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A Look Back at MLK (math)
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Filmic Techniques Based on the work of Brad Smilanich Mis-en-Scene: originally a French theatrical term arrangements of all the visual elements of the stage area in film โ โthe contents of the frame and the way those contents are organizedโ include: lighting, costume, dรฉcor, props, camera movement or distance . . . all photographic decisions etc. Proxemics: Spatial relationship among characters within the mis-en-scene Rule of Thirds: a compositional rule of thumb in painting, design, photography etc. suggests image divided into 9 equal parts with two vertical and two horizontal lines important elements of the mis-en-scene should be placed along these lines and their intersections some suggest aligning with intersections makes for more interesting pictures than just centreing the subject Proxemics Camera Distance: Quite literally, how far the camera is from the subject being filmed The Hand Camera Camera Distance: Quite literally, how far the camera is from the subject being filmed Extreme Close Up: Singles out one small portion of the body or object Used to intensify emotion, or show reaction Camera Distance: Close up Shot: Shows head of character or small significant object Used to show emotions Camera Distance: Medium Shot: shows figures from the waist up allows character to be seen within background Camera Distance: Long Shot: shows figures from feet up similar to the โstageโ in live theatre orients audience to figures within a location or surrounding Camera Distance: Extreme Long Shot: Sometimes called an โestablishing shotโ Panoramic view of an exterior location orients audience to a location Camera Distance: Camera Angle: Cameraโs angle of view relative to the subject being photographed High Angle Shot: looks down on the subject often used to make the subject look small and insignificant (in combination with camera distance) puts the camera (audience) in โpowerโ position Camera Angle: Low Angle Shot: looks up at the subject often used to make the subject look large and powerful puts the camera (audience) in a โsubmissiveโ position Camera Angle: Flat Angle Shot: camera on same plane as the subject feels most โnormalโ to an audience Camera Angle: Canted Shot: frame is unbalanced in relation to the subject may indicate a symbolic unbalance in the character Camera Angle: Camera Movement literally the camera moving with or around or to follow the subjects in the mis-en-scene or frame Camera Movement: Tilting Movement camera moves up or down on a horizontal axis similar to head nodding movement may be used to show subjects relation to surroundings Camera Movement: Panning Movement camera moves side to side on a vertical axis similar to head shaking movement may be used to establish setting Camera Movement: Dolly Movement camera mounted on a vehicle that moves along with the subject (camera moves, not pivots) follows the subject to signify something important Camera Movement: Crane Shot camera mounted on a crane or boom permits camera to move in & out, up & down, backward & forward often used for high aerial establishing shots Misc. Shots: Hand Held: camera carried to seem jerky, giving โrealistic feelโ Push In: camera moves up to a characterโs face to indicate an epiphany (realization) Spiral: camera circles subject for effect End for ELA 20-2 and 10-1 Shot Transitions/Editing: artificial editing done to string together multiple shots to create a narrative scene or sequence a cut is the change from one shot to another usually separated in to โsoftโ and โhardโ cuts Jump Cut: an instantaneous change from one shot to another this can be very natural or may disorient the audience, depending on how it is used Transitions/Editing Swish Pan: A pan where the speed of the camera is so fast that images are blurry used often to connect events in different settings that are connected by time Transitions/Editing Dissolve: transition where one shot gradually dissapears while another shot gradually appears often used to suggest change of setting or long time passage i.e. flashbacks Transitions/Editing Fade In/Out: transition where the shot gradually overexposes to white or underexposes to black often used to suggest a lengthy passage of time or change in location Transitions/Editing Wipe: transition where one shot is gradually eliminated as another shot moves onto the screen can be vertically or horizontally often suggests movement of the camera to another location Transitions/Editing Iris In/Out: transition where one shot gradually appears as an expanding circle in the middle of an old image suggests . . .??? Transitions/Editing Shot-Reverse Shot: one character is shown looking (often off-screen) at another character, and then the other character is shown looking "back" at the first character. Since the characters are shown facing in opposite directions, the viewer unconciously assumes that they are looking at each other. Transitions/Editing Two-Shot: Face-up shot of two people. Often used in interviews, or when two presenters are hosting a show. A "One-Shot" could be a mid-shot of either of these subjects. A "Three-Shot", unsurprisingly, contains three people. Transitions/Editing Shot Transitions/Editing: Sound: used to reflect or enhance what is shown visually on the screen