Five ways tools can help you tackle Twitter - Emphasis

Five ways tools can help you tackle Twitter Five ways tools can help you tackle Twitter The basic Twitter.com platform is surprisingly inflexible. For example, it doesnt allow you to schedule tweets for later, monitor how many people have clicked on your links, combine multiple accounts or view more than one stream of information at a time. So most people who embrace Twitter use a variety of tools and apps to improve their experience. 1. Dashboard Two of the most popular dashboards are Tweetdeck (which started out as a separate entity but was bought by Twitter in May 2011) and Hootsuite. Both are free and let you view several streams simultaneously (for example your own tweets, replies to your tweets, direct messages or your timeline) in adjacent columns. Theyre also good for managing multiple Twitter accounts at the same time, and scheduling tweets. The main difference is that Tweetdeck is a desktop app so its not ideal if you hotdesk or work from several locations, while Hootsuite is browser based and therefore more portable. 2. Scheduled tweets Buffer offers even easier tweet scheduling, where instead of programming in a time and date for each tweet, you simply set a pattern. For example, you could program it to send two tweets a day, at 12.30pm and 3.30pm, Monday to Friday. Then you just fill up the dashboard with your tweets and drag and drop them into the order you want. It also tracks the performance of tweets sent through Buffer, letting you know how many clicks, retweets, replies and favourites they received, as well as their potential reach. 3. Collaborative tweeting If youre setting up a Twitter account that several people will contribute to, GroupTweet is well worth a look. It allows multiple users to post tweets to one account, either through the GroupTweet dashboard, or via their personal account using the relevant @ address or hashtag. The basic version is free, but if you want to be able to moderate and schedule tweets, youll need to upgrade at a cost of $4.99 a month. 4. Collating tweets On Twitter.com, your tweets dont stay around for long. If you need to retrieve something that you tweeted, or was tweeted to you, more than a couple of weeks back, youll be lucky if you can still find it. Searching in Google can help, but it depends how far back you want to go. Rather than digging around to try and find important tweets after the fact, favourite them at the time. Or if youre having a discussion and you want to save all of it, use Storify. Its great for saving brainstorming sessions for later heres one of mine discussing the differences between lunch, tea and dinner (a brainstorm of such epic dimensions that I still havent written the article I intended to). 5. Performance analysis It can be tempting to try to measure your Twitter performance, but proceed with caution. Basically, youre already doing it right if people are talking to you, RTing you or opening your links, and if your number of followers is growing. However, if you do want a little feedback, there are services available. Just remember to take what they say with a pinch of salt, and not get too caught up in the idea of performance after all, its about communication and relationships, not numbers. One interesting service is Crowdbooster, which shows you which of your tweets have been most popular and how many people they have potentially reached (it calls these impressions). It also reminds you about tweets you havent yet replied to, offers you the opportunity to schedule tweets for later and even advises you about what it thinks is the best time of day to tweet to your followers. If you just want to use it with one Twitter account, its free. To add more, youll have to pay ($39 a month for ten accounts, $99 a month for 30 accounts). A more controversial service is Klout, which scores your social influence between 1 and 100 based on data such as follower and following numbers, retweets and interactions. Its accuracy, however, is debatable. For example, it thinks I am influential not just about Brighton (fair enough, I live there) but Afghanistan and the Chicago Bears (neither of which I recall ever tweeting about). Over to you What tools do you use and recommend, and why? Well be writing more about Twitter in the new year, so wed love to hear your tips. You can either comment below or tweet us on @EmphasisWriting. Want more guidance on how to write for Twitter? See our Four tips for effective tweeting.

