisor should involve the public, allowing them to call the leader to court to listen to their opinions. D. The leader should listen carefully to one private advisor with whom he always disagrees. E. Machiavelli thinks that advisors are not helpful because they will always try to flatter their leader.

http://www.constitution.org/mac/prince17.htm How does Machiavelli feel about cruelty versus clemency? A. Machiavelli equates clemency with being loved and cruelty with being despised, and suggests that being despised is acceptable. B. Machiavelli suggests that cruelty doesn’t always result in being despised and winning the love of your subjects is the most important thing. C. Machiavelli says that cruelty, when applied in a prudent manner, will be held in more esteem than too much mercy. D. Cruelty and clemency are identical; being merciful to one person means that you must be cruel to another. E. Clemency is equated with happiness, and a happy set of subjects is the ultimate goal of a successful leader. What is the difference between hatred and fear? A. Fear makes people respect you. Hatred makes them work against you. B. Fear and hatred follow one another. If you create fear you will eventually create hatred. All leaders should avoid this. C. Hatred from external powers breeds nationalism within your country, causing people to fear external powers. D. Fear and hatred are opposites. E. Hatred follows love; fear follows clemency. http://www.constitution.org/mac/prince23.htm According to Machiavelli, what is a flatterer? A. Someone who wants to lavish gifts upon you in exchange for power. B. An external power that wants to ally with you. C. Someone who will tell you what you think rather than giving their own opinion. D. Someone who tests your opinions against their own to make a good argument. E. An external power that wants to make strong trade alliances to weaken you over time. According to Machiavelli, what is the best way to seek truth from advisers? A. Advisors should present any complaints to you as a group. B. Advisors should be called upon when the leader has a question, otherwise they are to remain silent. C. An advisor should involve the public, allowing them to call the leader to court to listen to their opinions. D. The leader should listen carefully to one private advisor with whom he always disagrees. E. Machiavelli thinks that advisors are not helpful because they will always try to flatter their leader.

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Select Case 1, 2, or 8 in the back of the textbook. After you have read the case, select at least one of the questions presented at the end.-If you select only one question, then you will need to elaborate with more examples and perspectives than if you select more than one, but the choice is yours. Fair warning: It is possible to fall into the trap of repeating oneself. To avoid that threat, think in advance of the different perspectives that you wish to explore. If you select more than one question, each answer will naturally be shorter. This may be a good approach if you discern that the questions lack strong potential to elicit in-depth answers. Remember to reply to the contributions of two other students in this exercise. This is a rule that we are only observing in the case analyses, given the relative complexity of the cases, compared to the chapter discussion questions. Always add value, from the textbook, news, personal experience, or all three. Indicate the case and question at the beginning, but avoid restating the question in your answer. In this respect, use the same method as in the chapter discussion questions, described in the Week 2 forum. Write at least 500 words (no minimum for replies, but do add value). Quoted passages do not contribute to the word count (so you will need to write more if you insert any quoted material). Post-edit your work carefully to catch errors. Avoid plagiarism at all cost. ——— Note on anomalous questions. Some questions will require you to work around selected details to fit the requisite discussion format. For example, Question 2 in Case 1 asks how your proposal will solve certain problems noted in answer to the previous question. If you have not actually answered Question 1, then you will have to assert one or more problems from the case, a proposed solution, and then an explanation of how your proposal may help. Question 3 is similar, in that you will need to identify a problem and a solution, followed by an argument about the budget. Although Alistair was expecting to hire a Project Engineer rather than a Quality Compliance Manager, the methods used to make the decision should be similar. The main difference in the Quality Compliance Manager position is that it is in a joint venture with a Hungarian government backed firm. International Joint Ventures (IJV) makes HRM practices more complicated because HRM practices and strategies are required for each IJV entity (Dowling, Festing, & Engle, 2013). HRM must address IJV in four stages, in which, each stage has an impact on the next. It is important for HRM to very thorough with each stage and communication through each stage is vital. To be successful, HRM must combine the IJV strategy along with the recruitment, selection, training, and development processes (Dowling et al., 2013). In light of the needs of the company and the new Quality Compliance Manager position, Alistair should choose the first candidate, Marie Erten-Loiseau. The fact that the job requires travel to France and Germany is a positive for Marie because she was born in France and was educated in France and Germany. The familiarity of these locations will help her as she meets with new business partners because she will have a good understanding of the policy and procedures required for companies in these two countries. Dowling et al., (2013), points out that the manager needs to be able to assess the desires of the stakeholders and be able to implement strategies based on their desires. Another reason for choosing Marie is that she has the most experience and has worked with Trianon for 13 years. The experience she has with the company is invaluable because she knows the goals of the company and strategies for implementing those goals. The last reason for choosing Marie is that she has been successful in her previous positions. She has lead two projects in two different countries and both were successful. This shows that she is able to adapt to the different practices of each country. There are many factors that Alistair should take into consideration to determine the correct choice for the Quality Compliance Manager position. The major factors that require consideration are the specificities of the entire situation, the reason for the assignment, and type of assignment. The four main specificities include context specificities, firm specific variables, local unit specificities, and IHRM practices (Dowling et al., 2013). The context specificities would include the differences in cultures between the assignment in Hungary and the base location for the Trianon, Marseilles. The firm specific variable includes any changes in the way operations in Hungary are conducted, whether it is strategy or HRM policies. The local unit specificities include the role of the joint venture in relation to Trianon and how this joint venture will fit into the long-term plan of the company. The company hopes that it will provide a good working relationship with the state supported airline, which will lead to more business in the future. The IHRM practices determine the employees that are hired and the training that is available to the employees. The reason for the assignment also is a major factor in determining the correct candidate. In the situation of Trianon, a joint venture with a Hungarian government back firm created a position that needed filling. The Quality Compliance Manager position allows Trianon to manage the joint venture operation, make sure it is successful, and build a strong relationship with Malev. The last major factor is the type of assignment. The Quality Compliance Manager assignment is long-term assignment because it is 3 years in duration. The joint venture is the first that the company has been involved in outside the UK so there is less familiarity on the administrative/compliance side. The candidate must act as an agent of direct control (Dowling et al., 2013) by assuring that compliance policies are followed and company strategy is implemented. Assessing whether a male or female would be the best fit for the position is also a factor that deserves consideration. The low number of female expatriates led Jessens, Cappellen, &Zanoni (2006) to research the following three myths: women have no desire to be in positions of authority in a foreign country, companies do not desire to place females in positions of authority while a foreign country, and women would be ineffective because of the views towards women in foreign countries. The research indicated that female expatriates do have conflict that arises related to their gender but the successful ones were able to turn the conflicts around based on the qualities that these women possess (Jessens et al., 2006). With all of these factors considered, I believe Marie Erten-Loiseau is the best candidate for the Quality Compliance Manager. References Dowling, P.J., Festing, M., & Engle, A.D. Sr. (2013). International Human Resource Management (6th ed.). Stamford, CT: Cengage Learning Janssens, M., Cappellen, T., &Zanoni, P. (2006). Successful female expatriates as agents: Positioning oneself through gender, hierarchy, and culture. Journal of World Business, 1-16. doi:10.1016/j.jwb.2006.01.001 2.) Case 8 – Questions 1 & 4 Multinational firms are often faced with recruiting and staffing decisions that could ultimately enhance or diminish the firm’s ability to be successful in a competitive global market. Perlmutter identified four staffing approaches for MNEs