can include dialogue, music, sound effects, voiceover etc. Diegetic Sound: sound that has a source in the world of the story dialogue spoken by characters, sound made by objects, or music coming from a source grounded in the story of the film Non-diegetic Sound: sound that has a source outside the world of the story usually part of the score or the soundtrack Parallel Sound: sound that complements the image shown i.e. romantic music during a love scene Counterpoint Sound: sound that contradicts the โfeelingโ of the image a happy song played while images of graphic violence are portrayed Voiceover: voice of a non-visible narrator laid over the scene often provides some comment about the narrative of the film Sound Bridge: used to โsoftenโ the transition between one scene and another takes sound from the next shot and overlays it on the current shot 2-3 seconds earlier than we see the image Examples of Diegetic/Non-Diegetic: In the first clip, the non-diegetic music changes to diegetic music when the main character moves inside of the convenience store. In the second clip, the โduhn duhn duuuuhโ which often is non-diegetic becomes diegetic because it is the band in the passing bus playing that music! End for ELA 20-1 Lighting: Can be used by a director to: Control the mood of a scene guide a viewerโs eye to a specific place in mis-en-scene Emphasize and de-emphasize elements in frame Add texture and color Make people look beautiful, ugly, sinister, or angelic Standard 3-Point Lighting: uses three lights called theย key light,ย fill lightย andย back light forms the basis of most lighting. once you understand three point lighting you are well on the way to understanding all lighting. Key Light: main light usually the strongest and has the most influence on the look of the scene. it is placed to one side of the camera/subject so that side is well lit and other side has shadow. Fill Light: secondary light is placed on the opposite side of the key light used to fill the shadows created by key softer and less bright than key Back Light: placed behind the subject ; lights it from the rear. provides definition and subtle highlights around the subject's outlines. Separates subject from background provides a three-dimensional look. Standard 3-Point Lighting: http://www.zvork.fr/vls/ Try using this simulator to play with lighting with those 3 points.In this video we take a look at the 0:02 fetch to code 0:03 execute cycle including its effect on 0:06 the various registers we've previously 0:12 [Music] 0:14 discussed a computer is defined Definition 0:17 as an electronic device that takes an 0:20 input 0:22 processes data 0:25 and delivers output 0:29 in this simple example you can see we're 0:31 taking the input 5 0:35 we're multiplying it by 2 that's our 0:37 process 0:39 and we're outputting 10. 0:44 but this could be way more complex for 0:46 example of a game console 0:48 the input could be the buttons you press 0:50 on a controller 0:53 the processes would then be carried out 0:55 by the console itself 0:59 and the output would be some form of 1:01 update to a monitor 1:02 and sound out for a speaker possibly 1:04 vibration feedback through the 1:06 controller 1:10 to process data a computer follows a set 1:13 of instructions 1:14 known as a computer program 1:18 if we take the lid off a typical desktop 1:20 computer we can identify 1:22 two critical components the memory 1:26 that stores the program and the central 1:29 processing unit or processor 1:31 which is under this large fan and 1:33 carries out the instructions 1:37 a computer carries out its function by 1:40 fetching 1:41 instructions decoding them and then 1:43 executing them 1:44 in a continuous repetitive cycle 1:46 billions of times a second 1:48 let's look at each of these stages in a 1:50 little more detail Fetch 1:53 so let's start with the fetch stage the 1:55 very first thing that happens 1:57 is the program counter is checked as it 2:00 holds the address 2:01 of the next instruction to be executed 2:07 the address stored is then copied into 2:09 the memory address register 2:14 the address is then sent along the 2:16 address bus to main memory 2:18 where it waits to receive a signal from 2:21 the control 2:22 bus so it knows what to do 2:27 as we want to read the data that's 2:29 stored in memory address 2:30 0 0 0 0 the control unit sends 2:34 a read signal along the control bus to 2:36 main memory 2:41 now main memory knows the data needs to 2:44 be read 2:45 the content stored in memory address 000 2:49 can be sent along the data bus to the 2:51 memory data register 2:56 now as we're currently in the process of 2:58 fetching an instruction 3:00 the data received by the memory data 3:03 register gets copied 3:04 into the current instruction register 3:11 the instruction effectively has now been 3:14 fetched from memory 3:16 just before we proceed to the decode 3:18 phase we now 3:19 increment the program counter so that 3:22 the address it contains 3:24 points to the address of the next 3:26 instruction which will need to be 3:30 executed 3:32 the instruction now being held in the 3:33 current instruction register 3:35 is ready to be decoded 3:39 now as we mentioned in the previous 3:41 video the instruction is made up of two 3:43 parts 3:44 we have the op code that's what it is we 3:47 need to do 3:50 and we have the operand what