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table of contents section 4 ­ motion chapter 9 linear motion · relative speed · speed and velocity · graphing motion activity graphing motion labette graphing motion · acceleration · freefalling lab acceleration due to gravity · motion ­ putting it all together labette physics of a plastic toy popper 288 290 291 291 299 300 305 307 312 314 318 322 329 331 335 339 chapter 10 projectile motion activity the motion of projectiles labette horizontal projectile motion labette projectile motion at an angle section 5 ­ newton s laws chapter 11 newtons laws · the law of inertia · newton s first law of motion ­ rotational motion labette newton s first law of motion ­ torque · static equilibrium · the law of acceleration lab newton s second law of motion · using free body diagrams activity model rocket physics · newton s second law of motion ­ rotational motion · the law of action/reaction · the force of friction lab calculating friction · uniform circular motion · motion in a vertical circle labette centripetal force · gravity · satellite motion · dark matter 345 347 344 349 355 358 364 367 377 383 385 394 400 404 409 412 415 420 430 433 section 6 ­ energy and momentum chapter 12 energy · work and energy labette a calculation of personal power · conservation of energy activity conceptualizing conservation of energy lab conservation of energy 438 440 440 446 453 457 458

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chapter 13 momentum · the physics of soft · the physics of catastrophe · combining conservation laws · kinetic energy changes in collisions and explosions · conservation of angular momentum lab rocket altitude prediction 463 463 468 477 480 483 489 495 497 503 510 517 520 521 528 529 532 533 540 545 550 556 557 559 563 565 571 section 7 ­ modern physics chapter 14 modern physics early days · the photoelectric effect lab light diffraction and interference · spectroscopy · fluorescence and phosphorescence · the laser chapter 15 the atomic nucleus · nuclear radiation is all around you · transmutation equations · detecting nuclear radiation lab nuclear radiation · a history of self exposure to ionizing radiation · radioactive half-life · neutron activation · food irradiation · nuclear fission · nuclear weapons · nuclear energy chapter 16 the nature of nature appendices 574

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the important thing in science is not so much to obtain new facts as to discover new ways of thinking about them sir william bragg section 4 motion hysicists look for patterns patterns lead to understanding look carefully at the colorful explosions in the air during a fireworks display or at the stream of water from a fountain or at the path of a home-run baseball they all look about the same ­ they have the same pattern the mathematically inclined might guess correctly that all the trajectory paths are parabolas non-mathematically inclined types would say that all the curves have similar shapes but whether or not you recognize the shapes as parabolas isn t as important as whether or not you recognize that they all have the same pattern if you see the pattern the next step is to make two guesses if they all have the same pattern then perhaps they re all moving according to the same principle they are in fact and if these three very different types of projectiles are all moving according to the same principle then perhaps all projectiles move according to the same unique principle they do in fact one of the things you ll find in this unit is that all projectiles are doing exactly the same thing they are all moving horizontally at a p 288

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motion otion constant speed and freefalling vertically both motions are very simple and so no matter how seemingly complicated the curvy motion of a projectile is it is actually pretty simple this is probably the most important thing i ve learned in physics ­ to look for patterns the universe by design or chance depending on your theology is organized in a system of patterns as you begin to recognize the patterns you quickly begin to realize that the universe is not a chaotic place it may not be simple but it is always understandable in this unit we ll go back to the most basic ideas in physics and build a solid foundation of understanding around the idea of motion we ll look at two types of motion constant speed and acceleration constant speed is just about as easy as it sounds but acceleration is a different matter i don t think many people really understand the concept of acceleration very well i have a friend who used to jump out of airplanes for a living he was a member of the army s h.a.l.o high altitude low open program he was trained to jump at 30,000 feet but not to open his parachute until he was 1,000 feet above the ground he comments that it was a long trip but it ended very quickly at the end of this three unit series that begins with motion you ll be able to appreciate if only vicariously the thrill he experienced and you ll be able to explain why the thrill you experience at the typical amusement park is as great or greater than the h.a.l.o experience 289

