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Thank You Note Gr.2
Quiz by Khitam Mohamad
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MAY 1: "Thank you" note expressions & some information on the Thanksgiving holiday in the U.S.
Billy gets lost. Billy is a puppy. He lives in a big house with a blue roof. He loves to play fetch with Emmy. Emmy throws the ball. Billy chases it. Then, Billy sees Cat. He drops the ball and chases Cat. Cat runs down the street, and Billy chases him. Emmy cries, âCome back, Billy.â Cat runs through a farm, and Billy chases him. Cat runs into the forest, and Billy chases him. Cat climbs up a tree. Billy turns to go home. He cannot see the big house with a blue roof.â Oh, no, I am lost,â Billy says. Billy runs down a path. He sees Fox. âHow can I get home?â he asks Fox. âI have never been out of the forest,â says Fox. âAsk Cow in the farmerâs field,â Fox says. Billy runs to the farmerâs field. Billy says to Cow, âI am lost. âDo you know the way to my house?â Billy asks. âI have never been off the farm,â says Cow. âAsk Owl,â Cow says. Billy goes to Owl in the barn. âPlease wake up, Owl,â says Billy. âI need your help,â he says. âI am lost!â he cries. âDo you know a big house with a blue roof?â Billy asks. âYes, I do,â Owl says. Owl flies, and Billy chases her. Then, Billy sees Emmy at the big house with a blue roof. âThank you, Owl,â says Billy. Create an interactive "fill the gaps" quiz in seconds - complete with a 'Hall of Fame'! Instructions: 1. Edit the title of this quiz (above) to something appropriate. 2. COPY and PASTE your text into this box (TIP - plain text for best results, to avoid formatting glitches), and edit it as you wish. 3. DOUBLE-CLICK any word to turn it into a 'gap'. 4. To put the word back, simply double-click the gap again or drag the word from the top of the screen to the correct gap. 5. When you are finished, click 'save' to turn your work into an interactive quiz for your students - complete with a Leaderboard so you can see how quickly they finished! Note: When you save your work, you will provide a password which will allow you to edit the quiz again later.
Stages in the Sale of a Property Stage 1 â Getting to Instruction ⢠Initial contact with the vendor: need to check the following: type of property, contact details of vendor, address of property/Eircode and purpose of the contact - sale or valuation? If a sale, does the vendor need a quick sale? Qualify the lead i.e. is the vendor buying another property? If an investment property, is the tenant in situ? Check if there is a folio number available and confirm the ownership of the property. Schedule the viewing. ⢠Pre-viewing: Set up a file & record all info from initial contact on CRM system. Check the Property Price Register to help get a general idea of property valuation (subject to viewing, helps to display knowledge of area/market and set expectations for the vendor). Nature of property may affect pricing e.g. starter home vs. larger property with vendor seeking to downsize. Consideration for comparables may include similar/same location, size and condition of property, availability and type of parking, layout of property, plot size, orientation of garden, extensions undertaken etc. Nature of market conditions, state of wider economy, cost of capital and availability of credit may also be factors. ⢠Appraisal/viewing: Bring an advertising pack/sales & marketing brochures. Walk through property with client, note nice features/selling points for the brochure, let the client talk about upgrades/specific features of the property. It is very important to listen to the vendor and build rapport. Confirm property details e.g. condition and layout, plot size, orientation of garden. Check for certificates of compliance for any extensions, planning permissions for conversions, right of way if applicable etc. Check if a BER available/provide details for approved assessors. Demonstrate your/the practiceâs professional expertise, justify why you should get the instruction, discuss recent local sales and give your potential valuation. Discuss the sales fee, marketing fee and any additional charges e.g. professional photography, drone footage, virtual tours (walkthrough video, Matterport etc.) Ask how the vendor heard about you/your practice and why are they considering you for the sale. Where appropriate offer advice to help vendor increase potential sales price. (If possible, leave with signed Property Services Agreement/Letter of Engagement.) Thank you, send/email market appraisal, any queries/questions do get in touch and let the vendor know that weâll be in touch in coming days. ⢠Post appraisal â letter sent that pm/next morning with market appraisal; diary note to follow up. Check that market appraisal letter received and check for questions. If did not get sale, find out why not/debrief. If get the sale, email confirmation of instruction. Once PSRA sent and LOE returned signed = stage 2. Other details required â ID, proof of address, proof of ownership/title, solicitor details, BER certificate (refer to assessor if not available). All these should be uploaded to CRM. Stage 2 â Getting to âSale Agreedâ Set up appointment to measure & photograph, note any special features e.g., upgraded kitchen, south-facing garden. Provide ideas for improving sales potential (declutter, painting, tidy garden etc. Check if has vendor potential buyers in mind already e.g., relations, friends, other parties interested. Seek vendor approval for photos/text of