are we 3:53 going to do it to 3:55 now the operand could contain the actual 3:57 data 3:58 or indeed it could contain an address of 4:01 where the data is to be found 4:06 by decoding this instruction we can see 4:08 the operation we need 4:10 is a load operation so we need to load 4:14 the contents of memory location0101 4:18 into the cpus accumulator 4:25 in the exam a simple model will be used 4:27 to describe the 4:29 structure of any given instruction 4:32 you're not going to be expected to 4:34 define how an opcode is made up 4:36 but simply to interpret opcodes in the 4:39 given context of an exam 4:40 question in the example here 4:44 you can see there's a total of 16 4:46 different opcodes available 4:48 and this is because we're using four 4:50 bits for our representation 4:56 so now we've fetched the instruction and 4:59 we've decoded it so we know what we need 5:00 to do 5:01 we're finally ready to execute it 5:05 so we now send address 0101 5:08 to the memory dress register 5:13 now we're in the memory address register 5:15 we can finally send the address 5:18 down the address bus to main memory 5:24 this time we want to read the data 5:26 that's stored in memory 5:28 and so the control unit again sends a 5:30 read signal along the control bus 5:36 so main memories now receive an address 5:38 and a read signal 5:40 so the content stored at memory location 5:43 0101 5:44 can now be sent along the data bus back 5:46 to the cpu 5:47 and into the memory data register 5:54 finally the contents of the memory data 5:56 register are copied to the accumulator 5:59 and this is one of a number of general 6:00 purpose registers found in the cpu 6:04 this first instruction is now complete Branching 6:11 so what does this program actually do 6:14 you should be able to work it through 6:16 carefully and figure it out 6:19 we're now pointing instructions zero 6:21 zero zero one in the program counter 6:23 and we're ready to fetch the second 6:25 instruction 6:27 at the end of this video we're gonna 6:29 provide you with the answer 6:34 so let's talk a second about programs 6:37 that branch 6:40 on the left here we have a very simple 6:42 piece of pseudo code 6:44 line zero says first execute this line 6:46 of code 6:47 line 1 now execute this line and then 6:50 line 2 says 6:52 if the age is greater than 18 then 6:56 we're going to execute lines 3 and 4 6:58 otherwise 6:59 we're going to execute lines six and 7:02 seven 7:03 so this program doesn't necessarily 7:05 follow strictly in sequence from line 7:07 zero through to seven there's a chance 7:10 here the program may branch and jump 7:14 around 7:16 so we're going to pretend that this 7:17 program has been loaded into memory 7:20 each line of code on the left here has 7:23 ended up 7:24 as a location in memory now this is not 7:27 strictly how this would happen in this 7:28 one-to-one way 7:29 but for the purpose of example it's 7:31 absolutely fine 7:35 so the program counter starts by 7:37 pointing to memory address zero 7:39 and we fetch the first instruction 7:41 decode it and execute it 7:44 it then updates and tells us the next 7:47 instruction 7:48 is zero zero zero one because remember 7:50 the program counter is being incremented 7:52 so we fetch it decode it and we execute 7:55 line one of our program 7:59 we then fetch line two which in binary 8:01 is one 8:02 zero 8:06 now at this point depending on what 8:10 happens during the execution 8:11 of line two the program may be required 8:15 to fetch line three from memory or 8:18 line five from memory 8:25 so let's look at how this actually works 8:27 because we've said the program counter 8:28 simply gets incremented 8:31 well in the current instruction register 8:33 we have an instruction with the op code 8:36 0 1 1 0. 8:41 now when we look this up in the decode 8:43 unit we discover that this 8:45 code means branch always 8:51 this replaces the value held in the 8:54 program counter 8:56 with the contents of the operand that's 8:58 the second part of the instruction 9:01 from the current instruction register so 9:03 this case 9:04 one zero zero one 9:09 now when the next fetch cycle begins the 9:12 program counter is obviously checked 9:14 and as its contents have been previously 9:16 updated to a new memory location 9:19 and not simply incremented the program 9:22 effectively is able to jump 9:24 around memory 9:28 so having watched this video you should 9:30 be able to answer the following key 9:32 question 9:33 how does a cpu work 9:39 okay so let's um answer the question we 9:41 posed 9:42 earlier what did that program actually 9:48 do 9:50 so this is the first fetch to code 9:53 execute cycle 9:55 and this is the one that we ran through 9:57 in detail earlier 9:58 it effectively loaded the contents of 10:01 the memory 10:02 stored at location location0101 10:05 into the accumulator in other words 10:08 the dna number 3 is moved 10:11 from memory into the cpu 10:18 we then proceed onto the second fetch 10:20 decode execute cycle 10:23 now this one adds the contents of memory 10:27 located at 0 1 1 0 10:30 to the current contents of the 10:32 accumulator 10:34 so in other words the dna number one 10:38 because that's what's stored at address 10:40 zero one one zero 10:43 is added to the number three that was in 10:45 the accumulator 10:46 the results are stored back over the 