13 Kick-Ass Tips for Writing Fantasy Fiction

13 Kick-Ass Tips for Writing Fantasy Fiction 13 Kick-Ass Tips For Writing Fantasy From Professional Fantasy Editors Has there ever been a better time to be writing fantasy? Where once it was a fringe genre, now fantasy is everywhere in pop culture, from Harry Potter to the memes surrounding Jon Snow.There’s also never been a more exciting time to write fantasy. The genre is changing daily, as authors such as Neil Gaiman, Susanna Clarke, and Patrick Rothfuss continue to interpret, subvert, and stretch it to attain new pinnacles. What’s more, the public can't seem to get enough of it, proving that there is a market for fantasy - and it’s a big one.So, if you’re an author, where can you find a place for yourself in today’s talent-rich terrain?In our search for the finest writing tips in the realm, we spoke to seven of the top fantasy editors on our marketplace. They’ve worked with George R.R. Martin, James Dashner, Brandon Sanderson, and many more of the brilliant authors who are re-defining the genre. Here’s what they said.1. Identify your marketIf y ou don’t know your market, you’ve already made a mistake, says Erin Young, an agent for Dystel Goderich Bourret, which represents authors such as James Dashner of Maze Runner fame.â€Å"Oh, my market is fantasy,† you might say, waving your monthly subscription of Imagination And Me. But is your story steampunk, urban, or grimdark fantasy? Is it for children or  young adults? Are there elves or tech? Is it set in the modern world, or is it a re-imagining of an alternate past? Jonathan Strange and Mr. Norrell, for instance, doesn’t target Discworld’s readers, and no-one would instinctively group Harry Potter and Stephen King's The Dark Tower in the same category. Castle Ruins, art by Jeff Brown.â€Å"You’re absorbing ideas. You're absorbing grammar. You're absorbing sentence structure and rhythm and prose,† she says. â€Å"Read books with description or dialogue you admire. Read the books that are classics- they are classics for a reason- and read the books that are bestsellers and read the books that are award winners. Read and read and read, and you'll start to see your own writing improve.†To take specific action, Nieveen suggests picking the 10 books that you most admire. Then, it's just a matter of re-reading them and noting strengths in their plot, dialogue, characters, and scene structure.  Learn from the best - and then go forth and tilt the arena again yourself.What are your tips for writing fantasy? Leave them in the comments below. You can also check out our list of the 100 best fantasy series ever  for inspiration!

Social Media and Mobile Search Marketing in Saudi Arabia Research Proposal

Social Media and Mobile Search Marketing in Saudi Arabia - Research Proposal Example According to reports released recently, there are approximately over three million Saudi Arabian Internet users who spent over three billion dollars in making purchases through ecommerce in the year 2010 (Bartlett, 2001). The biggest selling products were electronics which came second to the sale of software products during the year 2010 (Hillman et al, 2008). This implies that businesses who had invested in the internet during the year made big profits as a result of their investment activities. Hotels and airports also recorded booming online business, as they were the top earners for online businesses in the kingdom (Borysowich, 2010). Currently, reports indicate that there are signs that these values will continue rising within the next few years. This is because more people in their populations are joining the Internet and the service providers have also upgraded their systems (Hillman et al, 2008). For instance, the STC Company within the country has upgraded her broadband leve ls of penetration from 4% to 22% in the remote areas of the nation which were previously not able to access the service (Ader, 2008). This means that there is great support for similar businesses from the providers as they will be able to reach and trade with more citizens along with non-citizens in a more effective manner (Vithal and Jansen, 2009). The marketers participating or rather using the Internet should therefore begin developing their campaigns in the service. This is in view of the infrastructural developments going on and the profitable nature of ecommerce within the country (Hillman et al, 2008). There are predictions made that suggest that Internet spending is going to be on the rise as more of the wealthy people in the nation get faster access to the Internet. This is... As the discussion stresses the marketers participating or rather using the Internet should therefore begin developing their campaigns in the service. This is in view of the infrastructural developments going on and the profitable nature of ecommerce within the country. There are predictions made that suggest that Internet spending is going to be on the rise as more of the wealthy people in the nation get faster access to the Internet. This is in addition to the improvements being made in payment gateways to facilitate safer and faster transfers of funds. It is therefore the ideal moment for investors willing to invest in the sector to start exploring safe avenues and businesses to indulge in. This paper discusses that the use of the Internet within the Saudi Arabian population has led to an increased awareness of their rights and has also helped reduce the oppression against their women. For example, a campaign was started in the country using YouTube videos to sensitize the people on the right of a woman to drive. This was after the site highlighted the plight of a woman who was arrested on two separate occasions for driving and put into custody despite her driving safely. The aired clip raised a great stir within the population and this is a good example of just how influential the Internet is within the country. The Internet has been widely used across many family lines and countries to connect people and businesses, which makes it a suitable tool for marketing products to the population.