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motion otion chapter 9 linear motion t he year is 3000 ad and an archaeologist has just unearthed a time capsule containing a dvd from the year 2010 ad thrilled to find an artifact from a primitive culture that lived 1,000 years in the past she anxiously prepares to view the dvd it chronicles the minute-by-minute activities of one person s day at an amusement park she is intrigued by the garments worn amused by the low technology figure 9.1 the yf-22 raptor is fast this judgment of its speed is but flabbergasted by one thing in relative though it s fast compared to a runner or compared to even the particular she marvels that in speediest car but compared to the earth s speed as it revolves around the eight hours of activity at the sun 66,000 mph the raptor lags pitifully behind perception of speed is park the person being videoed is always made by comparing the distance traveled to the time it takes to really only active for twelve travel that distance minutes the rest of the time he is standing in long long lines waiting to get onto what is fast short short rides why she thinks would someone in how do you know when something is going this long-dead culture waste so much time for so little fast well you just know you can look at cars on benefit the answer of course is because of the the freeway and if the traffic is light you can just tell thrill at an amusement park you can move in ways that they re going fast but your brain really doesn t that would be life threatening in any other place it s know fast it can measure distance pretty well and it a place of extreme physics it s a place where can measure time but to measure how fast conservation of energy is king it s a place of high something is going it has to compare distance and acceleration stomach-churning centripetal forces time so if two cars travel the same distance but one and frighteningly severe impulses does it in a shorter period of time that one is moving to understand the physics of amusement park the fastest the simplest concept in motion is average rides is to truly understand motion power work speed average speed is simply the total distance momentum acceleration impulse uniform circular moved compared to the time taken to move that motion forces and freefall are all there but we ll distance so average speed is start where we must start with the simplest concept of motion we ll start with speed d v av total t total figure 9.2 the recognition of speed depends on a comparison of distance and time in this photo taken by megan orlando class of 2008 each image of both walker and biker are separated in time by 0.8 seconds the photo shows that the speeds for both are constant same distance covered between successive images and that the biker is traveling approximately three times faster than the walker three times the distance covered in the same time 290

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motion otion how fast is fast and compared to what i m a runner and i ve run many races i m most proud of running a half-marathon in an hour and thirty-three minutes so when i hear that haile gebrselassie of ethiopia ran a full marathon in 2:03:59 on september 28 2008 i m amazed his world record-setting pace makes him fast but his average speed of 12.5 mph is nothing compared to a harrowing ride i had down mount tam when i was sixteen a friend of mine jeff atkinson seemed insane as he took every corner at 50 mph or more i really thought i might die that day but i ve gone over 500 mph many times when i ve taken commercial plane flights and i m not scared at all well maybe a bit during takeoff each of the speeds listed so far were made without reference to any fixed spot but the assumption is that i ve been speaking about speeds that are relative to the earth that is i ve assumed that the earth isn t moving to be rigorous a speed must always be given relative to some fixed frame of reference when we re earth-bound we usually agree that the earth is our frame of reference without actually specifying it opting for 25 mph rather than 25 mph relative to the earth sometimes we get fooled though i remember being stopped at a traffic light and noticed that it was time to go because the car next to me was pulling forward but then realized that the car next to me was actually stopped and i was slowly rolling backward in this case i had made my car a fixed frame of reference i thought i still had my foot on the brake it made the earth and everything fixed to it appear to be moving and according to my defined frame of reference these things were moving there s nothing special about using the earth as a fixed frame of reference you can choose any nonaccelerating frame of reference to be fixed and the laws of motion will work just the same more about accelerating frames of reference later figure 9.3 shows a blue car that would appear to be at rest if its hubcaps weren t blurry the car was actually moving at 70 mph relative to the earth but the photographer was moving at the same speed as the blue car this made the blue car appear stationary and the trees and other car in the background appear to be moving to the rear occupants of the blue car if they chose to could consider themselves to be totally at rest they could drop a ball inside the car and it would drop straight down in their reference frame they could even play a little game of catch and it would feel the same as if they were outside on the ground figure 9.3 the blue car in this photograph taken by john oh class of 2005 is the fixed frame of reference the blue car was moving at about 70 mph relative to the earth but the photographer was moving at the same speed as the blue car in the frame of reference of the blue car the trees and other car are speeding backward motion is truly relative we usually consider the earth to be at rest because we don t feel it moving but you and i are actually rotating on the earth at about 1,000 mph and revolving around the sun at about 66,000 mph both these speeds are in the reference frame of the sun or fixed stars yet even the sun and so-called fixed stars are spiraling at terrifically greater speeds about the center of the milky way in the reference frame of the center of the galaxy the milky way is home to 100 billion stars an almost unfathomably large number of suns but the milky way is just one of 100 billion other galaxies most hurtling away from each other at speeds that are faster still ­ but compared to what there is in fact no place no spot to point to as the true frame of reference for the universe any place is as good as another and so in some sense it is accurate to say that yes the world does indeed revolve around you however don t begin to think since motion is relative that fast has no limit there is a limit ­ the speed limit of the universe ­ the speed of light nothing can ever exceed or even get to the speed of light except light of course the speed of light ­ that s fast speed and velocity a term that is used almost synonymously with speed is velocity but average speed and average velocity can be very different i joke sometimes that over a lifetime my average velocity will probably be almost zero and that my average daily velocity had better be zero if i am to keep my dear wife happy 291