brochure. Check for access (tenants in situ/working from home etc) and confirm viewing times. If given a key for viewings â tag it! Check alarm codes & whether a sign is allowed on the property. Bring to market â upload to all websites e.g., daft/my home, in house websites and create window display. Match the property against your internal database of potential purchasers /CRM system. Set up appointments for viewings on CRM or arrange for open viewings. Confirm viewings with vendor & purchaser. Turn on lights, open windows, secure valuables, leave out brochures & business cards, bring viewings sheets to keep record of attendees. Introduce yourself and get attendee details. Let people view the property and address any questions. Point out key features. Record questions to be answered and any feedback from viewers. Ask are they selling property? Let viewers know of offers already received. Lock up/alarm property/close windows. Provide vendor with feedback on viewings - number of viewers / questions raised/overall reaction to property. Offers should be confirmed in writing & upload to on CRM/ offers will be input by bidders onto online bidding platforms âProof of fundsâ required for offers in some practices. Successful bidder will be chosen by vendor, who might want quick sale/no chain or prefer the highest bidder. Booking deposit will be sought from successful bidder. The amount varies by practice but must cover fees. Sales Advice Notice/letter should be sent to both solicitors (and may be ccâd to vendor/buyer or notify both that SAN have gone out). Booking deposit receipt should be issued. The BER certificate and report should go to the solicitor. Send requests for docs/info to successful bidder including steps they need to take to progress sale e.g., organise the bank valuation and/or schedule the survey. Once the deposit is paid the property is Sale Agreed, inform other bidders, and update all websites/sales board etc. Stage 3 â Getting to closing Access should be organised for the bank valuation/survey. Stay in touch with both solicitors âcontract-chasingâ i.e., check when contracts are issued, signed and queries answered. Legal searches undertaken by the solicitors may include checking boundaries, land registry, title, rights of way, compliance certs etc. When contracts are signed 10% purchase price/booking deposit should be sent to the vendorâs solicitor. Once all queries satisfied = drawdown of mortgage/funding, house/life insurance in place. Title deeds will be requested once contract is signed. Decide final closing date. Check that the property taxes have been paid. Check that vendor has vacated the property. When vacant, conduct the final walkthrough and take final readings (MPRNs ). Check with solicitor if the drawn down funds h, and once received the solicitor gives authorisation to the estate agent to release the keys. The agent will do up invoice, send the balance of funds to solicitor and provide gift to purchaser. Finally remove sign, mark as sold on CRM, seek testimonials, upload to social media and close a/c on CRM
What is an official invitation letter? The companies write a letter of invitation-business when they host business visitors from abroad or from the same region or country. The business visitors can be investors; potential buyers may be conference visitors, business partners, employees of any company, or mere individuals who come for training at the companyâs facilities. If a company is inviting any visitor, a representative of that company must write the letter. Also, the firms must have some specific people who would sign the invitation letters. These letters are very much precise, only containing the necessary information. The invitation letter should state the name of the business organization they represent and their relationship to the host (e.g., distributor, regional sales reps, etc.). The letter should articulate the planned dates of travel, and must be formatted professionally. What is a personal invitation letter? A Personal invitation letter is a letter one writes to invite people to a party or a social gathering at a very personal level. It is a formal request asking for the personâs presence at the event that is going to take place. All the relevant details regarding the event like the reason, date, time and venue and the dress code, if any, must be provided in the invitation letters. This will keep the guests informed, and they will feel happy to attend the event. The style and tone of the letter would depend upon the relationship between the sender and receiver. Through the letter, you should be able to make the receiver feel that you highly value his/her presence at the party or the event. A personal invitation letter can be written to invite a person to a birthday party, wedding, conference, meeting, dinner, etc. Before writing the letter, make sure you have a list of people whom you would like to invite to the party or the event. How to Write an Invitation Letter Writing an invitation letter becomes easy and swift once you get through the tips and the format of the invitation letter provided below. Usually block, semi-block or a modified block format is used for official invitation letters. The important aspects of any invitation letters are date, time, salutations and closing. For more advice refer to the tips provided. Tips for Invitation Letter Writing â Organize the Matter â Before you draft an invitation letter ensure that you have all the required material. This material refers to a list of the people