Consequences of the new deal Essay Example | Topics and Well Written Essays - 250 words

Consequences of the new deal - Essay Example Meanwhile the Republicans were either contrasting the whole New Deal as an adversary of growth and commerce or accepting part of it, undertaking to make it better. Historians have distinguished between a â€Å"First New Deal† in 1933 and a â€Å"Second New Deal† between 1934 and 1936. The â€Å"First New Deal† was apprehensive with sectors which demanded urgent economic recoveries like banking, industry and farming. The â€Å"Second New Deal† focused on the Wagner Act which aimed at promoting labor unions, the Social Security Act, the Works Progress Administration (WPA) which was a relief program. Other programs aided migrant workers and occupant farmers. The other significant legislation of New Deal is the Fair Labor Standards Act (1938). It set the maximum hours and minimum wages for most groups of workforce (Henretta, Brody, Fernlund and Benjamin p233). Though the New Deal never stopped the Depression, it did have some notable consequences. The WPA program increased employment opportunities. The public was also confident of the government and there was a substantial rise in the power and size of federal government. The Social Security Act was a key milestone relative to the New Deal programs. Finally, the national government took an active role in the welfare of its citizens (Henretta, Brody, Fernlund and Benjamin

Greenland Glaciers and Global Warming Essay Example for Free

Greenland Glaciers and Global Warming Essay Global warming, which is the increasing of the average temperature within the air near the Earths surface and the oceans, has caused the glaciers in Greenland to melt, causing the water levels to rise and the climate to change. Global warming is an unfortunate event that is taking place in numerous parts of the world, enabling bizarre and, in some instances, unnatural changes in the weather. Global warming has become most noticeable in the polar regions, amongst the polar icecaps, or in the more iced-over regions of the world, such as in Greenland and the Atlantic Ocean. In fact, Greenland has become the most common area for quickly-dissolving glaciers, making it the most notorious for climate and weather changes throughout the world. It is difficult to connect weather changes to global warming, though it has been proven that some more pronounced changes are likely to come about, and in fact, already are. One of the most obvious changes involves an increase in precipitation, as well as changes in the average patterns of precipitation, which can lead to flooding and, in turn, drought. The sea levels worldwide will rise, and are rising, as the glaciers melt, which will cause Arctic shrinkage the shrinking of the Arctic region due to climate change. In time, this shrinkage could possibly be seen in other areas, including the Atlantic Ocean. Some other irreversible affects include the frequency and intensity of extreme weather events, such as hurricanes and tsunamis. With the continuously melting Greenland glaciers, these risks are more likely to happen and these changes will only become more obvious and the melting becomes more rapid. Jason Box, a professor at Ohio State and a global warming researcher, has noticed a rapid and unsettling change in the amount of glaciers in Greenland. In an interview in regards to the melting glaciers and global warming, Box stated that we fly over the worlds fastest-deteriorating glacier; and in 2003, we didnt even recognize the place. It had doubled its speed (of shearing off ice) and lost about 6 miles of width (Feran). Box goes on to state the worries that he feels about global warming, as well as pointing out a slight change to weather happenings around the world for instance, a snowstorm in an area that, despite being cold, has never seen such harsh weather. Box feels that this weather event can be linked simultaneously with global warming from the Greenland region. In further studies done by scientists and other global warming researchers, it has been discovered that a huge portion of the Atlantic region is warming just as much and just as fast as the rest of the world (Wilkinson). The scientists have researched and discovered that the temperature has risen 2. 