Annotate article with highlight. there is steps to highlight which is to show the problem, purpose,object of study, and relevance which is what do the authors suggest is the significance of their work to the field? also main findings which is where does this source list some of the main findings or conclusions from the project? and connection to other source which is where do concepts and thoughts from this text connect to other sources that you have read? just highlight and brief comments in each part

Annotate article with highlight. there is steps to highlight which is to show the problem, purpose,object of study, and relevance which is what do the authors suggest is the significance of their work to the field? also main findings which is where does this source list some of the main findings or conclusions from the project? and connection to other source which is where do concepts and thoughts from this text connect to other sources that you have read? just highlight and brief comments in each part

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Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi Part B Find , the magnitude of the final velocity of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: Part C What is the change in the two-block system’s kinetic energy due to the collision? Express your answer numerically in joules. You did not open hints for this part. ANSWER: pi = kg m/s vf vf = m/s K = Kfinal − Kinitial K = J Conservation of Energy Ranking Task Six pendulums of various masses are released from various heights above a tabletop, as shown in the figures below. All the pendulums have the same length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released. Assume that the size of each bob is negligible. Part A Rank each pendulum on the basis of its initial gravitational potential energy (before being released) relative to the tabletop. Rank from largest to smallest To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: m h 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). Momentum and Kinetic Energy Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed and has mass . Object 2 moves with speed and has mass . Part A Which object has the larger magnitude of its momentum? You did not open hints for this part. ANSWER: Part B Which object has the larger kinetic energy? You did not open hints for this part. ANSWER: v1 = v m1 = 2m v2 = 2v m2 = m Object 1 has the greater magnitude of its momentum. Object 2 has the greater magnitude of its momentum. Both objects have the same magnitude of their momenta. Object 1 has the greater kinetic energy. Object 2 has the greater kinetic energy. The objects have the same kinetic energy. Projectile Motion and Conservation of Energy Ranking Task Part A Six baseball throws are shown below. In each case the baseball is thrown at the same initial speed and from the same height above the ground. Assume that the effects of air resistance are negligible. Rank these throws according to the speed of the baseball the instant before it hits the ground. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: H PSS 10.1 Conservation of Mechanical Energy Learning Goal: To practice Problem-Solving Strategy 10.1 for conservation of mechanical energy problems. Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 that makes an angle of 45 with the vertical, steps off his tree limb, and swings down and then up to Jane’s open arms. When he arrives, his vine makes an angle of 30 with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan’s speed just before he reaches Jane. You can ignore air resistance and the mass of the vine. PROBLEM-SOLVING STRATEGY 10.1 Conservation of mechanical energy MODEL: Choose a system without friction or other losses of mechanical energy. m   VISUALIZE: Draw a before-and-after pictorial representation. Define symbols that will be used in the problem, list known values, and identify what you’re trying to find. SOLVE: The mathematical representation is based on the law of conservation of mechanical energy: . ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model The problem does not involve friction, nor are there losses of mechanical energy, so conservation of mechanical energy applies. Model Tarzan and the vine as a pendulum. Visualize Part A Which of the following sketches can be used in drawing a before-and-after pictorial representation? ANSWER: Kf + Uf = Ki + Ui Solve Part B What is Tarzan’s speed just before he reaches Jane? Express your answer in meters per second to two significant figures. You did not open hints for this part. ANSWER: Assess Part C This question will be shown after you complete previous question(s). Bungee Jumping Diagram A Diagram B Diagram C Diagram D vf vf = m/s Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass , and the surface of the bridge is a height above the water. The bungee cord, which has length when unstretched, will first straighten and then stretch as Kate falls. Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant . Kate doesn’t actually jump but simply steps off the edge of the bridge and falls straight downward. Kate’s height is negligible compared to the length of the bungee cord. Hence, she can be treated as a point particle. Use for the magnitude of the acceleration due to gravity. Part A How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn’t touch the water. Express the distance in terms of quantities given in the problem introduction. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Spinning Mass on a Spring An object of mass is attached to a spring with spring constant whose unstretched length is , and whose far end is fixed to a shaft that is rotating with angular speed . Neglect gravity and assume that the mass rotates with angular speed as shown. When solving this problem use an inertial coordinate system, as drawn here. m h L k g d = M k L Part A Given the angular speed , find the radius at which the mass rotates without moving toward or away from the origin. Express the radius in terms of , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C R( ) k L M R( ) = This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). ± Baby Bounce with a Hooke One of the pioneers of modern science, Sir Robert Hooke (1635-1703), studied the elastic properties of springs and formulated the law that bears his name. Hooke found the relationship among the force a spring exerts, , the distance from equilibrium the end of the spring is displaced, , and a number called the spring constant (or, sometimes, the force constant of the spring). According to Hooke, the force of the spring is directly proportional to its displacement from equilibrium, or . In its scalar form, this equation is simply . The negative