10:48 accumulator 10:49 so effectively we've done three plus one 10:53 equals four 10:58 the third fetch to code execute cycle 11:00 stores the contents which are in the 11:02 accumulator 11:03 into memory location zero one one one 11:07 and that's because the op code the first 11:09 part of this current instruction 11:10 zero zero one one is the command to 11:13 store when we look it up in the decoder 11:15 unit 11:16 so in other words the result of the 11:17 previous calculation three plus one 11:19 equals four 11:20 is now written back into main memory 11:28 the fourth fetch decode execute cycle 11:30 outputs the contents of the accumulator 11:33 remember they were copied into main 11:34 memory but they're still held in the 11:35 accumulator 11:37 so in this simple abstraction the number 11:40 four is now 11:41 output to the user so they can see the 11:43 result of the calculation 11:49 the fifth and final fetch code execute 11:51 cycle 11:52 brings a halt to the current program 11:58 so this very simple program which has 12:01 five 12:02 fetch decode execute cycles has 12:04 performed the calculation 12:06 three plus one is then stored the result 12:09 in main memory 12:10 and displayed the result four to the 12:12 user 12:13 and in a high-level language this may 12:15 look something very similar to the 12:17 following two lines of code 12:20 sum variable equals num1 plus num2 12:24 print sum to the user 12:27 so you can start to get an appreciation 12:29 here of how the high level code you 12:32 write actually ends up being fetched 12:34 decoded 12:35 and executed inside a processor 12:38 of course your processor is doing 12:40 billions and billions of these 12:42 operations a second 12:43 which when you think about it is really 12:45 very impressive 12:52 [Music] 13:03 you. make 10 questions for a standerd of a levelA BAD CASE OF THE STRIPES By David Shannon Parts(18): Camilla Narrator 1 Narrator 2 Narrator 3 Narrator 4 Mr. Harms Mother Father Dr. Bumble Old Woman Environmental Therapist Dr. Grop Dr. Gourd Dr. Sponge Mr. Mellon Dr. Cricket Dr. Young <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Narrator 1: A BAD CASE OF THE STRIPES By David Shannon Narrator 2: Camilla Cream loved lima beans. But she never ate them. Narrator 3: All of her friends hated lima beans, and she wanted to fit in. Camilla always worried about what other people thought of her. Narrator 4: Today she was fretting even more than usual. It was the very first day of school, and she couldn't decide what to wear. There were so many people to impress! Narrator 1: She tried on forty-two outfits, but none seemed quite right. She put on a pretty red dress and looked in the mirror. Then she screamed. Narrator 2: Her mother ran into the room, and she screamed, too. Mother: "Oh my heavens! You're completely covered with stripes!" Narrator 3: she cried. This was certainly true. Camilla was striped from head to toe. She looked like a rainbow. Narrator 4: Mrs. Cream felt Camilla's forehead. Mother: "Do you feel all right?" Narrator 1: she asked. Camilla: "I feel fine, but just look at me!" Narrator 2: Camilla answered. Mother: "You get back in bed this instant. You're not going to school today." Narrator 3: her mother ordered. Camilla was relieved. She didn't want to miss the first day of school, but she was afraid of what the other kids would say. And she had no idea what to wear with those crazy stripes. Narrator 4: That afternoon, Dr. Bumble came to examine Camilla. Dr. Bumble: "Most extraordinary! I've never seen anything like it! Are you having any coughing, sneezing, runny nose, aches, pains, chills, hot flashes, dizziness, drowsiness, shortness of breath, or uncontrollable twitching?" Narrator 1: he asked. Camilla: "No, I feel fine." Narrator 2: Camilla told him. Dr. Bumble: "Well then, I don't see any reason why she shouldn't go to school tomorrow. Here's some ointment that should help clear up those stripes in a few days. If it doesn't, you know where to reach me." Narrator 3: Dr. Bumble said, turning to Mrs. Cream. And off he went. Narrator 4: The next day was a disaster. Everyone at school laughed at Camilla. They called her "Camilla Crayon" and "Night of the Living Lollipop." Narrator 1: She tried her best to act as if everything were normal, but when the class said the Pledge of Allegiance, her stripes turned red, white, and blue, and she broke out in stars! Narrator 2: The other kids thought this was great. One yelled out, Narrator 3: "Let's see some purple polka dots!" Narrator 4: Sure enough, Camilla turned all purple polka-dotty. Someone else shouted, Narrator 1: "Checkerboard!" Narrator 4: and a pattern of squares covered her skin. Soon everyone was calling out different shapes and colors, and poor Camilla was changing faster than you can change channels on a T.V. Narrator 2: That night, Mr. Harms, the school principal, called. Mr. Harms: "I'm sorry, Mrs. Cream, I'm going to have to ask you to keep Camilla home from school. She's just too much of a distraction, and I've been getting phone calls from the other parents. They're afraid those stripes may be contagious." Narrator 3: he said. Camilla was so embarrassed. She couldn't believe that two days ago everyone liked her. Now, nobody wanted to be in the same room with her. Narrator 1: Her father tried to make her feel better. Father: "Is there anything I can get you, sweetheart?" Narrator 2: he asked. Camilla: "No, thank you," Narrator 3: sighed Camilla. What she really wanted was a nice plate of lima beans, but she had been laughed at enough for one day. Dr. Bumble: "Hmm, well, yes, I see. I think I'd better bring in the Specialists. We'll be right over.