1. Of all the skills in Bloom’s taxonomy, which are you most successful with in your own schooling? Which are more challenging for you?

1. Of all the skills in Bloom’s taxonomy, which are you most successful with in your own schooling? Which are more challenging for you?

Bloom’s Classification of Cognitive Skills Successful Category Definition Related Behaviors … Read More...
. What are the main tenets and concerns of the Epicurean philosophy? Are you persuaded by this general approach? Why or why not?

. What are the main tenets and concerns of the Epicurean philosophy? Are you persuaded by this general approach? Why or why not?

You will discover 3 key tenets as well as concerns … Read More...
AUCS 340: Ethics in the Professions Homework Assignment: International and US Health Care Systems The following homework assignment will help you to discover some of the differences between the administration of health care in the United States and internationally. This is a research based assignment; remember the use of Wikipedia.com is not an acceptable reference site for this course. You must include a references cited page for this assignment; correctly formatted APA or MLA references are acceptable (simply stating s web address is NOT a complete reference). The answers should be presented in paragraph formation. Staple all pages together for presentation. The first question refers to a country other than the United States of America 1) Socialized Medicine – provide a definition of the term socialized medicine and discuss a country that currently has a socialized medicine system to cover all citizens; this discussion should include the types of services offered to the citizens of this country. When was this system first implemented in this country? What is the name of this country’s health insurance plan? Compare the ranking for the life expectancy for this country to that of the United States. Which is higher? Why? Compare the cost of financing healthcare in this country to the United States in comparison to the amount of annual funding in dollars and the percentage of gross domestic product spent on health care for each country. What rank does this country have in comparison to the United States for overall health of its citizens? (This portion of the assignment should be approximately one page in length and graphic data is acceptable to support some answers, however, graphic information should only be used to explain your written explanation not as the answer to the question.) Bonus: Is this country’s system currently financially stable? Why or why not? The following questions refer to the delivery of healthcare in the United States of America, as it was organized prior to the implementation of the Affordable Care Act (ACA). The ACA is currently being phased into coverage. It is estimated that the answers to the following questions will result in an additional two to three pages of written text in addition to the page for question number one. 2) Medicare – when was it enacted? Who does it cover? Who was President when Medicare was originally passed? What do the specific portions Part A, Part B and Part D cover? When was Part D enacted? Who was President when Part D was enacted? Is the Medicare system currently financially stable? Why or why not. Compare the average life expectancy for males and females when Medicare was originally passed and the average life expectancy of males and females as of 2010; more recent data is acceptable. Bonus: What does Part C cover and when was it enacted? 3) Health Maintenance Organization (HMO) – Define the term health maintenance organization. When did this type of health insurance plan become popular in the United States? How does this type of system provide medical care to the people enrolled? This answer should discuss in network versus out of network coverage. 4) Medicaid- when was it enacted? Who does it cover? Who was President when this insurance plan was enacted? Are the coverage benefits the same state to state? Why or why not? Is the system currently financially stable? Why or why not. What effect does passage of the ACA project to have on enrollment in the Medicaid system? Why? 5) Organ Transplants – What is the mechanism for placement of a patient’s name on the organ transplant list? What is the current length of time a patient must wait for a heart transplant? Explain at least one reason why transplants are considered an ethical issue. How are transplants financed? Give at least one example of how much any type of organ transplant would cost. 6) Health Insurance/Information Portability and Accountability Act (HIPAA) – When was it enacted? Who was President when this legislation as passed? What is the scope of this legislative for the medical community and the general community? (Hint: There are actually two reasons for HIPAA legislation; make sure to state both in your response) 7) Death with Dignity Act – what year was the Oregon Death with Dignity Act passed? What ethical issue is covered by the Death with Dignity Act? List the factors that must be met for a patient to use the Death with Dignity Act. List two additional states that have enacted Death with Dignity Acts and when was the legislation passed in these states? 8) Hospice – what is hospice care? When was it developed? What country was most instrumental in the development of hospice care? Do health insurance plans in the United States cover hospice care? What types of services are covered for hospice care? Grading: 1) Accuracy and completeness of responses = 60% of grade 2) Correct use of sentence structure, spelling and grammar = 30% of grade 3) Appropriate use of references and citations = 10% of grade Simply stating a web page is not an appropriate reference This assignment is due on the date published in the course syllabus.