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motion otion speed is a scalar measurement and velocity is a vector measurement scalars measure only an amount of something the temperature of a room 70°f the area of a house 2000 square feet and the distance recorded on a car odometer 67,232 miles are all scalars vectors measure both amount and direction so they are everything scalars are and a bit more although we don t often think of it this way weight is a vector if you ask me how much i weigh i would tell you 180 pounds but i would be leaving out the fullest meaning of what my weight is weight is a force and like all forces it has a direction my weight is always directed down toward the center of the earth to measure my weight i have to put the scale between the earth and me because that is the direction in which my weight is directed it would be silly to put a scale on my side or on top of my head my weight isn t pointing in those directions so weight a vector is a more sophisticated measurement than a scalar and velocity is a more sophisticated measurement than speed velocity doesn t measure the ratio of distance to time but rather the ratio of displacement to time displacement is change in position this may sound like distance but it s not think of distance as the odometer reading distance is the log of miles or inches or light years traveled displacement is entirely different when you measure displacement you only consider the starting and ending points what happens in between doesn t matter so if you are a pilot for an airline and you start your day in san francisco fly to los angeles then to washington d.c and finally to chicago your distance would be the tally of the miles flown over 4,000 miles however your displacement would be the change in position between where you started san francisco and where you ended chicago this would be approximately 2,000 miles east the direction is important to calculate average velocity you simply compare the displacement or change in position with the time taken to make that change so average velocity is rrdv av t the arrows above the v and the d are meant to r distinguish the vectors velocity and displacement v r and d from the scalars speed and distance v and d 292

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motion otion check yourself ­ introduction to motion choose the correct answer and then give an explanation below the question 1 the average speed of a horse that gallops a distance of 10 kilometers in a time of 30 minutes is a 10 km/h b 20 km/h c 30 km/h d more than 30 km/h 2 an average speed of zero means a no motion b possible motion c definite motion 3 an average velocity of zero means a no motion b possible motion c definite motion 4 an distance of zero means a no movement b possible movement c definite movement 5 an displacement of zero means a no movement b possible movement c definite movement 6 it is possible to have a changing velocity even if the speed is constant a true b false 7 it is possible to have a changing speed even if the velocity is constant a true b false 8 would it be possible for you to run at 200,000 m/s a yes without qualification b no not ever c maybe but it would depend on the reference frame being used 9 would it be possible to run at 3.1 x 108 m/s a yes without qualification b no not ever c maybe but it would depend on the reference frame being used 293

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motion otion use the following information to answer the next four questions you travel 60 miles in a straight line for one hour and then travel back to your starting point in two hours 10 what distance have you traveled a 0 miles b 60 miles c 120 miles d 180 miles 11 what is your total displacement a 0 miles b 60 miles c 120 miles d 180 miles 12 what was your average speed a 0 mph b 40 mph c 60 mph d 120 mph 13 what was your average velocity a 0 mph b 40 mph c 60 mph d 120 mph 14 a car travels 500 km in 6 hours and another car travels the same 500 km in 10 hours the cars have the same a acceleration b displacement c average speed d velocity 15 an automobile odometer shows that the car traveled 80 km during a 2 hour period from this information it can be concluded that a the car traveled at a constant speed of 40 km/hr b the car traveled at an average speed of 40 km/hr c the initial speed of the car was 40 km/hr and the car was not accelerated during the 2 hr trip d the final speed of the car was 80 km/hr 294

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motion otion questions and problems average speed and velocity 1 tracks a and b are exactly the same length track b just looks shorter because it has a dip that has been bent into it if the balls were simultaneously released from the positions shown which if either would reach the end of the track first explain using truth rather than intuition 2 in the following scenario all speeds given are in the earth s reference frame on a neighborhood road a boy walks west at 4 mph he is passed by a bicyclist moving at 12 mph west and a car moving at 25 mph west a second car passes him moving 35 mph east a in the boy s reference frame what are the speeds of the bicycle and two cars b in the reference frame of the car moving east what are the speeds of the boy the bicycle and the other car 3 describe a situation in which the magnitudes of average speed and average velocity are identical 4 describe a situation where your average speed is not zero but your average velocity is zero 5 a physics student leaves home walks to school 4 blocks east and then returns home for lunch after lunch she returns to school a what is the distance of her journey b what is the displacement of her journey 295