sign indicates that the force that the spring exerts and its displacement have opposite directions. The value of depends on the geometry and the material of the spring; it can be easily determined experimentally using this scalar equation. Toy makers have always been interested in springs for the entertainment value of the motion they produce. One well-known application is a baby bouncer,which consists of a harness seat for a toddler, attached to a spring. The entire contraption hooks onto the top of a doorway. The idea is for the baby to hang in the seat with his or her feet just touching the ground so that a good push up will get the baby bouncing, providing potentially hours of entertainment. F  x k F = −kx F = −kx k Part A The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer. Displacement from equilibrium, ( ) Force exerted on the spring, ( ) 0 0 0.005 2.5 0.010 5.0 0.015 7.5 0.020 10 What is the spring constant of the spring being tested for the baby bouncer? Express your answer to two significant figures in newtons per meter. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Shooting a ball into a box Two children are trying to shoot a marble of mass into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. The edge of the table is a height above the top of the box (the height of which is negligibly small), and the center of the box is a distance from the edge of the table. x m F N k k = N/m m H d The spring has a spring constant . The first child compresses the spring a distance and finds that the marble falls short of its target by a horizontal distance . Part A By what distance, , should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.) Express the distance in terms of , , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). k x1 d12 x2 m k g H d x2 = Elastic Collision in One Dimension Block 1, of mass , moves across a frictionless surface with speed . It collides elastically with block 2, of mass , which is at rest ( ). After the collision, block 1 moves with speed , while block 2 moves with speed . Assume that , so that after the collision, the two objects move off in the direction of the first object before the collision. Part A This collision is elastic. What quantities, if any, are conserved in this collision? You did not open hints for this part. ANSWER: Part B What is the final speed of block 1? m1 ui m2 vi = 0 uf vf m1 > m2 kinetic energy only momentum only kinetic energy and momentum uf Express in terms of , , and . You did not open hints for this part. ANSWER: Part C What is the final speed of block 2? Express in terms of , , and . You did not open hints for this part. ANSWER: Ballistic Pendulum In a ballistic pendulum an object of mass is fired with an initial speed at a pendulum bob. The bob has a mass , which is suspended by a rod of length and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement as shown . uf m1 m2 ui uf = vf vf m1 m2 ui vf = m v0 M L  Part A Find an expression for , the initial speed of the fired object. Express your answer in terms of some or all of the variables , , , and and the acceleration due to gravity, . You did not open hints for this part. ANSWER: Part B An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 and a .44 caliber. The guns are fired into a 10- pendulum bob of length . Assume that the 9.0- bullet has a mass of 6.0 and the .44-caliber bullet has a mass of 12 . If the 9.0- bullet causes the pendulum to swing to a maximum angular displacement of 4.3 and the .44-caliber bullet causes a displacement of 10.1 , find the ratio of the initial speed of the 9.0- bullet to the speed of the .44-caliber bullet, . Express your answer numerically. You did not open hints for this part. ANSWER: v0 m M L  g v0 = mm kg L mm g g mm   mm (v /( 0 )9.0 v0)44 Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. (v0 )9.0/(v0 )44 =

Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi Part B Find , the magnitude of the final velocity of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: Part C What is the change in the two-block system’s kinetic energy due to the collision? Express your answer numerically in joules. You did not open hints for this part. ANSWER: pi = kg m/s vf vf = m/s K = Kfinal − Kinitial K = J Conservation of Energy Ranking Task Six pendulums of various masses are released from various heights above a tabletop, as shown in the figures below. All the pendulums have the same length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released. Assume that the size of each bob is negligible. Part A Rank each pendulum on the basis of its initial gravitational potential energy (before being released) relative to the tabletop. Rank from largest to smallest To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: m h 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). Momentum and Kinetic Energy Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed and has mass . Object 2 moves with speed and has mass . Part A Which object has the larger magnitude of its momentum? You did not open hints for this part. ANSWER: Part B Which object has the larger kinetic energy? You did not open hints for this part. ANSWER: v1 = v m1 = 2m v2 = 2v m2 = m Object 1 has the greater magnitude of its momentum. Object 2 has the greater magnitude of its momentum. Both objects have the same magnitude of their momenta. Object 1 has the greater kinetic energy. Object 2 has the greater kinetic energy. The objects have the same kinetic energy. Projectile Motion and Conservation of Energy Ranking Task Part A Six baseball throws are shown below. In each case the baseball is thrown at the same initial speed and from the same height above the ground. Assume that the effects of air resistance are negligible. Rank these throws according to the speed of the baseball the instant before it hits the ground. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: H PSS 10.1 Conservation of Mechanical Energy Learning Goal: To practice Problem-Solving Strategy 10.1 for conservation of mechanical energy problems. Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 that makes an angle of 45 with the vertical, steps off his tree limb, and swings down and then up to Jane’s open arms. When he arrives, his vine makes an angle of 30 with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan’s speed just before he reaches Jane. You can ignore air resistance and the mass of the vine. PROBLEM-SOLVING STRATEGY 10.1 Conservation of mechanical energy MODEL: Choose a system without friction or other losses of mechanical energy. m   VISUALIZE: Draw a before-and-after pictorial representation. Define symbols that will be used in the problem, list known values, and identify what you’re trying to find. SOLVE: The mathematical representation is based on the law of conservation of mechanical energy: . ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model The problem does not involve friction, nor are there losses of mechanical energy, so conservation of mechanical energy applies. Model Tarzan and the vine as a pendulum. Visualize Part A Which of the following sketches can be used in drawing a before-and-after pictorial representation? ANSWER: Kf + Uf = Ki + Ui Solve Part B What is Tarzan’s speed just before he reaches Jane? Express your answer in meters per second to two significant figures. You did not open hints for this part. ANSWER: Assess Part C This question will be shown after you complete previous question(s). Bungee Jumping Diagram A Diagram B Diagram C Diagram D vf vf = m/s Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass , and the surface of the bridge is a height above the water. The bungee cord, which has length when unstretched, will first straighten and then stretch as Kate falls. Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant . Kate doesn’t actually jump but simply steps off the edge of the bridge and falls straight downward. Kate’s height is negligible compared to the length of the bungee cord. Hence, she can be treated as a point particle. Use for the magnitude of the acceleration due to gravity. Part A How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn’t touch the water. Express the distance in terms of quantities given in the problem introduction. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Spinning Mass on a Spring An object of mass is attached to a spring with spring constant whose unstretched length is , and whose far end is fixed to a shaft that is rotating with angular speed . Neglect gravity and assume that the mass rotates with angular speed as shown. When solving this problem use an inertial coordinate system, as drawn here. m h L k g d = M k L Part A Given the angular speed , find the radius at which the mass rotates without moving toward or away from the origin. Express the radius in terms of , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C R( ) k L M R( ) = This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). ± Baby Bounce with a Hooke One of the pioneers of modern science, Sir Robert Hooke (1635-1703), studied the elastic properties of springs and formulated the law that bears his name. Hooke found the relationship among the force a spring exerts, , the distance from equilibrium the end of the spring is displaced, , and a number called the spring constant (or, sometimes, the force constant of the spring). According to Hooke, the force of the spring is directly proportional to its displacement from equilibrium, or . In its scalar form, this equation is simply . The negative sign indicates that the force that the spring exerts and its displacement have opposite directions. The value of depends on the geometry and the material of the spring; it can be easily determined experimentally using this scalar equation. Toy makers have always been interested in springs for the entertainment value of the motion they produce. One well-known application is a baby bouncer,which consists of a harness seat for a toddler, attached to a spring. The entire contraption hooks onto the top of a doorway. The idea is for the baby to hang in the seat with his or her feet just touching the ground so that a good push up will get the baby bouncing, providing potentially hours of entertainment. F  x k F = −kx F = −kx k Part A The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer. Displacement from equilibrium, ( ) Force exerted on the spring, ( ) 0 0 0.005 2.5 0.010 5.0 0.015 7.5 0.020 10 What is the spring constant of the spring being tested for the baby bouncer? Express your answer to two significant figures in newtons per meter. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Shooting a ball into a box Two children are trying to shoot a marble of mass into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. The edge of the table is a height above the top of the box (the height of which is negligibly small), and the center of the box is a distance from the edge of the table. x m F N k k = N/m m H d The spring has a spring constant . The first child compresses the spring a distance and finds that the marble falls short of its target by a horizontal distance . Part A By what distance, , should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.) Express the distance in terms of , , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). k x1 d12 x2 m k g H d x2 = Elastic Collision in One Dimension Block 1, of mass , moves across a frictionless surface with speed . It collides elastically with block 2, of mass , which is at rest ( ). After the collision, block 1 moves with speed , while block 2 moves with speed . Assume that , so that after the collision, the two objects move off in the direction of the first object before the collision. Part A This collision is elastic. What quantities, if any, are conserved in this collision? You did not open hints for this part. ANSWER: Part B What is the final speed of block 1? m1 ui m2 vi = 0 uf vf m1 > m2 kinetic energy only momentum only kinetic energy and momentum uf Express in terms of , , and . You did not open hints for this part. ANSWER: Part C What is the final speed of block 2? Express in terms of , , and . You did not open hints for this part. ANSWER: Ballistic Pendulum In a ballistic pendulum an object of mass is fired with an initial speed at a pendulum bob. The bob has a mass , which is suspended by a rod of length and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement as shown . uf m1 m2 ui uf = vf vf m1 m2 ui vf = m v0 M L  Part A Find an expression for , the initial speed of the fired object. Express your answer in terms of some or all of the variables , , , and and the acceleration due to gravity, . You did not open hints for this part. ANSWER: Part B An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 and a .44 caliber. The guns are fired into a 10- pendulum bob of length . Assume that the 9.0- bullet has a mass of 6.0 and the .44-caliber bullet has a mass of 12 . If the 9.0- bullet causes the pendulum to swing to a maximum angular displacement of 4.3 and the .44-caliber bullet causes a displacement of 10.1 , find the ratio of the initial speed of the 9.0- bullet to the speed of the .44-caliber bullet, . Express your answer numerically. You did not open hints for this part. ANSWER: v0 m M L  g v0 = mm kg L mm g g mm   mm (v /( 0 )9.0 v0)44 Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. (v0 )9.0/(v0 )44 =

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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...