AUCS 340: Ethics in the Professions Homework Assignment: International and US Health Care Systems The following homework assignment will help you to discover some of the differences between the administration of health care in the United States and internationally. This is a research based assignment; remember the use of Wikipedia.com is not an acceptable reference site for this course. You must include a references cited page for this assignment; correctly formatted APA or MLA references are acceptable (simply stating s web address is NOT a complete reference). The answers should be presented in paragraph formation. Staple all pages together for presentation. The first question refers to a country other than the United States of America 1) Socialized Medicine – provide a definition of the term socialized medicine and discuss a country that currently has a socialized medicine system to cover all citizens; this discussion should include the types of services offered to the citizens of this country. When was this system first implemented in this country? What is the name of this country’s health insurance plan? Compare the ranking for the life expectancy for this country to that of the United States. Which is higher? Why? Compare the cost of financing healthcare in this country to the United States in comparison to the amount of annual funding in dollars and the percentage of gross domestic product spent on health care for each country. What rank does this country have in comparison to the United States for overall health of its citizens? (This portion of the assignment should be approximately one page in length and graphic data is acceptable to support some answers, however, graphic information should only be used to explain your written explanation not as the answer to the question.) Bonus: Is this country’s system currently financially stable? Why or why not? The following questions refer to the delivery of healthcare in the United States of America, as it was organized prior to the implementation of the Affordable Care Act (ACA). The ACA is currently being phased into coverage. It is estimated that the answers to the following questions will result in an additional two to three pages of written text in addition to the page for question number one. 2) Medicare – when was it enacted? Who does it cover? Who was President when Medicare was originally passed? What do the specific portions Part A, Part B and Part D cover? When was Part D enacted? Who was President when Part D was enacted? Is the Medicare system currently financially stable? Why or why not. Compare the average life expectancy for males and females when Medicare was originally passed and the average life expectancy of males and females as of 2010; more recent data is acceptable. Bonus: What does Part C cover and when was it enacted? 3) Health Maintenance Organization (HMO) – Define the term health maintenance organization. When did this type of health insurance plan become popular in the United States? How does this type of system provide medical care to the people enrolled? This answer should discuss in network versus out of network coverage. 4) Medicaid- when was it enacted? Who does it cover? Who was President when this insurance plan was enacted? Are the coverage benefits the same state to state? Why or why not? Is the system currently financially stable? Why or why not. What effect does passage of the ACA project to have on enrollment in the Medicaid system? Why? 5) Organ Transplants – What is the mechanism for placement of a patient’s name on the organ transplant list? What is the current length of time a patient must wait for a heart transplant? Explain at least one reason why transplants are considered an ethical issue. How are transplants financed? Give at least one example of how much any type of organ transplant would cost. 6) Health Insurance/Information Portability and Accountability Act (HIPAA) – When was it enacted? Who was President when this legislation as passed? What is the scope of this legislative for the medical community and the general community? (Hint: There are actually two reasons for HIPAA legislation; make sure to state both in your response) 7) Death with Dignity Act – what year was the Oregon Death with Dignity Act passed? What ethical issue is covered by the Death with Dignity Act? List the factors that must be met for a patient to use the Death with Dignity Act. List two additional states that have enacted Death with Dignity Acts and when was the legislation passed in these states? 8) Hospice – what is hospice care? When was it developed? What country was most instrumental in the development of hospice care? Do health insurance plans in the United States cover hospice care? What types of services are covered for hospice care? Grading: 1) Accuracy and completeness of responses = 60% of grade 2) Correct use of sentence structure, spelling and grammar = 30% of grade 3) Appropriate use of references and citations = 10% of grade Simply stating a web page is not an appropriate reference This assignment is due on the date published in the course syllabus.

PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

After reading the paragraph, answer the question(s) that follow. A woman has been trying to conceive for several years, unsuccessfully. At a fertility clinic, they discover that she has blocked fallopian tubes. Using modern technologies, some of her eggs are removed, fertilized with her husband’s sperm, and implanted into her uterus. The procedure is successful, but the couple discovers that their new son is color-blind and has blood type O. The woman claims that the child can’t be theirs since she has blood type A and her husband has type B. Also, neither parent is color-blind, although one grandparent (the woman’s father) is also color-blind In regard to the baby’s color blindness, a sex-linked recessive trait, you explain that

After reading the paragraph, answer the question(s) that follow. A woman has been trying to conceive for several years, unsuccessfully. At a fertility clinic, they discover that she has blocked fallopian tubes. Using modern technologies, some of her eggs are removed, fertilized with her husband’s sperm, and implanted into her uterus. The procedure is successful, but the couple discovers that their new son is color-blind and has blood type O. The woman claims that the child can’t be theirs since she has blood type A and her husband has type B. Also, neither parent is color-blind, although one grandparent (the woman’s father) is also color-blind In regard to the baby’s color blindness, a sex-linked recessive trait, you explain that

