## Lab 1: Introduction to Motion You must make the following changes to your lab manual before coming to lab, not during lab! Do not plan to consult this sheet during lab. There is not enough time. The required changes must be in your lab manual in the proper sequence to complete the lab in a smooth and timely manner. You should bring this paper to lab but only for reference to the images printed below. You have been warned! A note about vector addition: Adding Vectors: To add these two vectors: means to place them head-to-tail like so: and therefore they equal: Subtracting Vectors: Subtracting these two vectors: is the same as the sum of one vector and the negative of the other: which is the same as: which means to place them head-to-tail like so: and therefore they equal: Pg. 7 Activity 1-3 Cross off Step 1 Cross off Step 2 Pg. 7 Step 3) Replace “Try to make each of the graphs …” with “Try to make one of the graphs…” Pg. 7 Step 4) Replace this step with: “Describe how you must move to produce the graph you selected. Note if you selected graph C your description is at the top of page 8. Pg. 8 Activity 2-1 Step 2) Replace: “(Just draw smooth patterns; leave out…” with “(Quickly draw smooth patterns; leave out…” Then highlight this entire sentence. + − + (− ) + Pg. 10 Step 3) Where it states “(Be sure to adjust the time scale to 15 s.)” The way to do this is to click this clock icon And change the “Duration:” value Pg. 11 Question 2-3) At the end of the question add the following: “See the top of page 12 for the rest of the question.” Pg. 13 Step 2) Highlight the part that states: “Get the times right. Get the velocities right. Each person should take a turn.” At the end of the paragraph add: “But do not spend too much time getting things perfect.” Pg. 15 Step 1) Where is states: “Use the analysis feature of the software to read values of velocity…” Do this: Click here and then move the mouse over the graph. You can now quickly read data from the graph.

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

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## In the article, “The Moral Person” it talks about Lawrence Kohlberg’s stages of moral development. Briefly explain the 3 Conventional levels (pre-conventional, conventional, and post-conventional). How may these stages impact one’s ethics? Think about how culture or the social environment affects our framework for coming up with any moral or ethical answer. (Hei Lam Kwan) In the article, they talked about a push for a “global ethic” or “one world”. Do you think this is possible? Besides the Golden Rule are there any other examples of shared ethics around the world? (Nicole Thompson) The article explained that often people know the distinction between right and wrong, but still do the wrong thing. If people know what is morally right, why do they act in ways that are morally wrong? (Nicole Thompson) In McLaren’s reading, he gives us a description on an idea of personhood to help us understand a moral person. He mentions a quote from the philosopher, Sarvepalli Rhadakrishnan that caught my interest. He says, “The self is not an object which we can find in knowledge, for it is the very condition of knowledge. It is different from all objects, the body, the senses, the empirical self itself (36)”. In your opinion, what exactly does he mean by stating that? Does thinking of yourself this way help you morally? (Maggy Ergun) Video: In the video, Damon Horowitz talks about the different approaches to figuring out what is right and what is wrong. Some of them included Plato, who believed that he could uncover the “truths about Justice”, Aristotle, who thought that people should use their current knowledge to make the right decision of here and now to their best ability, and Utilitarianism, who thought it was about measuring out the options to see which one had the most benefit for the greatest amount of people. Which approach do you think is best? Would you suggest another approach? (Nicole Thompson) Damon Horowitz explains the huge power we have and that is knowledge and data we receive from technology. With all this power in our hands, you can have any information you would like to obtain whether it’s on an object or human being. And as technology keeps rising, the more advanced it keeps getting. When it comes to privacy and dignity, do you think it is fair for one another to have this huge power on us? Will this be better for our future or worse? (Maggy Ergun) Horowitz describes how we rely more on our smart devices then actual moral thinking. (Mobile operating system then moral operating system) If we were to create a moral operating system, do you think that will help provoke people from making bad/evil decisions and guide us to better? Or do those bad decisions just come instantly without much thought? (Maggy Ergun) In the video it states, “what we need is a moral operating system.” What are the possible flaws in relying on a machine/software for answering ethical problems? Discuss and list at least one problem we may encounter from relying on such a system for an ethical solution. (Hei Lam Kwan) Reviewing the answers to the previous questions given, do you think there is only one right answer to any ethical question and why? (Hei Lam Kwan) http://www.ted.com/talks/damon_horowitz?language=en this is the video

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## ) What two directors have had a profound influence on Kathryn Bigelow’s work, including her film The Hurt Locker?. 11) We watched two films by the up and coming director, Terry Gilliam. Did you like his films or not and why?

