Japan nears economy plan :: essays papers

Japan approaches economy plan TOKYO (Reuters) - Japanese policymakers moved nearer Tuesday to a concurrence on measures to expel two long-standing hindrances to a financial recuperation - banks' sloping awful credits and securities exchange shortcoming. The decision alliance government is relied upon to finish by Wednesday a bundle fixating on steps to assist keeps money with discarding their non-performing credits and an exceptional reserve to assimilate deals of offers held by banks. While the cutoff time was deliberate and authorities have been hesitant to promise it would be met, in question is the believability of political and budgetary pioneers who have been not able to haul the country out of financial doldrums for 10 years. The nation's benchmark Nikkei share value normal, which shot up in excess of 3 percent at one point Tuesday on good faith about the monetary bundle, chances a retreat towards a month ago's 16-year lows if no dependable arrangement is reached. One key purpose of dispute has been whethe r citizens' cash ought to be utilized by a proposed store to purchase shares from banks. The Financial Services Agency (FSA), Japan's budgetary controller, had been hesitant to channel open assets into the body, saying government mediation in the market ought to be as constrained as could reasonably be expected. Be that as it may, an individual from the alliance board examining the issue said the hole was narrowing. The FSA appeared to have inclined nearer toward us, despite the fact that there are still a few contrasts, he told journalists. The alliance has changed the name of the proposed body to a store to obtain banks' shareholdings from a progressively unrefined stock-purchasing reserve, determining that the point was to assist saves money with emptying enormous shareholdings, misfortunes in which are crushing their capital sufficiency proportions and choking loaning. The banks have developed tremendous arrangement of offers in bunch organizations and their customers as a way t o solidify business ties, however the drop in Japanese offer costs in the course of the most recent decade has carried calls to constrain banks' shareholdings. The Nihon Keizai Shimbun money related day by day announced not long ago that  ¥15 trillion, or $119 billion, of assets from the state-upheld banking security net, the Deposit Insurance Corp., could be diverted to the proposed stock-purchasing body. The legislature is booked to hold a gathering of its crisis team on monetary estimates Wednesday morning if understanding can be reached with the decision alliance parties on Tuesday, a LDP official said. Copyright  © 2001, CNN America, INC.

The Quiet American Essay -- Films Movies Vietnam War Essays

The Quiet American The film The Quiet American happens during the 1950’s in Vietnam. The film delineates the environment of Vietnam past to the Vietnam War and during the French control of the nation. The principle plot of the film spins around three characters: Fowler played by Michael Caine, Pyle played by Brendan Fraiser, and Phoung played by Do Thi Hai Yen. For the span of the film the three principle characters are engaged with a semi love triangle. This triangle and the feelings that the male characters feel towards Phoung start to describe the manner in which they feel about the nation of Vietnam itself. Vietnam becomes feminized, untouchable, and sexualized similarly as Phoung does in Pyle and Fowler’s eyes. The way where Fowler and Pyle battle over Phoung speaks to the methodology that Britain and America utilized in their battle to â€Å"save† Vietnam from socialism. Pyle’s’ goals toward Phoung, albeit comparable at times to Fowler’s, contrast extraordinarily simultaneously. The two men see Phoung as a kind of article that should be spared or requires a type of help with request to suffer life. At the point when Pyle begins to look all starry eyed at Phoung upon their first gathering, he concludes that he should do whatever he can or whatever he considers fundamental so as to â€Å"save† Phoung from a modest presence. This is precisely the same way that Pyle sees Vietnam and its current condition. He needs to safeguard Vietnam from what he accepts to be unadulterated shrewdness: socialism. Pyle does this in a...

Helping Kids Cope in a Time of Crisis and Fear

Helping Kids Cope in a Time of Crisis and Fear FutureFit RL RF ? Peruse an article that is intended for parents, but has useful advice for teachers. It details, by age levels, how to explain horrific events to children. Updated on: September 12, 2001 Helping Kids Cope in a Time of Crisis and Fear: Advice for Teachers and Parents by Katy Abel Editor's note: This article was written as a guide for helping children following the attacks of September 11, 2001. However, the content of the article will be useful for teachers and parents following any national or international tragedy. In times of national agony, as we sense our security vanishing in the flames and smoke of unforeseen terrorism and tragedy, many of us wonder whatâ€"and how muchâ€"to say to children. The very sudden and shocking nature of September 11 attack on America makes it all the more essential for Moms, Dads, and teachers to find the right words, and the right way to communicate a message of safety and family security. Here is family therapist Carleton Kendrick’s ages-and-stages advice for how to express thoughts and feelingsâ€"and listen to kids talkâ€"about what’s happened. Preschoolers: Limit Media Exposure During the Persian Gulf War and following the bombing of the Oklahoma federal building, many preschool teachers observed young children reenacting scenes from television news broadcasts in their classroom play. But while children may mimic scenes of tragedy, they lack the cognitive ability to fully comprehend what they see. Scenes of carnage may seem cartoon-like to some, truly terrifying to others. “Preschoolers are basically going to be mirroring what they hear and see around them,” observes Kendrick. “My strong suggestion is to keep preschoolers away from television images of what’s happened in New York and Washington.” Kendrick advises parents to share their own feelings with preschoolers on a “need-to-know” basis. No four-year-old can understand a terrorist plot, but she may think it’s her fault if Mom is upset and it’s unclear why. A simple explanation (“I’m sad because some people were hurt in an accident today”) may be all that’s needed. Other suggestions: Maintain the family schedule as much as possible. This is a time when a sit-down dinner and a bedtime story can signal young children that while big buildings are falling down, the family structure remains intact. oung elementary school students will get information about what’s happened from their peers, if no one else. “Just as you don’t want them to have knowledge of sex from the playground, so too you don’t want them to rely on their friends for information about these attacks,” cautions Kendrick. “You the parent have to filter the horror and the tragedy and somehow make it understandable and not paralyzing.” Since children this age are going to wonder first and foremost about their own physical safety, Kendrick suggests accenting the positive. “I’d say, ‘We’re going to be a lot safer now,’” Kendrick advises. “Tell kids that we’ve learned from this that we have to have better plans to protect buildings and planes. This is important reassurance because children may have fears about their parents flying off on a business trip, or the family’s upcoming visit to Grandma’s for the holidays.” ou can certainly initiate a conversation, but always with, ‘What have you heard?’ That tips you off to what kids bring to the table.” Children are also old enough by fourth grade to express their own feelings and hear about the full range of their parents’ emotions. At the same time, they still need reassurance that their parents are powerful caretakers who can protect them. “’I’m looking out for you as best I can, taking care of you and voting for leaders who will take care of our country,’” is one way to express a desire to protect a child from harm. Grade 7 and Up: Identity and Security Parents can expect many pre-teens and teens to feel a heightened sense of anxiety in the wake of Tuesday’s attacks, Kendrick believes. The current climate of uncertainty and fear mirrors the emotions that many teens are experiencing in their personal lives. “The adolescent needs a safe harbor to retreat to after going out and testing the limits,” Kendrick notes. “But now it appears to them that somebody’s gone out and blown up the harbor. So with teens it’s all the more important that you reinforce whatever you can about your family being the real safe harbor, even if there are choppy seas in the distance. This is a good time to tap into the strength of “we,” so they know they are not floundering out there.” Teens and even younger children will take comfort in hearing about the good deeds and heroics that always accompany human tragedy. Share accounts of successful rescues, and tell children about the many Americans who are lining up to donate blood. Children will also feel better when they themselves are given a chance “to do something.” Help children write condolence letters to the victims’ families, plant a tree or bush to honor their memory, or visit a local church to light a candle and say a prayer for comfort and peace. FamilyEducation

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Essay on Roosevelt and Hoover DBQ - 1428 Words

Roosevelt and Hoover DBQ The Great Depression quickly altered Americas view of liberalism and therefore, Roosevelt can be considered a liberal and Hoover a conservative, despite the fact that they did occasionally support very similar policies. The United States experienced political shifts during the Great Depression, which are described by Arthur Schlesinger’s analysis of eras in which public objectives were placed before personal concerns. It seems that the public view of what constitutes as liberal beliefs versus what is thought to be conservative beliefs shifts in a similar way. Laissez-faire ideas were considered liberal during the 1920s, but the coming of the Great Depression in 1929 altered the American view of liberalism.†¦show more content†¦The Second Industrial Revolution was ushered in with the invention of the production line. This made it possible for businessmen, such as Henry Ford, to prosper. Automobiles and a variety of other useful electrical appliances became accessible to the masses. The United States had become more success and this instilled a new confidence in the American people, which caused people to support the liberal policies of the 1920s. Hoover was beginning to demonstrate conservative beliefs even before the onset of the Great Depression. Document A shows Hoover’s wish to avoid being thought of as a complete supporter of laissez-faire ideas. He appeared irresolute when it came to preserving the capitalistic society of the 1920s. During this time, society was managed by corrupt political bosses, such as Tweed. The American economy had flourished under the private interest policies of Harding and Coolidge, which forced Hoover to promise the American people that he would not abandon the laissez-faire economics, which had been so successful during past presidencies. Hoover was sure, however, that working class Americans would not be opposed to restricting unfair business practices. Documents B an d C depict Hoover’s lack of support for private interest or public purpose policies. In these documents, Hoover stresses the significance of individual interestsShow MoreRelatedEssay on APUSH DBQ- Hoover vs. Roosevelt774 Words   |  4 Pagesï » ¿DBQ #3 President Franklin D. Roosevelt, the thirty-second president of the United States, was a central figure for the United States in the 20th Century. While leading his country out of The Great Depression, he also led the nation through World War II. Herbert Hoover, the thirty-first President, led the country during the Great Depression and his policies enforced at that time eventually led to his downfall because of their inability to end the downward economic spiral. Both of these PresidentsRead MoreSummary : Great Depression 1445 Words   |  6 PagesPhillip Durgin March 10th, 2016 G Block History Great Depression DBQ As â€Å"prosperity s decade† came to a symbolically harsh and sudden end on Thursday, October 24, 1929, the United States government, led by President Herbert Hoover, was thrown into the unknown. No such downturn had ever presented itself before, which compounded itself with the lack of economic understanding present at the time. Yet it had seemed that the economy was healthy before the crash. Employment was high and inflation wasRead MoreThe New Deal: DBQ1337 Words   |  6 PagesDBQ In 1929, the United States Stock Market crashed, heralding the tumble into world-wide depression. President Hoover tried to pacify the people by telling them it was temporary and would pass over. But a new figure rose out of the people, promising he would do anything and everything he could to restore their lives. In 1932, Franklin D. Roosevelt was elected to the presidency, and his new policies would soon sweep over the country. Roosevelts responses to the problems of the Great DepressionRead MoreApush Dbqs Essay2248 Words   |  9 Pages2011 DBQ: (Form A) 1. Analyze the international and domestic challenges the United States faced between 1968 and 1974, and evaluate how President Richard Nixon’s administration responded to them. (Form B) 1. Explain the ways that participation in political campaigns and elections in the United States changed between 1815 and 1840, and analyze forces and events that led to these changes. 2010 DBQ: (Form A) 1. In what ways did ideas and values held by Puritans influence the political