since color blindness is sex-linked, a son can inherit color … Read More...
Chapter 13 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Matter of Some Gravity Learning Goal: To understand Newton’s law of gravitation and the distinction between inertial and gravitational masses. In this problem, you will practice using Newton’s law of gravitation. According to that law, the magnitude of the gravitational force between two small particles of masses and , separated by a distance , is given by , where is the universal gravitational constant, whose numerical value (in SI units) is . This formula applies not only to small particles, but also to spherical objects. In fact, the gravitational force between two uniform spheres is the same as if we concentrated all the mass of each sphere at its center. Thus, by modeling the Earth and the Moon as uniform spheres, you can use the particle approximation when calculating the force of gravity between them. Be careful in using Newton’s law to choose the correct value for . To calculate the force of gravitational attraction between two uniform spheres, the distance in the equation for Newton’s law of gravitation is the distance between the centers of the spheres. For instance, if a small object such as an elephant is located on the surface of the Earth, the radius of the Earth would be used in the equation. Note that the force of gravity acting on an object located near the surface of a planet is often called weight. Also note that in situations involving satellites, you are often given the altitude of the satellite, that is, the distance from the satellite to the surface of the planet; this is not the distance to be used in the formula for the law of gravitation. There is a potentially confusing issue involving mass. Mass is defined as a measure of an object’s inertia, that is, its ability to resist acceleration. Newton’s second law demonstrates the relationship between mass, acceleration, and the net force acting on an object: . We can now refer to this measure of inertia more precisely as the inertial mass. On the other hand, the masses of the particles that appear in the expression for the law of gravity seem to have nothing to do with inertia: Rather, they serve as a measure of the strength of gravitational interactions. It would be reasonable to call such a property gravitational mass. Does this mean that every object has two different masses? Generally speaking, yes. However, the good news is that according to the latest, highly precise, measurements, the inertial and the gravitational mass of an object are, in fact, equal to each other; it is an established consensus among physicists that there is only one mass after all, which is a measure of both the object’s inertia and its ability to engage in gravitational interactions. Note that this consensus, like everything else in science, is open to possible amendments in the future. In this problem, you will answer several questions that require the use of Newton’s law of gravitation. Part A Two particles are separated by a certain distance. The force of gravitational interaction between them is . Now the separation between the particles is tripled. Find the new force of gravitational Fg m1 m2 r Fg = G m1m2 r2 G 6.67 × 10−11 N m2 kg2 r r rEarth F  = m net a F0 interaction . Express your answer in terms of . ANSWER: Part B A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite moves to a different orbit, so that its altitude is tripled. Find the new force of gravitational interaction . Express your answer in terms of . You did not open hints for this part. ANSWER: Part C A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite is brought back to the surface of the planet. Find the new force of gravitational interaction . Express your answer in terms of . ANSWER: F1 F0 F1 = F0 F2 F0 F2 = F0 F4 F0 Typesetting math: 81% Part D Two satellites revolve around the Earth. Satellite A has mass and has an orbit of radius . Satellite B has mass and an orbit of unknown radius . The forces of gravitational attraction between each satellite and the Earth is the same. Find . Express your answer in terms of . ANSWER: Part E An adult elephant has a mass of about 5.0 tons. An adult elephant shrew has a mass of about 50 grams. How far from the center of the Earth should an elephant be placed so that its weight equals that of the elephant shrew on the surface of the Earth? The radius of the Earth is 6400 . ( .) Express your answer in kilometers. ANSWER: The table below gives the masses of the Earth, the Moon, and the Sun. Name Mass (kg) Earth Moon Sun F4 = m r 6m rb rb r rb = r km 1 ton = 103 kg r = km 5.97 × 1024 7.35 × 1022 1.99 × 1030 Typesetting math: 81% The average distance between the Earth and the Moon is . The average distance between the Earth and the Sun is . Use this information to answer the following questions. Part F Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the new moon (when the moon is located directly between the Earth and the Sun). Express your answer in newtons to three significant figures. You did not open hints for this part. ANSWER: Part G Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the full moon (when the Earth is located directly between the moon and the sun). Express your answer in newtons to three significant figures. ANSWER: ± Understanding Newton’s Law of Universal Gravitation Learning Goal: To understand Newton’s law of universal gravitation and be able to apply it in two-object situations and (collinear) three-object situations; to distinguish between the use of and . 3.84 × 108 m 1.50 × 1011 m Fnet Fnet = N Fnet Fnet = N Typesetting math: 81% G g In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in the figure. Newton’s law of universal gravitation describes the magnitude of the attractive gravitational force between two objects with masses and as , where is the distance between the centers of the two objects and is the gravitational constant. The gravitational force is attractive, so in the figure it pulls to the right on (toward ) and toward the left on (toward ). The gravitational force acting on is equal in size to, but exactly opposite in direction from, the gravitational force acting on , as required by Newton’s third law. The magnitude of both forces is calculated with the equation given above. The gravitational constant has the value and should not be confused with the magnitude of the gravitational free-fall acceleration constant, denoted by , which equals 9.80 near the surface of the earth. The size of in SI units is tiny. This means that gravitational forces are sizeable only in the vicinity of very massive objects, such as the earth. You are in fact gravitationally attracted toward all the objects around you, such as the computer you are using, but the size of that force is too small to be noticed without extremely sensitive equipment. Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass and the sun has mass . They are separated, center to center, by . Part A What is the size of the gravitational force acting on the earth due to the sun? Express your answer in newtons. F  g m1 m2 Fg = G( ) m1m2 r2 r G m1 m2 m2 m1 m1 m2 G G = 6.67 × 10−11 N m2/kg2 g m/s2 G mearth = 5.98 × 1024 kg msun = 1.99 × 1030 kg r = 93 million miles = 150 million km Typesetting math: 81% You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F N Typesetting math: 81% This question will be shown after you complete previous question(s). Understanding Mass and Weight Learning Goal: To understand the distinction between mass and weight and to be able to calculate the weight of an object from its mass and Newton’s law of gravitation. The concepts of mass and weight are often confused. In fact, in everyday conversations, the word “weight” often replaces “mass,” as in “My weight is seventy-five kilograms” or “I need to lose some weight.” Of course, mass and weight are related; however, they are also very different. Mass, as you recall, is a measure of an object’s inertia (ability to resist acceleration). Newton’s 2nd law demonstrates the relationship among an object’s mass, its acceleration, and the net force acting on it: . Mass is an intrinsic property of an object and is independent of the object’s location. Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: , where is the weight of an object, is the mass of that object, and is the local acceleration due to gravity (in other words, the strength of the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the object and its location. Part A Which of the following quantities represent mass? Check all that apply. ANSWER: Fnet = ma w = mg w m g 12.0 lbs 0.34 g 120 kg 1600 kN 0.34 m 411 cm 899 MN Typesetting math: 81% Part B This question will be shown after you complete previous question(s). Using the universal law of gravity, we can find the weight of an object feeling the gravitational pull of a nearby planet. We can write an expression , where is the weight of the object, is the gravitational constant, is the mass of that object, is mass of the planet, and is the distance from the center of the planet to the object. If the object is on the surface of the planet, is simply the radius of the planet. Part C The gravitational field on the surface of the earth is stronger than that on the surface of the moon. If a rock is transported from the moon to the earth, which properties of the rock change? ANSWER: Part D This question will be shown after you complete previous question(s). Part E If acceleration due to gravity on the earth is , which formula gives the acceleration due to gravity on Loput? You did not open hints for this part. ANSWER: w = GmM/r2 w G m M r r mass only weight only both mass and weight neither mass nor weight g Typesetting math: 81% Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). ± Weight on a Neutron Star Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but a much smaller diameter. g 1.7 5.6 g 1.72 5.6 g 1.72 5.62 g 5.6 1.7 g 5.62 1.72 g 5.6 1.72 Typesetting math: 81% Part A If you weigh 655 on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 19.0 ? Take the mass of the sun to be = 1.99×1030 , the gravitational constant to be = 6.67×10−11 , and the acceleration due to gravity at the earth’s surface to be = 9.810 . Express your weight in newtons. You did not open hints for this part. ANSWER: ± Escape Velocity Learning Goal: To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass . The escape velocity is a function of the distance of the object from the center of the planet , but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question “How fast does my rocket have to go to escape from the surface of the planet?” Part A The key to making a concise mathematical definition of escape velocity is to consider the energy. If an object is launched at its escape velocity, what is the total mechanical energy of the object at a very large (i.e., infinite) distance from the planet? Follow the usual convention and take the gravitational potential energy to be zero at very large distances. You did not open hints for this part. ANSWER: N km ms kg G N m2/kg2 g m/s2 wstar wstar = N m M R Etotal Typesetting math: 81% Consider the motion of an object between a point close to the planet and a point very very far from the planet. Indicate whether the following statements are true or false. Part B Angular momentum about the center of the planet is conserved. ANSWER: Part C Total mechanical energy is conserved. ANSWER: Part D Kinetic energy is conserved. ANSWER: Etotal = true false true false Typesetting math: 81% Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). A Satellite in a Circular Orbit Consider a satellite of mass that orbits a planet of mass in a circle a distance from the center of the planet. The satellite’s mass is negligible compared with that of the planet. Indicate whether each of the statements in this problem is true or false. Part A The information given is sufficient to uniquely specify the speed, potential energy, and angular momentum of the satellite. You did not open hints for this part. ANSWER: true false m1 m2 r true false Typesetting math: 81% Part B The total mechanical energy of the satellite is conserved. You did not open hints for this part. ANSWER: Part C The linear momentum vector of the satellite is conserved. You did not open hints for this part. ANSWER: Part D The angular momentum of the satellite about the center of the planet is conserved. You did not open hints for this part. ANSWER: true false true false Typesetting math: 81% Part E The equations that express the conservation laws of total mechanical energy and linear momentum are sufficient to solve for the speed necessary to maintain a circular orbit at without using . You did not open hints for this part. ANSWER: At the Galaxy’s Core Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light years and an orbital speed of about 200 . Part A Determine the mass of the massive object at the center of the Milky Way galaxy. Take the distance of one light year to be . Express your answer in kilograms. You did not open hints for this part. true false R F = ma true false km/s M 9.461 × 1015 m Typesetting math: 81% ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Properties of Circular Orbits Learning Goal: To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth. M = kg Typesetting math: 81% The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit–a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass . For all parts of this problem, where appropriate, use for the universal gravitational constant. Part A Find the orbital speed for a satellite in a circular orbit of radius . Express the orbital speed in terms of , , and . You did not open hints for this part. ANSWER: Part B Find the kinetic energy of a satellite with mass in a circular orbit with radius . Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. ANSWER: Part C M G v R G M R v = K m R \texttip{K}{K} = Typesetting math: 81% This question will be shown after you complete previous question(s). Part D Find the orbital period \texttip{T}{T}. Express your answer in terms of \texttip{G}{G}, \texttip{M}{M}, \texttip{R}{R}, and \texttip{\pi }{pi}. You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F Find \texttip{L}{L}, the magnitude of the angular momentum of the satellite with respect to the center of the planet. Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. You did not open hints for this part. ANSWER: \texttip{T}{T} = Typesetting math: 81% Part G The quantities \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L} all represent physical quantities characterizing the orbit that depend on radius \texttip{R}{R}. Indicate the exponent (power) of the radial dependence of the absolute value of each. Express your answer as a comma-separated list of exponents corresponding to \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L}, in that order. For example, -1,-1/2,-0.5,-3/2 would mean v \propto R^{-1}, K \propto R^{-1/2}, and so forth. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. \texttip{L}{L} = Typesetting math: 81%