5 degrees in the past half century and that there has been a 140 percent ice loss within a decade. This has caused ice shelves to break up or disappear, exposing the glaciers behind them and speeding up the discharge of ice and fresh water into the ocean (Wilkinson). In the article, Dr. Ian Allison of the Australian Antarctic Division says that the activities taking place in the Atlantic are related to the rising of the air and water temperatures. Allison also stated that the melting of the Greenland glaciers are of the biggest concern, saying that its changes are even more noticeable than those of other regions. In Greenland, the rate of ice loss is getting greater over the last 10 years and the surface ice melt is definitely related to the warming. Allison, whos main focus is that of the Arctic and Atlantic regions, has been keeping close note on the melting glaciers, as well as trying to compare them to changes that have been taking place with weather. The more ice that the Atlantic loses, as well as the rest of the regions under the pressure of global warming, the more heat that comes back to it. When there is no ice to reflect the heat of the sun, the heat permeates through the water, causing the water to warm up even more. The heat is then spread to the remaining glaciers, which causes an almost domino effect, repeating itself until all that can happen is for the sea levels to rise. According to Alan Boyle, a science editor, Greenlands glaciers have been dumping ice into the Atlantic Ocean at a rate thats doubled over the past five years, as researchers have reported. Yet there are many scientists and researchers that are not as worried about the melting of the glaciers as others are; they claim that Greenland has gone through warming before, but the heat had been followed by cooling temperatures. Many of the researchers feel that the same thing is happening again. These scientists are not disregarding the possibility of global warming, but are wary to rule in Greenland as a current problem. Other scientists are against this, saying that Greenland has been warming up 2. 2 times faster than it has in previous years. Greenland is home to one of the worlds largest, and one of the most quickly dissolving, glacier, the Kangerdlugssuaq Glacier. The aforementioned glacier has gone from being completely stationary as of 1996 to flowing at a rate of fourteen kilometers a year by 2005; it is because of this that it is considered one of the fastest moving glaciers on the planet. It is also because of this, as well as Greenlands other quickly-melting glaciers, that will play a huge, unwanted role in the rising of the worlds sea levels (Biello). Greenland has become one of the biggest concerns of scientists, due to the alarming rate that its glaciers are melting, as well as to the obvious increase in the temperature. Since Greenland is home to some of the most quickly melting glaciers, as well as to the worlds largest, it will be one of the main purveyors of climate and weather changes throughout the world. Bizarre changes in weather have already been noticed, with many scientists blaming global warming on these changes. Regardless of the fact that Greenland is in a region of its own, what is taking place with its glaciers can affect the entire world; the weather will be the most pronouncedly changed. Horrific weather events will last longer than what is considered average, and they can take place in areas that would not normally see such conditions. Works Cited Biello, David. (17 Feb 2006. ) Greenlands glaciers: Melting and on the move. Scientific American. Retrieved March 24, 2009, from http://www. sciam. com/article. cfm? id=greenlands-glaciers-melti. Boyle, Alan. (16 Feb 2006. ) Greenlands glaciers losing ice at faster rate. Retrieved March 24, 2009, from http://www. msnbc. msn. com/id/11385475/. Feran, Tim. (24 March 2009. ) Glacier warning us, OSU researcher says. The Columbus Dispatch. Retrieved March 24, 2009, from http://www. columbusdispatch. com/live/content/life/stories/2009/03/24/2_NOVA_ICE. ART_ART_03-24-09_D5_9ADB1F1. html? sid=101. Wilkinson, Marian. (23 March 2009. ) The ice caps are in trouble. The Sydney Morning Herald. Retrieved March 24, 2009, from http://www. smh. com. au/environment/earth-hour/theice-caps-areintrouble-200