PHSX 220 Homework 13 D2L – Friday April 28 – 5:00 pm SHM and Pendula Problem 1: Shown below are 6 identical masses attached to springs and hung vertically. The masses are pulled down various distances and then released. The spring constant (k), spring sti ness, and the distance (d) that the mass is pulled down from its equilibrium position are given for each situation. The expression relating k and m to the angular frequency of the system is the same for both a horizontal and vertical spring-block system. Rank the situations based on the time it takes the mass to get from its maximum height to its minimum height from greatest to least. Problem 2: Shown below are systems containing a block resting on a frictionless surface and attached to the end of a spring. The springs are displaced to the right by a distance given in each gure and then released from rest. The blocks oscillate back and forth. The mass and spring constant are given for each system. Rank the cases based on the frequency of oscillation from greatest to least. Problem 3: Shown below are six masses hung on the ends of strings forming a pendulum. The masses have been pulled to the side and released so that they are swinging back and forth. For each pendulum the diagrams give the mass of the swinging object, the frequency of the swing, and how far, in terms of the angle from the vertical, that the masses were initially pulled to the side. Rank the six cases based on the length of the string from greatest to least. Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the gure. Rank the cases shown based on their frequency of oscillation from greatest to least.

PHSX 220 Homework 13 D2L – Friday April 28 – 5:00 pm SHM and Pendula Problem 1: Shown below are 6 identical masses attached to springs and hung vertically. The masses are pulled down various distances and then released. The spring constant (k), spring sti ness, and the distance (d) that the mass is pulled down from its equilibrium position are given for each situation. The expression relating k and m to the angular frequency of the system is the same for both a horizontal and vertical spring-block system. Rank the situations based on the time it takes the mass to get from its maximum height to its minimum height from greatest to least. Problem 2: Shown below are systems containing a block resting on a frictionless surface and attached to the end of a spring. The springs are displaced to the right by a distance given in each gure and then released from rest. The blocks oscillate back and forth. The mass and spring constant are given for each system. Rank the cases based on the frequency of oscillation from greatest to least. Problem 3: Shown below are six masses hung on the ends of strings forming a pendulum. The masses have been pulled to the side and released so that they are swinging back and forth. For each pendulum the diagrams give the mass of the swinging object, the frequency of the swing, and how far, in terms of the angle from the vertical, that the masses were initially pulled to the side. Rank the six cases based on the length of the string from greatest to least. Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the gure. Rank the cases shown based on their frequency of oscillation from greatest to least.

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2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ à _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4à 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0à __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: 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). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ à _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4à 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0à __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: 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). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

info@checkyourstudy.com 2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm … Read More...
Chapter 4 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Advice for the Quarterback A quarterback is set up to throw the football to a receiver who is running with a constant velocity directly away from the quarterback and is now a distance away from the quarterback. The quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates that the receiver must catch the ball a time interval after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is and that the horizontal position of the quaterback is . Use for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem. Part A Find , the vertical component of the velocity of the ball when the quarterback releases it. Express in terms of and . Hint 1. Equation of motion in y direction What is the expression for , the height of the ball as a function of time? Answer in terms of , , and . v r D  tc y = 0 x = 0 g v0y v0y tc g y(t) t g v0y ANSWER: Incorrect; Try Again Hint 2. Height at which the ball is caught, Remember that after time the ball was caught at the same height as it had been released. That is, . ANSWER: Answer Requested Part B Find , the initial horizontal component of velocity of the ball. Express your answer for in terms of , , and . Hint 1. Receiver’s position Find , the receiver’s position before he catches the ball. Answer in terms of , , and . ANSWER: Football’s position y(t) = v0yt− g 1 2 t2 y(tc) tc y(tc) = y0 = 0 v0y = gtc 2 v0x v0x D tc vr xr D vr tc xr = D + vrtc Typesetting math: 100% Find , the horizontal distance that the ball travels before reaching the receiver. Answer in terms of and . ANSWER: ANSWER: Answer Requested Part C Find the speed with which the quarterback must throw the ball. Answer in terms of , , , and . Hint 1. How to approach the problem Remember that velocity is a vector; from solving Parts A and B you have the two components, from which you can find the magnitude of this vector. ANSWER: Answer Requested Part D xc v0x tc xc = v0xtc v0x = + D tc vr v0 D tc vr g v0 = ( + ) + D tc vr 2 ( ) gtc 2 2 −−−−−−−−−−−−−−−−−−−  Typesetting math: 100% Assuming that the quarterback throws the ball with speed , find the angle above the horizontal at which he should throw it. Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give your answer in terms of already known quantities, , , and . Hint 1. Find angle from and Think of velocity as a vector with Cartesian coordinates and . Find the angle that this vector would make with the x axis using the results of Parts A and B. ANSWER: Answer Requested Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. v0  v0x v0y v0  v0x v0y v0xx^ v0yy^   = atan( ) v0y v0x Typesetting math: 100% Part A Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Algebraic sign of velocity The algebraic sign of the velocity is determined solely by comparing the direction in which the object is moving with the direction that is defined to be positive. In this example, to the right is defined to be the positive x direction and upward the positive y direction. Therefore, any object moving to the right, whether speeding up, slowing down, or even simultaneously moving upward or downward, has a positive x velocity. Similarly, if the object is moving downward, regardless of any other aspect of its motion, its y velocity is negative. Hint 2. Sketch Alex’s initial velocity On the diagram below, sketch the vector representing Alex’s velocity the instant after he leaves the ground at the beginning of the jump. ANSWER: ANSWER: Typesetting math: 100% Answer Requested Part B Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he lands at the end of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Sketch Alex’s final velocity On the diagram below, sketch the vector representing Alex’s velocity the instant before he safely lands on the other side of the crevasse. ANSWER: Answer Requested ANSWER: Answer Requested Typesetting math: 100% At the buzzer, a basketball player shoots a desperation shot. The ball goes in! Part C Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s initial velocity On the diagram below, sketch the vector representing the velocity of the basketball the instant after it leaves the player’s hands. ANSWER: Typesetting math: 100% ANSWER: Correct Part D Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s velocity at maximum height Typesetting math: 100% On the diagram below, sketch the vector representing the velocity of the basketball the instant it reaches its maximum height. ANSWER: ANSWER: Answer Requested PSS 4.1 Projectile Motion Problems Learning Goal: Typesetting math: 100% To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 9.00 and launch angle 30.0 (above the horizontal) travels a horizontal distance of = 17.0 before hitting the ground. From what height was the rock thrown? Use the value = 9.810 for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Make simplifying assumptions, such as treating the object as a particle. Is it reasonable to ignore air resistance? VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols, and identify what you are trying to find. SOLVE: The acceleration is known: and . Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are , . is the same for the horizontal and vertical components of the motion. Find from one component, and then use that value for the other component. ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly. Visualize Part A Which diagram represents an accurate sketch of the rock’s trajectory? Hint 1. The launch angle In a projectile’s motion, the angle of the initial velocity above the horizontal is called the launch angle. ANSWER: m/s  d m g m/s2 ax = 0 ay = −g xf = xi +vixt, yf = yi +viyt− g(t 1 2 )2 vfx = vix = constant, and vfy = viy − gt t t v i Typesetting math: 100% Typesetting math: 100% Correct Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile’s acceleration, , is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn’t change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? ANSWER: ay At ground level below the point where the rock is launched At the point where the rock strikes the ground At the peak of the trajectory At the point where the rock is released At ground level below the peak of the trajectory Typesetting math: 100% Correct It’s best to place the origin of the coordinate system at ground level below the launching point because in this way all the points of interest (the launching point and the landing point) will have positive coordinates. (Based on your experience, you know that it’s generally easier to work with positive coordinates.) Keep in mind, however, that this is an arbitrary choice. The correct solution of the problem will not depend on the location of the origin of your coordinate system. Now, define symbols representing initial and final position, velocity, and time. Your target variable is , the initial y coordinate of the rock. Your pictorial representation should be complete now, and similar to the picture below: Solve Part C Find the height from which the rock was launched. Express your answer in meters to three significant figures. yi yi Typesetting math: 100% Hint 1. How to approach the problem The time needed to move horizontally to the final position = 17.0 is the same time needed for the rock to rise from the initial position to the peak of its trajectory and then fall to the ground. Use the information you have about motion in the horizontal direction to solve for . Knowing this time will allow you to use the equations of motion for the vertical direction to solve for . Hint 2. Find the time spent in the air How long ( ) is the rock in the air? Express your answer in seconds to three significant figures. Hint 1. Determine which equation to use Which of the equations given in the strategy and shown below is the most appropriate to calculate the time the rock spent in the air? ANSWER: Hint 2. Find the x component of the initial velocity What is the x component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: t xf = d m yi t yi t t xf = xi + vixt yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt vix = 7.79 m/s Typesetting math: 100% Hint 3. Find the y component of the initial velocity What is the y component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: Answer Requested Assess Part D A second rock is thrown straight upward with a speed 4.500 . If this rock takes 2.181 to fall to the ground, from what height was it released? Express your answer in meters to three significant figures. Hint 1. Identify the known variables What are the values of , , , and for the second rock? Take the positive y axis to be upward and the origin to be located on the ground where the rock lands. Express your answers to four significant figures in the units shown to the right, separated by commas. ANSWER: t = 2.18 s viy = 4.50 m/s yi = 13.5 m m/s s H yf viy t a Typesetting math: 100% Answer Requested Hint 2. Determine which equation to use to find the height Which equation should you use to find ? Keep in mind that if the positive y axis is upward and the origin is located on the ground, . ANSWER: ANSWER: Answer Requested Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both rocks were thrown