to be invited, sequential order of the events, timings of the events, special guest, official documents, photocopies and any other required item. Some items may also need to be attached along with the letter, keep them alongside. Refer to these as and when required. All the relevant documents will help you in drafting the letter. â Drafting â You donât just write a letter straightway and post it. It has to be reviewed and finalized. One of these processes is drafting. Drafting ensures that your mistakes and their rectification arenât passed on to the invitation itself. Make all the mistakes in the draft itself. Drafting an invitation letter is important as sometimes we may make mistakes that we are not able to see but they are visible to others. One may require a draft to be approved by seniors before it is finalized. A second opinion from a friend or peer etc. may be required as well to determine certain things. â Politeness â You donât need to be told that you have to use polite language while writing an invitation letter, why would you be rude when sending an invitation? True, but you have to remind yourself of certain manners and etiquettes required of an invitation. Your invitation is your initiative, not the recipients so you need to be gracious. Always begin the letter with a welcome note instead of straightforward information of the invitation. Words of respect and gratitude are symbols of courtesy and politeness, always expressing your gratitude in the beginning and the end of the letter. â Positive Tone â The gesture of welcome and gratitude themselves are positive points of an invitation letter. Apart from these, gestures of appreciation and anticipation are other positive points which can persuade a guest to attend the event. When you show your appreciation and anticipation towards the recipient through your words, it is an acknowledgement of his importance and thereby a positive approach. Towards this effect two tenses are used within the invitation letter, the present and the future. The present tense conveys information about the event and the future tense conveys an anticipated presence of the guest. â Offer Assistance â An invitation being the responsibility of the sender, the assistance to the recipient by default becomes a responsibility of the host. The more facilities you provide the better the chances of someoneâs attendance. You can offer pick up and drop services, accommodation, meals, provide them contact numbers in case you are not present at the venue and other required assistance. Relevant facts like date, time and venue of the event in the beginning itself is itself assisting. These assistances encourage a positive response from the invitees. â Special Instructions â Some occasions require special instructions for the guests. These instructions can be: 1. Dress code 2. Road or route map 3. Purpose of the occasion â birthday, honor, anniversary etc. 4. Return gift 5. Response or confirmation to the invitation 6. Attire and items required for the guest to bring 7. No eatables allowed 8. Entrance only by invitation 9. 2 people per pass 10. No weapons allowed â Length of the Matter â A simple invitation letter will only contain only the relevant facts. A simple invitation letter features an introduction which allows the sender to introduce themselves and or the organization they represent. A simple background of the individual or company is enough. Though invitations are meant to be concise and straightforward, it isnât necessary. You can vary the length as per your need and requirement. Wedding and party invitation letters are not lengthy as compared to visit and certain personal invitation letters. â Using Letterhead â As a rule official Invitation letters require a letterhead. Letterhead represents the sender and its inclusion is authority established. If you have a pre printed letterhead then use that. Personal Invitation letters donât require letterheads and one can use it as per oneâs desire. â Gesture of Appreciation â Next, the appreciation for the guest to attend an activity or event must be shown. This can be completed with a formal note, stating that you look forward to seeing the individual at the event. â Donât forget the Enclosure â Some requests require certain documents to be attached; these can be the photocopies of documents like agreements, hard copies of email received, earlier correspondence, receipts, warranty etc. Keep original copies of all your letters, faxes, e-mails, and other related documents. â Closing the Letter â Start the letter with Gratitude and end it with the same. It is a professional and social courtesy. At the end of your last paragraph is written, a complimentary close of the likes of âSincerelyâ, âThank youâ, âTrulyâ is essential. Close the letter by restating your appreciation and gratitude. â Proofreading â Check for - awkward phrases, grammatical errors, incomplete sentences and spelling mistakes. Fix them with appropriate punctuation and remove dull or lifeless sentences and replace them with clever phrasing, poetry or a themed approach. This is the final step; the draft will be reviewed and revised before it acquires a proper form. Read it aloud to yourself to figure out mistakes which are missed out in writing. â Inform in Advance â Invitation letters need to be sent in advance. Try to send the invitation letter two weeks or more in advance. The recipient needs to know in advance so that they can adjust their schedules, book tickets or make other arrangements which are essential.