Lamb The Gospel According to Biff, Christ’s Childhood Pal Chapter 2 Free Essays

Chapter 2 The angel wants me to convey more of Joshua’s grace. Grace? I’m trying to write about a six-year-old, for Christ’s sakes, how much grace could he have? It’s not like Joshua walked around professing that he was the Son of God every day of the week. He was a pretty normal kid, for the most part. We will write a custom essay sample on Lamb: The Gospel According to Biff, Christ’s Childhood Pal Chapter 2 or any similar topic only for you Order Now There was the trick he did with the lizards, and once we found a dead meadowlark and he brought it back to life, and there was the time, when we were eight, when he healed his brother Judah’s fractured skull after a game of â€Å"stone the adulteress† got out of hand. (Judah could never get the knack of being an adulteress. He’d stand there stiff as Lot’s wife. You can’t do that. An adulteress has to be wily and nimble-footed.) The miracles Joshua performed were small and quiet, as miracles tend to be, once you get used to them. But trouble came from the miracles that happened around him, without his volition, as it were. Bread and serpents come to mind. It was a few days before the Passover feast, and many of the families of Nazareth were not making the pilgrimage to Jerusalem that year. There had been little rain through our winter season, so it was going to be a hard year. Many farmers could not afford the time away from their fields to travel to and from the holy city. My father and Joshua’s were both working in Sepphoris, and the Romans wouldn’t give them time off work beyond the actual feast days. My mother had been making the unleavened bread when I came in from playing in the square. She held a dozen sheets of the flatbread before her and she looked as if she was going to dash it to the floor any second. â€Å"Biff, where is your friend Joshua?† My little brothers grinned at me from behind her skirts. â€Å"At home, I suppose. I just left him.† â€Å"What have you boys been doing?† â€Å"Nothing.† I tried to remember if I had done anything that should make her this angry, but nothing came to mind. It was a rare day and I’d made no trouble. Both my little brothers were unscathed as far as I knew. â€Å"What have you done to cause this?† She held out a sheet of the flatbread, and there, in crispy brown relief on the golden crust, was the image of my friend Joshua’s face. She snatched up another sheet of bread, and there, again, was my friend Josh. Graven images – big sin. Josh was smiling. Mother frowned on smiling. â€Å"Well? Do I need to go to Joshua’s house and ask his poor, insane mother?† â€Å"I did this. I put Joshua’s face on the bread.† I just hoped that she didn’t ask me how I had done it. â€Å"Your father will punish you when he comes home this evening. Now go, get out of here.† I could hear my little brother’s giggling as I slunk out the door, but once outside, things worsened. Women were coming away from their baking stones, and each held a sheet of unleavened bread, and each was muttering some variation of â€Å"Hey, there’s a kid on my bread.† I ran to Joshua’s house and stormed in without knocking. Joshua and his brothers were at the table eating. Mary was nursing Joshua’s newest little sister, Miriam. â€Å"You are in big trouble,† I whispered in Josh’s ear with enough force to blow out an eardrum. Joshua held up the flatbread he was eating and grinned, just like the face on his bread. â€Å"It’s a miracle.† â€Å"Tastes good too,† said James, crunching a corner off of his brother’s head. â€Å"It’s all over town, Joshua. Not just your house. Everyone’s bread has your face on it.† â€Å"He is truly the Son of God,† Mary said with a beatific smile. â€Å"Oh, jeez, Mother,† James said. â€Å"Yeah, jeez Mom,† said Judah. â€Å"His mug is all over the Passover feast. We have to do something.† They didn’t seem to get the gravity of the situation. I was already in trouble, and my mother didn’t even suspect anything supernatural. â€Å"We have to cut your hair.† â€Å"What?† â€Å"We cannot cut his hair,† Mary said. She had always let Joshua wear his hair long, like an Essene, saying that he was a Nazarite like Samson. It was just another reason why many of the townspeople thought her mad. The rest of us wore our hair cut short, like the Greeks who had ruled our country since the time of Alexander, and the Romans after them. â€Å"If we cut his hair he looks like the rest of us. We can say it’s someone else on the bread.† â€Å"Moses,† Mary said. â€Å"Young Moses.† â€Å"Yes!† â€Å"I’ll get a knife.† â€Å"James, Judah, come with me,† I said. â€Å"We have to tell the town that the face of Moses has come to visit us for the Passover feast.† Mary pulled Miriam from her breast, bent, and kissed me on the forehead. â€Å"You are a good friend, Biff.† I almost melted in my sandals, but I caught Joshua frowning at me. â€Å"It’s not the truth,† he said. â€Å"It will keep the Pharisees from judging you.† â€Å"I’m not afraid of them,† said the nine-year-old. â€Å"I didn’t do this to the bread.† â€Å"Then why take the blame and the punishment for it?† â€Å"I don’t know, seems like I should, doesn’t it?† â€Å"Sit still so your mother can cut your hair.† I dashed out the door, Judah and James on my heels, the three of us bleating like spring lambs. â€Å"Behold! Moses has put his face on the bread for Passover! Behold!† Miracles. She kissed me. Holy Moses on a matzo! She kissed me. The miracle of the serpent? It was an omen, in a way, although I can only say that because of what happened between Joshua and the Pharisees later on. At the time, Joshua thought it was the fulfillment of a prophecy, or that’s how we tried to sell it to his mother and father. It was late summer and we were playing in a wheat field outside of town when Joshua found the nest of vipers. â€Å"A nest of vipers,† Joshua shouted. The wheat was so tall I couldn’t see where he was calling from. â€Å"A pox on your family,† I replied. â€Å"No, there’s a nest of vipers over here. Really.† â€Å"Oh, I thought you were taunting me. Sorry, a pox off of your family.† â€Å"Come, see.† I crashed through the wheat to find Joshua standing by a pile of stones a farmer had used to mark the boundary of his field. I screamed and backpedaled so quickly that I lost my balance and fell. A knot of snakes writhed at Joshua’s feet, skating over his sandals and wrapping themselves around his ankles. â€Å"Joshua, get away from there.† â€Å"They won’t hurt me. It says so in Isaiah.† â€Å"Just in case they haven’t read the Prophets†¦Ã¢â‚¬  Joshua stepped aside, sending the snakes scattering, and there, behind him, was the biggest cobra I had ever seen. It reared up until it was taller than my friend, spreading a hood like a cloak. â€Å"Run, Joshua.† He smiled. â€Å"I’m going to call her Sarah, after Abraham’s wife. These are her children.† â€Å"No kidding? Say good-bye now, Josh.† â€Å"I want to show Mother. She loves prophecy.† With that, he was off toward the village, the giant serpent following him like a shadow. The baby snakes stayed in the nest and I backed slowly away before running after my friend. I once brought a frog home, hoping to keep him as a pet. Not a large frog, a one-handed frog, quiet and well mannered. My mother made me release him, then cleanse myself in the immersion pool (the mikveh) at the synagogue. Still she wouldn’t let me in the house until after sunset because I was unclean. Joshua led a fourteen-foot-long cobra into his house and his mother squealed with joy. My mother never squealed. Mary slung the baby to her hip, kneeled in front of her son, and quoted Isaiah: â€Å"‘The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them. And the cow and the bear shall feed; their young ones shall lie down together: and the lion shall eat straw like the ox. And the sucking child shall play on the hole of the asp, and the weaned child shall put his hand on the cockatrice’s den.'† James, Judah, and Elizabeth cowered in the corner, too frightened to cry. I stood outside the doorway watching. The snake swayed behind Joshua as if preparing to strike. â€Å"Her name is Sarah.† â€Å"They were cobras, not asps,† I said. â€Å"A whole pile of cobras.† â€Å"Can we keep her?† Joshua asked. â€Å"I’ll catch rats for her, and make a bed for her next to Elizabeth’s.† â€Å"Definitely not asps. I’d know an asp if I saw one. Probably not a cockatrice either. I’d say a cobra.† (Actually, I didn’t know an asp from a hole in the ground.) â€Å"Shush, Biff,† Mary said. My heart broke with the harshness in my love’s voice. Just then Joseph rounded the corner and went through the door before I could catch him. No worry, he was back outside in an instant. â€Å"Jumpin’ Jehoshaphat!† I checked to see if Joseph’s heart had failed, having quickly decided that once Mary and I were married the snake would have to go, or at least sleep outside, but the burly carpenter seemed only shaken, and a little dusty from his backward dive through the door. â€Å"Not an asp, right?† I asked. â€Å"Asps are made small to fit the breasts of Egyptian queens, right?† Joseph ignored me. â€Å"Back away slowly, son. I’ll get a knife from my workshop.† â€Å"She won’t hurt us,† Joshua said. â€Å"Her name is Sarah. She’s from Isaiah.† â€Å"It is in the prophecy, Joseph,† Mary said. I could see Joseph searching his memory for the passage. Although only a layman, he knew his scripture as well as anyone. â€Å"I don’t remember the part about Sarah.† â€Å"I don’t think it’s prophecy,† I offered. â€Å"It says asps, and that is definitely not an asp. I’d say she’s going to bite Joshua’s ass off if you don’t grab her, Joseph.† (A guy has to try.) â€Å"Can I keep her?† Joshua asked. Joseph had regained his composure by now. Evidently, once you accept that your wife slept with God, extraordinary events seem sort of commonplace. â€Å"Take her back where you found her, Joshua, the prophecy has been fulfilled now.† â€Å"But I want to keep her.† â€Å"No, Joshua.† â€Å"You’re not the boss of me.† I suspected that Joseph had heard that before. â€Å"Just so,† he said, â€Å"please take Sarah back where you found her.† Joshua stormed out of the house, his snake following close behind. Joseph and I gave them a wide berth. â€Å"Try not to let anyone see you,† Joseph said. â€Å"They won’t understand.† He was right, of course. On our way out of the village we ran into a gang of older boys, led by Jakan, the son of Iban the Pharisee. They did not understand. There were perhaps a dozen Pharisees in Nazareth: learned men, working-class teachers, who spent much of their time at the synagogue debating the Law. They were often hired as judges and scribes, and this gave them great influence over the people of the village. So much influence, in fact, that the Romans often used them as mouthpieces to our people. With influence comes power, with power, abuse. Jakan was only the son of a Pharisee. He was only two years older than Joshua and me, but he was well on his way to mastering cruelty. If there is a single joy in having everyone you have ever known two thousand years dead, it is that Jakan is one of them. May his fat crackle in the fires of hell for eternity! Joshua taught us that we should not hate – a lesson that I was never able to master, along with geometry. Blame Jakan for the former, Euclid for the latter. Joshua ran behind the houses and shops of the village, the snake behind him by ten steps, and me behind her ten steps more. As he rounded the corner by the smith’s shop, Joshua ran into Jakan, knocking him to the ground. â€Å"You idiot!† Jakan shouted, rising and dusting himself off. His three friends laughed and he spun on them like an angry tiger. â€Å"This one needs to have his face washed in dung. Hold him.† The boys turned their focus on Joshua, two grabbing his arms while the third punched him in the stomach. Jakan turned to look for a pile to rub Joshua’s face in. Sarah slithered around the corner and reared up behind Joshua, spreading her glorious hood wide above our heads. â€Å"Hey,† I called as I rounded the corner. â€Å"You guys think this is an asp?† My fear of the snake had changed into a sort of wary affection. She seemed to be smiling. I know I was. Sarah swayed from side to side like a wheat stalk in the wind. The boys dropped Joshua’s arms and ran to Jakan, who had turned and slowly backed away. â€Å"Joshua was talking about asps,† I continued, â€Å"but I’d have to say that this here is a cobra.† Joshua was bent over, still trying to catch his breath, but he looked back at me and grinned. â€Å"Of course, I’m not the son of a Pharisee, but – â€Å" â€Å"He’s in league with the serpent!† Jakan screamed. â€Å"He consorts with demons!† â€Å"Demons!† the other boys shouted, trying to crowd behind their fat friend. â€Å"I will tell my father of this and you’ll be stoned.† A voice from behind Jakan said, â€Å"What is all this shouting?† And a sweet voice it was. She came out of the house by the smith’s shop. Her skin shone like copper and she had the light blue eyes of the northern desert people. Wisps of reddish-brown hair showed at the edges of her purple shawl. She couldn’t have been more than nine or ten, but there was something very old in her eyes. I stopped breathing when I saw her. Jakan puffed up like a toad. â€Å"Stay back. These two are consorting with a demon. I will tell the elders and they will be judged.† She spit at his feet. I had never seen a girl spit before. It was charming. â€Å"It looks like a cobra to me.† â€Å"See there, I told you.† She walked up to Sarah as if she were approaching a fig tree looking for fruit, not a hint of fear, only interest. â€Å"You think this is a demon?† she said, without looking back at Jakan. â€Å"Won’t you be embarrassed when the elders find that you mistook a common snake of the field for a demon?† â€Å"It is a demon.† The girl reached her hand up, and the snake made as if to strike, then lowered its head until its forked tongue was brushing the girl’s fingers. â€Å"This is definitely a cobra, little boy. And these two were probably leading it back to the fields where it would help the farmers by eating rats.† â€Å"Yep, that’s what we were doing,† I said. â€Å"Absolutely,† Joshua said. The girl turned to Jakan and his friends. â€Å"A demon?† Jakan stomped like an angry donkey. â€Å"You are in league with them.† â€Å"Don’t be silly, my family has only just arrived from Magdala, I’ve never seen these two before, but it’s obvious what they were doing. We do it all the time in Magdala. But then, this is a backwater village.† â€Å"We do it here too,† Jakan said. â€Å"I was – well – these two make trouble.† â€Å"Trouble,† his friends said. â€Å"Why don’t we let them get on with what they were doing.† Jakan, his eyes bouncing from the girl to the snake to the girl again, began to lead his friends away. â€Å"I will deal with you two another time.† As soon as they were around the corner, the girl jumped back from the snake and ran toward the door of her house. â€Å"Wait,† Joshua called. â€Å"I have to go.† â€Å"What is your name?† â€Å"I’m Mary of Magdala, daughter of Isaac,† she said. â€Å"Call me Maggie.† â€Å"Come with us, Maggie.† â€Å"I can’t, I have to go.† â€Å"Why?† â€Å"Because I’ve peed myself.† She disappeared through the door. Miracles. Once we were back in the wheat field Sarah headed for her den. We watched from a distance as she slid down the hole. â€Å"Josh. How did you do that?† â€Å"I have no idea.† â€Å"Is this kind of thing going to keep happening?† â€Å"Probably.† â€Å"We are going to get into a lot of trouble, aren’t we?† â€Å"What am I, a prophet?† â€Å"I asked you first.† Joshua stared into the sky like a man in a trance. â€Å"Did you see her? She’s afraid of nothing.† â€Å"She’s a giant snake, what’s to be afraid of?† Joshua frowned. â€Å"Don’t pretend to be simple, Biff. We were saved by a serpent and a girl, I don’t know what to think about that.† â€Å"Why think about it at all? It just happened.† â€Å"Nothing happens but by God’s will,† Joshua said. â€Å"It doesn’t fit with the testament of Moses.† â€Å"Maybe it’s a new testament,† I said. â€Å"You aren’t pretending, are you?† Joshua said. â€Å"You really are simple.† â€Å"I think she likes you better than she likes me,† I said. â€Å"The snake?† â€Å"Right, I’m the simple one.† I don’t know if now, having lived and died the life of a man, I can write about little-boy love, but remembering it now, it seems the cleanest pain I’ve known. Love without desire, or conditions, or limits – a pure and radiant glow in the heart that could make me giddy and sad and glorious all at once. Where does it go? Why, in all their experiments, did the Magi never try to capture that purity in a bottle? Perhaps they couldn’t. Perhaps it is lost to us when we become sexual creatures, and no magic can bring it back. Perhaps I only remember it because I spent so long trying to understand the love that Joshua felt for everyone. In the East they taught us that all suffering comes from desire, and that rough beast would stalk me through my life, but on that afternoon, and for a time after, I touched grace. At night I would lie awake, listening to my brothers’ breathing against the silence of the house, and in my mind’s eye I could see her eyes like blue fire in the dark. Exquisite torture. I wonder now if Joshua didn’t make her whole life like that. Maggie, she was the strongest of us all. After the miracle of the serpent, Joshua and I made up excuses to pass by the smith’s shop where we might run into Maggie. Every morning we would rise early and go to Joseph, volunteering to run to the smith for some nails or the repair of a tool. Poor Joseph took this as enthusiasm for carpentry. â€Å"Would you boys like to come to Sepphoris with me tomorrow?† Joseph asked us one day when we were badgering him about fetching nails. â€Å"Biff, would your father let you start learning the work of a carpenter?† I was mortified. At ten a boy was expected to start learning his father’s trade, but that was a year away – forever when you’re nine. â€Å"I?CI am still thinking about what I will do when I grow up,† I said. My own father had made a similar offer to Joshua the day before. â€Å"So you won’t become a stonecutter?† â€Å"I was thinking about becoming the village idiot, if my father will allow it.† â€Å"He has a God-given talent,† Joshua said. â€Å"I’ve been talking to Bartholomew the idiot,† I said. â€Å"He’s going to teach me to fling my own dung and run headlong into walls.† Joseph scowled at me. â€Å"Perhaps you two are yet too young. Next year.† â€Å"Yes,† Joshua said, â€Å"next year. May we go now, Joseph? Biff is meeting Bartholomew for his lesson.† Joseph nodded and we were off before he inflicted more kindness upon us. We actually had befriended Bartholomew, the village idiot. He was foul and drooled a lot, but he was large, and offered some protection against Jakan and his bullies. Bart also spent most of his time begging near the town square, where the women came to fetch water from the well. From time to time we caught a glimpse of Maggie as she passed, a water jar balanced on her head. â€Å"You know, we are going to have to start working soon,† Joshua said. â€Å"I won’t see you, once I’m working with my father.† â€Å"Joshua, look around you, do you see any trees?† â€Å"No.† â€Å"And the trees we do have, olive trees – twisted, gnarly, knotty things, right?† â€Å"Right.† â€Å"But you’re going to be a carpenter like your father?† â€Å"There’s a chance of it.† â€Å"One word, Josh: rocks.† â€Å"Rocks?† â€Å"Look around. Rocks as far as the eye can see. Galilee is nothing but rocks, dirt, and more rocks. Be a stonemason like me and my father. We can build cities for the Romans.† â€Å"Actually, I was thinking about saving mankind.† â€Å"Forget that nonsense, Josh. Rocks, I tell you.† How to cite Lamb: The Gospel According to Biff, Christ’s Childhood Pal Chapter 2, Essay examples