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## Use the links provided to answer the questions below. http://www.youtube.com/watch?v=9tt6BQDVKu0 http://assets.soomopublishing.com/courses/AG/Fragile_Superpower.pdf NIE Report Why does the report suggest that China and India may or may not become dominant powers in the near future? A. Both countries have high economic and social hurdles to overcome. B. Both countries are only somewhat democratic. C. Both countries lack the military strength and nuclear weaponry to challenge even smaller states. D. Neither country is a member of the UN Security Council. E. Neither country is concerned about global warming and is therefore unfit to become a great power player. According to the U.S. intelligence report discussed in the video, why will the use of nuclear weapons grow more likely? A. Irresponsible powerful countries will want to strike the United States to take over its dominant role in the world. B. There will be a tendency to forget just how dangerous they are as we over-emphasize the importance of international trade. C. Rogue states and terrorist groups may be able to gain greater access to these weapons. D. Since the United States and the Soviet Union are rapidly increasing their weapons building programs, the chances of a nuclear incident becomes higher. E. China is likely to produce nuclear weapons to use against the United States and the Soviet Union. According to the video, is the United States likely to lose its position in the world soon? A. Yes, given the rapid rise of China, we will be seeing a challenge from China in the next 5-10 years. B. Yes, China, in conjunction with India, will rise up against the United States. C. Yes, the Russians are working to undermine the U.S. position actively. D. No, although there appears to be decline, the replacement of the United States as the world leader is not likely to come in the next 10 years. E. No, the United States will actually lose its position after its departure from Iraq in 2012. The Rise of a Fierce Yet Fragile Superpower Why does Susan Shirk say that China is fragile? A. China is fragile because it isn’t a democratic country and will have a difficult time managing relations with other states because of this. B. China is fragile because it has a shrinking economy, so despite its size, China is actually very weak. C. China is fragile because its leaders tend to exacerbate the tensions between states like the Soviet Union and the United States. D. China is fragile because it cannot develop a strong sense of human rights and so its people may try to revolt against it. E. China is fragile because its rate of expansion has created gaps between the wealthy and poor and it has a problem of control with decentralized local governing structures. According to scholars, is a war between the rising power and the current power leader inevitable? A. No, while some scholars believe this is true, others suggest that a “peaceful rise” is possible. B. No, history indicates that all great power transitions have been peaceful. C. Yes, scholars indicate that all of our historical examples of great power transition have been through war. D. Yes, although there are examples of peaceful rise, there is too much cultural difference for that to occur with China. E. Yes, since tension between the United States and China is so strong, scholars agree that a war is coming.