Land warfare is a complex domain that involves the application of military power on the ground to achieve political and strategic objectives. Modern military doctrine, such as that used by the U.S. Army and the Indian Army, categorizes these elements into Combat Power and the Principles of War. 1. The 8 Elements of Combat Power Combat power is the total means of destructive, constructive, and information capabilities that a military unit can apply. It is typically broken down into eight key elements: ElementDescriptionLeadershipThe "multiplier" of all other elements. It provides purpose, direction, and motivation to soldiers.InformationEnables commanders to make informed decisions and creates opportunities to achieve results.Mission CommandThe system used to integrate the other elements. It focuses on decentralized execution based on the commander's intent.Movement & ManeuverThe movement of forces to gain a positional advantage over the enemy to deliver lethal or non-lethal effects.IntelligenceThe understanding of the enemy, terrain, weather, and civil considerations.FiresThe use of weapon systems (artillery, mortars, air support) to create specific lethal or non-lethal effects.SustainmentThe logistics required to maintain operations, including ammunition, fuel, food, and medical support.ProtectionThe preservation of the force so that the commander can apply maximum combat power.2. The Principles of War These are the enduring "rules of thumb" that guide how land forces are employed strategically and tactically: Objective: Direct every operation toward a clearly defined and attainable goal. Offensive: Seize, retain, and exploit the initiative. You cannot win by defending alone. Mass: Concentrate the effects of combat power at the most advantageous place and time. Economy of Force: Allocate the minimum essential combat power to secondary efforts so you can "mass" elsewhere. Maneuver: Place the enemy in a position of disadvantage through flexible movement. Unity of Command: Ensure all forces operate under a single responsible commander toward a common objective. Security: Prevent the enemy from gaining an unexpected advantage. Surprise: Strike the enemy at a time, place, or in a manner for which they are unprepared. Simplicity: Prepare clear, uncomplicated plans to minimize confusion in the "fog of war." 3. The Modern Legal Framework Land warfare is also governed by the Law of Land Warfare (International Humanitarian Law), which rests on four pillars: Military Necessity: Actions must be necessary to achieve a legitimate military goal. Distinction: Forces must distinguish between combatants and non-combatants (civilians). Proportionality: The anticipated harm to civilians must not be excessive in relation to the concrete military advantage gained. Unnecessary Suffering: Weapons and methods must not cause gratuitous or superfluous injury. Note: Contemporary land warfare is increasingly "Multi-Domain," meaning land forces must now integrate with cyber, space, and electronic warfare to be effective. , While land warfare uses many tools, the two primary "philosophies" of how to win a war are Attrition and Maneuver. Most modern conflicts are a spectrum of both, but understanding the pure form of each helps explain military strategy. 1. Attrition Warfare: The "Sledgehammer" Attrition warfare is a strategy where one side attempts to win by wearing down the enemy to the point of collapse through continuous losses in personnel, equipment, and supplies. Core Logic: "I have more than you." It assumes that if you can destroy the enemyâs resources faster than they can replace them, you will eventually win. Focus: Firepower and mass. Success is measured by "body counts," equipment destroyed, and the steady seizing of terrain. Command Style: Usually centralized and methodical. It requires strict synchronization of massive resources (artillery, logistics, manpower). Historical Example: The Battle of Verdun (WWI). German Chief of Staff Erich von Falkenhayn famously stated his goal was to "bleed France white" by forcing them to defend a position they could not afford to lose, regardless of the cost in lives. 2. Maneuver Warfare: The "Scalpel" Maneuver warfare seeks to shatter the enemyâs moral and physical cohesionâtheir ability to act as a unified forceârather than simply destroying every soldier. Core Logic: "I am faster and more unpredictable than you." It aims to create a state of chaos where the enemy's leadership can no longer make effective decisions. Focus: Speed, surprise, and dislocation (forcing the enemy to be in the wrong place at the wrong time). The OODA Loop: Developed by Col. John Boyd, this is the heart of maneuver theory. It stands for Observe, Orient, Decide, Act. The goal is to cycle through these steps faster than the enemy, essentially "getting inside" their decision-making process until they collapse from confusion. Historical Example: The 1940 Invasion of France (Blitzkrieg). Instead of fighting a line-by-line battle of attrition, German forces used speed and concentrated armor to bypass strongpoints, cut communication lines, and cause a total systemic collapse of the French military in weeks. 