to consider based on the primary attitudes of international executives that would lay the foundation for MNEs during the recruitment and hiring process (Dowling, Festing, & Engle, 2013). At one point or another throughout the MacDougall family journey Lachlan and Lisa have served in one of the four capacities as an ethnocentric, polycentric, geocentric, and regiocentric employee. The ability to encompass all four attitudes that Perlmutter set forth is something that the MacDougall family has managed to do extremely well. The possibility for a multinational firm to recruit a family of this caliber that has been exposed and has an understanding of the positive and negative aspects of each attitude is phenomenal. This would be resourceful for any multinational firm. The MacDougal family’s exposure to cross-cultural management is also valuable. The diverse cultural background that the family has encountered on their international journey is a rarity. Cultural diversity and cross-cultural management play a critical role in MNEs because it produces a work environment that can transform the workplace into a place of learning and give the firm the availability to create new ideas for a more productive and competitive advantage over other firms (Sultana, Rashid, Mohiuddin, &Mazumder, 2013). This is something that is easy for the MacDougall family to bring to the table with the family’s given history. The expatriate lifestyle that has become second nature to the MacDougall family is beneficial for multinational firms for multifarious reasons Being raised around different cultures and then choosing to work internationally and learn different cultures has attributed to Lachlan’s successful career. The family’s ability to communicate and blend in socially among diverse cultures is an important aspect for international firms that want to stay competitive and be successful. The family has acclimated fairly easy to all of the places they have been and this is something that can be favorable when firms are recruiting employees. The MacDougall family has an upper-hand in the international marketplace naturally due to previous experiences with other countries and cultures. The exceptional way that the family has managed to conform to a multitude of other cultures and flourish is not an easy task. Marriage is not easy and many families experience a greater challenge avoiding divorcees when international mobility is involved. Lachlan and Lisa have been able to move together and this is an important aspect to the success of their marriage. Based on the case study they have a common desire to travel and both are successful in their careers. Lisa’s devotion to her husband’s successful career has put some strain on the marriage as she has had times where she felt she did not have her own identity. Military spouses experience this type of stress during long deployments and times that they have to hold the household together on their own. Another example is with employers who are transferred internationally for a short period of time or travel often. Separation of spouses can strain any marriage, but Lisa and Lachlan have been fortunate to avoid separation for any extended length of time. References Dowling, P.J., Festing, M., & Engle, A.D.Sr.(2013). International Human Resource Management. (6thed.). Stamford, CT: Cengage Sultana, M., Rashid, M., Mohiuddin, M. &Mazumder, M. (2013).Cross-cultural management and organizational performance.A Contnet analysis perspective.International Journal of Business and Management, 8(8), 133-146.

Select Case 1, 2, or 8 in the back of the textbook. After you have read the case, select at least one of the questions presented at the end.-If you select only one question, then you will need to elaborate with more examples and perspectives than if you select more than one, but the choice is yours. Fair warning: It is possible to fall into the trap of repeating oneself. To avoid that threat, think in advance of the different perspectives that you wish to explore. If you select more than one question, each answer will naturally be shorter. This may be a good approach if you discern that the questions lack strong potential to elicit in-depth answers. Remember to reply to the contributions of two other students in this exercise. This is a rule that we are only observing in the case analyses, given the relative complexity of the cases, compared to the chapter discussion questions. Always add value, from the textbook, news, personal experience, or all three. Indicate the case and question at the beginning, but avoid restating the question in your answer. In this respect, use the same method as in the chapter discussion questions, described in the Week 2 forum. Write at least 500 words (no minimum for replies, but do add value). Quoted passages do not contribute to the word count (so you will need to write more if you insert any quoted material). Post-edit your work carefully to catch errors. Avoid plagiarism at all cost. ——— Note on anomalous questions. Some questions will require you to work around selected details to fit the requisite discussion format. For example, Question 2 in Case 1 asks how your proposal will solve certain problems noted in answer to the previous question. If you have not actually answered Question 1, then you will have to assert one or more problems from the case, a proposed solution, and then an explanation of how your proposal may help. Question 3 is similar, in that you will need to identify a problem and a solution, followed by an argument about the budget. Although Alistair was expecting to hire a Project Engineer rather than a Quality Compliance Manager, the methods used to make the decision should be similar. The main difference in the Quality Compliance Manager position is that it is in a joint venture with a Hungarian government backed firm. International Joint Ventures (IJV) makes HRM practices more complicated because HRM practices and strategies are required for each IJV entity (Dowling, Festing, & Engle, 2013). HRM must address IJV in four stages, in which, each stage has an impact on the next. It is important for HRM to very thorough with each stage and communication through each stage is vital. To be successful, HRM must combine the IJV strategy along with the recruitment, selection, training, and development processes (Dowling et al., 2013). In light of the needs of the company and the new Quality Compliance Manager position, Alistair should choose the first candidate, Marie Erten-Loiseau. The fact that the job requires travel to France and Germany is a positive for Marie because she was born in France and was educated in France and Germany. The familiarity of these locations will help her as she meets with new business partners because she will have a good understanding of the policy and procedures required for companies in these two countries. Dowling et al., (2013), points out that the manager needs to be able to assess the desires of the stakeholders and be able to implement strategies based on their desires. Another reason for choosing Marie is that she has the most experience and has worked with Trianon for 13 years. The experience she has with the company is invaluable because she knows the goals of the company and strategies for implementing those goals. The last reason for choosing Marie is that she has been successful in her previous positions. She has lead two projects in two different countries and both were successful. This shows that she is able to adapt to the different practices of each country. There are many factors that Alistair should take into consideration to determine the correct choice for the Quality Compliance Manager position. The major factors that require consideration are the specificities of the entire situation, the reason for the assignment, and type of assignment. The four main specificities include context specificities, firm specific variables, local unit specificities, and IHRM practices (Dowling et al., 2013). The context specificities would include the differences in cultures between the assignment in Hungary and the base location for the Trianon, Marseilles. The firm specific variable includes any changes in the way operations in Hungary are conducted, whether it is strategy or HRM policies. The local unit specificities include the role of the joint venture in relation to Trianon and how this joint venture will fit into the long-term plan of the company. The company hopes that it will provide a good working relationship with the state supported airline, which will lead to more business in the future. The IHRM practices determine the employees that are hired and the training that is available to the employees. The reason for the assignment also is a major factor in determining the correct candidate. In the situation of Trianon, a joint venture with a Hungarian government back firm created a position that needed filling. The Quality Compliance Manager position allows Trianon to manage the joint venture operation, make sure it is successful, and build a strong relationship with Malev. The last major factor is the type of assignment. The Quality Compliance Manager assignment is long-term assignment because it is 3 years in duration. The joint venture is the first that the company has been involved in outside the UK so there is less familiarity on the administrative/compliance side. The candidate must act as an agent of direct control (Dowling et al., 2013) by assuring that compliance policies are followed and company strategy is implemented. Assessing whether a male or female would be the best fit for the position is also a factor that deserves consideration. The low number of female expatriates led Jessens, Cappellen, &Zanoni (2006) to research the following three myths: women have no desire to be in positions of authority in a foreign country, companies do not desire to place females in positions of authority while a foreign country, and women would be