with the same initial vertical velocity, 4.500 , and fell the same vertical distance of 13.5 , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part C correctly. ± Arrow Hits Apple An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity. Part A , , , = 0,4.500,2.181,-yf viy t a 9.810 m, m/s, s, m/s2 H yi = H yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt = − 2g( − ) v2f y v2i y yf yi H = 13.5 m viy = m/s m  = 45 D = 220 m g = 9.8 m/s2 Typesetting math: 100% Find , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Hint 1. Find the initial upward component of velocity in terms of D. Introduce the (unknown) variables and for the initial components of velocity. Then use kinematics to relate them and solve for . What is the vertical component of the initial velocity? Express your answer symbolically in terms of and . Hint 1. Find Find the horizontal component of the initial velocity. Express your answer symbolically in terms of and given symbolic quantities. ANSWER: Hint 2. Find What is the vertical component of the initial velocity? Express your answer symbolically in terms of . ANSWER: ANSWER: ta vy0 vx0 ta vy0 ta D vx0 vx0 ta vx0 = D ta vy0 vy0 vx0 vy0 = vx0 vy0 = D ta Typesetting math: 100% Hint 2. Find the time of flight in terms of the initial vertical component of velocity. From the change in the vertical component of velocity, you should be able to find in terms of and . Give your answer in terms of and . Hint 1. Find When applied to the y-component of velocity, in this problem the formula for with constant acceleration is What is , the vertical component of velocity when the arrow hits the tree? Answer symbolically in terms of only. ANSWER: ANSWER: Hint 3. Put the algebra together to find symbolically. If you have an expression for the initial vertical velocity component in terms in terms of and , and another in terms of and , you should be able to eliminate this initial component to find an expression for Express your answer symbolically in terms of given variables. ANSWER: ta vy0 g vy0 g vy(ta) v(t) −g vy(t) = vy0 − g t vy(ta ) vy0 vy(ta) = −vy0 ta = 2vy0 g ta D ta g ta ta2 t2 = a 2D g Typesetting math: 100% ANSWER: Answer Requested Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Express your answer numerically in seconds, to two significant figures. Hint 1. When should the apple be dropped The apple should be dropped at the time equal to the total time it takes the arrow to reach the tree minus the time it takes the apple to fall 6.0 meters. Hint 2. Find the time it takes for the apple to fall 6.0 meters How long does it take an apple to fall 6.0 meters? Express your answer numerically in seconds, to two significant figures. ANSWER: Answer Requested ANSWER: ta = 6.7 s tf = 1.1 s td = 5.6 s Typesetting math: 100% Answer Requested Video Tutor: Ball Fired Upward from Accelerating Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment? Hint 1. Determine how long the ball is in the air How will doubling the initial upward speed of the ball change the time the ball spends in the air? A kinematic equation may be helpful here. The time in the air will ANSWER: be cut in half. stay the same. double. quadruple. Typesetting math: 100% Hint 2. Determine the appropriate kinematic expression Which of the following kinematic equations correctly describes the horizontal distance between the ball and the cart at the moment the ball lands? The cart’s initial horizontal velocity is , its horizontal acceleration is , and is the time elapsed between launch and impact. ANSWER: ANSWER: Correct The ball will spend twice as much time in the air ( , where is the ball’s initial upward velocity), so it will land four times farther behind the cart: (where is the cart’s horizontal acceleration). Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. d v0x ax t d = v0x t d = 1 2 axv0x t2 d = v0x t+ 1 2 axt2 d = 1 2 axt2 the same distance twice as far half as far four times as far by a factor not listed above t = 2v0y/g v0y d = 1 2 axt2 ax Typesetting math: 100% Part A The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance. Hint 1. How to approach the problem While the crate is on the plane, it shares the plane’s velocity. What is the crate’s velocity immediately after it is released? Hint 2. What affects the motion of the crate? Gravity will accelerate the crate downward. What, if anything, affects the crate’s horizontal motion? (Keep in mind that we are told to ignore air resistance, even though that’s not very realistic in this situation.) ANSWER: Correct At the moment it is released, the crate shares the plane’s horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell. Score Summary: Your score on this assignment is 0%. Before the plane is directly over the target After the plane has flown over the target When the plane is directly over the target Typesetting math: 100% You received 0 out of a possible total of 0 points. Typesetting math: 100%

Chapter 4 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Advice for the Quarterback A quarterback is set up to throw the football to a receiver who is running with a constant velocity directly away from the quarterback and is now a distance away from the quarterback. The quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates that the receiver must catch the ball a time interval after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is and that the horizontal position of the quaterback is . Use for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem. Part A Find , the vertical component of the velocity of the ball when the quarterback releases it. Express in terms of and . Hint 1. Equation of motion in y direction What is the expression for , the height of the ball as a function of time? Answer in terms of , , and . v r D  tc y = 0 x = 0 g v0y v0y tc g y(t) t g v0y ANSWER: Incorrect; Try Again Hint 2. Height at which the ball is caught, Remember that after time the ball was caught at the same height as it had been released. That is, . ANSWER: Answer Requested Part B Find , the initial horizontal component of velocity of the ball. Express your answer for in terms of , , and . Hint 1. Receiver’s position Find , the receiver’s position before he catches the ball. Answer in terms of , , and . ANSWER: Football’s position y(t) = v0yt− g 1 2 t2 y(tc) tc y(tc) = y0 = 0 v0y = gtc 2 v0x v0x D tc vr xr D vr tc xr = D + vrtc Typesetting math: 100% Find , the horizontal distance that the ball travels before reaching the receiver. Answer in terms of and . ANSWER: ANSWER: Answer Requested Part C Find the speed with which the quarterback must throw the ball. Answer in terms of , , , and . Hint 1. How to approach the problem Remember that velocity is a vector; from solving Parts A and B you have the two components, from which you can find the magnitude of this vector. ANSWER: Answer Requested Part D xc v0x tc xc = v0xtc v0x = + D tc vr v0 D tc vr g v0 = ( + ) + D tc vr 2 ( ) gtc 2 2 −−−−−−−−−−−−−−−−−−−  Typesetting math: 100% Assuming that the quarterback throws the ball with speed , find the angle above the horizontal at which he should throw it. Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give your answer in terms of already known quantities, , , and . Hint 1. Find angle from and Think of velocity as a vector with Cartesian coordinates and . Find the angle that this vector would make with the x axis using the results of Parts A and B. ANSWER: Answer Requested Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. v0  v0x v0y v0  v0x v0y v0xx^ v0yy^   = atan( ) v0y v0x Typesetting math: 100% Part A Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Algebraic sign of velocity The algebraic sign of the velocity is determined solely by comparing the direction in which the object is moving with the direction that is defined to be positive. In this example, to the right is defined to be the positive x direction and upward the positive y direction. Therefore, any object moving to the right, whether speeding up, slowing down, or even simultaneously moving upward or downward, has a positive x velocity. Similarly, if the object is moving downward, regardless of any other aspect of its motion, its y velocity is negative. Hint 2. Sketch Alex’s initial velocity On the diagram below, sketch the vector representing Alex’s velocity the instant after he leaves the ground at the beginning of the jump. ANSWER: ANSWER: Typesetting math: 100% Answer Requested Part B Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he lands at the end of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Sketch Alex’s final velocity On the diagram below, sketch the vector representing Alex’s velocity the instant before he safely lands on the other side of the crevasse. ANSWER: Answer Requested ANSWER: Answer Requested Typesetting math: 100% At the buzzer, a basketball player shoots a desperation shot. The ball goes in! Part C Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s initial velocity On the diagram below, sketch the vector representing the velocity of the basketball the instant after it leaves the player’s hands. ANSWER: Typesetting math: 100% ANSWER: Correct Part D Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s velocity at maximum height Typesetting math: 100% On the diagram below, sketch the vector representing the velocity of the basketball the instant it reaches its maximum height. ANSWER: ANSWER: Answer Requested PSS 4.1 Projectile Motion Problems Learning Goal: Typesetting math: 100% To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 9.00 and launch angle 30.0 (above the horizontal) travels a horizontal distance of = 17.0 before hitting the ground. From what height was the rock thrown? Use the value = 9.810 for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Make simplifying assumptions, such as treating the object as a particle. Is it reasonable to ignore air resistance? VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols, and identify what you are trying to find. SOLVE: The acceleration is known: and . Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are , . is the same for the horizontal and vertical components of the motion. Find from one component, and then use that value for the other component. ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly. Visualize Part A Which diagram represents an accurate sketch of the rock’s trajectory? Hint 1. The launch angle In a projectile’s motion, the angle of the initial velocity above the horizontal is called the launch angle. ANSWER: m/s  d m g m/s2 ax = 0 ay = −g xf = xi +vixt, yf = yi +viyt− g(t 1 2 )2 vfx = vix = constant, and vfy = viy − gt t t v i Typesetting math: 100% Typesetting math: 100% Correct Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile’s acceleration, , is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn’t change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? ANSWER: ay At ground level below the point where the rock is launched At the point where the rock strikes the ground At the peak of the trajectory At the point where the rock is released At ground level below the peak of the trajectory Typesetting math: 100% Correct It’s best to place the origin of the coordinate system at ground level below the launching point because in this way all the points of interest (the launching point and the landing point) will have positive coordinates. (Based on your experience, you know that it’s generally easier to work with positive coordinates.) Keep in mind, however, that this is an arbitrary choice. The correct solution of the problem will not depend on the location of the origin of your coordinate system. Now, define symbols representing initial and final position, velocity, and time. Your target variable is , the initial y coordinate of the rock. Your pictorial representation should be complete now, and similar to the picture below: Solve Part C Find the height from which the rock was launched. Express your answer in meters to three significant figures. yi yi Typesetting math: 100% Hint 1. How to approach the problem The time needed to move horizontally to the final position = 17.0 is the same time needed for the rock to rise from the initial position to the peak of its trajectory and then fall to the ground. Use the information you have about motion in the horizontal direction to solve for . Knowing this time will allow you to use the equations of motion for the vertical direction to solve for . Hint 2. Find the time spent in the air How long ( ) is the rock in the air? Express your answer in seconds to three significant figures. Hint 1. Determine which equation to use Which of the equations given in the strategy and shown below is the most appropriate to calculate the time the rock spent in the air? ANSWER: Hint 2. Find the x component of the initial velocity What is the x component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: t xf = d m yi t yi t t xf = xi + vixt yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt vix = 7.79 m/s Typesetting math: 100% Hint 3. Find the y component of the initial velocity What is the y component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: Answer Requested Assess Part D A second rock is thrown