3. Key Differences at a Glance FeatureAttrition WarfareManeuver WarfareObjectivePhysical destruction of the enemy army.Functional/Psychological collapse of the enemy.TargetThe enemy's strength (mass).The enemy's weakness (vulnerability).Primary ToolMassed Firepower.Movement and Tempo.Command"Command Push" (Top-down, rigid)."Recon Pull" (Decentralized, flexible).Success MetricExchange ratios (Kill counts).Disruption and loss of enemy control.4. The Modern Synthesis: "Schwerpunkt" In practice, no army is purely "maneuver" or "attrition." To maneuver successfully, you often need a period of attrition to punch a hole in the enemy's line. A critical concept here is the Schwerpunkt (Center of Gravity/Focus of Effort). A commander identifies the single most important place to strike and concentrates all available "elements of power" there. While the rest of the front might look like attrition, the Schwerpunkt is where the maneuver happens to achieve a breakthrough. Modern Reality: In high-intensity conflicts today (like the war in Ukraine), we see a "return to attrition" because modern sensors (drones, satellites) make it very difficult to achieve the surprise needed for pure maneuver warfare. When you can see everything, it's hard to be "unexpected."
To understand melody in music, think about some music youâre familiar with. If you were asked to hum it, what would that sound like? The part of the music that youâd hum is the melody. Itâs the main thread of sound that your brain tracks and holds onto when youâre listening to music. In vocal music, the melody is sung by the lead singer. Other vocalists can provide harmony and instruments can add accompaniment, but the melody is the star of the show.What are the characteristics of melody in music? How do you describe a melody in music? A melody needs to have two things. The first is a sequence of notes, or pitches, which range from high to low. The second is rhythm, which is the timing and duration of each note. These two simple elements can create an incredible variety of combinations. Even though a melody only consists of one note at a time, it can convey so much energy and emotion. Melodies can be fast and sparkly, like âThe Flight of the Bumblebee.â They can be slow and majestic, like âFinlandia.â They might be sweeping and graceful, like a Strauss waltz. Or they can be fun and exciting, like your favorite pop tunes that you love to sing along with. Melodies often tell you a lot about where a piece of music comes from. Itâs easy to recognize and identify melodies from different folk traditions such as the Japanese folk song âSakuraâ or the Irish tune âStar of the County Down.â Learn how to play your favorite melodies on piano, and more! Sign up now. What is melody in music? Here are some examples. Here is the famous melody for the song âLean on Meâ written out on a staff. Notice the way that the notes move up, down, and then repeat. What is melody in music? Example of Lean On Me notes on treble staff. A melody all by itself is great, but music can be even more fun when thereâs an accompaniment. Here are a few bars of âLean on Meâ with the accompaniment written out. As you listen to this song, notice how the accompaniment has a very similar rhythm and movement to the melody. Then thereâs that one note in the bass line that comes along every measure with its own rhythm, which adds some extra energy and movement to the song. What makes a good melody? When you create a melody, there are four types of movement you can use: Repeat (same note) Step (up or down) Skip (up or down) Leap (up or down) Stepping and repeating are the most common types of melodic motion, and this makes a melody easier to sing. Most âhummableâ tunes use steps and repeats almost exclusively. This kind of melody is called conjunct. Beethovenâs âOde to Joy,â one of the most famous melodies of all time.Skips and leaps are generally more sparing in melodies, but when thoughtfully placed they can have a powerful emotional impact. Tunes with a lot of leaps are called disjunct. Listen to Sarah Brightman sing All I Ask of You from The Phantom of the Opera starting at 0:39. This is a very disjunct melody, and challenging to sing. Great melodies also incorporate patterns that blend unity, repetition, and contrast. Our ears love patterns, but they also love novelty and growth. A good melody incorporates all of these elements. For example, listen to John Williamâs âPrincess Leia Theme.