Take Care by Drake free essay sample

Take Careof this album. It was a chilly Novemburr afternoon when I heard Drake’s â€Å"Headlines† on the radio. It made me want to nod my head along and rap like a G and I knew right away that I wanted to hear the entire album. Famous rapper and Canadian hit-show actor? Yes. Native Canadian, Aubrey Graham’s rise to fame was on a TV show called Degrassi. Aubrey played a quadriplegic basketball player who was very popular and learned how to solve typical, everyday, teenage problems throughout the course of an episode. His role ended in 2009 where he went on to pursue his rapping career. Drake’s first few songs like,â€Å"Best I Ever Had† and, â€Å"Successful† were instant hits. â€Å"Sweatpants, hair tied, chillin’ with no makeup on, that’s when you the prettiest I hope that you don’t take it wrong† is a very popular line and made him famous with the ladies. We will write a custom essay sample on Take Care by Drake or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The tracks on Take Care all had a couple of themes in common like, his failures in love and his fears of living an unhappy life. In his song â€Å"Look What You’ve Done†, it features a voicemail from his grandmother at the end of the song. In â€Å"Shot For Me†, he is talking about how his ex-girlfriend left him and he says to her, â€Å"Girl I can’t lie, I miss you. You and music were the only things that I commit to.† I bet she’s really regretting that decision! Ha-ha. My overall opinion of this album is A-plus-plus. Although I wouldn’t play it at a party to dance along to, I would recommend it for having a chill night with your Bros. It’s full of introspection and some smooth beats perfect for a late night. Take Care by Drake free essay sample Rap. Hip hop. They have long been associated with demeaning of women, promotion of drugs, alcohol, crude language, and arrogancy. These views were challenged by a 25 year old from Toronto named Aubrey Graham, better known by his middle name: Drake. His new album, Take Care, not only is not filled with hate and arrogance, but is filled with powerful messages hidden in the lyrics of his music. The albums opening track, Over My Dead Body, is one of my favorites. He does use profane language, but he also appeals to the pain of being an underdog. In the song, he talks about how he had someone great, and then she was taken away by something. The song says that the girl is okay and everyone else but Drake is okay because these kids wear crowns, meaning they are the top crowd, the popular kids, the ones with power. Another significant track on the album is the albums namesake, Take Care featuring Rihanna. We will write a custom essay sample on Take Care by Drake or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page In this song, Drake talks about a girl who he has known, and who he feels very strongly for, but is having difficulty with. He wants to be with her, but she pushing me away so I give her space, feeling with a heart that I didnt break. What hes saying is he would do whatever to please this girl, and he will use all his efforts to make that happen. Now how is that not beautiful? Its rap, it has swears in it, but it is filled with emotion, love, and struggle. In the song, Marvins Room, he talks about missing a past love. He says he is drunk, and even though she has a new man, he calls her and tells her how he feels, and that Im just saying you could do better. Tell me have you heard that lately? He talks about the struggles of fame and women. When you have fame you tend to abuse women, but Drake doesnt realize hes doing this before he is in very deep, and he wants his old life, his old girl. Doesnt everyone think like that once in a while? Doesnt everyone feel the rush of time? Doesnt that make people scared, and make them act out? Drake expresses themes that the young person who is coming of age deals with everyday. This album is by far, the best released in 2011, and the best Drake has ever done.

Monster of a Headache free essay sample

I have a loud-mouthed green monster inside my head. He has been my ever-present companion for five years, and I have, as is human nature, grown accustomed to him. We fight nearly every day; he is greedy for my energy and clear thinking, and he uses every drop of power he has to drain them out of me. But he, my monster of a headache – the searing, arrow-sharp, deafening pain-bringer – is not all that I am. Not anymore. His creation was not unlike that of the universe: he came into being with a bang, a concussion. He was just a baby then, but as time passed and I had seven more concussions, he became full-grown. In his prime, he had the power to dictate my every move – or lack thereof. He had my academics and social life firmly in his grip, and he slowly tore them to pieces; I struggled to grasp the pieces of my life and put them back together. We will write a custom essay sample on Monster of a Headache or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page My headache was my captor, my abuser, and worst of all, part of me. I spent too many days in darkness, in bed, watching the blending forms, geometric patterns, and bold flashes of color that were my monster’s boot prints behind my eyelids. The headaches crippled me physically and emotionally. I had no sense of balance, or even muscle memory to walk; my thoughts were catastrophic and my feelings hopeless. I almost let my life slip away to an eternity in bed. However, one day I remembered that I have dreams, dreams that consist of more than darkness and a duvet. Thoughts of flower shops and freshly baked bread were oxygen for a small flame inside me, and they ignited a fire that cannot be extinguished by any amount of pounding, squeezing, or crushing. I will never forget the feeling in my stomach – of nervousness, strength, and extreme pride – when I decided to conquer my monster. I knew that for my life to have direction or purpose, I had to stand up, literally, and take back what my monster had so viciously usurped. The idea of a battle for power was daunting, and I felt wildly unsure that I would come out on top. I started the fight regardless, slowly and deliberately. Doctors and countless appointments helped me to forge weapons to use in my battle against my monster. Each day I practiced focusing on my breathing and relaxing my muscles, and with the slow, measured beating of my heart and a full sense of peace in myself, I pushed my monster to the edges of my skull. I found the will to fight day after day, brandishing my headache-shrinking mind power and breathing techniques. The fire in me burned brighter each day, and I found that having faith in myself was one of my most powerful weapons. I don’t regret that a monster moved into my head. I have learned priceless lessons from my struggle, lessons that have shaped me and will guide me for the rest of my life. I learned to have nearly infinite patience for myself and others, and that problems can’t be solved by being ignored. Most importantly, I learned through battling a headache every day that I am the only one who can take charge of my life. I am responsible for creating my own success. Though the monster is still a tenant in my head, he doesn’t define or rule me anymore.

American Industry essays

American Industry essays The Industrial Giant Known as America Many factors led to America having a tremendous rise in industry. The five points that made the most impact were technology, mass distribution and production, education, railroads, management ideas and structure, and immigrant labor. These five points not only improved the existing industry, but they revolutionized how the American industry would be run for the next generation. As with any change in an existing system, there were a few problems, the main problems where with workers so management just replaced them with machines. Many people werent ready to make the adjustment from small town farming to big city living but the benefits far out-weighed any unusual situations, so the people and the nation when along with it. In the 1850s and on, most Americans were wondering about the benefit of a society dominated by cities, factories, and masses of wage earners. Along with cities and factories, pollution, and unhygienic situations was rising as well. Industrializing of the nation was wanted by many people but on the other hand, many people did not want to see the nation industrialize. The United States, at this point, mostly an agricultural society, and most of the people lived on farms or in small towns, and had lots of open space to live in. These caused a slowing of the United States transforming into a industrial nation. Depression set and there was unrest in the work force. This began to change in the 1870s when the Populist Party gained a strong foothold. In 1897, the economic depression finally came to an end. In 1910, the United States firming planted itself as the worlds Probably the most important feature aiding the nations growth was technology. Two major inventions during this period were the invention of the gasoline-powered, internal combustion engine and harnessing of electric power. H ...

Pollocks Revolutionary Transgressions Essay Example | Topics and Well Written Essays - 500 words

Pollocks Revolutionary Transgressions - Essay Example The essay "Pollock’s Revolutionary Transgressions" discusses what were Pollock's break throughs and innovations in Painting in relation to the painting of his time. The painter was very active in his painting, making observers appreciate the energy involved in the visual pieces as well as the idea of the oneness and physical interaction between the artist and his art. Harold Rosenberg, the art critique who coined action painting, remarked that Pollock’s work led to a movement wherein the canvas began to appear as an arena in which to act rather than as a space in which to reproduce, redesign, analyze or express an object. This is the reason why Pollock is credited to have influenced several modern abstract painters. One of those that benefited from Pollock’s innovation was Willem de Kooning, who explained that the painter broke the ice in abstract expressionism (Hess 7). Like Pollock, de Kooning became known for painting through gestures and actions. De Kooningâ €™s style, however, is different from that of Pollock’s since he is considered to be more conservative in his techniques and in his materials. For instance, he primarily used oil in his artworks and did not experiment on resins like Pollock. Pollock’s influence can best be identified when one examines de Kooning’s masterpieces in the context of the fact that they were created through a deliberate modification of artistic procedures. Another important painter that considers Pollock as an inspiration and major influence is Helen Frankenthaler.

FREQUENCY DISTRIBUTIONS Assignment Example | Topics and Well Written Essays - 750 words

FREQUENCY DISTRIBUTIONS - Assignment Example The average minutes that I use in physical fitness training, every day, is equal to 50.8. The figure is from data collected for duration of 10 days. The list number of minutes spent on physical fitness training is 38 minutes and the highest number of minutes is 60. The standard deviation is the square root of the variance. The standard deviation of the above data is 9.33 meaning that, on average, every value of the collected data is far from the mean by 9.33 units. Data falling within the range include 60,60,38,38,58,58,58,41,41,56, meaning that 100 percent of the sample is within the range. For normally distributed data, only 5 percent of the value should fall outside the above range. Therefore, the above data is normally distributed. Additionally, the data does not have any outlets, which reflects the fact that it is normally distributed. A curve for a normally distributed data is bell shaped and symmetric, meaning that the data has an equal spread on both sides of the curve (William, 2003). The data is also continuous on both sides of the bell shape. Comparing normally distributed data and non-normal data, the estimates from normal data are more accurate compared to estimates from data that is not normally distributed (Bryc, 2013). When defining normally distributed data, one must specify two quantities, including the mean ( µ) and the standard deviation (ÏÆ').which reflects the spread of the curve. Different values of the mean and standard deviation yield different normal curves thus different normal distributions. Besides the 95 percent test, 99.7 percent test is also applicable while determining if data is normally distributed. 99.7 percent of all the values should fall within three standard deviations from the mean. In other words, they should fall between  µ-3ÏÆ' and  µ+3ÏÆ' (Berman, 2013). More than 99.7% of the data fall within the range reflecting the fact that the data has a normal distribution. One of it implications