Chapter 13 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Matter of Some Gravity Learning Goal: To understand Newton’s law of gravitation and the distinction between inertial and gravitational masses. In this problem, you will practice using Newton’s law of gravitation. According to that law, the magnitude of the gravitational force between two small particles of masses and , separated by a distance , is given by , where is the universal gravitational constant, whose numerical value (in SI units) is . This formula applies not only to small particles, but also to spherical objects. In fact, the gravitational force between two uniform spheres is the same as if we concentrated all the mass of each sphere at its center. Thus, by modeling the Earth and the Moon as uniform spheres, you can use the particle approximation when calculating the force of gravity between them. Be careful in using Newton’s law to choose the correct value for . To calculate the force of gravitational attraction between two uniform spheres, the distance in the equation for Newton’s law of gravitation is the distance between the centers of the spheres. For instance, if a small object such as an elephant is located on the surface of the Earth, the radius of the Earth would be used in the equation. Note that the force of gravity acting on an object located near the surface of a planet is often called weight. Also note that in situations involving satellites, you are often given the altitude of the satellite, that is, the distance from the satellite to the surface of the planet; this is not the distance to be used in the formula for the law of gravitation. There is a potentially confusing issue involving mass. Mass is defined as a measure of an object’s inertia, that is, its ability to resist acceleration. Newton’s second law demonstrates the relationship between mass, acceleration, and the net force acting on an object: . We can now refer to this measure of inertia more precisely as the inertial mass. On the other hand, the masses of the particles that appear in the expression for the law of gravity seem to have nothing to do with inertia: Rather, they serve as a measure of the strength of gravitational interactions. It would be reasonable to call such a property gravitational mass. Does this mean that every object has two different masses? Generally speaking, yes. However, the good news is that according to the latest, highly precise, measurements, the inertial and the gravitational mass of an object are, in fact, equal to each other; it is an established consensus among physicists that there is only one mass after all, which is a measure of both the object’s inertia and its ability to engage in gravitational interactions. Note that this consensus, like everything else in science, is open to possible amendments in the future. In this problem, you will answer several questions that require the use of Newton’s law of gravitation. Part A Two particles are separated by a certain distance. The force of gravitational interaction between them is . Now the separation between the particles is tripled. Find the new force of gravitational Fg m1 m2 r Fg = G m1m2 r2 G 6.67 × 10−11 N m2 kg2 r r rEarth F  = m net a F0 interaction . Express your answer in terms of . ANSWER: Part B A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite moves to a different orbit, so that its altitude is tripled. Find the new force of gravitational interaction . Express your answer in terms of . You did not open hints for this part. ANSWER: Part C A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite is brought back to the surface of the planet. Find the new force of gravitational interaction . Express your answer in terms of . ANSWER: F1 F0 F1 = F0 F2 F0 F2 = F0 F4 F0 Typesetting math: 81% Part D Two satellites revolve around the Earth. Satellite A has mass and has an orbit of radius . Satellite B has mass and an orbit of unknown radius . The forces of gravitational attraction between each satellite and the Earth is the same. Find . Express your answer in terms of . ANSWER: Part E An adult elephant has a mass of about 5.0 tons. An adult elephant shrew has a mass of about 50 grams. How far from the center of the Earth should an elephant be placed so that its weight equals that of the elephant shrew on the surface of the Earth? The radius of the Earth is 6400 . ( .) Express your answer in kilometers. ANSWER: The table below gives the masses of the Earth, the Moon, and the Sun. Name Mass (kg) Earth Moon Sun F4 = m r 6m rb rb r rb = r km 1 ton = 103 kg r = km 5.97 × 1024 7.35 × 1022 1.99 × 1030 Typesetting math: 81% The average distance between the Earth and the Moon is . The average distance between the Earth and the Sun is . Use this information to answer the following questions. Part F Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the new moon (when the moon is located directly between the Earth and the Sun). Express your answer in newtons to three significant figures. You did not open hints for this part. ANSWER: Part G Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the full moon (when the Earth is located directly between the moon and the sun). Express your answer in newtons to three significant figures. ANSWER: ± Understanding Newton’s Law of Universal Gravitation Learning Goal: To understand Newton’s law of universal gravitation and be able to apply it in two-object situations and (collinear) three-object situations; to distinguish between the use of and . 3.84 × 108 m 1.50 × 1011 m Fnet Fnet = N Fnet Fnet = N Typesetting math: 81% G g In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in the figure. Newton’s law of universal gravitation describes the magnitude of the attractive gravitational force between two objects with masses and as , where is the distance between the centers of the two objects and is the gravitational constant. The gravitational force is attractive, so in the figure it pulls to the right on (toward ) and toward the left on (toward ). The gravitational force acting on is equal in size to, but exactly opposite in direction from, the gravitational force acting on , as required by Newton’s third law. The magnitude of both forces is calculated with the equation given above. The gravitational constant has the value and should not be confused with the magnitude of the gravitational free-fall acceleration constant, denoted by , which equals 9.80 near the surface of the earth. The size of in SI units is tiny. This means that gravitational forces are sizeable only in the vicinity of very massive objects, such as the earth. You are in fact gravitationally attracted toward all the objects around you, such as the computer you are using, but the size of that force is too small to be noticed without extremely sensitive equipment. Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass and the sun has mass . They are separated, center to center, by . Part A What is the size of the gravitational force acting on the earth due to the sun? Express your answer in newtons. F  g m1 m2 Fg = G( ) m1m2 r2 r G m1 m2 m2 m1 m1 m2 G G = 6.67 × 10−11 N m2/kg2 g m/s2 G mearth = 5.98 × 1024 kg msun = 1.99 × 1030 kg r = 93 million miles = 150 million km Typesetting math: 81% You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F N Typesetting math: 81% This question will be shown after you complete previous question(s). Understanding Mass and Weight Learning Goal: To understand the distinction between mass and weight and to be able to calculate the weight of an object from its mass and Newton’s law of gravitation. The concepts of mass and weight are often confused. In fact, in everyday conversations, the word “weight” often replaces “mass,” as in “My weight is seventy-five kilograms” or “I need to lose some weight.” Of course, mass and weight are related; however, they are also very different. Mass, as you recall, is a measure of an object’s inertia (ability to resist acceleration). Newton’s 2nd law demonstrates the relationship among an object’s mass, its acceleration, and the net force acting on it: . Mass is an intrinsic property of an object and is independent of the object’s location. Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: , where is the weight of an object, is the mass of that object, and is the local acceleration due to gravity (in other words, the strength of the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the object and its location. Part A Which of the following quantities represent mass? Check all that apply. ANSWER: Fnet = ma w = mg w m g 12.0 lbs 0.34 g 120 kg 1600 kN 0.34 m 411 cm 899 MN Typesetting math: 81% Part B This question will be shown after you complete previous question(s). Using the universal law of gravity, we can find the weight of an object feeling the gravitational pull of a nearby planet. We can write an expression , where is the weight of the object, is the gravitational constant, is the mass of that object, is mass of the planet, and is the distance from the center of the planet to the object. If the object is on the surface of the planet, is simply the radius of the planet. Part C The gravitational field on the surface of the earth is stronger than that on the surface of the moon. If a rock is transported from the moon to the earth, which properties of the rock change? ANSWER: Part D This question will be shown after you complete previous question(s). Part E If acceleration due to gravity on the earth is , which formula gives the acceleration due to gravity on Loput? You did not open hints for this part. ANSWER: w = GmM/r2 w G m M r r mass only weight only both mass and weight neither mass nor weight g Typesetting math: 81% Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). ± Weight on a Neutron Star Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but a much smaller diameter. g 1.7 5.6 g 1.72 5.6 g 1.72 5.62 g 5.6 1.7 g 5.62 1.72 g 5.6 1.72 Typesetting math: 81% Part A If you weigh 655 on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 19.0 ? Take the mass of the sun to be = 1.99×1030 , the gravitational constant to be = 6.67×10−11 , and the acceleration due to gravity at the earth’s surface to be = 9.810 . Express your weight in newtons. You did not open hints for this part. ANSWER: ± Escape Velocity Learning Goal: To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass . The escape velocity is a function of the distance of the object from the center of the planet , but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question “How fast does my rocket have to go to escape from the surface of the planet?” Part A The key to making a concise mathematical definition of escape velocity is to consider the energy. If an object is launched at its escape velocity, what is the total mechanical energy of the object at a very large (i.e., infinite) distance from the planet? Follow the usual convention and take the gravitational potential energy to be zero at very large distances. You did not open hints for this part. ANSWER: N km ms kg G N m2/kg2 g m/s2 wstar wstar = N m M R Etotal Typesetting math: 81% Consider the motion of an object between a point close to the planet and a point very very far from the planet. Indicate whether the following statements are true or false. Part B Angular momentum about the center of the planet is conserved. ANSWER: Part C Total mechanical energy is conserved. ANSWER: Part D Kinetic energy is conserved. ANSWER: Etotal = true false true false Typesetting math: 81% Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). A Satellite in a Circular Orbit Consider a satellite of mass that orbits a planet of mass in a circle a distance from the center of the planet. The satellite’s mass is negligible compared with that of the planet. Indicate whether each of the statements in this problem is true or false. Part A The information given is sufficient to uniquely specify the speed, potential energy, and angular momentum of the satellite. You did not open hints for this part. ANSWER: true false m1 m2 r true false Typesetting math: 81% Part B The total mechanical energy of the satellite is conserved. You did not open hints for this part. ANSWER: Part C The linear momentum vector of the satellite is conserved. You did not open hints for this part. ANSWER: Part D The angular momentum of the satellite about the center of the planet is conserved. You did not open hints for this part. ANSWER: true false true false Typesetting math: 81% Part E The equations that express the conservation laws of total mechanical energy and linear momentum are sufficient to solve for the speed necessary to maintain a circular orbit at without using . You did not open hints for this part. ANSWER: At the Galaxy’s Core Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light years and an orbital speed of about 200 . Part A Determine the mass of the massive object at the center of the Milky Way galaxy. Take the distance of one light year to be . Express your answer in kilograms. You did not open hints for this part. true false R F = ma true false km/s M 9.461 × 1015 m Typesetting math: 81% ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Properties of Circular Orbits Learning Goal: To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth. M = kg Typesetting math: 81% The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit–a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass . For all parts of this problem, where appropriate, use for the universal gravitational constant. Part A Find the orbital speed for a satellite in a circular orbit of radius . Express the orbital speed in terms of , , and . You did not open hints for this part. ANSWER: Part B Find the kinetic energy of a satellite with mass in a circular orbit with radius . Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. ANSWER: Part C M G v R G M R v = K m R \texttip{K}{K} = Typesetting math: 81% This question will be shown after you complete previous question(s). Part D Find the orbital period \texttip{T}{T}. Express your answer in terms of \texttip{G}{G}, \texttip{M}{M}, \texttip{R}{R}, and \texttip{\pi }{pi}. You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F Find \texttip{L}{L}, the magnitude of the angular momentum of the satellite with respect to the center of the planet. Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. You did not open hints for this part. ANSWER: \texttip{T}{T} = Typesetting math: 81% Part G The quantities \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L} all represent physical quantities characterizing the orbit that depend on radius \texttip{R}{R}. Indicate the exponent (power) of the radial dependence of the absolute value of each. Express your answer as a comma-separated list of exponents corresponding to \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L}, in that order. For example, -1,-1/2,-0.5,-3/2 would mean v \propto R^{-1}, K \propto R^{-1/2}, and so forth. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. \texttip{L}{L} = Typesetting math: 81%