â Can you hear the repeated pattern in the melody that gradually moves higher as the theme progresses? Now listen to the way it changes and develops into something that fits with what came before but sounds new at the same time. This is some great melodic writing! Can melody exist without rhythm? There is no way for a melody to exist without rhythm. Even if your melody only has one note, that note has a duration, and thatâs the rhythm. If your melody has two notes, how long those notes last and how much time passes between hearing them is also a rhythm. A melody in music can often be recognized even when itâs performed with different rhythms. This frequently happens in live performances of pop, rock, and jazz, in which singers typically improvise slight rhythmic differences with each performance. No two renditions are exactly the same, and this constant reinterpretation keeps the music fresh. How to make a melody for a song on piano Creating your own melodies on the piano is easy and fun! There are so many ways you can discover a melody all your own. Here are a few ideas. Get some inspiration from the world around you. What can you hear right now? A clock ticking? A bird song? A car passing by your house? See if you can find some notes on the piano that imitate the sounds you hear. Think of a feeling youâd like to put into a melody. What are some ways you could make a string of notes sound happy, sad, angry, or maybe just thoughtful. Choose a line from a poem you like, or write your own. Read it out loud and put some feeling into it. Did your voice rise and fall in pitch as you were reading? Now go to the piano, start on any note you like, and try to imitate what happened when you read. Go up when your voice naturally went up, go down when your voice naturally went down. How did that sound? Now you have the perfect melody to go with those words. Too many keys on the piano? The truth is, most melodies use only a limited number of different notes. Try creating a melody using only the black keys. These form whatâs called a pentatonic scale. Itâs used in a lot of folk music traditions around the world and can be a great place to start if you want to create your own melodies. Remember, when you create your melody, keep it simple. Use repeated notes and steps, but add a few skips to keep things interesting. One tip about leaps: when you do put in a big leap, try doubling back and filling in the empty space you leaped over. This keeps the melody self-contained and easier to sing. Also, see if you can use the same patterns of notes and rhythms to give the melody unity, but also change those patterns to give it variety. There is no right or wrong way to create your own music. Keep trying combinations of notes and rhythms until you find something that you like. How many bars and notes are in a melody? Many types of music tend to have a prescribed number of bars, or measures. This will vary widely between different genres, and creates an overall sense of musical structure. If youâre writing a pop song, a verse will usually have between eight and sixteen bars. The prechorus that follows often has just four bars, and this âforeshorteningâ creates a sense of acceleration, driving the listener toward the chorus. The number of notes can also vary widely. A melody in music needs at least two notes, and a long and complex one can have hundreds or even thousands of notes. What is a countermelody in music? How many melodies should a song have? A counter melody is a melodic line that interacts with the primary melody as an independent but supportive voice. A great example of this is the song âWe Donât Talk about Bruno.â Each character sings their own melody during the piece, but these melodies all combine at the end as countermelodies. This produces a musical texture known as counterpoint. The same thing happens in âOne Day Moreâ from Les Miserables. The different melodies are first sung separately, but end up being combined in a splendid, complex texture that leads the music to its thrilling conclusion. The difference between a countermelody and regular harmony is that harmony usually supports the rhythms of the melody. A countermelody will move more independently, with different rhythms from those of the melody, and will often sound âmelodicâ when sung or played all by itself. A melodic song should have one main melody. This is the part that the lead voice sings. Itâs usually in the spotlight, and will be the most memorable part of the music. Anything else is either harmony, countermelody, or accompaniment. Does all music have to have a melody? A piece of music doesnât have to have a melody. There are many different kinds of music without melody. For example, a lot of music played on percussion instruments wonât have a melody. Listen to this example of Tahitian drumming. This is some great music, exciting and fun to listen to, but youâd have a hard time humming it. Itâs music, but it doesnât have a melody. Rap music is another style of music where there doesnât have to be a melody. In rap, words are chanted rather than sung. The performer will raise and lower the pitch of their voice for emphasis, but itâs the rhythm of the words that creates most of the music. Music can even lack any melody, at least in some sections. Listen to the opening chords of âDuel of the Fates.