Impact of Conflict on Human Capital Development

Impact of Conflict on Human Capital Development Living Amid Conflict and its Implications to Human Capital Development By Alexander Ken P. Libranza Introduction The adverse effects of the outbreak and recurrence of conflict can be dangerous because of its long-term economic implications that may force a country into a vicious cycle of low human capital development and conflict (Kim et al, 2010). A common stand among recent literature suggests that conflict destroys the process of accumulating physical and human capital, which deteriorates the labor force and in turn affects institutional capacity (Justino, 2011; Nkurunziza, 2008; Serneels et al, 2010). Most researches on civil wars and armed conflict has been focused on the macro-level of analysis, as noted by Stewart Valpy (2001), that largely address the economic and social consequences concentrating on the prevalence of underdevelopment among conflict-affected countries. However, very few researchers talk about the micro-level impacts of conflicts on household and individual. One possible reason is the unavailability of household-level data in conflict-affected countries. Second, even wh en such data are available the reliability of the source and the sample is also being questioned. Although, empirical works are growing, the increasing micro-level researches has been greatly focused on the effects of war to household living standards and direct impacts of combats that involves narratives of individuals in conflict areas. Very limited works has addressed the long term effects of violent conflict on children and child development, most especially on the Philippine context. Drawing on a review of both theoretical and empirical literature, this paper frames the connection between armed conflict and human capital development within a conceptual framework in which the accumulation of nutrition and education and levels of human development are linked. This paper further shows that while armed conflict might be caused by many factors, low levels of human development increase the risks of conflict outbreaks and recurrence. Figure 1: Adopted from Kim Conceià §Ãƒ £o (2010), â€Å"The Economic Crisis, Violent Conflict, and Human Development† Figure 1 shows the conceptual framework of the study. This framework suggests a self-reinforcing cycle from the roots and cause of armed conflict to low human capital development, and vice versa. The decade-long armed conflict in the Philippines is a proof of this loop. Concentrated in rural areas, variations of insecurities and violence has affected communities especially children and women who are forced to suffer physical and psychological trauma as consequences from shooting, combat operations, and rights abuse. While conflict maybe caused by many factors, Risser (2007) traces its roots to the issues of poverty, economic distribution disparities, and scarcity of state social and welfare services. These becomes a problem because it limits access to health care services and basic education which is critical for the accumulation of physical, social, and human capital. The framework further notes that a country experiencing conflict cannot secure long term returns for investments in both physical and human capital, resulting in low investment in health and education which lead to low levels of human development. A country with low levels of human development has a difficulty in improving institutions which lowers productivity and potential growth. As such, lower growth rates heighten the risk of conflict, potentially trapping a country in a self-reinforcing cycle of conflict, low human development, and vice versa (Kim Conceicao, 2010). In the period of 2001-2005, IBON Foundation monitored 1,061 armed confrontations between the government forces and various armed groups and recorded 569 killing of innocent, unarmed civilians – 52 of which are minors under 18-years old, 63 women, and 199 who were killed during the crossfire. Over the last decade, millions of children were killed in armed conflicts all over the world (Machel, 1996). While others are exploited as soldiers and exposed to extreme brutality and violence (Camacho, 2003). It is estimated that 45 percent of the direct victims of armed conflict are 15 years old and younger. Moreover, there were 819 incident of human rights violations involving children from 2001 to April 2005. Children suffered effects of sexual violence, harassment and psychological trauma, intimidation, illegal detention, and exposure to hunger and disease. There were 75 cases of children who were orphaned when their parents were killed during the conflict, however this number may be underreported due to the lack of data, limited information, and unreliability of the sources. Exposure to actual combats and being caught in the crossfire of battles has left them physically disabled, emotionally scarred, and psychologically traumatized which are detrimental in accumulating the proper human and social capital to become well-adjusted and productive workers. This research relates to various fields in the literature, in particular for development economics, health and nutrition, and education. I briefly mention below the key areas in the mentioned field of study that motivates this research. First is on the established link between economic conditions and conflict. There has been a great deal of work analyzing the causal effects of conflict and war. Most of these studies extensively focused on establishing a strong link between poverty to armed conflict and violence (Justino, 2006; Justino, 2009; Miguel et al., 2004). Macro-level analysis, as noted by Stewart, F. Valpy F. (2001), has provided an insight on the economic and social consequences of conflict focusing on the prevalence of underdevelopment among conflict-affected countries. However, there has been limited number of studies focusing at the micro-level impacts of conflicts on household and individual. The increasing micro-level data has been greatly focused on the effects of war to household living standards, direct impacts of combats, and very limited on children and child development especially on the Philippine context. Second is the relationship of health to socio-economic characteristics, and its implications to consumption patterns. Serdan (2008) gave an overview of how armed conflict affects food intakes, food availability, and a clear measurement indicators of nutritional outcomes for children. In addition, Straus and Thomas (2008) noted how health and nutrition affects the accumulation of human capital, as well as its positive effects to productivity and living standards. Third is relating nutrition to academic performance. In fact, academic performance and nutrition, as important elements in the accumulation of proper human and social capital, has been the subject of the growing literature demonstrating the long term impacts of conflict to the productivity of the workforce, their well-being, as well as living standards (Thomas, 2007; Berhman et al., 2004; Malluccio et al., 2006, Serdan, 2008). Furthermore, a unanimous agreement establishes health as an important factor for determining the well-being of the population which affects schooling, income, and labor force participation (Serdan, 2008; Alderman et al., 2006; Shemyakina, 2006; Swee 2009). In all, existing researches are clear: the effects or armed conflict and violence represent a significant challenge to the health and education systems. This further qualifies both the short-term and long-term economic implications of armed conflict to the different sectors of the economy. This paper examines the possible causal effects of armed conflict and violence on health outcomes and education of children. In particular, I analyzed if the exposure to armed conflict and violence has a differential effect on the nutrition and academic performance of conflict-affected children, and comparing these results to those children from non-armed conflict areas. When it comes to peace development, this quantitative research will contribute to the lack of data around conflict-affected areas towards creating an impact assessment for conflict and post-conflict rehabilitation programs. The main issue is the gap between academic studies and practitioner works that has been due to the limited information and reliance on sources of data from mass media and humanitarian monitoring mechanism. I want to establish a closer link between academic studies and policy making in conflict-affected areas. The paper seek to assess how armed conflict and violence affect the health and education of children living in conflict areas. More specifically, this research looks into the anthropometric indicators that would suggest disruptions on the nutritional intakes, academic performance, and schooling of children. In doing so, the study evaluates the current status of health and education of children living amid conflict and violence, and compares the nutritional outcomes and academic performance of children from armed conflict areas to non-armed conflict areas. LIBRANZA | 1

What Massage Is the Poet Trying to Convey About “The Charge of the Light Brigade”

What massage is the poet trying to convey about â€Å"The Charge Of The Light Brigade†? In the poem â€Å"The Charge Of The Light Brigade† Alfred Tennyson tries to convey the readers to honor the qualities of the actual Light Brigade. With the use of figurative language, effective structure and techniques he achieve to show the determination and bravery of the six hundred soldiers that fought in the Brigade. Tennyson firstly introduce us to the heroes of the poem in the first stanza when he says â€Å"All in the valley of Death rode the six hundred†.This metaphor show the bravery of the â€Å"six hundred† because they where riding towards their death. The personification of Death suggest that something terrible happened to the soldiers, and the phrase â€Å"valley of Death† helps the creation of an image of the setting,uncertain and terrible, which the six hundred where riding towards. Tennyson then decides to put a man shouting a military order, â €Å"Charge for the guns†. He leaves the person unknown to emphasize at the brave men and that they were following orders. The word â€Å"guns† confirms that the destination of the Brigade was towards their death.The stanza ends with the repetition of the lines † into the valley of death rode the six hundred† to emphasize more their fatal lost and their strength to face death. The message of the poem is described using a variety of techniques. The rhetorical question â€Å"Was there a man dismayed? † Suggest that the soldiers didn't lost their courage and they didn't overcomes by terror while facing the death. This shows the loyalty and toughness of the heroes. The rhetorical question is contrasting with the following group of lines â€Å"Theirs not to make reply, theirs not to reason why, theirs but to do and die†.There is alliteration being used. These lines sum up the heroism and nobility of the six hundred, which they did their job without reasoning, without replying even that their lives where based on that. Tennyson attempts to make us feel the way the soldiers did when they where surrounded, by using onomatopoeia through the lines â€Å"Cannon to right of them, Cannon to left of them, Cannon in front of them†. The use of senses(optic and hearing) successfully help the reader to feel the moment, the terror of the soldiers as well as understanding better the quality of heir pride and strength to keep fighting and not be overcome by their fears. Their bravery is being described by the phrase â€Å"Bodly they rode and well†. There is a powerful personification of â€Å"jaws of Death/mouth of Hell† which represent the battlefield and the dangers, which again emphasize how heroic the men fought but it contrasting again with their fatal lost. Tennyson tries to show the response of the world to this charge by saying † charging an army while all the world wondered†. Tennyson imagines that th e viewers of the battle are wondering with awe and amazement.At the end of stanza four, the poet through the phrase â€Å"Then they rode back, but not, not the six hundred† shows that the charge has ended, the soldiers are turning back. The repetition of the word â€Å"not† shows the terrible casualties of the Light Brigade, the lost of many men out of the six hundred. Furthermore, Tennyson recognize the soldiers as heroes as he emphasizes to the lost of their life † while horse and hero fell†. There is a vivid image been created of the horse and the hero fall to the ground dead. The poem last stanza begins with a rhetorical question â€Å"When can their glory fade?The speaker tries to make the soldiers of the Light Brigade legends, to emphasize that their glory should never fade. Tennyson want us to remember the Light Brigade as a â€Å"wild charge† and repeats the line â€Å"all the world wondered† this time Tennyson is referring to us, to show that we should be amazed with the wild charge of the brave heroes and we should wonder for their strength and pride. The poem ends with some commands â€Å"Honour the charge they made! Honour the Light Brigade, Noble six hundred†. These commands summarize the purpose of the poem, to tell us, that we should remember and respect these noble war heroes, to honor their lives.