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## Chapter 1 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Curved Motion Diagram The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet. Part A What is the direction of the acceleration of the object at moment 5? Enter the letter of the arrow with this direction from the compass rose in the figure. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again Part B What is the direction of the acceleration of the object at moments 0 and 10? Enter the letters corresponding to the arrows with these directions from the compass rose in the figure, separated by commas. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again PSS 1.1 Motion Diagrams Learning Goal: To practice Problem-Solving Strategy 1.1 for motion diagram problems. A car is traveling with constant velocity along a highway. The driver notices he is late for work, so he stomps down on the gas pedal and the car begins to speed up. The car has just achieved double its directions at time step 0, time step 10 = initial velocity when the driver spots a police officer behind him and applies the brakes. The car then slows down, coming to rest at a stoplight ahead. Draw a complete motion diagram for this situation. PROBLEM-SOLVING STRATEGY 1.1 Motion diagrams MODEL: Represent the moving object as a particle. Make simplifying assumptions when interpreting the problem statement. VISUALIZE: A complete motion diagram consists of: The position of the object in each frame of the film, shown as a dot. Use five or six dots to make the motion clear but without overcrowding the picture. More complex motions may need more dots. The average velocity vectors, found by connecting each dot in the motion diagram to the next with a vector arrow. There is one velocity vector linking each set of two position dots. Label the row of velocity vectors . The average acceleration vectors, found using Tactics Box 1.3. There is one acceleration vector linking each set of two velocity vectors. Each acceleration vector is drawn at the dot between the two velocity vectors it links. Use to indicate a point at which the acceleration is zero. Label the row of acceleration vectors . Model It is appropriate to use the particle model for the car. You should also make some simplifying assumptions. v 0 a Part A The car’s motion can be divided into three different stages: its motion before the driver realizes he’s late, its motion after the driver hits the gas (but before he sees the police car), and its motion after the driver sees the police car. Which of the following simplifying assumptions is it reasonable to make in this problem? During each of the three different stages of its motion, the car is moving with constant A. acceleration. B. During each of the three different stages of its motion, the car is moving with constant velocity. C. The highway is straight (i.e., there are no curves). D. The highway is level (i.e., there are no hills or valleys). Enter all the correct answers in alphabetical order without commas. For example, if statements C and D are correct, enter CD. ANSWER: Correct In addition to the assumptions listed above, in the rest of this problem assume that the car is moving in a straight line to the right. Visualize Part B In the three diagrams shown to the left, the position of the car at five subsequent instants of time is represented by black dots, and the car’s average velocity is represented by green arrows. Which of these diagrams best describes the position and the velocity of the car before the driver notices he is late? ANSWER: Correct Part C Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver hits the gas, but before he notices the police officer? ANSWER: Correct A B C A B C Part D Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver notices the police officer? ANSWER: Correct Part E Which of the diagrams shown below most accurately depicts the average acceleration vectors of the car during the events described in the problem introduction? ANSWER: A B C Correct You can now draw a complete motion diagram for the situation described in this problem. Your diagram should look like this: Measurements in SI Units Familiarity with SI units will aid your study of physics and all other sciences. Part A What is the approximate height of the average adult in centimeters? Hint 1. Converting between feet and centimeters The distance from your elbow to your fingertips is typically about 50 . A B C cm ANSWER: Correct If you’re not familiar with metric units of length, you can use your body to develop intuition for them. The average height of an adult is 5 6.4 . The distance from elbow to fingertips on the average adult is about 50 . Ten (1 ) is about the width of this adult’s little finger and 10 is about the width of the average hand. Part B Approximately what is the mass of the average adult in kilograms? Hint 1. Converting between pounds and kilograms Something that weighs 1 has a mass of about . ANSWER: Correct Something that weighs 1 has a mass of about . This is a useful conversion to keep in mind! ± A Trip to Europe 100 200 300 cm cm cm feet inches cm mm cm cm pound 1 kg 2 80 500 1200 kg kg kg pound (1/2) kg Learning Goal: To understand how to use dimensional analysis to solve problems. Dimensional analysis is a useful tool for solving problems that involve unit conversions. Since unit conversion is not limited to physics problems but is part of our everyday life, correct use of conversion factors is essential to working through problems of practical importance. For example, dimensional analysis could be used in problems involving currency exchange. Say you want to calculate how many euros you get if you exchange 3600 ( ), given the exchange rate , that is, 1 to 1.20 . Begin by writing down the starting value, 3600 . This can also be written as a fraction: . Next, convert dollars to euros. This conversion involves multiplying by a simple conversion factor derived from the exchange rate: . Note that the “dollar” unit, , should appear on the bottom of this conversion factor, since appears on the top of the starting value. Finally, since dollars are divided by dollars, the units can be canceled and the final result is . Currency exchange is only one example of many practical situations where dimensional analysis may help you to work through problems. Remember that dimensional analysis involves multiplying a given value by a conversion factor, resulting in a value in the new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one. You and your friends are organizing a trip to Europe. Your plan is to rent a car and drive through the major European capitals. By consulting a map you estimate that you will cover a total distance of 5000 . Consider the euro-dollar exchange rate given in the introduction and use dimensional analysis to work through these simple problems. Part A You select a rental package that includes a car with an average consumption of 6.00 of fuel per 100 . Considering that in Europe the average fuel cost is 1.063 , how much (in US dollars) will you spend in fuel on your trip? Express your answer numerically in US dollars to three significant figures. You did not open hints for this part. ANSWER: US dollars USD 1 EUR = 1.20 USD euro US dollars USD 3600 USD 1 1.00 EUR 1.20 USD USD USD ( )( ) = 3000 EUR 3600 USD 1 1.00 EUR 1.20 USD km liters km euros/liter Part B How many gallons of fuel would the rental car consume per mile? Express your answer numerically in gallons per mile to three significant figures. You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. Cost of fuel = USD gallons/mile

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## Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F F = −kx x k m k x = 0 block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = -60 % s t = 0 s cm cm/s 0 = -2.09 rad Correct Part B What is the phase at ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: t = 0.5 s = 0 rad t = 1.0 s = 2.09 rad t = 1.5 s = 4.19 rad Correct Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct g cm s 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 0.628 s 5.00 Nm -0.785 rad Part E The initial coordinate of the mass. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part F The initial velocity. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part G The maximum speed. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 1.41 cm 14.1 cms 20.0 cms Part H The total energy. Express your answer to one decimal place and include the appropriate units. ANSWER: Correct Part I The velocity at . Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? 1.0 mJ t = 0.40 s 1.46 cms N/m cm s Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum m = 110 g vmax = 49 cms A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. m L T T L T = 2 Lg −− g T/2 T ‘2T 2T g/6 ANSWER: Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. T/6 T/’6 ‘6T 6T It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. g % s L = 19 cm m lmoon = 0.35 m m g 1.0 MHz Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 94.2%. You received 135.71 out of a possible total of 144 points. N amax = 6.6 μm vmax = 41 ms

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