â This choral passage is all about harmony, with little rhythmic variance or sense of melody. But it makes an effective contrast with the next section, which is bustling with rapid instrumental melodies. In some pieces, there are multiple melodic lines but there is no one main melody. When music is made up of equally important countermelodies, it creates a contrapuntal texture. Baroque composer J.S. Bach was one of the greatest masters of this style, such as in his Little Fugue in G minor. It starts with a single melodic line, the subject, but then a countermelody is added, and then more and more until several melodic lines are playing together. Itâs fun to listen to, but once all the countermelodies are playing together it becomes hard to decide which part to hum along with! Youâll also hear a lot of counterpoint in jazz music, in which the different instruments are all playing together and improvising their own melodies that combine to create a rich, thick musical texture. Experience the wonder of melody in music! Whether youâre humming your favorite tune, or creating a new song all your own, melody is a memorable, shareable part of music. Enrich your music experience by being aware of, listening for, and enjoying the melodies all around you.
Changes. Things are always changing, like the clock, the weather, and even me. It seems nothing ever stays the same. My life has been full of changes. Sometimes I don't feel good about them, but then later it gets better. Taffy, my kitty, ran away. We have looked for him all over, but we cannot find him anywhere. I miss Taffy a lot, and I am sad. Dad says that we can get another kitty. That makes me feel better. I don't know what I will name him, but I will always remember Taffy. My best friend, Robin, just moved away. The moving van took away everything, and the house is empty. I wish Robin were here to play with me. Robin now lives in the mountains. I have never seen mountains, but they sound like fun to visit. Mom says we can take an airplane, so I can see Robin and play with her again. The day I started the new school year, I was scared of all the new children in my class. I was afraid that they wouldn't like me, and that I couldn't run as fast as they do. Now I am happy because I have made lots of new friends. I like Sarah and Ana, and Mary Lou, who makes me laugh. I love my class and my teacher. Mom just took a new job at an office downtown. She's not here when I come home from school. My Aunt Barbara is here to give me cookies and milk. Then I wait and wait for Mom to come home. When the hands of the clock point straight up and down, she comes home, and that makes me happy. Things are always changing, even with me. Yesterday I looked in the mirror. My face looked like a Halloween pumpkin because I lost my first tooth. I had a big surprise when I woke up this morning. My tooth was gone from under my pillow. There was a note from the tooth fairy and a whole quarter. I'm going to save it to buy some colored pencils. In school I learned that crawly caterpillars change into butterflies. And tiny acorn nuts grow into great big oak trees. Mom says that long ago, she was little like me. Do you think some day I will change and be a grownup? I think I will be an artist.
Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: ⢠Free-falling objects do not encounter air resistance. ⢠All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs ⢠Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 ⢠(-8.00 m/s2) ⢠d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) ⢠d (16.0 m/s2) ⢠d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) ⢠(4.1 s) + ½ ⢠(6.00 m/s2) ⢠(4.10 s)2 d = (0 m) + ½ ⢠(6.00 m/s2) ⢠(16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: ⢠An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. ⢠If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) ⢠(t) + ½ ⢠(-9.8 m/s2) ⢠(t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) ⢠(t)2 -8.52 m = (-4.9 m/s2) ⢠(t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 â˘(-9.8m/s2) â˘d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) â˘d (-19.6 m/s2) ⢠d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) ⢠d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.