Physics Notes

Gravitation Gravitational field strength at a point is defined as the gravitational force per unit mass at that point. Newton's law of gravitation: The (mutual) gravitational force F between two point masses M and m separated by a distance r is given by F =| GMm| (where G: Universal gravitational constant)| | r2| | or, the gravitational force of between two point masses is proportional to the product of their masses ; inversely proportional to the square of their separation. Gravitational field strength at a point is the gravitational force per unit mass at that point. It is a vector and its S. I. unit is N kg-1.By definition, g = F / m By Newton Law of Gravitation, F = GMm / r2 Combining, magnitude of g = GM / r2 Therefore g = GM / r2, M = Mass of object â€Å"creating† the field Example 1: Assuming that the Earth is a uniform sphere of radius 6. 4 x 106 m and mass 6. 0 x 1024 kg, find the gravitational field strength g at a point: (a) on the surface, g = GM / r2 = (6. 67 ? 1 0-11)(6. 0 x 1024) / (6. 4 x 106)2 = 9. 77ms-2 (b) at height 0. 50 times the radius of above the Earth's surface. g = GM / r2 = (6. 67 ? 10-11)(6. 0 x 1024) / ( (1. 5 ? 6. 4 x 106)2 = 4. 34ms-2 Example 2: The acceleration due to gravity at the Earth's surface is 9. 0ms-2. Calculate the acceleration due to gravity on a planet which has the same density but twice the radius of Earth. g = GM / r2 gP / gE = MPrE2 / MErP2 = (4/3) ? rP3rE2? P / (4/3) ? rE3rP2? E = rP / rE = 2 Hence gP = 2 x 9. 81 = 19. 6ms-2 Assuming that Earth is a uniform sphere of mass M. The magnitude of the gravitational force from Earth on a particle of mass m, located outside Earth a distance r from the centre of the Earth is F = GMm / r2. When a particle is released, it will fall towards the centre of the Earth, as a result of the gravitational force with an acceleration ag. FG = mag ag = GM / r2Hence ag = g Thus gravitational field strength g is also numerically equal to the acceleration of free fall. Example 1: A ship is at rest on the Earth's equator. Assuming the earth to be a perfect sphere of radius R and the acceleration due to gravity at the poles is go, express its apparent weight, N, of a body of mass m in terms of m, go, R and T (the period of the earth's rotation about its axis, which is one day). At the North Pole, the gravitational attraction is F = GMEm / R2 = mgo At the equator, Normal Reaction Force on ship by Earth = Gravitational attraction – centripetal force N = mgo – mR? = mgo – mR (2? / T)2 Gravitational potential at a point is defined as the work done (by an external agent) in bringing a unit mass from infinity to that point (without changing its kinetic energy). ? = W / m = -GM / r Why gravitational potential values are always negative? As the gravitational force on the mass is attractive, the work done by an ext agent in bringing unit mass from infinity to any point in the field will be negative work {as the force exerted by the ext agent is opp osite in direction to the displacement to ensure that ? KE = 0} Hence by the definition of negative work, all values of ? re negative. g = -| d? | = – gradient of ? -r graph {Analogy: E = -dV/dx}| | dr| | Gravitational potential energy U of a mass m at a point in the gravitational field of another mass M, is the work done in bringing that mass m {NOT: unit mass, or a mass} from infinity to that point. ; U = m ? = -GMm / r Change in GPE, ? U = mgh only if g is constant over the distance h; {; h;; radius of planet} otherwise, must use: ? U = m? f-m? i | Aspects| Electric Field| Gravitational Field| 1. | Quantity interacting with or producing the field| Charge Q| Mass M| 2. Definition of Field Strength| Force per unit positive charge E = F / q| Force per unit mass g = F / M| 3. | Force between two Point Charges or Masses| Coulomb's Law: Fe = Q1Q2 / 4 or2| Newton's Law of Gravitation: Fg = G (GMm / r2)| 4. | Field Strength of isolated Point Charge or Mass| E = Q / 4 or2| g = G (G M / r2)| 5. | Definition of Potential| Work done in bringing a unit positive charge from infinity to the point; V = W /Q| Work done in bringing a unit mass from infinity to the point; ? = W / M| 6. | Potential of isolated Point Charge or Mass| V = Q / 4 or| ? -G (M / r)| 7. | Change in Potential Energy| ? U = q ? V| ? U = m | Total Energy of a Satellite = GPE + KE = (-GMm / r) + ? (GMm / r) Escape Speed of a Satellite By Conservation of Energy, Initial KE| +| Initial GPE| =| Final KE| +| Final GPE| (? mvE2)| +| (-GMm / r)| =| (0)| +| (0)| Thus escape speed, vE = v(2GM / R) Note : Escape speed of an object is independent of its mass For a satellite in circular orbit, â€Å"the centripetal force is provided by the gravitational force† {Must always state what force is providing the centripetal force before following eqn is used! Hence GMm / r2 = mv2 / r = mr? 2 = mr (2? / T)2 A satellite does not move in the direction of the gravitational force {ie it stays in its circular orbi t} because: the gravitational force exerted by the Earth on the satellite is just sufficient to cause the centripetal acceleration but not enough to also pull it down towards the Earth. {This explains also why the Moon does not fall towards the Earth} Geostationary satellite is one which is always above a certain point on the Earth (as the Earth rotates about its axis. For a geostationary orbit: T = 24 hrs, orbital radius (; height) are fixed values from the centre of the Earth, ang velocity w is also a fixed value; rotates fr west to east. However, the mass of the satellite is NOT a particular value ; hence the ke, gpe, ; the centripetal force are also not fixed values {ie their values depend on the mass of the geostationary satellite. } A geostationary orbit must lie in the equatorial plane of the earth because it must accelerate in a plane where the centre of Earth lies since the net orce exerted on the satellite is the Earth's gravitational force, which is directed towards the c entre of Earth. {Alternatively, may explain by showing why it's impossible for a satellite in a non-equatorial plane to be geostationary. } Thermal Physics Internal Energy: is the sum of the kinetic energy of the molecules due to its random motion ; the potential energy of the molecules due to the intermolecular forces. Internal energy is determined by the values of the current state and is independent of how the state is arrived at. You can read also Thin Film Solar CellThus if a system undergoes a series of changes from one state A to another state B, its change in internal energy is the same, regardless of which path {the changes in the p ; V} it has taken to get from A to B. Since Kinetic Energy proportional to temp, and internal energy of the system = sum of its Kinetic Energy and Potential Energy, a rise in temperature will cause a rise in Kinetic Energy and thus an increase in internal energy. If two bodies are in thermal equilibrium, there is no net flow of heat energy between them and they have the same temperature. NB: this does not imply they must have the same internal energy as internal energy depends also on the number of molecules in the 2 bodies, which is unknown here} Thermodynamic (Kelvin) scale of temperature: theoretical scale that is independent of the properties of any particular substance. An absolute scale of temp is a temp scale which does not depend on the property of any particular subs tance (ie the thermodynamic scale) Absolute zero: Temperature at which all substances have a minimum internal energy {NOT: zero internal energy. } T/K = T/ °C + 273. 15, by definition of the Celsius scale.Specific heat capacity is defined as the amount of heat energy needed to produce unit temperature change {NOT: by 1 K} for unit mass {NOT: 1 kg} of a substance, without causing a change in state. c = Q / m? T Specific latent heat of vaporisation is defined as the amount of heat energy needed to change unit mass of a substance from liquid phase to gaseous phase without a change of temperature. Specific latent heat of fusion is defined as the amount of heat energy needed to change unit mass of a substance from solid phase to liquid phase without a change of temperature L = Q / m {for both cases of vaporisation ; melting}The specific latent heat of vaporisation is greater than the specific latent heat of fusion for a given substance because * During vaporisation, there is a greater increase in volume than in fusion, * Thus more work is done against atmospheric pressure during vaporisation, * The increase in vol also means the INCREASE IN THE (MOLECULAR) POTENTIAL ENERGY, ; hence, internal energy, during vaporisation more than that during melting, * Hence by 1st Law of Thermodynamics, heat supplied during vaporisation more than that during melting; hence lv ; lf {since Q = ml = ?U – W}. Note: 1. the use of comparative terms: greater, more, and; 2. the increase in internal energy is due to an increase in the PE, NOT KE of molecules 3. the system here is NOT to be considered as an ideal gas system Similarly, you need to explain why, when a liq is boiling, thermal energy is being supplied, and yet, the temp of the liq does not change. | Melting| Boiling| Evaporation| Occurrence| Throughout the substance, at fixed temperature and pressure| On the surface, at all temperatures|Spacing(vol) ; PE of molecules| Increase slightly| Increase significantly| | Tempera ture ; hence KE of molecules| Remains constant during process| Decrease for remaining liquid| First Law of Thermodynamics: The increase in internal energy of a system is equal to the sum of the heat supplied to the system and the work done on the system. ?U = W + Q| ? U: Increase in internal energy of the system Q: Heat supplied to the system W: work done on the system| {Need to recall the sign convention for all 3 terms} Work is done by a gas when it expands; work is done on a gas when it is ompressed. W = area under pressure – volume graph. For constant pressure {isobaric process}, Work done = pressure x ? Volume Isothermal process: a process where T = const {? U = 0 for ideal gas} ? U for a cycle = 0 {since U ? T, ; ? T = 0 for a cycle } Equation of state for an ideal gas: p V = n R T, where T is in Kelvin {NOT:  °C}, n: no. of moles. p V = N k T, where N: no. of molecules, k:Boltzmann const Ideal Gas: a gas which obeys the ideal gas equation pV = nRT FOR ALL VALUES OF P , V ; T Avogadro constant: defined as the number of atoms in 12g of carbon-12.It is thus the number of particles (atoms or molecules) in one mole of substance. For an ideal gas, internal energy U = Sum of the KE of the molecules only {since PE = 0 for ideal gas} U = N x? m ;c2; = N x (3/2)kT {for monatomic gas} * U depends on T and number of molecules N * U ? T for a given number of molecules Ave KE of a molecule, ? m ;c2; ? T {T in K: not  °C} Dynamics Newton's laws of motion: Newton's First Law Every body continues in a state of rest or uniform motion in a straight line unless a net (external) force acts on it. Newton's Second LawThe rate of change of momentum of a body is directly proportional to the net force acting on the body, and the momentum change takes place in the direction of the net force. Newton's Third Law When object X exerts a force on object Y, object Y exerts a force of the same type that is equal in magnitude and opposite in direction on object X. The two force s ALWAYS act on different objects and they form an action-reaction pair. Linear momentum and its conservation: Mass: is a measure of the amount of matter in a body, ; is the property of a body which resists change in motion.Weight: is the force of gravitational attraction (exerted by the Earth) on a body. Linear momentum: of a body is defined as the product of its mass and velocity ie p = m v Impulse of a force (I): is defined as the product of the force and the time ? t during which it acts ie I = F x ? t {for force which is const over the duration ? t} For a variable force, the impulse I = Area under the F-t graph { ? Fdt; may need to â€Å"count squares†} Impulse is equal in magnitude to the change in momentum of the body acted on by the force.Hence the change in momentum of the body is equal in mag to the area under a (net) force-time graph. {Incorrect to define impulse as change in momentum} Force: is defined as the rate of change of momentum, ie F = [ m (v – u) ] / t = ma or F = v dm / dt The {one} Newton: is defined as the force needed to accelerate a mass of 1 kg by 1 m s-2. Principle of Conservation of Linear Momentum: When objects of a system interact, their total momentum before and after interaction are equal if no net (external) force acts on the system. * The total momentum of an isolated system is constant m1 u1 + m2 u2 = m1 v1 + m2 v2 if net F = 0 {for all collisions } NB: Total momentum DURING the interaction/collision is also conserved. (Perfectly) elastic collision: Both momentum ; kinetic energy of the system are conserved. Inelastic collision: Only momentum is conserved, total kinetic energy is not conserved. Perfectly inelastic collision: Only momentum is conserved, and the particles stick together after collision. (i. e. move with the same velocity. ) For all elastic collisions, u1 – u2 = v2 – v1 ie. relative speed of approach = relative speed of separation or, ? m1u12 + ? m2u22 = ? m1v12 + ? 2v22 In inelastic collisions, total energy is conserved but Kinetic Energy may be converted into other forms of energy such as sound and heat energy. Current of Electricity Electric current is the rate of flow of charge. {NOT: charged particles} Electric charge Q passing a point is defined as the product of the (steady) current at that point and the time for which the current flows, Q = I t One coulomb is defined as the charge flowing per second pass a point at which the current is one ampere. Example 1: An ion beam of singly-charged Na+ and K+ ions is passing through vacuum. If the beam current is 20 ?A, calculate the total number of ions passing any fixed point in the beam per second. (The charge on each ion is 1. 6 x 10-19 C. ) Current, I = Q / t = Ne / t where N is the no. of ions and e is the charge on one ion. No. of ions per second = N / t = I / e = (20 x 10-6) / (1. 6 x 10-19) = 1. 25 x 10-14 Potential difference is defined as the energy transferred from electrical energy to other forms of e nergy when unit charge passes through an electrical device, V = W / Q P. D. = Energy Transferred / Charge = Power / Current or, is the ratio of the power supplied to the device to the current flowing, V = P / IThe volt: is defined as the potential difference between 2 pts in a circuit in which one joule of energy is converted from electrical to non-electrical energy when one coulomb passes from 1 pt to the other, ie 1 volt = One joule per coulomb Difference between Potential and Potential Difference (PD): The potential at a point of the circuit is due to the amount of charge present along with the energy of the charges. Thus, the potential along circuit drops from the positive terminal to negative terminal, and potential differs from points to points. Potential Difference refers to the difference in potential between any given two points.For example, if the potential of point A is 1 V and the potential at point B is 5 V, the PD across AB, or VAB , is 4 V. In addition, when there is no energy loss between two points of the circuit, the potential of these points is same and thus the PD across is 0 V. Example 2: A current of 5 mA passes through a bulb for 1 minute. The potential difference across the bulb is 4 V. Calculate: (a) The amount of charge passing through the bulb in 1 minute. Charge Q = I t = 5 x 10-3 x 60 = 0. 