Random Essays :: essays research papers

31) After the attack on Pearl Harbor, the feelings of animosity in America against Japan increased. By late 1945, the Allied leaders met in Germany with news of a secret new weapon, called the atomic bomb, created by American scientists, that was powerful enough to destroy an entire city. However, there were some feelings that the bomb was too powerful, and the leaders chose instead to send the Potsdam Declaration to Japan warning them to surrender. The Japanese military did not know about the atomic bomb and ignored the warning, so on August 6th 1945, an American bomber called the Enola Gay was dropped on Hiroshima, Japan. This blast killed an approximated 70,000 people and destroyed more than eighty percent of the city, but the Japanese still did not surrender. The US dropped a second atomic bomb, and after a furious debate in the Japanese cabinet, the emperor of Japan announced a surrender. This day on the 14th of August became known as V-J Day, for Victory over Japan. 32) a & b) The approach to bring discrimination cases before the courts that I would have disagreed with most would have been using violence to gain attention. This approach only caused an uproar that required law enforcement and resulted in injuries of many people. Although it did bring attention, it brought the wrong sort of attention that they were seeking. The courts possibly would have been less eager to see their cases after acts of violence, since it only demonstrated rebellion. 33) a & b) President Lyndon Johnson proposed the development of a plan called the Great Society, which was a plan with an ambitious goal to improve the standard of living of every American. One of these important Great Society programs was Medicare. This plan helped to pay the hospital bills of citizens over the age of 65. Similar to this program, Medicaid gave states money to help poor people of all ages with medical bills. Along with this, he fought to help Americans who lived below the poverty line. The Economic Opportunity Act was passed in 1964 to set up job-training programs for the poor. It also gave loans to businesses poor sections of the cities and offered loans to poor farmers. 34) Among the recent advances in science and technology, the development of computers has become a part of everyday life in American culture. Random Essays :: essays research papers 31) After the attack on Pearl Harbor, the feelings of animosity in America against Japan increased. By late 1945, the Allied leaders met in Germany with news of a secret new weapon, called the atomic bomb, created by American scientists, that was powerful enough to destroy an entire city. However, there were some feelings that the bomb was too powerful, and the leaders chose instead to send the Potsdam Declaration to Japan warning them to surrender. The Japanese military did not know about the atomic bomb and ignored the warning, so on August 6th 1945, an American bomber called the Enola Gay was dropped on Hiroshima, Japan. This blast killed an approximated 70,000 people and destroyed more than eighty percent of the city, but the Japanese still did not surrender. The US dropped a second atomic bomb, and after a furious debate in the Japanese cabinet, the emperor of Japan announced a surrender. This day on the 14th of August became known as V-J Day, for Victory over Japan. 32) a & b) The approach to bring discrimination cases before the courts that I would have disagreed with most would have been using violence to gain attention. This approach only caused an uproar that required law enforcement and resulted in injuries of many people. Although it did bring attention, it brought the wrong sort of attention that they were seeking. The courts possibly would have been less eager to see their cases after acts of violence, since it only demonstrated rebellion. 33) a & b) President Lyndon Johnson proposed the development of a plan called the Great Society, which was a plan with an ambitious goal to improve the standard of living of every American. One of these important Great Society programs was Medicare. This plan helped to pay the hospital bills of citizens over the age of 65. Similar to this program, Medicaid gave states money to help poor people of all ages with medical bills. Along with this, he fought to help Americans who lived below the poverty line. The Economic Opportunity Act was passed in 1964 to set up job-training programs for the poor. It also gave loans to businesses poor sections of the cities and offered loans to poor farmers. 34) Among the recent advances in science and technology, the development of computers has become a part of everyday life in American culture.