โ Narrator 4: said Dr. Bumble to Mr. Cream on the phone. About an hour later, Dr. Bumble arrived with four people in long white coats. He introduced them to the Creams. Dr. Bumble: "This is Dr. Grop, Dr. Sponge, Dr. Cricket, and Dr. Young." Narrator 1: Then the Specialists went to work on Camilla. They squeezed and jabbed, tapped and tested. It was very uncomfortable. Dr. Grop: "Well, it's not the mumps." Dr. Sponge: "Or the measles." Dr. Cricket:"Definitely not chicken pox." Dr. Young: "Or sunburn." Narrator 2: replied the Specialists. Specialists:"Try these. Take one of each before bed." Narrator 4: said the specialists. They each handed her a bottle filled with different colored pills. Then they filed out the front door followed by Dr. Bumble. Narrator 1: That night, Camilla took her medicine. It was awful. Narrator 2: When she woke up the next morning, she did feel different, but when she got dressed, her clothes didn't fit right. She looked in the mirror, and there, staring back at her, was a giant, multi-colored pill with a face on it. Narrator 3: Dr. Bumble rushed over as soon as Mrs. Cream called. But this time, instead of the Specialists, he brought the Experts. Narrator 4: Dr. Gourd and Mr. Mellon were the finest scientific minds in the land. Once again, Camilla was poked and prodded, looked at and listened to. Narrator 1: The Experts wrote down lots of numbers. Then they huddled together and whispered. Dr. Gourd finally spoke. Dr. Gourd: "It might be a virus," Narrator 2: he announced with authority. Suddenly, fuzzy little virus balls appeared all over Camilla. Mr. Mellon: "Or possibly some form of bacteria," Narrator 3: said Mr. Mellon. Out popped squiggly little bacteria tails. Dr. Gourd: "Or it could be a fungus," Narrator 4: added Dr. Gourd. Instantly, Camilla was covered with different colored fungus blotches. The experts looked at Camilla, then each other. Experts: "We need to go over these numbers again back at the lab. Weโll call you when we know something," Narrator 1: said the Experts. But the Experts didn't have a clue, much less a cure. Narrator 2: By now, the T.V. news had found out about Camilla. Reporters from every channel were outside her house, telling the story of "The Bizarre Case of the Incredible Changing Kid." Narrator 3: Soon a huge crowd was camped out on the front lawn. Narrator 4: The Creams were swamped with all kinds of remedies from psychologists, allergists, herbalists, nutritionists, psychics, an old medicine man, a guru, and even a veterinarian. Narrator 1: Each so-called cure only added to poor Camilla's strange appearance until it was hard to even recognize her. She sprouted roots and berries and crystals and feathers and a long furry tail. But nothing worked. Narrator 2: One day, a woman who called herself an Environmental Therapist claimed she could cure Camilla. She said, Environmental Therapist: "Close your eyes, breathe deeply, and become one with your room." Camilla: "I wish you hadn't said that," Narrator 3: Camilla groaned. Slowly, she started to melt into the walls of her room. Her bed became her mouth, her nose was a dresser, and two paintings were her eyes. The therapist screamed and ran from the house. Mother: "What are we going to do? It just keeps getting worse and worse!" Narrator 4: cried Mrs. Cream. She began to sob. Narrator 1: At that moment, Mr. Cream heard a quiet little knock at the front door. He opened it, and there stood an old woman who was just as plump and sweet as a strawberry. Old Woman: "Excuse me, but I think I can help." Narrator 2: she said brightly. Narrator 3: She went into Camilla's room and looked around. Old Woman: "My goodness, what we have here is a bad case of the stripes. One of the worst I've ever seen!" Narrator 4: she said with a shake of her head. She pulled a container of small green beans from her bag. She said, Old Woman: "Here. These might do the trick." Mother: "Are those magic beans?" Narrator 1: asked Mrs. Cream. The old woman replied, Old Woman: "Oh my, no, there's no such thing. These are just plain old lima beans. I'll bet you'd like some, wouldn't you?" Narrator 2: she asked Camilla. Camilla wanted a big, heaping plateful of lima beans more than just about anything, but she was still afraid to admit it. She said, Camilla: "Yuck! No one likes lima beans, especially me!" Old Woman: "Oh, dear, I guess I was wrong about you." Narrator 3: said the old woman sadly. She put the beans back in her bag and started toward the door. Narrator 4: Camilla watched the old woman walk away. Those beans would taste so good. And being laughed at for eating them was nothing, compared to what she'd been going through. She finally couldn't stand it. Camilla: "Wait! The truth is...I really love lima beans." Narrator 1: she cried. The old woman smiled, popping a handful of beans into Camilla's mouth, and said, Old Woman: "I thought so." Camilla: "Mmmmmmm," Narrator 2: said Camilla. Suddenly the branches, feathers, and squiggly tails began to disappear.Then the whole room swirled around. When it stopped, there stood