3 C (b) The work done to operate the bulb for 1 minute. Potential difference across the bulb = W / Q 4 = W / 0. Work done to operate the bulb for 1 minute = 0. 3 x 4 = 1. 2 J Electrical Power, P = V I = I2 / R = V2 / R {Brightness of a lamp is determined by the power dissipated, NOT: by V, or I or R alone} Example 3: A high-voltage transmission line with a resistance of 0. 4 ? km-1 carries a current of 500 A. The line is at a potential of 1200 kV at the power station and carries the current to a city located 160 km from the power station. Calculate (a) the power loss in the line. The power loss in the line P = I2 R = 5002 x 0. 4 x 160 = 16 MW (b) the fraction of the transmitted power that is lost.The total power transmitted = I V = 500 x 1200 x 103 = 600 MW The fraction of power loss = 16 / 600 = 0. 267 Resistance is defined as the ratio of the potential difference across a component to the current flowing through it , R = VI {It is NOT defined as the gradient of a V-I graph; however for an ohmic conductor, its resistance equals the gradient of its V-I graph as this graph is a straight line which passes through the origin} The Ohm: is the resistance of a resistor if there is a current of 1 A flowing through it when the pd across it is 1 V, ie, 1 ? = One volt per ampere Example 4:In the circuit below, the voltmeter reading is 8. 00 V and the ammeter reading is 2. 00 A. Calculate the resistance of R. Resistance of R = V / I = 8 / 2 = 4. 0 ? | | Temperature characteristics of thermistors: The resistance (i. e. the ratio V / I) is constant because metallic conductors at constant temperature obey Ohm's Law. | As V increases, the temperature increases, resulting in an increase in the amplitude of vibration of ions and the collision frequency of electrons with the lattice ions. Hence the resistance of the filament increases with V. | A thermistor is made from semi-conductors.As V increases, temperature increases. This releases more charge carriers (electrons and holes) from the lattice, thus reducing the resistance of the thermistor. Hence, resistance decreases as temperature increases. | In forward bias, a diode has low resistance. In reverse bias, the diode has high resistance until the breakdown voltage is reached. | Ohm's law: The current in a component is proportional to the potential difference across it provided physical conditions (eg temp) stay constant. R = ? L / A {for a conductor of length l, uniform x-sect area A and resistivity ? Resistivity is defined as the resistance of a material of unit cross-sectional area and unit length. {From R = ? l / A , ? = RA / L} Example 5: Calculate the resistanc e of a nichrome wire of length 500 mm and diameter 1. 0 mm, given that the resistivity of nichrome is 1. 1 x 10-6 ? m. Resistance, R = ? l / A = [(1. 1 x 10-6)(500 x 10-3)] / ? (1 x 10-3 / 2)2 = 0. 70 ? Electromotive force (Emf) is defined as the energy transferred / converted from non-electrical forms of energy into electrical energy when unit charge is moved round a complete circuit. ie EMF = Energy Transferred per unit charge E = WQEMF refers to the electrical energy generated from non-electrical energy forms, whereas PD refers to electrical energy being changed into non-electrical energy. For example, EMF Sources| Energy Change| PD across| Energy Change| Chemical Cell| Chem ; Elec| Bulb| Elec ; Light| Generator| Mech ; Elec| Fan| Elec ; Mech| Thermocouple| Thermal ; Elec| Door Bell| Elec ; Sound| Solar Cell| Solar ; Elec| Heating element| Elec ; Thermal| Effects of the internal resistance of a source of EMF: Internal resistance is the resistance to current flow within the power source.It reduces the potential difference (not EMF) across the terminal of the power supply when it is delivering a current. Consider the circuit below: The voltage across the resistor, V = IR, The voltage lost to internal resistance = Ir Thus, the EMF of the cell, E = IR + Ir = V + Ir Therefore If I = 0A or if r = 0? , V = E Motion in a Circle Kinematics of uniform circular motion Radian (rad) is the S. I. unit for angle, ? and it can be related to degrees in the following way. In one complete revolution, an object rotates through 360 ° , or 2? rad. As the object moves through an angle ? , with respect to the centre of rotation, this angle ? s known as the angular displacement. Angular velocity (? ) of the object is the rate of change of angular displacement with respect to time. ? = ? / t = 2? / T (for one complete revolution) Linear velocity, v, of an object is its instantaneous velocity at any point in its circular path. v = arc length / time taken = r? / t = r? * The directi on of the linear velocity is at a tangent to the circle described at that point. Hence it is sometimes referred to as the tangential velocity * ? is the same for every point in the rotating object, but the linear velocity v is greater for points further from the axis.A body moving in a circle at a constant speed changes velocity {since its direction changes}. Thus, it always experiences an acceleration, a force and a change in momentum. Centripetal acceleration a = r? 2 = v2 / r {in magnitude} Centripetal force Centripetal force is the resultant of all the forces that act on a system in circular motion. {It is not a particular force; â€Å"centripetal† means â€Å"centre-seeking†. Also, when asked to draw a diagram showing all the forces that act on a system in circular motion, it is wrong to include a force that is labelled as â€Å"centripetal force†. } Centripetal force, F = m r ? 2 = mv2 / r {in magnitude}A person in a satellite orbiting the Earth experience s â€Å"weightlessness† although the gravi field strength at that height is not zero because the person and the satellite would both have the same acceleration; hence the contact force between man ; satellite / normal reaction on the person is zero {Not because the field strength is negligible}. D. C. Circuits Circuit Symbols: Open Switch| Closed Switch| Lamp| Cell| Battery| Voltmeter| Resistor| Fuse| Ammeter| Variable resistor| Thermistor| Light dependent resistor (LDR)| Resistors in Series: R = R1 + R2 + †¦ Resistors in Parallel: 1/R = 1/R1 + 1/R2 + †¦ Example 1:Three resistors of resistance 2 ? , 3 ? and 4 ? respectively are used to make the combinations X, Y and Z shown in the diagrams. List the combinations in order of increasing resistance. Resistance for X = [1/2 + 1/(4+3)]-1 = 1. 56 ? Resistance for Y = 2 + (1/4 + 1/3)-1 = 3. 71 ? Resistance for Z = (1/3 + 1/2 + 1/4)-1 = 0. 923 ? Therefore, the combination of resistors in order of increasing resistance is Z X Y. Example: Referring to the circuit drawn, determine the value of I1, I and R, the combined resistance in the circuit. E = I1 (160) = I2 (4000) = I3 (32000) I1 = 2 / 160 = 0. 0125 A I2 = 2 / 4000 = 5 x 10-4 AI3 = 2 / 32000 = 6. 25 x 10-5 ASince I = I1 + I2 + I3, I = 13. 1 mAApplying Ohm’s Law, R = 213. 1 x 10-3 = 153 ? | | Example: A battery with an EMF of 20 V and an internal resistance of 2. 0 ? is connected to resistors R1 and R2 as shown in the diagram. A total current of 4. 0 A is supplied by the battery and R2 has a resistance of 12 ?. Calculate the resistance of R1 and the power supplied to each circuit component. E – I r = I2 R2 20 – 4 (2) = I2 (12) I2 = 1A Therefore, I1 = 4 – 1 = 3 AE – I r = I1 R1 12 = 3 R1 Therefore, R1 = 4Power supplied to R1 = (I1)2 R1 = 36 W Power supplied to R2 = (I2)2 R2 = 12 W| |For potential divider with 2 resistors in series, Potential drop across R1, V1 = R1 / (R1 + R2) x PD across R1 ; R2 Potential drop acro ss R2, V1 = R2 / (R1 + R2) x PD across R1 ; R2 Example: Two resistors, of resistance 300 k? and 500 k? respectively, form a potential divider with outer junctions maintained at potentials of +3 V and -15 V. Determine the potential at the junction X between the resistors. The potential difference across the 300 k? resistor = 300 / (300 + 500) [3 – (-15)] = 6. 75 V The potential at X = 3 – 6. 75 = -3. 75 V A thermistor is a resistor whose resistance varies greatly with temperature.Its resistance decreases with increasing temperature. It can be used in potential divider circuits to monitor and control temperatures. Example: In the figure on the right, the thermistor has a resistance of 800 ? when hot, and a resistance of 5000 ? when cold. Determine the potential at W when the temperature is hot. When thermistor is hot, potential difference across it = [800 / (800 + 1700)] x (7 – 2) = 1. 6 VThe potential at W = 2 + 1. 6 V = 3. 6 V| | A Light dependent resistor (LDR) is a resistor whose resistance varies with the intensity of light falling on it. Its resistance decreases with increasing light intensity.It can be used in a potential divider circuit to monitor light intensity. Example: In the figure below, the resistance of the LDR is 6. 0 M in the dark but then drops to 2. 0 k in the light Determine the potential at point P when the LDR is in the light. In the light the potential difference across the LDR= [2k / (3k + 2k)] x (18 – 3) = 6 VThe potential at P = 18 – 6= 12 V| | The potential difference along the wire is proportional to the length of the wire. The sliding contact will move along wire AB until it finds a point along the wire such that the galvanometer shows a zero reading.When the galvanometer shows a zero reading, the current through the galvanometer (and the device that is being tested) is zero and the potentiometer is said to be â€Å"balanced†. If the cell has negligible internal resistance, and if the potent iometer is balanced, EMF / PD of the unknown source, V = [L1 / (L1 + L2)] x E Example: In the circuit shown, the potentiometer wire has a resistance of 60 ?. Determine the EMF of the unknown cell if the balanced point is at B. Resistance of wire AB= [0. 65 / (0. 65 + 0. 35)] x 60 = 39 ? EMF of the test cell= [39 / (60 + 20)] x 12| Work, Energy and PowerWork Done by a force is defined as the product of the force and displacement (of its point of application) in the direction of the force W = F s cos ? Negative work is said to be done by F if x or its compo. is anti-parallel to F If a variable force F produces a displacement in the direction of F, the work done is determined from the area under F-x graph. {May need to find area by â€Å"counting the squares†. } By Principle of Conservation of Energy, Work Done on a system = KE gain + GPE gain + Work done against friction} Consider a rigid object of mass m that is initially at rest.To accelerate it uniformly to a speed v, a cons tant net force F is exerted on it, parallel to its motion over a displacement s. Since F is constant, acceleration is constant, Therefore, using the equation: v2 = u2 +2as, as = 12 (v2 – u2) Since kinetic energy is equal to the work done on the mass to bring it from rest to a speed v, The kinetic energy, EK| = Work done by the force F = Fs = mas = ? m (v2 – u2)| Gravitational potential energy: this arises in a system of masses where there are attractive gravitational forces between them.The gravitational potential energy of an object is the energy it possesses by virtue of its position in a gravitational field. Elastic potential energy: this arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them. Electric potential energy: this arises in a system of charges where there are either attractive or repulsive electric forces between them. The potential energy, U, of a body in a force field {whether gravitationa l or electric field} is related to the force F it experiences by: F = – dU / dx.Consider an object of mass m being lifted vertically by a force F, without acceleration, from a certain height h1 to a height h2. Since the object moves up at a constant speed, F is equal to mg. The change in potential energy of the mass| = Work done by the force F = F s = F h = m g h| Efficiency: The ratio of (useful) output energy of a machine to the input energy. ie =| Useful Output Energy| x100% =| Useful Output Power| x100%| | Input Energy| | Input Power| | Power {instantaneous} is defined as the work done per unit time. P =| Total Work Done| =| W| | Total Time| | t|Since work done W = F x s, P =| F x s| =| Fv| | t| | | * for object moving at const speed: F = Total resistive force {equilibrium condition} * for object beginning to accelerate: F = Total resistive force + ma Forces Hooke's Law: Within the limit of proportionality, the extension produced in a material is directly proportional to the force/load applied F = kx Force constant k = force per unit extension (F/x) Elastic potential energy/strain energy = Area under the F-x graph {May need to â€Å"count the squares†} For a material that obeys Hooke? s law, Elastic Potential Energy, E = ? F x = ? x2 Forces on Masses in Gravitational Fields: A region of space in which a mass experiences an (attractive) force due to the presence of another mass. Forces on Charge in Electric Fields: A region of space where a charge experiences an (attractive or repulsive) force due to the presence of another charge. Hydrostatic Pressure p = ? gh {or, pressure difference between 2 points separated by a vertical distance of h } Upthrust: An upward force exerted by a fluid on a submerged or floating object; arises because of the difference in pressure between the upper and lower surfaces of the object.Archimedes' Principle: Upthrust = weight of the fluid displaced by submerged object. ie Upthrust = Volsubmerged x ? fluid x g Frict ional Forces: * The contact force between two surfaces = (friction2 + normal reaction2)? * The component along the surface of the contact force is called friction * Friction between 2 surfaces always opposes relative motion {or attempted motion}, and * Its value varies up to a maximum value {called the static friction} Viscous Forces: * A force that opposes the motion of an object in a fluid * Only exists when there is (relative) motion Magnitude of viscous force increases with the speed of the object Centre of Gravity of an object is defined as that pt through which the entire weight of the object may be considered to act. A couple is a pair of forces which tends to produce rotation only. Moment of a Force: The product of the force and the perpendicular distance of its line of action to the pivot Torque of a Couple: The produce of one of the forces of the couple and the perpendicular distance between the lines of action of the forces. (WARNING: NOT an action-reaction pair as they a ct on the same body. ) Conditions for Equilibrium (of an extended object): 1.The resultant force acting on it in any direction equals zero 2. The resultant moment about any point is zero If a mass is acted upon by 3 forces only and remains in equilibrium, then 1. The lines of action of the 3 forces must pass through a common point 2. When a vector diagram of the three forces is drawn, the forces will form a closed triangle (vector triangle), with the 3 vectors pointing in the same orientation around the triangle. Principle of Moments: For a body to be in equilibrium, the sum of all the anticlockwise moments about any point must be equal to the sum of all the clockwise moments about that same point.Measurement Base quantities and their units; mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol): Base Quantities| SI Units| | Name| Symbol| Length| metre| m| Mass| kilogram| kg| Time| second| s| Amount of substance| mole| mol| Temperature| Kelvin| K| C urrent| ampere| A| Luminous intensity| candela| cd| Derived units as products or quotients of the base units: Derived| Quantities Equation| Derived Units| Area (A)| A = L2| m2| Volume (V)| V = L3| m3| Density (? )| ? = m / V| kg m-3| Velocity (v)| v = L / t| ms-1| Acceleration (a)| a = ? v / t| ms-1 / s = ms-2|Momentum (p)| p = m x v| (kg)(ms-1) = kg m s-1| Derived Quantities| Equation| Derived Unit| Derived Units| | | Special Name| Symbol| | Force (F)| F = ? p / t| Newton| N| [(kg m s-1) / s = kg m s-2| Pressure (p)| p = F / A| Pascal| Pa| (kg m s-2) / m2 = kg m-1 s-2| Energy (E)| E = F x d| joule| J| (kg m s-2)(m) = kg m2 s-2| Power (P)| P = E / t| watt| W| (kg m2 s-2) / s = kg m2 s-3| Frequency (f)| f = 1 / t| hertz| Hz| 1 / s = s-1| Charge (Q)| Q = I x t| coulomb| C| A s| Potential Difference (V)| V = E / Q| volt| V| (kg m2 s-2) / A s = kg m2 s-3 A-1| Resistance (R)| R = V / I| ohm| ? (kg m2 s-3 A-1) / A = kg m2 s-3 A-2| Prefixes and their symbols to indicate decimal sub-multipl es or multiples of both base and derived units: Multiplying Factor| Prefix| Symbol| 10-12| pico| p| 10-9| nano| n| 10-6| micro| ? | 10-3| milli| m| 10-2| centi| c| 10-1| decid| d| 103| kilo| k| 106| mega| M| 109| giga| G| 1012| tera| T| Estimates of physical quantities: When making an estimate, it is only reasonable to give the figure to 1 or at most 2 significant figures since an estimate is not very precise. Physical Quantity| Reasonable Estimate| Mass of 3 cans (330 ml) of Coke| 1 kg|Mass of a medium-sized car| 1000 kg| Length of a football field| 100 m| Reaction time of a young man| 0. 