straight upward with a speed 4.500 . If this rock takes 2.181 to fall to the ground, from what height was it released? Express your answer in meters to three significant figures. Hint 1. Identify the known variables What are the values of , , , and for the second rock? Take the positive y axis to be upward and the origin to be located on the ground where the rock lands. Express your answers to four significant figures in the units shown to the right, separated by commas. ANSWER: t = 2.18 s viy = 4.50 m/s yi = 13.5 m m/s s H yf viy t a Typesetting math: 100% Answer Requested Hint 2. Determine which equation to use to find the height Which equation should you use to find ? Keep in mind that if the positive y axis is upward and the origin is located on the ground, . ANSWER: ANSWER: Answer Requested Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both rocks were thrown with the same initial vertical velocity, 4.500 , and fell the same vertical distance of 13.5 , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part C correctly. ± Arrow Hits Apple An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity. Part A , , , = 0,4.500,2.181,-yf viy t a 9.810 m, m/s, s, m/s2 H yi = H yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt = − 2g( − ) v2f y v2i y yf yi H = 13.5 m viy = m/s m  = 45 D = 220 m g = 9.8 m/s2 Typesetting math: 100% Find , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Hint 1. Find the initial upward component of velocity in terms of D. Introduce the (unknown) variables and for the initial components of velocity. Then use kinematics to relate them and solve for . What is the vertical component of the initial velocity? Express your answer symbolically in terms of and . Hint 1. Find Find the horizontal component of the initial velocity. Express your answer symbolically in terms of and given symbolic quantities. ANSWER: Hint 2. Find What is the vertical component of the initial velocity? Express your answer symbolically in terms of . ANSWER: ANSWER: ta vy0 vx0 ta vy0 ta D vx0 vx0 ta vx0 = D ta vy0 vy0 vx0 vy0 = vx0 vy0 = D ta Typesetting math: 100% Hint 2. Find the time of flight in terms of the initial vertical component of velocity. From the change in the vertical component of velocity, you should be able to find in terms of and . Give your answer in terms of and . Hint 1. Find When applied to the y-component of velocity, in this problem the formula for with constant acceleration is What is , the vertical component of velocity when the arrow hits the tree? Answer symbolically in terms of only. ANSWER: ANSWER: Hint 3. Put the algebra together to find symbolically. If you have an expression for the initial vertical velocity component in terms in terms of and , and another in terms of and , you should be able to eliminate this initial component to find an expression for Express your answer symbolically in terms of given variables. ANSWER: ta vy0 g vy0 g vy(ta) v(t) −g vy(t) = vy0 − g t vy(ta ) vy0 vy(ta) = −vy0 ta = 2vy0 g ta D ta g ta ta2 t2 = a 2D g Typesetting math: 100% ANSWER: Answer Requested Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Express your answer numerically in seconds, to two significant figures. Hint 1. When should the apple be dropped The apple should be dropped at the time equal to the total time it takes the arrow to reach the tree minus the time it takes the apple to fall 6.0 meters. Hint 2. Find the time it takes for the apple to fall 6.0 meters How long does it take an apple to fall 6.0 meters? Express your answer numerically in seconds, to two significant figures. ANSWER: Answer Requested ANSWER: ta = 6.7 s tf = 1.1 s td = 5.6 s Typesetting math: 100% Answer Requested Video Tutor: Ball Fired Upward from Accelerating Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment? Hint 1. Determine how long the ball is in the air How will doubling the initial upward speed of the ball change the time the ball spends in the air? A kinematic equation may be helpful here. The time in the air will ANSWER: be cut in half. stay the same. double. quadruple. Typesetting math: 100% Hint 2. Determine the appropriate kinematic expression Which of the following kinematic equations correctly describes the horizontal distance between the ball and the cart at the moment the ball lands? The cart’s initial horizontal velocity is , its horizontal acceleration is , and is the time elapsed between launch and impact. ANSWER: ANSWER: Correct The ball will spend twice as much time in the air ( , where is the ball’s initial upward velocity), so it will land four times farther behind the cart: (where is the cart’s horizontal acceleration). Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. d v0x ax t d = v0x t d = 1 2 axv0x t2 d = v0x t+ 1 2 axt2 d = 1 2 axt2 the same distance twice as far half as far four times as far by a factor not listed above t = 2v0y/g v0y d = 1 2 axt2 ax Typesetting math: 100% Part A The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance. Hint 1. How to approach the problem While the crate is on the plane, it shares the plane’s velocity. What is the crate’s velocity immediately after it is released? Hint 2. What affects the motion of the crate? Gravity will accelerate the crate downward. What, if anything, affects the crate’s horizontal motion? (Keep in mind that we are told to ignore air resistance, even though that’s not very realistic in this situation.) ANSWER: Correct At the moment it is released, the crate shares the plane’s horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell. Score Summary: Your score on this assignment is 0%. Before the plane is directly over the target After the plane has flown over the target When the plane is directly over the target Typesetting math: 100% You received 0 out of a possible total of 0 points. Typesetting math: 100%

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1. Describe two applications where lenses are used. What does the lens do in each of these cases. 2. Draw a diagram showing how a camera lens forms an image of a distant object on the film. Explain what is done to obtain clear pictures of far and near objects using a camera.

1. Describe two applications where lenses are used. What does the lens do in each of these cases. 2. Draw a diagram showing how a camera lens forms an image of a distant object on the film. Explain what is done to obtain clear pictures of far and near objects using a camera.

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

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

Section 9.1 “Angular velocity,” of an object is its instantaneous … Read More...