ineffective because of the views towards women in foreign countries. The research indicated that female expatriates do have conflict that arises related to their gender but the successful ones were able to turn the conflicts around based on the qualities that these women possess (Jessens et al., 2006). With all of these factors considered, I believe Marie Erten-Loiseau is the best candidate for the Quality Compliance Manager. References Dowling, P.J., Festing, M., & Engle, A.D. Sr. (2013). International Human Resource Management (6th ed.). Stamford, CT: Cengage Learning Janssens, M., Cappellen, T., &Zanoni, P. (2006). Successful female expatriates as agents: Positioning oneself through gender, hierarchy, and culture. Journal of World Business, 1-16. doi:10.1016/j.jwb.2006.01.001 2.) Case 8 – Questions 1 & 4 Multinational firms are often faced with recruiting and staffing decisions that could ultimately enhance or diminish the firm’s ability to be successful in a competitive global market. Perlmutter identified four staffing approaches for MNEs to consider based on the primary attitudes of international executives that would lay the foundation for MNEs during the recruitment and hiring process (Dowling, Festing, & Engle, 2013). At one point or another throughout the MacDougall family journey Lachlan and Lisa have served in one of the four capacities as an ethnocentric, polycentric, geocentric, and regiocentric employee. The ability to encompass all four attitudes that Perlmutter set forth is something that the MacDougall family has managed to do extremely well. The possibility for a multinational firm to recruit a family of this caliber that has been exposed and has an understanding of the positive and negative aspects of each attitude is phenomenal. This would be resourceful for any multinational firm. The MacDougal family’s exposure to cross-cultural management is also valuable. The diverse cultural background that the family has encountered on their international journey is a rarity. Cultural diversity and cross-cultural management play a critical role in MNEs because it produces a work environment that can transform the workplace into a place of learning and give the firm the availability to create new ideas for a more productive and competitive advantage over other firms (Sultana, Rashid, Mohiuddin, &Mazumder, 2013). This is something that is easy for the MacDougall family to bring to the table with the family’s given history. The expatriate lifestyle that has become second nature to the MacDougall family is beneficial for multinational firms for multifarious reasons Being raised around different cultures and then choosing to work internationally and learn different cultures has attributed to Lachlan’s successful career. The family’s ability to communicate and blend in socially among diverse cultures is an important aspect for international firms that want to stay competitive and be successful. The family has acclimated fairly easy to all of the places they have been and this is something that can be favorable when firms are recruiting employees. The MacDougall family has an upper-hand in the international marketplace naturally due to previous experiences with other countries and cultures. The exceptional way that the family has managed to conform to a multitude of other cultures and flourish is not an easy task. Marriage is not easy and many families experience a greater challenge avoiding divorcees when international mobility is involved. Lachlan and Lisa have been able to move together and this is an important aspect to the success of their marriage. Based on the case study they have a common desire to travel and both are successful in their careers. Lisa’s devotion to her husband’s successful career has put some strain on the marriage as she has had times where she felt she did not have her own identity. Military spouses experience this type of stress during long deployments and times that they have to hold the household together on their own. Another example is with employers who are transferred internationally for a short period of time or travel often. Separation of spouses can strain any marriage, but Lisa and Lachlan have been fortunate to avoid separation for any extended length of time. References Dowling, P.J., Festing, M., & Engle, A.D.Sr.(2013). International Human Resource Management. (6thed.). Stamford, CT: Cengage Sultana, M., Rashid, M., Mohiuddin, M. &Mazumder, M. (2013).Cross-cultural management and organizational performance.A Contnet analysis perspective.International Journal of Business and Management, 8(8), 133-146.

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Project Four: Revisiting English 1010 (Literacy, Language, and Culture: An Exploration of the African American Experience) The MultiMedia Reflective Portfolio Project Overview This project will provide us with the opportunity to use a combination of textual, digital, and oral tools to: 1) reflect on and display what we have learned about African American literacy, language, and culture; and 2) reflect on and display what we have learned about the process of composing a literacy narrative, informative summary, media analysis, and multimedia reflective portfolio project. Ultimately, this project will provide us with the opportunity to use multimedia tools and applications to reflect on and display our experience as knowledge users and knowledge makers in this course (specifically as it relates to the English 1010 Learning Outcomes). ___________________________________________________________________ Introduction/Rationale/Assignment Prompt: This reflective assignment, which is the last major assignment of the semester, consists of two parts: Part One Part One consists of a 2-3 page reflective essay in which you reflect on and display: (1) what you learned about African American literacy, language, and culture; and (2) what you learned about the process of composing a literacy narrative, informative summary, media analysis, and multimedia reflective portfolio project–specifically as the process relates to the Learning Outcomes (Reading, Writing, Reflection, and Technology Use). To do so, you must look back over the work you produced during the semester in order to locate and discuss your learning and accomplishments in these areas. While your discussion of achievements with respect to ENG 1010 Learning Outcomes is perhaps the most important goal in the Reflective Essay, the written expression of these achievements can be strengthened when it is integrated into a broader narrative that describes where you are coming from and who you are as a student. In this narrative, you may discuss, for example, how you learned and used various reading strategies in the course, or you may describe, for example, how your ability to use composition and course management technologies, like Word and Blackboard, increased. You may also address, as appropriate, how your culture, identity, or background shaped your experiences as a student in ENG 1010. You may wish to discuss, for example, some of the following issues. • Transition to college and the larger first-year experience • Negotiation of a new identity as college student (how you adjusted; how you handled it) • Membership in groups historically underrepresented in college • Language diversity • Managing life circumstances to be able to give enough time and energy to academic work In sum, the Reflective Essay should make claims about your learning and accomplishments with respect to the two areas identified above. Essentially, the reflective essay should demonstrate what you have learned and what you can do as a result of your work in ENG 1010. In this way, a successful Reflective Essay will inspire confidence that you are prepared to move forward into your next composition courses, beginning with ENG 1020, and into the larger academic discourse community. Part Two Part Two consists of an electronic multimedia portfolio containing 3-5 selected pieces of the work you produced this semester (essay topic proposals, reading responses, essay outlines, essay first or final drafts, in-class assignments, etc.) that you can use as evidence of your learning and accomplishments and to support the claims you made in your reflective essay. ___________________________________________________________________ English 1010 Learning Outcomes Reading ● Develop reading strategies to explain, paraphrase, and summarize college-level material. ● Analyze college-level material to identify evidence that supports broader claims. Writing ● Plan and compose a well-organized thesis-driven text that engages with college-level material and is supported by relevant and sufficient evidence. ● Develop a flexible revision process that incorporates feedback to rewrite multiple drafts of a text for clarity (e.g. argument, organization, support, and audience awareness). Reflection ● Use reflective writing to evaluate and revise writing processes and drafts ● Use reflective writing to assess and articulate skill development in relation to course learning outcomes. Technology Use ● Navigate institutional web-based interfaces, such as course websites, university email, and Blackboard Learn™, to find, access and submit course material. ● Use computer-based composition technologies, including word processing software (e.g. Microsoft Word, PowerPoint), to compose college-level texts. ● Use computer-based composition technologies to read and annotate course readings and texts authored by students (e.g. peer review). Your Final Draft Should: • meet the requirements as outlined in the “Introduction/Rationale/Assignment Prompt” section above. Points for This Project • First Draft: 20 Points • Final Draft: 130 Points • Oral Presentation: 30 Points Refer to the Course Schedule (Syllabus) for Assignment Due Dates. _______________________________________________________________ Evaluation: You will be evaluated based on content, organization, and mechanics.