2 s| * Occasionally, students are asked to estimate the area under a graph. The usual method of counting squares within the enclosed area is used. (eg. Topic 3 (Dynamics), N94P2Q1c) * Often, when making an estimate, a formula and a simple calculation may be involved. EXAMPLE 1: Estimate the average running speed of a typical 17-year-old? s 2. 4-km run. velocity = distance / time = 2400 / (12. 5 x 60) = 3. 2 ? 3 ms-1 EXAMPLE 2: Which estimate is realistic? | Option| Explanation|A| The kinetic energy of a bus travelling on an expressway is 30000J| A bus of mass m travelling on an expressway will travel between 50 to 80 kmh-1, which is 13. 8 to 22. 2 ms-1. Thus, its KE will be approximately ? m(182) = 162m. Thus, for its KE to be 30000J: 162m = 30000. Thus, m = 185kg, which is an absurd weight for a bus; ie. This is not a realistic estimate. | B| The power of a domestic light is 300W. | A single light bulb in the house usually runs at about 20W to 60W. Thus, a domestic light is unlikely to run at more than 200W; this estimate is rather high. | C| The temperature of a hot oven is 300 K. 300K = 27 0C. Not very hot. | D| The volume of air in a car tyre is 0. 03 m3. | | Estimating the width of a tyre, t, is 15 cm or 0. 15 m, and estimating R to be 40 cm and r to be 30 cm,volume of air in a car tyre is = ? (R2 – r2)t = ? (0. 42 – 0. 32)(0. 15) = 0. 033 m3 ? 0. 03 m3 (t o one sig. fig. )| Distinction between systematic errors (including zero errors) and random errors and between precision and accuracy: Random error: is the type of error which causes readings to scatter about the true value. Systematic error: is the type of error which causes readings to deviate in one direction from the true value.Precision: refers to the degree of agreement (scatter, spread) of repeated measurements of the same quantity. {NB: regardless of whether or not they are correct. } Accuracy: refers to the degree of agreement between the result of a measurement and the true value of the quantity. | ; ; R Error Higher ; ; ; ; ; ; Less Precise ; ; ;| v v vS Error HigherLess Accuratev v v| | | | | | Assess the uncertainty in a derived quantity by simple addition of actual, fractional or percentage uncertainties (a rigorous statistical treatment is not required). For a quantity x = (2. 0  ± 0. 1) mm,Actual/ Absolute uncertainty, ? x =  ± 0. 1 mm Fractional uncertainty, ? x x = 0. 05 Percentage uncertainty, ? xx 100% = 5 % If p = (2x + y) / 3 or p = (2x – y) / 3, ? p = (2? x + ? y) / 3 If r = 2xy3 or r = 2x / y3, ? r / r = ? x / x + 3? y / y Actual error must be recorded to only 1 significant figure, ; The number of decimal places a calculated quantity should have is determined by its actual error. For eg, suppose g has been initially calculated to be 9. 80645 ms-2 ; ? g has been initially calculated to be 0. 04848 ms-2. The final value of ? g must be recorded as 0. 5 ms-2 {1 sf }, and the appropriate recording of g is (9. 81  ± 0. 05) ms-2. Distinction between scalar and vector quantities: | Scalar| Vector| Definition| A scalar quantity has a magnitude only. It is completely described by a certain number and a unit. | A vector quantity has both magnitude and direction. It can be described by an arrow whose length represents the magnitude of the vector and the arrow-head represents the direction of the vector. | Examples| Distance, speed, mass , time, temperature, work done, kinetic energy, pressure, power, electric charge etc. Common Error:Students tend to associate kinetic energy and pressure with vectors because of the vector components involved. However, such considerations have no bearings on whether the quantity is a vector or scalar. | Displacement, velocity, moments (or torque), momentum, force, electric field etc. | Representation of vector as two perpendicular components: In the diagram below, XY represents a flat kite of weight 4. 0 N. At a certain instant, XY is inclined at 30 ° to the horizontal and the wind exerts a steady force of 6. 0 N at right angles to XY so that the kite flies freely.By accurate scale drawing| By calculations using sine and cosine rules, or Pythagoras? theorem| Draw a scale diagram to find the magnitude and direction of the resultant force acting on the kite. R = 3. 2 N (? 3. 2 cm) at ? = 112 ° to the 4 N vector. | Using cosine rule, a2 = b2 + c2 – 2bc cos A R2 = 42 + 62 -2( 4)(6)(cos 30 °) R = 3. 23 NUsing sine rule: a / sin A = b / sin B 6 / sin ? = 3. 23 / sin 30 ° ? = 68 ° or 112 ° = 112 ° to the 4 N vector| Summing Vector Components| | Fx = – 6 sin 30 ° = – 3 NFy = 6 cos 30 ° – 4 = 1. 2 NR = v(-32 + 1. 22) = 3. 23 Ntan ? = 1. 2 / 3 = 22 °R is at an angle 112 ° to the 4 N vector. (90 ° + 22 °)|Kinematics Displacement, speed, velocity and acceleration: Distance: Total length covered irrespective of the direction of motion. Displacement: Distance moved in a certain direction. Speed: Distance travelled per unit time. Velocity: is defined as the rate of change of displacement, or, displacement per unit time {NOT: displacement over time, nor, displacement per second, nor, rate of change of displacement per unit time} Acceleration: is defined as the rate of change of velocity. Using graphs to find displacement, velocity and acceleration: * The area under a velocity-time graph is the change in displacement. The gr adient of a displacement-time graph is the {instantaneous} velocity. * The gradient of a velocity-time graph is the acceleration. The ‘SUVAT' Equations of Motion The most important word for this chapter is SUVAT, which stands for: * S (displacement), * U (initial velocity), * V (final velocity), * A (acceleration) and * T (time) of a particle that is in motion. Below is a list of the equations you MUST memorise, even if they are in the formula book, memorise them anyway, to ensure you can implement them quickly. 1. v = u +at| derived from definition of acceleration: a = (v – u) / t| 2. | s = ? (u + v) t| derived from the area under the v-t graph| 3. | v2 = u2 + 2as| derived from equations (1) and (2)| 4. | s = ut + ? at2| derived from equations (1) and (2)| These equations apply only if the motion takes place along a straight line and the acceleration is constant; {hence, for eg. , air resistance must be negligible. } Motion of bodies falling in a uniform gravitational field with air resistance: Consider a body moving in a uniform gravitational field under 2 different conditions: Without Air Resistance:Assuming negligible air resistance, whether the body is moving up, or at the highest point or moving down, the weight of the body, W, is the only force acting on it, causing it to experience a constant acceleration. Thus, the gradient of the v-t graph is constant throughout its rise and fall. The body is said to undergo free fall. With Air Resistance: If air resistance is NOT negligible and if it is projected upwards with the same initial velocity, as the body moves upwards, both air resistance and weight act downwards. Thus its speed will decrease at a rate greater than . 81 ms-2 . This causes the time taken to reach its maximum height reached to be lower than in the case with no air resistance. The max height reached is also reduced. At the highest point, the body is momentarily at rest; air resistance becomes zero and hence the only force acting on it is the weight. The acceleration is thus 9. 81 ms-2 at this point. As a body falls, air resistance opposes its weight. The downward acceleration is thus less than 9. 81 ms-2. As air resistance increases with speed, it eventually equals its weight (but in opposite direction).From then there will be no resultant force acting on the body and it will fall with a constant speed, called the terminal velocity. Equations for the horizontal and vertical motion: | x direction (horizontal – axis)| y direction (vertical – axis)| s (displacement)| sx = ux t sx = ux t + ? ax t2| sy = uy t + ? ay t2 (Note: If projectile ends at same level as the start, then sy = 0)| u (initial velocity)| ux| uy| v (final velocity)| vx = ux + axt (Note: At max height, vx = 0)| vy = uy + at vy2 = uy2 + 2asy| a (acceleration)| ax (Note: Exists when a force in x direction present)| ay (Note: If object is falling, then ay = -g)| (time)| t| t| Parabolic Motion: tan ? = vy / vx ?: direction of tangenti al velocity {NOT: tan ? = sy / sx } Forces Hooke's Law: Within the limit of proportionality, the extension produced in a material is directly proportional to the force/load applied F = kx Force constant k = force per unit extension (F/x) Elastic potential energy/strain energy = Area under the F-x graph {May need to â€Å"count the squares†} For a material that obeys Hooke? s law, Elastic Potential Energy, E = ? F x = ? k x2 Forces on Masses in Gravitational Fields: A region of space in which a mass experiences an (attractive) force due to the presence of another mass.Forces on Charge in Electric Fields: A region of space where a charge experiences an (attractive or repulsive) force due to the presence of another charge. Hydrostatic Pressure p = ? gh {or, pressure difference between 2 points separated by a vertical distance of h } Upthrust: An upward force exerted by a fluid on a submerged or floating object; arises because of the difference in pressure between the upper and l ower surfaces of the object. Archimedes' Principle: Upthrust = weight of the fluid displaced by submerged object. ie Upthrust = Volsubmerged x ? fluid x g Frictional Forces: The contact force between two surfaces = (friction2 + normal reaction2)? * The component along the surface of the contact force is called friction * Friction between 2 surfaces always opposes relative motion {or attempted motion}, and * Its value varies up to a maximum value {called the static friction} Viscous Forces: * A force that opposes the motion of an object in a fluid * Only exists when there is (relative) motion * Magnitude of viscous force increases with the speed of the object Centre of Gravity of an object is defined as that pt through which the entire weight of the object may be considered to act.A couple is a pair of forces which tends to produce rotation only. Moment of a Force: The product of the force and the perpendicular distance of its line of action to the pivot Torque of a Couple: The produ ce of one of the forces of the couple and the perpendicular distance between the lines of action of the forces. (WARNING: NOT an action-reaction pair as they act on the same body. ) Conditions for Equilibrium (of an extended object): 1. The resultant force acting on it in any direction equals zero 2. The resultant moment about any point is zero If a mass is acted upon by 3 forces only and remains in equilibrium, then 1.The lines of action of the 3 forces must pass through a common point 2. When a vector diagram of the three forces is drawn, the forces will form a closed triangle (vector triangle), with the 3 vectors pointing in the same orientation around the triangle. Principle of Moments: For a body to be in equilibrium, the sum of all the anticlockwise moments about any point must be equal to the sum of all the clockwise moments about that same point. Work, Energy and Power Work Done by a force is defined as the product of the force and displacement (of its point of application) in the direction of the force W = F s cos ?Negative work is said to be done by F if x or its compo. is anti-parallel to F If a variable force F produces a displacement in the direction of F, the work done is determined from the area under F-x graph. {May need to find area by â€Å"counting the squares†. } By Principle of Conservation of Energy, Work Done on a system = KE gain + GPE gain + Work done against friction} Consider a rigid object of mass m that is initially at rest. To accelerate it uniformly to a speed v, a constant net force F is exerted on it, parallel to its motion over a displacement s. Since F is constant, acceleration is constant, Therefore, using the equation: 2 = u2 +2as, as = 12 (v2 – u2) Since kinetic energy is equal to the work done on the mass to bring it from rest to a speed v, The kinetic energy, EK| = Work done by the force F = Fs = mas = ? m (v2 – u2)| Gravitational potential energy: this arises in a system of masses where there are at tractive gravitational forces between them. The gravitational potential energy of an object is the energy it possesses by virtue of its position in a gravitational field. Elastic potential energy: this arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them.Electric potential energy: this arises in a system of charges where there are either attractive or repulsive electric forces between them. The potential energy, U, of a body in a force field {whether gravitational or electric field} is related to the force F it experiences by: F = – dU / dx. Consider an object of mass m being lifted vertically by a force F, without acceleration, from a certain height h1 to a height h2. Since the object moves up at a constant speed, F is equal to mg. The change in potential energy of the mass| = Work done by the force F = F s = F h = m g h|Efficiency: The ratio of (useful) output energy of a machine to the input energy. ie =| U seful Output Energy| x100% =| Useful Output Power| x100%| | Input Energy| | Input Power| | Power {instantaneous} is defined as the work done per unit time. P =| Total Work Done| =| W| | Total Time| | t| Since work done W = F x s, P =| F x s| =| Fv| | t| | | * for object moving at const speed: F = Total resistive force {equilibrium condition} * for object beginning to accelerate: F = Total resistive force + ma Wave Motion Displacement (y): Position of an oscillating particle from its equilibrium position.Amplitude (y0 or A): The maximum magnitude of the displacement of an oscillating particle from its equilibrium position. Period (T): Time taken for a particle to undergo one complete cycle of oscillation. Frequency (f): Number of oscillations performed by a particle per unit time. Wavelength (? ): For a progressive wave, it is the distance between any two successive particles that are in phase, e. g. it is the distance between 2 consecutive crests or 2 troughs. Wave speed (v): The sp eed at which the waveform travels in the direction of the propagation of the wave.Wave front: A line or surface joining points which are at the same state of oscillation, i. e. in phase, e. g. a line joining crest to crest in a wave. Ray: The path taken by the wave. This is used to indicate the direction of wave propagation. Rays are always at right angles to the wave fronts (i. e. wave fronts are always perpendicular to the direction of propagation). From the definition of speed, Speed = Distance / Time A wave travels a distance of one wavelength, ? , in a time interval of one period, T. The frequency, f, of a wave is equal to 1 / T Therefore, speed, v = ? / T = (1 / T)? f? v = f? Example 1: A wave travelling in the positive x direction is showed in the figure. Find the amplitude, wavelength, period, and speed of the wave if it has a frequency of 8. 