Chemical Reactions Essay

Introduction In this paper you learn about the reactions that occur between backing soda and lemon juice. We will also describe what is occurring with the molecules on a molecular level. Lastly we will explain what chemical bonds are formed and or broken when lemon juice and backing soda. Observations of the Reactants When most people hear baking soda they think of the bright orange box sitting in their pantry or refrigerator soaking up the foul odors that have come about from the onions or fish. Some may think of pancakes or baking a cake. Baking powder is a fine white substance with the consistency of powdered sugar. Baking soda is a chemical base. Another substance most people do not recognize as a chemical in their household is Lemon Juice. This is a liquid mixture of water and citric acid. Its color is mildly foggy and a pale yellow. Lemon juice is a chemical acid and when mixed with a base like baking soda creates a reaction. Reactions that occur Mixing lemon juice with baking soda gives you a chemical reaction. The lemon juice contains citric acid. The citric acid from the lemon juice will donate a hydrogen ion (H+) to the bicarbonate or baking soda (NaHCO3). When the bicarbonate is mixed into solution, the bicarbonate acts as a base and takes the H+ ion from the citric acid to form carbonic acid (H2CO3) and carbon dioxide (CO2). Whenever a chemical reaction produces gas, it will be highly favored due to its large increase in entropy associated with the gas formation. In this reaction, you will notice the solution bubbling and foaming due to the CO2 production. The reaction of lemon juice and baking soda is as follows: C6H8O7 + 3NaHCO3 Na3C6H5O7 + 3H2CO Essentially, one molecule of citric acid will react with three molecules of sodium bicarbonate. This will form one molecule of sodium citrate and three molecules of carbonic acid. It is a very exothermic chemical reaction. Molecular Level Baking soda or sodium bicarbonate is a salt while lemon juice is a citric acid. When combined, on a molecular basis, the acid in the lemon juice is able to lose a hydrogen (H+) ion while the sodium bicarbonate (NaHCO3) of the baking soda is able to gain an ion. Mixed in a solution, the NaHCO3 dissociates into a sodium (Na+) and bicarbonate (HCO3-) ion. The HCO3- then takes the H+ ion to form H2CO3 (carbonic acid). Bonds that formed and broken The bonds that are forming between the lemon juices and backing soda are polar covalent bonds. The bonds have an uneven electron share which is known as a dipole moment that makes them insoluble. Each the backing soda and the lemon juice have bonds that are broken. The bonds that are broken in the citric acid are when the H+ ions are taken away to form the H2CO3 and CO2. While this is happening the two molecules are sharing there atoms which is making then fight one another. So in return the baking soda does not naturalize the lemon juice like most acids and bases do. This is the violent bubbling reaction you see occur when the two are mixed. Conclusion Backing soda and lemon juice are two very few reactants that react the way they do. Normally a base and an acid turn neutral. This is not the case between these two chemicals. The molecules fight on another casing them to react violently resulting in the bubbling situation that is observer. As you have learned these two chemicals react in a way to form a gas called carbon dioxide. The color changed mildly to form a fogy white color. When it is compared on a pH level it is stronger than stomach acid. This experience has showed us that different reactants react in many different ways and that is why it is important to observe them many different items before make an assumption. Reference Swindells, J. (n.d.). What does lemon juice and baking soda do?. Retrieved from http://www.blurtit.com/q7839108.html Tro, N. J. (2009). Introductory chemistry. (3rd ed.). Upper Saddle River, NJ: Pearson/Prentice Hall. What is the chemical equation for lemon juice and baking soda. (n.d.). Retrieved from http://wiki.answers.com/Q/What_is_the_chemial_equation_for_lemon_juice_and_baking_soda