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Doppler Shift 73 Because of the Doppler Effect, light emitted by an object can appear to change wavelength due to its motion toward or away from an observer. When the observer and the source of light are moving toward each other, the light is shifted to shorter wavelengths (blueshifted). When the observer and the source of light are moving away from each other, the light is shifted to longer wavelengths (redshifted). Part I: Motion of Source Star is not . rnovrng r ABCD 1) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to shorter wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? 2) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to longer wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? . 74 Doppler Shift 3) In which of the srtuations shown (A—D) will theobserver receive light that Is not Doppler Shifted at all? Explain your reasoning. – 4) Imagine our solar system Is moving In the Milky Way toward a group of three stars. Star A is a blue star that is slightly closer to us than the other two. Star B is a red star that is farthest away from us. Star C is a yellow star that is halfway between Stars A end B. a) Which of these three stars, if any, will give off light that appears to be blueshifted? Explain your reasoning. . / b) Which of these three stars, if any, will give off light that appears to be redshifted? Explain your reasoning. c) Which of these three stars, if any, will give off light that appears to have no shift? Explain your reasoning. — 5) You overhear two students discussing the topic of Doppler Shift. Student 1: Since Betelgeuse is a red star, it must be going away from us, and since Rigel is a blue star it must be coming toward us. Student 2: 1 disagree, the color of the star does not tell you if it is moving. You have to look at the shift in wavelength of the lines in the star’s absorption spectrum to determine whether it’s moving toward or away from you. Do you agree or disagree with either or both of the students? Explain your reasoning. 5 Part II: Shift in Absorption Spectra When we study an astronomical object like a star or galaxy, we examine the spectrum of light it gives off. Since the lines of a spectrum occur at specific wavelengths we can determine that an object is moving when we see that the lines have been shifted to either longer or shorter wavelengths. For the absorption line spectra shown on the next page, short-wavelength light (the blue end of the spectrum) is shown on the left-hand side and long-wavelength light (the red end of the spectrum) is shown on the right-hand side. Doppler Shift 75 For the three absorption line spectra shown below (A, B, and C), one of the spectra corresponds to a star that is not moving relative to you, one of the spectra is from a star that is moving toward you, and one of the spectra is from a star that is moving away from you. A B Blue J___ ..‘ C 6) Which of the three spectra above corresponds with the star moving toward you? Explain your reasoning. If two sources of llght are moving relative to an observer, the light from the star that is moving faster will appear to undergo a greater Doppler Consider the four spectra at the right. The spectrum labeled F is an absorption line spectrum from a star that is at rest. Again, note that short-wavelength (blue) light is shown on the left-hand side of each spectrum and long-wavelength (red) light is shown on the right-hand side of each spectrum. 7) Which of the three spectra corresponds with the star moving away from you? Explain your reasoning. Part 111: Size of Shift and Speed Blue Red . – 76 Doppler Shift 8) Which of the four spectra would be from the star that is moving the fastest? Would this star be moving toward or away from the observer? 9) Of the stars that are moving, which spectra would be from the star that is moving the slowest? Describe the motion of this star, – (fJ 1O)An Important line In the absorption spectrum of stars occurs at a wavelength of 656 nm for stars at rest. Irna me that you observe five stars (H—L) from Earth and discover that this Important absorption line Is measured at the wavelength shown in the table below for each of the five stars, Star Wavelength of Absorption Line H 649nm I 660 nm J 656nrn K 658nrn L 647nm a) Which of the stars are gMng off light that appears blueshifted? Explain your reasoning. b) Which of the stars are gMng off light that appears redshifted? Explain your reasoning. d) Which star is moving the fastest? Is it moving toward or away from the observer? Explain your reasoning. , . . c) Which star is giving off light that appears shifted by the greatest amount? Is this light shifted to longer or shorter wavelengths? Explain your reasoning. a) Which planets will receive a radio signal that Is redshifted? Explain your reasoning. b) Which planets wfll receive a radio signal that is shifted to shorter wavelengths? Explain your reasoning. a a . ii) The figure at right shows a spaceprobe and five planets. The motion of the spaceprobe is indicated by the arrow. The spaceprobe is continuously broadcasting a radio signal in all directions. 4 C E not to scale c) Will all the planets receive radio signals from the spaceprobe that are Doppler shifted? Explain your reasoning. d) How will the size of the Doppler Shift in the radio signals detected at Planets A and B compare? Explain your reasoning. Cats r , ‘, e) How Will the slz of 1h Dupler Shift in the radio signals deteed °lane E and B compare? Explain your reasoning. ‘