0 Hz. Amplitude (A) = 0. 15 mWavelength (? ) = 0. 40 mPeriod (T) = 1f = 18. 0 ? 0. 125 sSpeed (v) =f? = 8. 0 x 0. 40 = 3. 20 m s-1A wa ve which results in a net transfer of energy from one place to another is known as a progressive wave. | | Intensity {of a wave}: is defined as the rate of energy flow per unit time {power} per unit cross-sectional area perpendicular to the direction of wave propagation.Intensity = Power / Area = Energy / (Time x Area) For a point source (which would emit spherical wavefronts), Intensity = (? m? 2xo2) / (t x 4? r2) where x0: amplitude ; r: distance from the point source. Therefore, I ? xo2 / r2 (Pt Source) For all wave sources, I ? (Amplitude)2 Transverse wave: A wave in which the oscillations of the wave particles {NOT: movement} are perpendicular to the direction of the propagation of the wave. Longitudinal wave: A wave in which the oscillations of the wave particles are parallel to the direction of the propagation of the wave.Polarisation is said to occur when oscillations are in one direction in a plane, {NOT just â€Å"in one direction†} normal to the direction of propag ation. {Only transverse waves can be polarized; longitudinal waves can’t. }Example 2: The following stationary wave pattern is obtained using a C. R. O. whose screen is graduated in centimetre squares. Given that the time-base is adjusted such that 1 unit on the horizontal axis of the screen corresponds to a time of 1. 0 ms, find the period and frequency of the wave. Period, T = (4 units) x 1. 0 = 4. 0 ms = 4. 0 x 10-3 sf = 1 / T = 14 x 10-3 250 Hz| | Superposition Principle of Superposition: When two or more waves of the same type meet at a point, the resultant displacement of the waves is equal to the vector sum of their individual displacements at that point. Stretched String A horizontal rope with one end fixed and another attached to a vertical oscillator. Stationary waves will be produced by the direct and reflected waves in the string. Or we can have the string stopped at one end with a pulley as shown below. Microwaves A microwave emitter placed a distance away from a metal plate that reflects the emitted wave.By moving a detector along the path of the wave, the nodes and antinodes could be detected. Air column A tuning fork held at the mouth of a open tube projects a sound wave into the column of air in the tube. The length of the tube can be changed by varying the water level. At certain lengths of the tube, the air column resonates with the tuning fork. This is due to the formation of stationary waves by the incident and reflected sound waves at the water surface. Stationary (Standing) Wave) is one * whose waveform/wave profile does not advance {move}, where there is no net transport of energy, and * where the positions of antinodes and nodes do not change (with time). A stationary wave is formed when two progressive waves of the same frequency, amplitude and speed, travelling in opposite directions are superposed. {Assume boundary conditions are met} | Stationary waves| Stationary Waves Progressive Waves| Amplitude| Varies from maximum at th e anti-nodes to zero at the nodes. | Same for all particles in the wave (provided no energy is lost). | Wavelength| Twice the distance between a pair of adjacent nodes or anti-nodes. The distance between two consecutive points on a wave, that are in phase. | Phase| Particles in the same segment/ between 2 adjacent nodes, are in phase. Particles in adjacent segments are in anti-phase. | All particles within one wavelength have different phases. | Wave Profile| The wave profile does not advance. | The wave profile advances. | Energy| No energy is transported by the wave. | Energy is transported in the direction of the wave. | Node is a region of destructive superposition where the waves always meet out of phase by ? radians. Hence displacement here is permanently zero {or minimum}.Antinode is a region of constructive superposition where the waves always meet in phase. Hence a particle here vibrates with maximum amplitude {but it is NOT a pt with a permanent large displacement! } Dist between 2 successive nodes / antinodes = ? / 2 Max pressure change occurs at the nodes {NOT the antinodes} because every node changes fr being a pt of compression to become a pt of rarefaction {half a period later} Diffraction: refers to the spreading {or bending} of waves when they pass through an opening {gap}, or round an obstacle (into the â€Å"shadow† region). Illustrate with diag} For significant diffraction to occur, the size of the gap ? ? of the wave For a diffraction grating, d sin ? = n ? , d = dist between successive slits {grating spacing} = reciprocal of number of lines per metre When a â€Å"white light† passes through a diffraction grating, for each order of diffraction, a longer wavelength {red} diffracts more than a shorter wavelength {violet} {as sin ? ? ? }. Diffraction refers to the spreading of waves as they pass through a narrow slit or near an obstacle. For diffraction to occur, the size of the gap should approximately be equal to the wavelengt h of the wave.Coherent waves: Waves having a constant phase difference {not: zero phase difference / in phase} Interference may be described as the superposition of waves from 2 coherent sources. For an observable / well-defined interference pattern, the waves must be coherent, have about the same amplitude, be unpolarised or polarised in the same direction, ; be of the same type. Two-source interference using: 1. Water Waves Interference patterns could be observed when two dippers are attached to the vibrator of the ripple tank.The ripples produce constructive and destructive interference. The dippers are coherent sources because they are fixed to the same vibrator. 2. Microwaves Microwave emitted from a transmitter through 2 slits on a metal plate would also produce interference patterns. By moving a detector on the opposite side of the metal plate, a series of rise and fall in amplitude of the wave would be registered. 3. Light Waves (Young? s double slit experiment) Since light is emitted from a bulb randomly, the way to obtain two coherent light sources is by splitting light from a single slit.The 2 beams from the double slit would then interfere with each other, creating a pattern of alternate bright and dark fringes (or high and low intensities) at regular intervals, which is also known as our interference pattern. Condition for Constructive Interference at a pt P: Phase difference of the 2 waves at P = 0 {or 2? , 4? , etc} Thus, with 2 in-phase sources, * implies path difference = n? ; with 2 antiphase sources: path difference = (n + ? )? Condition for Destructive Interference at a pt P: Phase difference of the 2 waves at P = ? { or 3? , 5? , etc } With 2 in-phase sources, + implies path difference = (n+ ? ), with 2 antiphase sources: path difference = n ? Fringe separation x = ? D / a, if a;;D {applies only to Young's Double Slit interference of light, ie, NOT for microwaves, sound waves, water waves} Phase difference betw the 2 waves at any pt X {be tw the central & 1st maxima) is (approx) proportional to the dist of X from the central maxima. Using 2 sources of equal amplitude x0, the resultant amplitude of a bright fringe would be doubled {2Ãâ€"0}, & the resultant intensity increases by 4 times {not 2 times}. { IResultant ? (2 x0)2 } Electric FieldsElectric field strength / intensity at a point is defined as the force per unit positive charge acting at that point {a vector; Unit: N C-1 or V m-1} E = F / q > F = qE * The electric force on a positive charge in an electric field is in the direction of E, while * The electric force on a negative charge is opposite to the direction of E. * Hence a +ve charge placed in an electric field will accelerate in the direction of E and gain KE {& simultaneously lose EPE}, while a negative charge caused to move (projected) in the direction of E will decelerate, ie lose KE, { & gain EPE}. Representation of electric fields by field lines | | | | | Coulomb's law: The (mutual) electric force F acting between 2 point charges Q1 and Q2 separated by a distance r is given by: F = Q1Q2 / 4 or2 where ? 0: permittivity of free space or, the (mutual) electric force between two point charges is proportional to the product of their charges ; inversely proportional to the square of their separation. Example 1: Two positive charges, each 4. 18 ? C, and a negative charge, -6. 36 ? C, are fixed at the vertices of an equilateral triangle of side 13. 0 cm. Find the electrostatic force on the negative charge. | F = Q1Q2 / 4 or2= (8. 99 x 109) [(4. 18 x 10-6)(6. 6 x 10-6) / (13. 0 x 10-2)2]= 14. 1 N (Note: negative sign for -6. 36 ? C has been ignored in the calculation)FR = 2 x Fcos300= 24. 4 N, vertically upwards| Electric field strength due to a Point Charge Q : E = Q / 4 or2 {NB: Do NOT substitute a negative Q with its negative sign in calculations! } Example 2: In the figure below, determine the point (other than at infinity) at which the total electric field strength is zero. From t he diagram, it can be observed that the point where E is zero lies on a straight line where the charges lie, to the left of the -2. 5 ? C charge. Let this point be a distance r from the left charge.Since the total electric field strength is zero, E6? = E-2? [6? / (1 + r)2] / 4 or2 = [2. 5? / r2] / 4 or2 (Note: negative sign for -2. 5 ? C has been ignored here) 6 / (1 + r)2 = 2. 5 / r2 v(6r) = 2. 5 (1 + r) r = 1. 82 m The point lies on a straight line where the charges lie, 1. 82 m to the left of the -2. 5 ? C charge. Uniform electric field between 2 Charged Parallel Plates: E = Vd, d: perpendicular dist between the plates, V: potential difference between plates Path of charge moving at 90 ° to electric field: parabolic. Beyond the pt where it exits the field, the path is a straight line, at a tangent to the parabola at exit.Example 3: An electron (m = 9. 11 x 10-31 kg; q = -1. 6 x 10-19 C) moving with a speed of 1. 5 x 107 ms-1, enters a region between 2 parallel plates, which are 20 mm apart and 60 mm long. The top plate is at a potential of 80 V relative to the lower plate. Determine the angle through which the electron has been deflected as a result of passing through the plates. Time taken for the electron to travel 60 mm horizontally = Distance / Speed = 60 x 10-3 / 1. 5 x 107 = 4 x 10-9 s E = V / d = 80 / 20 x 10-3 = 4000 V m-1 a = F / m = eE / m = (1. 6 x 10-19)(4000) / (9. 1 x 10-31) = 7. 0 x 1014 ms-2 vy = uy + at = 0 + (7. x 1014)( 4 x 10-9) = 2. 8 x 106 ms-1 tan ? = vy / vx = 2. 8 x 106 / 1. 5 x 107 = 0. 187 Therefore ? = 10. 6 ° Effect of a uniform electric field on the motion of charged particles * Equipotential surface: a surface where the electric potential is constant * Potential gradient = 0, ie E along surface = 0 } * Hence no work is done when a charge is moved along this surface. { W=QV, V=0 } * Electric field lines must meet this surface at right angles. * {If the field lines are not at 90 ° to it, it would imply that there is a non- zero component of E along the surface. This would contradict the fact that E along an equipotential = 0. Electric potential at a point: is defined as the work done in moving a unit positive charge from infinity to that point, { a scalar; unit: V } ie V = W / Q The electric potential at infinity is defined as zero. At any other point, it may be positive or negative depending on the sign of Q that sets up the field. {Contrast gravitational potential. } Relation between E and V: E = – dV / dr i. e. The electric field strength at a pt is numerically equal to the potential gradient at that pt. NB: Electric field lines point in direction of decreasing potential {ie from high to low pot}.Electric potential energy U of a charge Q at a pt where the potential is V: U = QV Work done W on a charge Q in moving it across a pd ? V: W = Q ? V Electric Potential due to a point charge Q : V = Q / 4 or {NB: Substitute Q with its sign} Electromagnetism When a conductor carrying a current is plac ed in a magnetic field, it experiences a magnetic force. The figure above shows a wire of length L carrying a current I and lying in a magnetic field of flux density B. Suppose the angle between the current I and the field B is ? , the magnitude of the force F on the conductor is iven by F = BILsin? The direction of the force can be found using Fleming? s Left Hand Rule (see figure above). Note that the force is always perpendicular to the plane containing both the current I and the magnetic field B. * If the wire is parallel to the field lines, then ? = 0 °, and F = 0. (No magnetic force acts on the wire) * If the wire is at right angles to the field lines, then ? = 90 °, and the magnetic force acting on the wire would be maximum (F = BIL) Example The 3 diagrams below each show a magnetic field of flux density 2 T that lies in the plane of the page.In each case, a current I of 10 A is directed as shown. Use Fleming's Left Hand Rule to predict the directions of the forces and wo rk out the magnitude of the forces on a 0. 5 m length of wire that carries the current. (Assume the horizontal is the current) | | | F = BIL sin? = 2 x 10 x 0. 5 x sin90 = 10 N| F = BIL sin? = 2 x 10 x 0. 5 x sin60 = 8. 66 N| F = BIL sin ? = 2 x 10 x 0. 5 x sin180 = 0 N| Magnetic flux density B is defined as the force acting per unit current in a wire of unit length at right-angles to the field B = F / ILsin ? > F = B I L sin ? {? Angle between the B and L} {NB: write down the above defining equation & define each symbol if you're not able to give the â€Å"statement form†. } Direction of the magnetic force is always perpendicular to the plane containing the current I and B {even if ? ? 0} The Tesla is defined as the magnetic flux density of a magnetic field that causes a force of one newton to act on a current of one ampere in a wire of length one metre which is perpendicular to the magnetic field. By the Principle of moments, Clockwise moments = Anticlockwise moments mg â⠂¬ ¢ x = F †¢ y = BILsin90 †¢ yB = mgx / ILy Example A 100-turn rectangular coil 6. 0 cm by 4. 0 cm is pivoted about a horizontal axis as shown below. A horizontal uniform magnetic field of direction perpendicular to the axis of the coil passes through the coil. Initially, no mass is placed on the pan and the arm is kept horizontal by adjusting the counter-weight. When a current of 0. 50 A flows through the coil, equilibrium is restored by placing a 50 mg mass on the pan, 8. 0 cm from the pivot. Determine the magnitude of the magnetic flux density and the direction of the current in the coil.Taking moments about the pivot, sum of Anti-clockwise moments = Clockwise moment (2 x n)(FB) x P = W x Q (2 x n)(B I L) x P = m g x Q, where n: no. of wires on each side of the coil (2 x 100)(B x 0. 5 x 0. 06) x 0. 02 = 50 x 10