Project Four: Revisiting English 1010 (Literacy, Language, and Culture: An Exploration of the African American Experience) The MultiMedia Reflective Portfolio Project Overview This project will provide us with the opportunity to use a combination of textual, digital, and oral tools to: 1) reflect on and display what we have learned about African American literacy, language, and culture; and 2) reflect on and display what we have learned about the process of composing a literacy narrative, informative summary, media analysis, and multimedia reflective portfolio project. Ultimately, this project will provide us with the opportunity to use multimedia tools and applications to reflect on and display our experience as knowledge users and knowledge makers in this course (specifically as it relates to the English 1010 Learning Outcomes). ___________________________________________________________________ Introduction/Rationale/Assignment Prompt: This reflective assignment, which is the last major assignment of the semester, consists of two parts: Part One Part One consists of a 2-3 page reflective essay in which you reflect on and display: (1) what you learned about African American literacy, language, and culture; and (2) what you learned about the process of composing a literacy narrative, informative summary, media analysis, and multimedia reflective portfolio project–specifically as the process relates to the Learning Outcomes (Reading, Writing, Reflection, and Technology Use). To do so, you must look back over the work you produced during the semester in order to locate and discuss your learning and accomplishments in these areas. While your discussion of achievements with respect to ENG 1010 Learning Outcomes is perhaps the most important goal in the Reflective Essay, the written expression of these achievements can be strengthened when it is integrated into a broader narrative that describes where you are coming from and who you are as a student. In this narrative, you may discuss, for example, how you learned and used various reading strategies in the course, or you may describe, for example, how your ability to use composition and course management technologies, like Word and Blackboard, increased. You may also address, as appropriate, how your culture, identity, or background shaped your experiences as a student in ENG 1010. You may wish to discuss, for example, some of the following issues. • Transition to college and the larger first-year experience • Negotiation of a new identity as college student (how you adjusted; how you handled it) • Membership in groups historically underrepresented in college • Language diversity • Managing life circumstances to be able to give enough time and energy to academic work In sum, the Reflective Essay should make claims about your learning and accomplishments with respect to the two areas identified above. Essentially, the reflective essay should demonstrate what you have learned and what you can do as a result of your work in ENG 1010. In this way, a successful Reflective Essay will inspire confidence that you are prepared to move forward into your next composition courses, beginning with ENG 1020, and into the larger academic discourse community. Part Two Part Two consists of an electronic multimedia portfolio containing 3-5 selected pieces of the work you produced this semester (essay topic proposals, reading responses, essay outlines, essay first or final drafts, in-class assignments, etc.) that you can use as evidence of your learning and accomplishments and to support the claims you made in your reflective essay. ___________________________________________________________________ English 1010 Learning Outcomes Reading ● Develop reading strategies to explain, paraphrase, and summarize college-level material. ● Analyze college-level material to identify evidence that supports broader claims. Writing ● Plan and compose a well-organized thesis-driven text that engages with college-level material and is supported by relevant and sufficient evidence. ● Develop a flexible revision process that incorporates feedback to rewrite multiple drafts of a text for clarity (e.g. argument, organization, support, and audience awareness). Reflection ● Use reflective writing to evaluate and revise writing processes and drafts ● Use reflective writing to assess and articulate skill development in relation to course learning outcomes. Technology Use ● Navigate institutional web-based interfaces, such as course websites, university email, and Blackboard Learn™, to find, access and submit course material. ● Use computer-based composition technologies, including word processing software (e.g. Microsoft Word, PowerPoint), to compose college-level texts. ● Use computer-based composition technologies to read and annotate course readings and texts authored by students (e.g. peer review). Your Final Draft Should: • meet the requirements as outlined in the “Introduction/Rationale/Assignment Prompt” section above. Points for This Project • First Draft: 20 Points • Final Draft: 130 Points • Oral Presentation: 30 Points Refer to the Course Schedule (Syllabus) for Assignment Due Dates. _______________________________________________________________ Evaluation: You will be evaluated based on content, organization, and mechanics.

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Assignment 10 Due: 11:59pm on Wednesday, April 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.3 Part A The figure shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies to . Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: Ka Kc Correct Conceptual Question 12.6 You have two steel solid spheres. Sphere 2 has twice the radius of sphere 1. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: I2 I1 Correct Problem 12.2 A high-speed drill reaches 2500 in 0.59 . Part A What is the drill’s angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Through how many revolutions does it turn during this first 0.59 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct I2/I1 = 32 rpm s  = 440 rad s2 s  = 12 rev Constant Angular Acceleration in the Kitchen Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second. Hint 1. How to approach the problem Recall from your study of kinematics the three equations of motion derived for systems undergoing constant linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to work with the three analogous equations of motion. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find the angular acceleration . Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it What is the angular velocity of the salad spinner as Dario is spinning it? Express your answer numerically in degrees per second. Hint 1. Converting rotations to degrees When the salad spinner spins through one revolution, it turns through 360 degrees. ANSWER: Hint 3. Find the angular distance the salad spinner travels as it comes to rest Through how many degrees does the salad spinner rotate as it comes to rest? Express your answer numerically in degrees. Hint 1. Converting rotations to degrees  0 = 1440 degrees/s  =  − 0 One revolution is equivalent to 360 degrees. ANSWER: Hint 4. Determine which equation to use You know the initial and final velocities of the system and the angular distance through which the spinner rotates as it comes to a stop. Which equation should be used to solve for the unknown constant angular acceleration ? ANSWER: ANSWER: Correct Part B How long does it take for the salad spinner to come to rest? Express your answer numerically in seconds.  = 2160 degrees   = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0  = -480 degrees/s2 Hint 1. How to approach the problem Again, you will need the equations of rotational kinematics that apply to situations of constant angular acceleration. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find . Hint 2. Determine which equation to use You have the initial and final velocities of the system and the angular acceleration, which you found in the previous part. Which is the best equation to use to solve for the unknown time ? ANSWER: ANSWER: Correct ± A Spinning Electric Fan An electric fan is turned off, and its angular velocity decreases uniformly from 540 to 250 in a time interval of length 4.40 . Part A Find the angular acceleration in revolutions per second per second. Hint 1. Average acceleration Recall that if the angular velocity decreases uniformly, the angular acceleration will remain constant. Therefore, the angular acceleration is just the total change in angular velocity divided by t t  = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0 t = 3.00 s rev/min rev/min s  the total change in time. Be careful of the sign of the angular acceleration. ANSWER: Correct Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. Hint 1. Determine the correct kinematic equation Which of the following kinematic equations is best suited to this problem? Here and are the initial and final angular velocities, is the elapsed time, is the constant angular acceleration, and and are the initial and final angular displacements. Hint 1. How to chose the right equation Notice that you were given in the problem introduction the initial and final speeds, as well as the length of time between them. In this problem, you are asked to find the number of revolutions (which here is the change in angular displacement, ). If you already found the angular acceleration in Part A, you could use that as well, but you would end up using a more complex equation. Also, in general, it is somewhat favorable to use given quantities instead of quantities that you have calculated. ANSWER:  = -1.10 rev/s2 0  t  0   − 0  = 0 + t  = 0 + t+  1 2 t2 = + 2( − ) 2 20 0 − 0 = (+ )t 1 2 0 ANSWER: Correct Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? Hint 1. Finding the total time for spin down To find the total time for spin down, just calculate when the velocity will equal zero. This is accomplished by setting the initial velocity plus the acceleration multipled by the time equal to zero and then solving for the time. One can then just subtract the time it took to reach 250 from the total time. Be careful of your signs when you set up the equation. ANSWER: Correct Problem 12.8 A 100 ball and a 230 ball are connected by a 34- -long, massless, rigid rod. The balls rotate about their center of mass at 130 . Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units. ANSWER: 29.0 rev rev/min 3.79 s g g cm rpm g Correct Problem 12.10 A thin, 60.0 disk with a diameter of 9.00 rotates about an axis through its center with 0.200 of kinetic energy. Part A What is the speed of a point on the rim? Express your answer with the appropriate units. ANSWER: Correct Problem 12.12 A drum major twirls a 95- -long, 470 baton about its center of mass at 150 . Part A What is the baton’s rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 3.2 ms g cm J 3.65 ms cm g rpm K = 4.4 J Correct Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord’s weight can be ignored. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply. Hint 1. Conditions for equilibrium If the blocks had the same mass, the system would be in equilibrium. The blocks would have zero acceleration and the tension in each part of the cord would equal the weight of each block. Both parts of the cord would then pull with equal force on the pulley, resulting in a zero net torque and no rotation of the pulley. Is this still the case in the current situation where block B has twice the mass of block A? Hint 2. Rotational analogue of Newton’s second law The net torque of all the forces acting on a rigid body is proportional to the angular acceleration of the body net  and is given by , where is the moment of inertia of the body. Hint 3. Relation between linear and angular acceleration A particle that rotates with angular acceleration has linear acceleration equal to , where is the distance of the particle from the axis of rotation. In the present case, where there is no slipping or stretching of the cord, the cord and the pulley must move together at the same speed. Therefore, if the cord moves with linear acceleration , the pulley must rotate with angular acceleration , where is the radius of the pulley. ANSWER: Correct Part B What happens when block B moves downward? Hint 1. How to approach the problem To determine whether the tensions in both parts of the cord are equal, it is convenient to write a mathematical expression for the net torque on the pulley. This will allow you to relate the tensions in the cord to the pulley’s angular acceleration. Hint 2. Find the net torque on the pulley Let’s assume that the tensions in both parts of the cord are different. Let be the tension in the right cord and the tension in the left cord. If is the radius of the pulley, what is the net torque acting on the pulley? Take the positive sense of rotation to be counterclockwise. Express your answer in terms of , , and . net = I I  a a = R R a  = a R R The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. T1 T2 R net T1 T2 R Hint 1. Torque The torque of a force with respect to a point is defined as the product of the magnitude times the perpendicular distance between the line of action of and the point . In other words, . ANSWER: ANSWER: Correct Note that if the pulley were stationary (as in many systems where only linear motion is studied), then the tensions in both parts of the cord would be equal. However, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration. Problem 12.18 Part A In the figure , what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.  F  O F l F  O  = Fl net = R(T2 − T1 ) The left cord pulls on the pulley with greater force than the right cord. The left and right cord pull with equal force on the pulley. The right cord pulls on the pulley with greater force than the left cord. ANSWER: Correct Part B What is the direction of net torque about the axle? ANSWER: Correct Problem 12.22 An athlete at the gym holds a 3.5 steel ball in his hand. His arm is 78 long and has a mass of 3.6 . Assume the center of mass of the arm is at the geometrical center of the arm. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer to two significant figures and include the appropriate units.  = 0.20 Nm Clockwise Counterclockwise kg cm kg ANSWER: Correct Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Parallel Axis Theorem The parallel axis theorem relates , the moment of inertia of an object about an axis passing through its center of mass, to , the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is , where is the perpendicular distance from the center of mass to the axis that passes through point p, and is the mass of the object. Part A Suppose a uniform slender rod has length and mass . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . Find , the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the center of mass Find the distance appropriate to this problem. That is, find the perpendicular distance from the center of mass of the rod to the axis passing through one end of the rod.  = 41 Nm 45  = 29 Nm Icm Ip Ip = Icm + Md2 d M L m Icm = m 1 12 L2 Iend Iend m L d ANSWER: ANSWER: Correct Part B Now consider a cube of mass with edges of length . The moment of inertia of the cube about an axis through its center of mass and perpendicular to one of its faces is given by . Find , the moment of inertia about an axis p through one of the edges of the cube Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the axis Find the perpendicular distance from the center of mass axis to the new edge axis (axis labeled p in the figure). ANSWER: d = L 2 Iend = mL2 3 m a Icm Icm = m 1 6 a2 Iedge Iedge m a o p d ANSWER: Correct Problem 12.26 Starting from rest, a 12- -diameter compact disk takes 2.9 to reach its operating angular velocity of 2000 . Assume that the angular acceleration is constant. The disk’s moment of inertia is . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: d = a 2 Iedge = 2ma2 3 cm s rpm 2.5 × 10−5 kg m2 = 1.8×10−3  Nm Correct Problem 12.23 An object’s moment of inertia is 2.20 . Its angular velocity is increasing at the rate of 3.70 . Part A What is the total torque on the object? ANSWER: Correct Problem 12.31 A 5.1 cat and a 2.5 bowl of tuna fish are at opposite ends of the 4.0- -long seesaw. N = 48 rev kgm2 rad/s2 8.14 N  m kg kg m Part A How far to the left of the pivot must a 3.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass , length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance from the scapula. The deltoid muscle makes an angle of with the horizontal, as shown. Use throughout the problem. Part A kg d = 1.4 m M1 = 3.6 kg L = 0.66 m L1 = 0.33 m L2 = 0.15 m  = 17 g = 9.8 m/s2 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. Hint 1. Nature of the problem Remember that this is a statics problem, so all forces and torques are balanced (their sums equal zero). Hint 2. Origin of torque Calculate the torque about the point at which the arm attaches to the rest of the body. This allows one to balance the torques without having to worry about the undefined forces at this point. Hint 3. Adding up the torques Add up the torques about the point in which the humerus attaches to the body. Answer in terms of , , , , , and . Remember that counterclockwise torque is positive. ANSWER: ANSWER: Correct Part B Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). Express your answer in newtons, to the nearest integer. T L1 L2 M1 g T  total = 0 = L1M1g − Tsin()L2 T = 265 N Fy Hint 1. Total forces involved Recall that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body). ANSWER: Correct Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. Express your answer in newtons, to the nearest integer. ANSWER: Correct ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: , , and . Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). |Fy| = 42 N Fx |Fx| = 254 N F 1 F  2 F  3 Part A If and , what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. Hint 1. Finding torque about pivot from What is the magnitude of the torque | | provided by around the pivot point? Give your answer numerically in newton-meters to two significant figures. ANSWER: ANSWER: Correct Part B If the L-shaped rod has a moment of inertia , , , and again , how long a time would it take for the object to move through ( /4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures. F3 = 0 F1 = 12 N F 2 F 1   1 F  1 |  1 | = 0.36 N  m F2 = 4.5 N I = 9 kg m2 F1 = 12 N F2 = 27 N F3 = 0 t 45  Hint 1. Find the net torque about the pivot What is the magnitude of the total torque around the pivot point? Answer numerically in newton-meters to two significant figures. ANSWER: Hint 2. Calculate Given the total torque around the pivot point, what is , the magnitude of the angular acceleration? Express your answer numerically in radians per second squared to two significant figures. Hint 1. Equation for If you know the magnitude of the total torque ( ) and the rotational inertia ( ), you can then find the rotational acceleration ( ) from ANSWER: Hint 3. Description of angular kinematics Now that you know the angular acceleration, this is a problem in rotational kinematics; find the time needed to go through a given angle . For constant acceleration ( ) and starting with (where is angular speed) the relation is given by which is analogous to the expression for linear displacement ( ) with constant acceleration ( ) starting from rest, | p ivot| | p ivot| = 1.8 N  m    vot Ivot  pivot = Ipivot.  = 0.20 radians/s2    = 0   = 1  , 2 t2 x a . ANSWER: Correct Part C Now consider the situation in which and , but now a force with nonzero magnitude is acting on the rod. What does have to be to obtain equilibrium? Give a numerical answer, without trigonometric functions, in newtons, to two significant figures. Hint 1. Find the required component of Only the tangential (perpendicular) component of (call it ) provides a torque. What is ? Answer in terms of . You will need to evaluate any trigonometric functions. ANSWER: ANSWER: Correct x = 1 a 2 t2 t = 2.8 s F1 = 12 N F2 = 0 F3 F3 F 3 F  3 F3t F3t F3 F3t = 1 2 F3 F3 = 9.0 N Problem 12.32 A car tire is 55.0 in diameter. The car is traveling at a speed of 24.0 . Part A What is the tire’s rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units. ANSWER: cm m/s 833 rpm 48.0 ms 0 ms Correct Problem 12.33 A 460 , 8.00-cm-diameter solid cylinder rolls across the floor at 1.30 . Part A What is the can’s kinetic energy? Express your answer with the appropriate units. ANSWER: Correct Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? g m/s 0.583 J g ANSWER: Correct Part B What is the direction of the angular momentum of the bar ? ANSWER: Correct Problem 12.46 Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? 3.27 kgm2/s into the page out of the page kg ANSWER: Correct Part B What is its direction? ANSWER: Correct Problem 12.60 A 3.0- -long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.46. 3.66×10−2 kgm /s 2 x direction -x direction y direction -y direction z direction -z direction m Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.61 The 3.0- -long, 90 rigid beam in the following figure is supported at each end. An 70 student stands 2.0 from support 1.  = 47 m kg kg m Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 12.63 A 44 , 5.5- -long beam is supported, but not attached to, the two posts in the figure . A 22 boy starts walking along the beam. You may want to review ( pages 330 – 334) . For help with math skills, you may want to review: F1 = 670 N F2 = 900 N kg m kg The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture of the four forces acting on the beam, indicating both their direction and the place on the beam that the forces are acting. Choose a coordinate system with a direction for the axis along the beam, and indicate the position of the boy. What is the net force on the beam if it is stationary? Just before the beam tips, the force of the left support on the beam is zero. Using the zero net force condition, what is the force due to the right support just before the beam tips? For the beam to remain stationary, what must be zero besides the net force on the beam? Choose a point on the beam, and compute the net torque on the beam about that point. Be sure to choose a positive direction for the rotation axis and therefore the torques. Using the zero torque condition, what is the position of the boy on the beam just prior to tipping? How far is this position from the right edge of the beam? ANSWER: Correct d = 2.0 m Problem 12.68 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.6 diameter and a mass of 270 . Its maximum angular velocity is 1500 . Part A A motor spins up the flywheel with a constant torque of 54 . How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.2 . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: m kg rpm N  m t = 250 s = 1.1×106 E J s Correct Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.71 The 3.30 , 40.0-cm-diameter disk in the figure is spinning at 350 . Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2.10 ? P = 2.4×105 W  = 1800 Nm kg rpm s Express your answer with the appropriate units. ANSWER: Correct Problem 12.74 A 5.0 , 60- -diameter cylinder rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. Part A What is the magnitude of the cylinder’s initial angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: 5.76 N kg cm  = 22 rad s2 Correct Part B What is the magnitude of the cylinder’s angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.82 A 45 figure skater is spinning on the toes of her skates at 0.90 . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 , 20 average diameter, 160 tall) plus two rod-like arms (2.5 each, 67 long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 , 20- -diameter, 200- -tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Score Summary:  = 6.6 rad s kg rev/s kg cm cm kg cm kg cm cm 2 = Your score on this assignment is 95.7%. You received 189.42 out of a possible total of 198 points.