Doppler Shift 73 Because of the Doppler Effect, light emitted by an object can appear to change wavelength due to its motion toward or away from an observer. When the observer and the source of light are moving toward each other, the light is shifted to shorter wavelengths (blueshifted). When the observer and the source of light are moving away from each other, the light is shifted to longer wavelengths (redshifted). Part I: Motion of Source Star is not . rnovrng r ABCD 1) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to shorter wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? 2) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to longer wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? . 74 Doppler Shift 3) In which of the srtuations shown (A—D) will theobserver receive light that Is not Doppler Shifted at all? Explain your reasoning. – 4) Imagine our solar system Is moving In the Milky Way toward a group of three stars. Star A is a blue star that is slightly closer to us than the other two. Star B is a red star that is farthest away from us. Star C is a yellow star that is halfway between Stars A end B. a) Which of these three stars, if any, will give off light that appears to be blueshifted? Explain your reasoning. . / b) Which of these three stars, if any, will give off light that appears to be redshifted? Explain your reasoning. c) Which of these three stars, if any, will give off light that appears to have no shift? Explain your reasoning. — 5) You overhear two students discussing the topic of Doppler Shift. Student 1: Since Betelgeuse is a red star, it must be going away from us, and since Rigel is a blue star it must be coming toward us. Student 2: 1 disagree, the color of the star does not tell you if it is moving. You have to look at the shift in wavelength of the lines in the star’s absorption spectrum to determine whether it’s moving toward or away from you. Do you agree or disagree with either or both of the students? Explain your reasoning. 5 Part II: Shift in Absorption Spectra When we study an astronomical object like a star or galaxy, we examine the spectrum of light it gives off. Since the lines of a spectrum occur at specific wavelengths we can determine that an object is moving when we see that the lines have been shifted to either longer or shorter wavelengths. For the absorption line spectra shown on the next page, short-wavelength light (the blue end of the spectrum) is shown on the left-hand side and long-wavelength light (the red end of the spectrum) is shown on the right-hand side. Doppler Shift 75 For the three absorption line spectra shown below (A, B, and C), one of the spectra corresponds to a star that is not moving relative to you, one of the spectra is from a star that is moving toward you, and one of the spectra is from a star that is moving away from you. A B Blue J___ ..‘ C 6) Which of the three spectra above corresponds with the star moving toward you? Explain your reasoning. If two sources of llght are moving relative to an observer, the light from the star that is moving faster will appear to undergo a greater Doppler Consider the four spectra at the right. The spectrum labeled F is an absorption line spectrum from a star that is at rest. Again, note that short-wavelength (blue) light is shown on the left-hand side of each spectrum and long-wavelength (red) light is shown on the right-hand side of each spectrum. 7) Which of the three spectra corresponds with the star moving away from you? Explain your reasoning. Part 111: Size of Shift and Speed Blue Red . – 76 Doppler Shift 8) Which of the four spectra would be from the star that is moving the fastest? Would this star be moving toward or away from the observer? 9) Of the stars that are moving, which spectra would be from the star that is moving the slowest? Describe the motion of this star, – (fJ 1O)An Important line In the absorption spectrum of stars occurs at a wavelength of 656 nm for stars at rest. Irna me that you observe five stars (H—L) from Earth and discover that this Important absorption line Is measured at the wavelength shown in the table below for each of the five stars, Star Wavelength of Absorption Line H 649nm I 660 nm J 656nrn K 658nrn L 647nm a) Which of the stars are gMng off light that appears blueshifted? Explain your reasoning. b) Which of the stars are gMng off light that appears redshifted? Explain your reasoning. d) Which star is moving the fastest? Is it moving toward or away from the observer? Explain your reasoning. , . . c) Which star is giving off light that appears shifted by the greatest amount? Is this light shifted to longer or shorter wavelengths? Explain your reasoning. a) Which planets will receive a radio signal that Is redshifted? Explain your reasoning. b) Which planets wfll receive a radio signal that is shifted to shorter wavelengths? Explain your reasoning. a a . ii) The figure at right shows a spaceprobe and five planets. The motion of the spaceprobe is indicated by the arrow. The spaceprobe is continuously broadcasting a radio signal in all directions. 4 C E not to scale c) Will all the planets receive radio signals from the spaceprobe that are Doppler shifted? Explain your reasoning. d) How will the size of the Doppler Shift in the radio signals detected at Planets A and B compare? Explain your reasoning. Cats r , ‘, e) How Will the slz of 1h Dupler Shift in the radio signals deteed °lane E and B compare? Explain your reasoning. ‘