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motion otion 6 a skydiver with parachute unopened falls 625 m in 15.0 s then he opens his parachute and falls another 356 m in 142 s what is his average speed for the entire fall 7 a car drives according to the diagram to the right assume that there is a 1.0-hour rest period after the first leg of the trip a determine the average speed for the trip 60 mph for 0.25 h 40 mph for 0.50 h 60 mph for 0.25 h 30 mph for 0.50 h b determine the average velocity for the trip 8 you maintain a speed of 115 mph for 2.0 hours after resting for 45 minutes you then return along the same route to where you started on the way back you hold it down to 55 mph what is your average speed for the entire trip 9 the f-15 is one of the u.s air force s fastest jets capable of a maximum speed of mach 2.5 two-and-a-half times the speed of sound if an f-15 at travis afb were required to scramble to a problem in sacramento 50 miles away what is the fewest number of minutes it would take to get there 296

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motion otion 10 one of the methods that the washington d.c police department uses to catch speeders is to trigger multiple photographs of cars that pass through an automated radar zone at excessive speed the photographs below were taken 0.20 s apart the marker lines are five feet apart the speed limit in this zone was 45 mph by how much was this car exceeding the speed limit 11 a physics teacher who lives 30 miles from school is frustrated by the low speed limit of 65 mph he decides to go 80 mph instead how many minutes of time does he save driving at the higher speed 12 high school cross-country courses are 5 km long let s say the fastest person on the team can complete the course with an average speed of 5.21 m/s and the slowest can complete the course with an average speed of 4.27 m/s if the fastest runner wants to run the course so that he crosses the finish line at the same time as the slowest runner how much time must he wait to start running after the slowest runner begins 297

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motion otion 13 a car drives for 1.5 hours at 60 mph east then the driver rests for an hour finally the car drives for 3.0 hours at 40 mph south a determine the average speed for the trip b determine the average velocity for the trip 14 a speed trap is set up over a distance of 1,000 m you are moving at a speed of 35 m/s for 425 m before you become aware of the police department airplane overhead tracking your motion what is the maximum speed you can travel over the remainder of the 1,000 m in order for your average speed to be under the posted speed limit of 25 m/s 15 two bullies want to get you the three of you are on a narrow path that you can t get off and you re in the middle they re separated by one mile when they start running toward you they each run at six mph but you can run at 10 mph if you initially start out right in front of one of them and run back and forth the full distance between bullies how much distance will you have covered by the time they finally catch you 298

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motion otion introduction to graphing motion onstant speed is really not very interesting in fact it s boring you never hear about people falling asleep on a windy mountain road but a quick look at the glazed eyes of some drivers on the freeway when the traffic is light and they can set their cruise control tells you that they are not being very stimulated figure 9.4 this photograph was taken by keeping the shutter open on the the equation for average camera while the flash was activated every second it is clearly not constant speed v av d t is a very speed since the distance covered varies for the same increment of time if the simple equation and isn t distance between images were known a graph of the motion distance vs time able to tell you very much could be made in order to understand the nature of the motion more clearly about any motion that isn t constant speed for example when i drive freefall is a very important type of motion and from school to home on a typical afternoon after probably the most common type on the planet 4:30 it can take me 50 minutes to go 30 miles the everyone knows that things go faster as they fall but average speed equation can only determine that my how much faster do they go in one second compared average speed on the way home is to the previous second and do falling objects keep 30 miles 0.83 hours or 36 mph but this simplistic gaining speed at the same rate to answer these record of my trip cannot take into account that there questions we need to check where the objects are at were segments where i traveled at 70 mph and points regular intervals of time to see how far they ve gone where i was completely stopped there is no record and if there are any patterns of how many times i was speeding up or slowing in figure 9.4 bobby buchanan has set a flash to down or how quickly i sped up one time compared to go off every second while he walks in front of a any other time indeed the only thing the average camera with its shutter held open every second the speed tells me is that if another driver had started out flash illuminates the darkness and exposes bobby s on the same trip as me and kept his speed constant at position this is not constant speed in equal 36 mph it would take him the same time to complete increments of time his position changes unequally the trip big deal the distance between his successive positions in order to understand more complicated motion increases ­ he s speeding up if we knew the distance which really means more interesting motion we between his images we could not only calculate his need to be able to look at the details of that motion average speed but also his incremental speed and we need to be able to take a peek at it in small we could check to see if the increase in speed was increments and then compare one increment to uniform the same increase each second another c 299

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