Camilla, and everything was back to normal. Camilla: "I'm cured!" Narrator 3: she shouted. The old woman said, Old Woman: "Yes, I knew the real you was in there somewhere." Narrator 4: She patted Camilla on the head and went outside and vanished into the crowd. Narrator 1: Afterward, Camilla wasn't quite the same. Narrator 2: Some of the kids at school said she was weird, but she didn't care a bit. Narrator 3: She ate all the lima beans she wanted, and she never had even a touch of stripes again.Employee: Welcome to ABC. How may I help you? Jessica: Can I take a look at the shoes behind a glass window? Employee: Yay yay yay yay! Of course, of course. Follow me. Employee: You have a good taste! These shoes are the most popular in ABC! Jessica: I really like the style. How much are these? Employee: It is a brand new product! Hot piece of cake right out of an oven! It's 68 dollars Jessica: Oh no! It's too expensive! I only have a few dollars in my pocket. Can I have some discount? Employee: Ohhh no... I'm really sorry sweety. This is the fixed price. Why don't you take a look at the products in the corner? They are all on sale! Jessica: Do you have size 5 for these? Employee: Of course! Try these. Jessica: Ummmm. I think these are too small for me. Can I have 1 size bigger? Employee: size 6? Let me get back to you in a sec. Employee: Let's try these sweetie. How are these? Jessica: Perfect! I love it! I will take these! Employee: How do you like to make your payment? Credit card or cash? Jessica: Cash. Here you are. Employee: Here's your 5 dollars change. Thanks for coming. Have a wonderful day! Jessica: Thank you! I really love the shoes!According to ใใซใใใฐ add to ๅขใใ add up ๅ่จใใ after a while ใใฐใใใใฆ against the idea ใใฎ่ใใซๅๅฏพใใฆ all of a sudden ็ช็ถใซ all the time ใใคใ all through the night ไธๆฉไธญ along with ใใจไธ็ทใซ apply for ใใซ็ณใ่พผใ apply to ใใซ้ฉ็จใใ as a rule ๅๅใจใใฆ aside from ใใฎใปใใซ / ใใ้คใใฆ at any cost ใฉใใช็ ็ฒใๆใฃใฆใ at heart ๅฟใฎๅบใงใฏ at last ใคใใซ at least ๅฐใชใใจใ at length ่ฉณ็ดฐใซ at most ๅคใใฆใ at once ใใใซ / ไธๅบฆใซ at the sight of ใใ่ฆใฆ at times ๆใ
attach to ใใซไปใใ / ใใซ็ตใณใคใใ back up ๆฏๆดใใใใใใฏใขใใใใ based on ใใซๅบใฅใใฆ be absent from ใใๆฌ ๅธญใใฆใใ be against ๅๅฏพใใ be based on ใใซๅบใฅใใฆใใ be confident of ใใซ่ชไฟกใใใ be curious about ใใซๅฅฝๅฅๅฟใๆใค be derived from ใใซ็ฑๆฅใใ be filled with ใใงๆบใใใใฆใใ be full of ใใงใใฃใฑใใงใใ be made up of ใใงๆงๆใใใฆใใ be pleased with ใใซๆบ่ถณใใฆใใ be short of ไธ่ถณใใฆใใ be similar to ใใซไผผใฆใใ because of ใใฎใใใง / ใใฎใใใใง before long ใพใใชใ break out ็ช็บใใ break out in ๏ผๆฅใซ๏ผใใซใชใ break up ่งฃๆฃใใ / ๅฅใใ bring out ๅผใๅบใ / ๅ
ฌ่กจใใ bring up ่ฒใฆใ / ๆใกๅบใ burst into ๆฅใซใใๅงใใ by heart ๆ่จใใฆ by mistake ้้ใใฆ by now ไป้ ใพใงใซใฏ by the way ใจใใใง by way of ใใ้ใใฆ call for ่ฆๆฑใใ / ๅผใณใใใ call out ๅคงๅฃฐใงๅผใถ carry on ็ถใใ carry out ๅฎ่กใใใ่กใ catch up with ใใซ่ฟฝใใคใ close to ใใซ่ฟใ come across ๅถ็ถๅบไผใ / ่ฆใคใใ come into ใใซๅ
ฅใ / ใใซใชใ come out ๅบใฆใใ / ๅ
ฌ่กจใใใ come up with ใใๆใใคใ compared with ใใจๆฏในใฆ depend on ใใซไพๅญใใ do him good ๅฝผใซๅฉ็ใใใใใ drive at ๆๅณใใใ็ใ drop by ็ซใกๅฏใ drop down ่ฝใกใ feel at home ใใคใใ feel like doing ใใใใๆฐๅ feel sorry ๆฐใฎๆฏใซๆใ figure out ็่งฃใใ find fault with ใใซๆๅฅใใคใใ find out ็ฅใใ่งฃๆใใ for fear of ใใๆใใฆ for free ็กๆใง for good ๆฐธ้ ใซใๅฎๅ
จใซ for once ไธๅบฆใ ใ / ไปๅใ ใใฏ for sale ๅฃฒใ็ฉใฎ for the best ๆๅใฎใใใซ get over ไนใ่ถใใ get ready ๆบๅใใ get rid of ใใๅใ้คใ give away ไธใใใๅฏไปใใ give in to ใใซๅฑใใ give off ๆพใค give out ้
ใ / ็บ่กจใใ go ahead ็ถใใฆ่กใ go down ไธใใ / ๆฒใ hand in ๆๅบใใ hand over ๆๆธกใ hang on ๅพ
ใค / ้ ๅผตใ hang up ๅ่ฉฑๅจใ็ฝฎใ hear from ใใใ้ฃ็ตกใใใใ help yourself ่ช็ฑใซๅใ / ่ช็ฑใซใฉใใ hold back ๆงใใ hold on ๅพ
ใค / ๆใกใใใใ hold up ๅๆญขใใใใ้
ใใใ in a jacket ใธใฃใฑใใใ็ใฆ in a word ไธ่จใง่จใใฐ in advance ๅใใฃใฆ in case ใใฎๅ ดๅใซ in common ๅ
ฑ้ใใฆ in detail ่ฉณ็ดฐใซ in hand ๆๅ
ใซ in part ้จๅ็ใซ in place of ใใฎไปฃใใใซ in return ่ฆ่ฟใใซ in terms of ใใฎ่ฆณ็นใใ in the distance ้ ใใซ in the habit of ใใใ็ฟๆ
ฃใใใ in the way ๅฆจใใซใชใฃใฆ instead of ใใฎไปฃใใใซ keep a secret ็งๅฏใๅฎใ keep an eye on ่ฆๅฎใ keep away from ่ฟใฅใใชใใใใซใใ keep on Ving ใใ็ถใใ keep pace with ใใซ้
ใใใซใคใใฆใใ keep the change ใ้ฃใใฏใใใพใใ keep track of ่จ้ฒใใคใใ / ่ฟฝ่ทกใใ keep up with ใใซ้
ใใใซใคใใฆใใ lay it down ใใใ็ฝฎใ / ่ฆๅฎใใ less than ใๆชๆบ / ใใใๅฐใชใ look after ไธ่ฉฑใใใ look back on ใใๆฏใ่ฟใ look down on ใใ่ฆไธใ look like ใใฎใใใซ่ฆใใ look up ่ชฟในใ / ่ฆไธใใ made up of ใใงๆงๆใใใฆใใ major in ใใๅฐๆปใใ make efforts ๅชๅใใ make it out ็่งฃใใ / ๆใ้ใใ make out ่ฆๅใใใใใพใใใ make progress ้ฒๆญฉใใ make sense ็่งฃใงใใใๆๅณใๆใ make up your mind ๆฑบๅฟใใ mind your own business ่ชๅใฎใใจใซ้ไธญใใ move on ๆฌกใซ้ฒใ no longer ใใฏใใใชใ not always ๅฟ
ใใใใใงใชใ nothing but ใใ ใใ ใ on air ๆพ้ไธญ on behalf of ใใไปฃ่กจใใฆ on business ไปไบใง on fire ็ซใใคใใฆใใ on purpose ใใใจ on the point ใใฎ็นใง on time ๆ้้ใใซ one another ใไบใใซ out of the question ๅ้กๅคใง pass by ้ใ้ใใ pay attention ๆณจๆใๆใ play a part in ใใงๅฝนๅฒใๆใใ pour out ๆณจใๅบใใๆบขใๅบใ prefer A to B BใใAใๅฅฝใ put away ็ไปใใ put off ๅปถๆใใ put on ็ใ / ๆผใใใ(weightใงๅคชใ๏ผ put out ๆถใ / ็บ่กจใใ reach for ๆใไผธใฐใ rely on ใใซ้ ผใ result in ใ่ชๅ่ฉใ็ตๆใจใใฆใใซใชใ run it over ใใใใฒใ / ่ชญใฟ่ฟใ run out of ใใไฝฟใๆใใ run over ใฒใใฆใใพใใ่ตฐใๅใ see about ๆ้
ใใ / ่ชฟในใ see off ่ฆ้ใ see through ่ฆๆใ / ่ฆ้ใ set out ๅบ็บใใใๅงใใ set up ่จญ็ฝฎใใ / ่จญๅฎใใ show off ่ชๆ