  ANSWERS Part 1 1 C is the answer because … Read More...
WEEKLY ASSIGNMENT #5 (WOW THAT TOOK A WHILE) NAME: 1. Find the linear approximation of the function f(x; y; z) = p x2 + y2 + z2 at some point to approximate a value of the number p (3:02)2 + (1:97)2 + (5:99)2. 1 2. Consider your favorite function, the Cobb-Douglas production function. P(L;K) = 1:5L:65K:35 modeling the production of the state of Idaho. Over time we discover that capitol is gradually increasing at an approximate rate of 0:02 units per year. If we decide as a group that we are perfectly happy with our production level and would rather have additional vacation time then how much can we decrease labor by each year and keep the same level of production. In how long(rounded up to the nearest year) will we have an additional week of vacation? 2 3. Use the chain rule to find dz dt or dw=dt (a) z = x?y x+2y x = et; y = e?t. (b) w = sin x cos x x = p t; y = 1=t. 4. Use the chain rule to find @z=@t or @z=@s (a) z = (x ? y)5 x = s2t; y = st2 (b) z = er cos  r = st;  = p x2 + y2. 3 5. The temperature at a point (x; y; z) is given by the function T(x; y; z) = 200e?x2?3y2?9z2 where T is measure in C and x; y; z in meters. (a) Find the rate of change of temperature at the point (2;?1; 2) in the direction toward the point (3;?3; 3). (b) In which direction does the temperature increase fastest, and what is that fastest rate? 4 6. Suppose (1; 1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f. (a) fxx(1; 1) = 4; fxy(1; 1) = 1; fyy(1; 1) = 2 (b) fxx(1; 1) = 4; fxy(1; 1) = 3; fyy(1; 1) = 2 (c) fxx(1; 1) = ?1; fxy(1; 1) = 6; fyy(1; 1) = 1 (d) fxx(1; 1) = ?1; fxy(1; 1) = 2; fyy(1; 1) = ?8 (e) fxx(1; 1) = 4; fxy(1; 1) = 6; fyy(1; 1) = 9 5 Bonus Show that f(x; y) = x2 + 4y2 ? 4xy + 2 has an infinite number of critical points, and for all of them D = 0 at each one. Then show that f has a local (and absolute) minimum at each critical point. 6