Assignment 10 Due: 11:59pm on Wednesday, April 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.3 Part A The figure shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies to . Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: Ka Kc Correct Conceptual Question 12.6 You have two steel solid spheres. Sphere 2 has twice the radius of sphere 1. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: I2 I1 Correct Problem 12.2 A high-speed drill reaches 2500 in 0.59 . Part A What is the drill’s angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Through how many revolutions does it turn during this first 0.59 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct I2/I1 = 32 rpm s  = 440 rad s2 s  = 12 rev Constant Angular Acceleration in the Kitchen Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second. Hint 1. How to approach the problem Recall from your study of kinematics the three equations of motion derived for systems undergoing constant linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to work with the three analogous equations of motion. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find the angular acceleration . Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it What is the angular velocity of the salad spinner as Dario is spinning it? Express your answer numerically in degrees per second. Hint 1. Converting rotations to degrees When the salad spinner spins through one revolution, it turns through 360 degrees. ANSWER: Hint 3. Find the angular distance the salad spinner travels as it comes to rest Through how many degrees does the salad spinner rotate as it comes to rest? Express your answer numerically in degrees. Hint 1. Converting rotations to degrees  0 = 1440 degrees/s  =  − 0 One revolution is equivalent to 360 degrees. ANSWER: Hint 4. Determine which equation to use You know the initial and final velocities of the system and the angular distance through which the spinner rotates as it comes to a stop. Which equation should be used to solve for the unknown constant angular acceleration ? ANSWER: ANSWER: Correct Part B How long does it take for the salad spinner to come to rest? Express your answer numerically in seconds.  = 2160 degrees   = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0  = -480 degrees/s2 Hint 1. How to approach the problem Again, you will need the equations of rotational kinematics that apply to situations of constant angular acceleration. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find . Hint 2. Determine which equation to use You have the initial and final velocities of the system and the angular acceleration, which you found in the previous part. Which is the best equation to use to solve for the unknown time ? ANSWER: ANSWER: Correct ± A Spinning Electric Fan An electric fan is turned off, and its angular velocity decreases uniformly from 540 to 250 in a time interval of length 4.40 . Part A Find the angular acceleration in revolutions per second per second. Hint 1. Average acceleration Recall that if the angular velocity decreases uniformly, the angular acceleration will remain constant. Therefore, the angular acceleration is just the total change in angular velocity divided by t t  = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0 t = 3.00 s rev/min rev/min s  the total change in time. Be careful of the sign of the angular acceleration. ANSWER: Correct Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. Hint 1. Determine the correct kinematic equation Which of the following kinematic equations is best suited to this problem? Here and are the initial and final angular velocities, is the elapsed time, is the constant angular acceleration, and and are the initial and final angular displacements. Hint 1. How to chose the right equation Notice that you were given in the problem introduction the initial and final speeds, as well as the length of time between them. In this problem, you are asked to find the number of revolutions (which here is the change in angular displacement, ). If you already found the angular acceleration in Part A, you could use that as well, but you would end up using a more complex equation. Also, in general, it is somewhat favorable to use given quantities instead of quantities that you have calculated. ANSWER:  = -1.10 rev/s2 0  t  0   − 0  = 0 + t  = 0 + t+  1 2 t2 = + 2( − ) 2 20 0 − 0 = (+ )t 1 2 0 ANSWER: Correct Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? Hint 1. Finding the total time for spin down To find the total time for spin down, just calculate when the velocity will equal zero. This is accomplished by setting the initial velocity plus the acceleration multipled by the time equal to zero and then solving for the time. One can then just subtract the time it took to reach 250 from the total time. Be careful of your signs when you set up the equation. ANSWER: Correct Problem 12.8 A 100 ball and a 230 ball are connected by a 34- -long, massless, rigid rod. The balls rotate about their center of mass at 130 . Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units. ANSWER: 29.0 rev rev/min 3.79 s g g cm rpm g Correct Problem 12.10 A thin, 60.0 disk with a diameter of 9.00 rotates about an axis through its center with 0.200 of kinetic energy. Part A What is the speed of a point on the rim? Express your answer with the appropriate units. ANSWER: Correct Problem 12.12 A drum major twirls a 95- -long, 470 baton about its center of mass at 150 . Part A What is the baton’s rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 3.2 ms g cm J 3.65 ms cm g rpm K = 4.4 J Correct Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord’s weight can be ignored. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply. Hint 1. Conditions for equilibrium If the blocks had the same mass, the system would be in equilibrium. The blocks would have zero acceleration and the tension in each part of the cord would equal the weight of each block. Both parts of the cord would then pull with equal force on the pulley, resulting in a zero net torque and no rotation of the pulley. Is this still the case in the current situation where block B has twice the mass of block A? Hint 2. Rotational analogue of Newton’s second law The net torque of all the forces acting on a rigid body is proportional to the angular acceleration of the body net  and is given by , where is the moment of inertia of the body. Hint 3. Relation between linear and angular acceleration A particle that rotates with angular acceleration has linear acceleration equal to , where is the distance of the particle from the axis of rotation. In the present case, where there is no slipping or stretching of the cord, the cord and the pulley must move together at the same speed. Therefore, if the cord moves with linear acceleration , the pulley must rotate with angular acceleration , where is the radius of the pulley. ANSWER: Correct Part B What happens when block B moves downward? Hint 1. How to approach the problem To determine whether the tensions in both parts of the cord are equal, it is convenient to write a mathematical expression for the net torque on the pulley. This will allow you to relate the tensions in the cord to the pulley’s angular acceleration. Hint 2. Find the net torque on the pulley Let’s assume that the tensions in both parts of the cord are different. Let be the tension in the right cord and the tension in the left cord. If is the radius of the pulley, what is the net torque acting on the pulley? Take the positive sense of rotation to be counterclockwise. Express your answer in terms of , , and . net = I I  a a = R R a  = a R R The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. T1 T2 R net T1 T2 R Hint 1. Torque The torque of a force with respect to a point is defined as the product of the magnitude times the perpendicular distance between the line of action of and the point . In other words, . ANSWER: ANSWER: Correct Note that if the pulley were stationary (as in many systems where only linear motion is studied), then the tensions in both parts of the cord would be equal. However, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration. Problem 12.18 Part A In the figure , what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.  F  O F l F  O  = Fl net = R(T2 − T1 ) The left cord pulls on the pulley with greater force than the right cord. The left and right cord pull with equal force on the pulley. The right cord pulls on the pulley with greater force than the left cord. ANSWER: Correct Part B What is the direction of net torque about the axle? ANSWER: Correct Problem 12.22 An athlete at the gym holds a 3.5 steel ball in his hand. His arm is 78 long and has a mass of 3.6 . Assume the center of mass of the arm is at the geometrical center of the arm. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer to two significant figures and include the appropriate units.  = 0.20 Nm Clockwise Counterclockwise kg cm kg ANSWER: Correct Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Parallel Axis Theorem The parallel axis theorem relates , the moment of inertia of an object about an axis passing through its center of mass, to , the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is , where is the perpendicular distance from the center of mass to the axis that passes through point p, and is the mass of the object. Part A Suppose a uniform slender rod has length and mass . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . Find , the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the center of mass Find the distance appropriate to this problem. That is, find the perpendicular distance from the center of mass of the rod to the axis passing through one end of the rod.  = 41 Nm 45  = 29 Nm Icm Ip Ip = Icm + Md2 d M L m Icm = m 1 12 L2 Iend Iend m L d ANSWER: ANSWER: Correct Part B Now consider a cube of mass with edges of length . The moment of inertia of the cube about an axis through its center of mass and perpendicular to one of its faces is given by . Find , the moment of inertia about an axis p through one of the edges of the cube Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the axis Find the perpendicular distance from the center of mass axis to the new edge axis (axis labeled p in the figure). ANSWER: d = L 2 Iend = mL2 3 m a Icm Icm = m 1 6 a2 Iedge Iedge m a o p d ANSWER: Correct Problem 12.26 Starting from rest, a 12- -diameter compact disk takes 2.9 to reach its operating angular velocity of 2000 . Assume that the angular acceleration is constant. The disk’s moment of inertia is . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: d = a 2 Iedge = 2ma2 3 cm s rpm 2.5 × 10−5 kg m2 = 1.8×10−3  Nm Correct Problem 12.23 An object’s moment of inertia is 2.20 . Its angular velocity is increasing at the rate of 3.70 . Part A What is the total torque on the object? ANSWER: Correct Problem 12.31 A 5.1 cat and a 2.5 bowl of tuna fish are at opposite ends of the 4.0- -long seesaw. N = 48 rev kgm2 rad/s2 8.14 N  m kg kg m Part A How far to the left of the pivot must a 3.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass , length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance from the scapula. The deltoid muscle makes an angle of with the horizontal, as shown. Use throughout the problem. Part A kg d = 1.4 m M1 = 3.6 kg L = 0.66 m L1 = 0.33 m L2 = 0.15 m  = 17 g = 9.8 m/s2 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. Hint 1. Nature of the problem Remember that this is a statics problem, so all forces and torques are balanced (their sums equal zero). Hint 2. Origin of torque Calculate the torque about the point at which the arm attaches to the rest of the body. This allows one to balance the torques without having to worry about the undefined forces at this point. Hint 3. Adding up the torques Add up the torques about the point in which the humerus attaches to the body. Answer in terms of , , , , , and . Remember that counterclockwise torque is positive. ANSWER: ANSWER: Correct Part B Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). Express your answer in newtons, to the nearest integer. T L1 L2 M1 g T  total = 0 = L1M1g − Tsin()L2 T = 265 N Fy Hint 1. Total forces involved Recall that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body). ANSWER: Correct Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. Express your answer in newtons, to the nearest integer. ANSWER: Correct ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: , , and . Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). |Fy| = 42 N Fx |Fx| = 254 N F 1 F  2 F  3 Part A If and , what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. Hint 1. Finding torque about pivot from What is the magnitude of the torque | | provided by around the pivot point? Give your answer numerically in newton-meters to two significant figures. ANSWER: ANSWER: Correct Part B If the L-shaped rod has a moment of inertia , , , and again , how long a time would it take for the object to move through ( /4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures. F3 = 0 F1 = 12 N F 2 F 1   1 F  1 |  1 | = 0.36 N  m F2 = 4.5 N I = 9 kg m2 F1 = 12 N F2 = 27 N F3 = 0 t 45  Hint 1. Find the net torque about the pivot What is the magnitude of the total torque around the pivot point? Answer numerically in newton-meters to two significant figures. ANSWER: Hint 2. Calculate Given the total torque around the pivot point, what is , the magnitude of the angular acceleration? Express your answer numerically in radians per second squared to two significant figures. Hint 1. Equation for If you know the magnitude of the total torque ( ) and the rotational inertia ( ), you can then find the rotational acceleration ( ) from ANSWER: Hint 3. Description of angular kinematics Now that you know the angular acceleration, this is a problem in rotational kinematics; find the time needed to go through a given angle . For constant acceleration ( ) and starting with (where is angular speed) the relation is given by which is analogous to the expression for linear displacement ( ) with constant acceleration ( ) starting from rest, | p ivot| | p ivot| = 1.8 N  m    vot Ivot  pivot = Ipivot.  = 0.20 radians/s2    = 0   = 1  , 2 t2 x a . ANSWER: Correct Part C Now consider the situation in which and , but now a force with nonzero magnitude is acting on the rod. What does have to be to obtain equilibrium? Give a numerical answer, without trigonometric functions, in newtons, to two significant figures. Hint 1. Find the required component of Only the tangential (perpendicular) component of (call it ) provides a torque. What is ? Answer in terms of . You will need to evaluate any trigonometric functions. ANSWER: ANSWER: Correct x = 1 a 2 t2 t = 2.8 s F1 = 12 N F2 = 0 F3 F3 F 3 F  3 F3t F3t F3 F3t = 1 2 F3 F3 = 9.0 N Problem 12.32 A car tire is 55.0 in diameter. The car is traveling at a speed of 24.0 . Part A What is the tire’s rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units. ANSWER: cm m/s 833 rpm 48.0 ms 0 ms Correct Problem 12.33 A 460 , 8.00-cm-diameter solid cylinder rolls across the floor at 1.30 . Part A What is the can’s kinetic energy? Express your answer with the appropriate units. ANSWER: Correct Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? g m/s 0.583 J g ANSWER: Correct Part B What is the direction of the angular momentum of the bar ? ANSWER: Correct Problem 12.46 Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? 3.27 kgm2/s into the page out of the page kg ANSWER: Correct Part B What is its direction? ANSWER: Correct Problem 12.60 A 3.0- -long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.46. 3.66×10−2 kgm /s 2 x direction -x direction y direction -y direction z direction -z direction m Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.61 The 3.0- -long, 90 rigid beam in the following figure is supported at each end. An 70 student stands 2.0 from support 1.  = 47 m kg kg m Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 12.63 A 44 , 5.5- -long beam is supported, but not attached to, the two posts in the figure . A 22 boy starts walking along the beam. You may want to review ( pages 330 – 334) . For help with math skills, you may want to review: F1 = 670 N F2 = 900 N kg m kg The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture of the four forces acting on the beam, indicating both their direction and the place on the beam that the forces are acting. Choose a coordinate system with a direction for the axis along the beam, and indicate the position of the boy. What is the net force on the beam if it is stationary? Just before the beam tips, the force of the left support on the beam is zero. Using the zero net force condition, what is the force due to the right support just before the beam tips? For the beam to remain stationary, what must be zero besides the net force on the beam? Choose a point on the beam, and compute the net torque on the beam about that point. Be sure to choose a positive direction for the rotation axis and therefore the torques. Using the zero torque condition, what is the position of the boy on the beam just prior to tipping? How far is this position from the right edge of the beam? ANSWER: Correct d = 2.0 m Problem 12.68 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.6 diameter and a mass of 270 . Its maximum angular velocity is 1500 . Part A A motor spins up the flywheel with a constant torque of 54 . How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.2 . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: m kg rpm N  m t = 250 s = 1.1×106 E J s Correct Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.71 The 3.30 , 40.0-cm-diameter disk in the figure is spinning at 350 . Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2.10 ? P = 2.4×105 W  = 1800 Nm kg rpm s Express your answer with the appropriate units. ANSWER: Correct Problem 12.74 A 5.0 , 60- -diameter cylinder rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. Part A What is the magnitude of the cylinder’s initial angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: 5.76 N kg cm  = 22 rad s2 Correct Part B What is the magnitude of the cylinder’s angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.82 A 45 figure skater is spinning on the toes of her skates at 0.90 . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 , 20 average diameter, 160 tall) plus two rod-like arms (2.5 each, 67 long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 , 20- -diameter, 200- -tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Score Summary:  = 6.6 rad s kg rev/s kg cm cm kg cm kg cm cm 2 = Your score on this assignment is 95.7%. You received 189.42 out of a possible total of 198 points.

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Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11<Z<0.22) (f) P(-0.11<Z<0.5) Q.19. Use normal distribution table to find the missing values (?). (a) P(Z< ?)=0.40 (b) P(Z< ?)=0.76 (c) P(Z> ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11 ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

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When researchers say, “preferences need no inferences” with respect to emotion, what are they really arguing? Appraisal does not need to come first in the emotion process. Appraisal must come first in the emotion process. Personality traits are more important than situations for determining emotions. Attitudes are more important than personality traits for determining emotions.

When researchers say, “preferences need no inferences” with respect to emotion, what are they really arguing? Appraisal does not need to come first in the emotion process. Appraisal must come first in the emotion process. Personality traits are more important than situations for determining emotions. Attitudes are more important than personality traits for determining emotions.

When researchers say, “preferences need no inferences” with respect to … Read More...