ขใใใ่ฆใใณใใใ show up ็พใใ / ๅฐ็ใใ sit up ๅบงใใ่ตทใไธใใ speak up ใฏใฃใใ่ฉฑใ stand out ็ฎ็ซใค stand out ็ฎ็ซใค stand up for ใใๆฏๆใใ suffer from ใใซ่ฆใใ take away ๆใกๅปใ / ๅฅชใ take in ็่งฃใใใๅใๅ
ฅใใ take notice of ๆณจๆใๆใ take on ๅผใๅใใ / ๆใ take out ๅใๅบใ / ๆใกๅธฐใ take over ๅผใ็ถใใไนใฃๅใ take part ๅๅ ใใ take place ่ตทใใ / ้ๅฌใใใ take risks ๅฑ้บใๅใ take turns ไบคไปฃใง่กใ talk over ็ธ่ซใใ tear off ๅผใ่ฃใ the second largest ไบ็ช็ฎใซๅคงใใ think better of ่ใ็ดใ throw away ๆจใฆใ try on ่ฉฆ็ใใ turn in ๆๅบใใ turn off ๆถใ / ๅใ turn on ๏ผในใคใใใ๏ผๅ
ฅใใ turn out ็ตๆ็ใซใใซใชใ turn over ใฒใฃใใ่ฟใ under control ๅถๅพกไธใซใใ up to date ๆๆฐใฎ with ease ๅฎนๆใซ with regard to ใใซ้ขใใฆOstinato Music Definition Ostinato (plural โ ostinati or ostinatos) is an Italian word meaning obstinate or persistent and is used in music to describe a musical phrase or rhythm that is repeated persistently. The repeated pattern could be a melody, a figure in the bass โ called a basso ostinato or simply a repeated rhythmic idea. An ostinato may be played for an entire piece of music or just during one section. The key aspect to remember in the definition of an ostinato is that it is a pattern that is repeated persistently in a piece of music. Rhythmic Ostinato A rhythmic ostinato is a rhythmic pattern that is persistently repeated. It will often be played on an untuned percussion instrument (e.g. snare drum, triangle, etc..). However, rhythmic ostinati can also be found in parts played on pitched instruments where the note pitch stays the same or where the pitches change as the phrase is repeated. The key characteristic is that it is the rhythm that is persistently repeated.In Maurice Ravelโs โBoleroโ the use of a rhythmic ostinato brings a magical and almost hypnotic feel to the piece as the percussive pattern contrasts with the sweeping and almost improvisatory nature of the flute melody. Have a look at the pattern below and listen to its use in the audio extract: Rhythmic Ostinato Example from Ravel Bolero.A rhythmic ostinato is an excellent technique that composers use for creating drama and tension. One of the most famous examples of this is from โMarsโ by Gustav Holst. Have a look/listen to the rhythmic pattern: Rhythmic Ostinato Example from Gustav Holst Mars. This rhythmic pattern is played relentlessly throughout the piece and forms the basis for the intense drama associated with the subject โ Mars, the god of war! Have a listen to this extract of the piece performed by the United States Air Force Band:You can hear how the relentless sound of a rhythmic ostinato is extremely effective at building tension as the music around it changes and develops. This effect is heightened in the extract from Mars as the bass note remains on a G throughout the extract and acts as a pedal point. Not surprisingly, rhythmic ostinati are used widely in dramatic film music. Hans Zimmer is a film composer who makes considerable use of this technique across the many film scores he has written. Have a listen to the opening from his theme for the film โPirates of the Caribbeanโ performed by the Auckland Symphony Orchestra:You can hear that there are a number of different ostinati in many of the different parts that are layered to produce the overall sound. Here is the rhythmic ostinato that forms the basis of the melody line: Rhythmic Ostinato Example Hans ZimmerMelodic ostinato A melodic ostinato is a repeated pattern where both the rhythm and the melody form the basis for the repeated pattern. These often occur in the bass part where they are called a basso ostinato. Basso Ostinato A basso ostinato is a repeated pattern in the bass part of a piece. This technique became particularly popular in the 17th century where a number of Baroque dances were based upon ostinati in the bass part. In dances such as the passacaglia the bass remained constant throughout the piece whilst the other parts developed. This technique is called โground bassโ and you can have a look at my lesson on ground bass for some examples of this. The most famous example of a basso ostinato is Pachelbelโs Canon in D. Ostinati Examples in Contemporary Music Rhythmic and melodic ostinatos have had a massive influence on contemporary popular music across a wide range of genres. This can be seen in 2 main ways: Riffs (short melodic phrases) โ these are effectively contemporary expressions of ostinato. Loops โ rhythmic and melodic phrases are repeated to create the characteristic sound of contemporary productions. As a result, you will probably be able to find examples of the use of repeated patterns/ostinati in most contemporary songs. However, there are some songs where the use of an ostinato provides the clear foundation for the song and these are useful examples to listen to. Examples of Ostinati Riffs Seven Nation Army by White Stripes The guitar riff from Seven Nation Army is one of the most famous modern guitar riffs and is used as an ostinato that plays throughout the song. It is an excellent example of a melodic ostinato:Back in Black by AC/DC The opening guitar riff in this song is another great example:Examples of Loops Loops are repeated patterns that are clearly built on the concept of ostinati. They are used widely in contemporary music. Hip hop songs often use loops as the foundation for the track. Still D.R.E by Dr. Dre ft. Snoop Dogg In this song a piano loop plays