WEEKLY ASSIGNMENT #5 (WOW THAT TOOK A WHILE) NAME: 1. Find the linear approximation of the function f(x; y; z) = p x2 + y2 + z2 at some point to approximate a value of the number p (3:02)2 + (1:97)2 + (5:99)2. 1 2. Consider your favorite function, the Cobb-Douglas production function. P(L;K) = 1:5L:65K:35 modeling the production of the state of Idaho. Over time we discover that capitol is gradually increasing at an approximate rate of 0:02 units per year. If we decide as a group that we are perfectly happy with our production level and would rather have additional vacation time then how much can we decrease labor by each year and keep the same level of production. In how long(rounded up to the nearest year) will we have an additional week of vacation? 2 3. Use the chain rule to find dz dt or dw=dt (a) z = x?y x+2y x = et; y = e?t. (b) w = sin x cos x x = p t; y = 1=t. 4. Use the chain rule to find @z=@t or @z=@s (a) z = (x ? y)5 x = s2t; y = st2 (b) z = er cos  r = st;  = p x2 + y2. 3 5. The temperature at a point (x; y; z) is given by the function T(x; y; z) = 200e?x2?3y2?9z2 where T is measure in C and x; y; z in meters. (a) Find the rate of change of temperature at the point (2;?1; 2) in the direction toward the point (3;?3; 3). (b) In which direction does the temperature increase fastest, and what is that fastest rate? 4 6. Suppose (1; 1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f. (a) fxx(1; 1) = 4; fxy(1; 1) = 1; fyy(1; 1) = 2 (b) fxx(1; 1) = 4; fxy(1; 1) = 3; fyy(1; 1) = 2 (c) fxx(1; 1) = ?1; fxy(1; 1) = 6; fyy(1; 1) = 1 (d) fxx(1; 1) = ?1; fxy(1; 1) = 2; fyy(1; 1) = ?8 (e) fxx(1; 1) = 4; fxy(1; 1) = 6; fyy(1; 1) = 9 5 Bonus Show that f(x; y) = x2 + 4y2 ? 4xy + 2 has an infinite number of critical points, and for all of them D = 0 at each one. Then show that f has a local (and absolute) minimum at each critical point. 6

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

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

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