throughout the whole track and forms the foundation of the song:Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: โข Free-falling objects do not encounter air resistance. โข All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs โข Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 โข a โข d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 โข (-8.00 m/s2) โข d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) โข d (16.0 m/s2) โข d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi โข t + ยฝ โข a โข t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) โข (4.1 s) + ยฝ โข (6.00 m/s2) โข (4.10 s)2 d = (0 m) + ยฝ โข (6.00 m/s2) โข (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: โข An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. โข If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. โข If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. โข If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi โข t + ยฝ โข a โข t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) โข (t) + ยฝ โข (-9.8 m/s2) โข (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) โข (t)2 -8.52 m = (-4.9 m/s2) โข (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 โข a โข d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 โข(-9.8m/s2) โขd 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) โขd (-19.6 m/s2) โข d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) โข d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.Gr''ade 3 Questions based on this chapter: English Alexander was a king of the ancient Greek kingdom of Macedonia. By the age of thirty, he had created one of the largest empires in the world, stretching from Greece to northwestern India. When Alexander was young, a trader brought a horse which was difficult to mount. Let us read about how Alexander tames the horse. One day King Philip bought a fine horse. He was a strong animal and the king paid a high price for him. But he was wild and no man could mount him, or do anything at all with him. This horse is really wild. It cannot be tamed by the royal men. Many have tried and failed. We tried everything possible, your Majesty. We tried to whip him but that only made him worse. Glossary wild rough/harsh mount a horse to climb onto the back of a horse to tame to control whip to beat using a long rope King Philip asked his men to take the horse away. It is a pity to send such a fine horse away. I think the men do not know how to tame him. I can try taming this beautiful horse. Perhaps you can do better than them. But be careful, my son. You are still very young to mount this violent animal. Alexander wanted to (mount/feed/tame/ ride) the horse. If you would give me the order, I will try. I am sure I can manage this horse better than anyone else. Antonym(s) worse x better young x old fail x succeed If I fail, I will pay you the price of the horse, Father. The courtiers told Alexander that it might be dangerous for a young boy to try taming the wild horse. They laughed at him. Alexander went near the horse and turned his head towards the sun. He had noticed that the horse was afraid of his own shadow. I will name you Bucephalus. Stay calm and I will do no harm. The horse was afraid of his own (body/courtiers/King Philip/shadow). English He then spoke gently to the horse. Bucephalus means 'ox-head'โ head of an ox, in Ancient Greek. When he had quietened him a little, he made a quick spring and leapt upon the horse's back. I thought the little prince would be killed by this dangerous animal. What a miracle! The horse has recognized the young prince as his master. Alexander let the horse run. When Bucephalus had become tired of running, Alexander reined him in and rode back to the place where his father was standing. Glossary noticed (here) to see afraid scared/frightened calm quiet gently softly quietened to become calmer and less noisy a miracle a wonder/unusual event to rein to check or guide a horse Look at the young prince! He is mounted well! But the horse is still wild! Antonym(s); laughed x cried afraid x brave. English When he reached the place where his father was standing, he leapt to the ground. His father ran and kissed him. Dear Father! I shall add My son! Macedonia is a small kingdom more territories and bring for you. You must seek a larger kingdom glory to our kingdom. that will be worthy of you. Fascinating Fact(s) Alexandria Bucephalus was a city founded by Alexander in memory of his loyal horse Bucephalus. During Alexander's invasion of India, he had fought against the Indian King, Porus, near the river Hydaspes (modern day river Jhelum, Pakistan). His horse Bucephalus died there and he honoured his horse by naming the city after it. Antonym(s) worthy x unworthy proud x ashamed You have carried me across countries and stood bravely beside me as I fought to win the numerous fierce battles. You have saved my life many times. I am truly proud of you, Bucephalus. (Mesopotamia/Minneapolis/ Macedonia/Minnesota) was a small kingdom for Alexander to rule. Glossary numerous many fierce strong and violent Alexander and Bucephalus were said to be always together, for when one of them was seen, the other was sure to be not far away. Bucephalus would never allow anyone to mount him, but his master. Alexander became the most famous king and warrior, and for that reason, he is called 'Alexander the Great!.