Electromechanical Energy Conversion

Introduction Chapter 3 Electromechanical Energy Conversion Topics to cover: 1. Introduction 3. Force and Torque 5. Friction 2. Electro-Motive Force (EMF) 4. Doubly-Excited Actuators 6. Mechanical Components Introduction (Cont. ) For energy conversion between electrical and mechanical forms, electromechanical devices are developed. In general, electromechanical energy conversion devices can be divided into three categories: – Transducers (for measurement and control), which transform signals of different forms. Examples are microphones, pickups, and speakers Force producing devices (linear motion devices), which produce forces mostly for linear motion drives, such as relays, solenoids (linear actuators), and electromagnets. – Continuous energy conversion equipment, which operate in rotating mode. A device would be known as a generator if it convert mechanical energy into electrical energy, or as a motor if it does the other way around (from electrical to mechanical). Lor entz Force & EMF Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fieldsF ? q(E? v? B) The induced emf in a conductor of length l moving with a speed v in a uniform magnetic field of flux density B can be determined by a e ? ?v? B? ? dl ? b In a coil of N turns, the induced emf can be calculated by e ? ? Concept map of electromechanical system modeling d? dt where ? is the flux linkage of the coil and the minus sign indicates that the induced current opposes the variation of the field. It makes no difference whether the variation of the flux linkage is a result of the field variation or coil movement. EMF EMF – Example: EMF in a Linear Actuator – Example SolutionSketch L(x) and calculate the induced emf in the excitation coil for a linear actuator shown below. Assuming infinite permeability for the magnetic core and ignore the fringing effect, we can express the self inductance of the coil as L? x ? ? where Rg ? x? ? N2 ?o N 2 l ?d ? x? ? Rg ? x ? 2g L(x) L(0) 2g ?o ? d ? x? l O is the air gap reluctance. ? e? ? N 2l d? d ? Li ? di dL dx di ? ? L ? i =L? x ? ? i o v 2g dt dt dt dx dt dt EMF – A Single Conductor in a Uniform Field e ? ? I dc If i=Imsin? t , e? Force and Torque – Example Solution (Cont. ) If i=Idc , ?o N 2 l 2g ? Im ? Im ?o N 2l 2gFor a single conductor in a uniform magnetic field, we have v ? d ? x I m cos ? t ? vI m sin ? t ?o N l 2 2g ?o N 2 l 2g d Fm ? Il ? B ?o N 2 l In a rotating system, the torque about an axis can be calculated by 2g d ? x cos? t ? v sin ? t ? ? T? r ? Fm v ? ? ? ? d ? x ? ? ? ? d ? x ? 2 ? 2 ? v 2 cos t ? arctan? ? where r is the radius vector from the axis towards the conductor. B Fm l I X Force and Torque – A Singly Excited Actuator Consider a singly excited linear actuator. After a time interval dt, we notice that the plunger has moved for a distance dx under the action of the force F.The mechanical work done by the force acting on the plunger during this time interval is thus dWm ? Fdx Force and Torque – A Singly Excited Actuator The amount of electrical energy that has been transferred into the magnetic field and converted into the mechanical work during dt is dWe ? dWf ? dWm ; dWe ? eidt ? vidt? Ri2dt e ? d? dt ? v ? Ri Because dWf ? dW ? dW ? eidt ? Fdx ? id? ? Fdx e m we obtain From the total differential dW f ? ? , x ? ? ? W f , x ? i? Therefore, ? W f , x ? d? ? and ? W f , x ? ?x F dx ?W f ? ? , x ? ?x Force and Torque Force and Torque – A Singly Excited Actuator (Cont. ) A Singly Excited Actuator (Cont. ) From the knowledge of electromagnetics, the energy stored in a magnetic field can be expressed as ? Wf ? ? , x? ? ? i? ? , x? d? In the diagram below, it is shown that the magnetic energy is equivalent to the area above the magnetization or ? -i curve. Mathematically, if we define the area underneath the magnetization curve a s the coenergy (which does not exist physically), i. e. 0 For a magnetically linear (with a constant permeability or a straight line magnetization curve such that the inductance of the coil is independent of the excitation current) system, the above expression becomes 1 ? Wf ? ?, x? ? 2 L? x? and the force acting on the plunger is then F ?Wf ? ?, x? ?x 1 ? ? ? dL? x? 1 2 dL? x? ?i 2 ? L? x? ? dx 2 dx ? 2 we can obtain Wf ‘ ? i, x? ? i? ?Wf , x? ? Wf (? , x ) dW f ‘ ? i , x ? ? ? di ? id? ? dW f ? ? , x ? ? ? di ? Fdx Therefore, ? ?W f ‘ ? i , x ? ?i ? W f ‘ ? i , x ? ?i di ? and ?W f ‘ ? i , x ? ?x F? dx ? W f ‘ ? i , x ? ?x (? , i ) Wf ‘ ( i, x ) O i Force and Torque Force and Torque – A Singly Excited Actuator (Cont. ) – Example 1 Calculate the force acting on the plunger of a linear actuator as shown below. From the definition, the coenergy can be calculated by iWf ‘ ? i , x? ? ? ? ? i , x? di ? 0 Wf ‘ ? i, x? ? ? (? , i ) Wf (? , x ) For a magnetically linear system, the above expression becomes Rg 1 L? x? i 2 2 Ni Wf ‘ ( i, x ) Rg and the force acting on the plunger is then F? ?Wf ‘ ? i , x ? ?x 1 dL? x ? ? i2 dx 2 O i (c) Force and Torque Force and Torque – Singly Excited Rotating Actuator – Solution to Example 1 Assume infinite permeability for the actuator core. The self inductance of the excitation winding can be readily obtained as L? x? ? N 2 ? o N 2l? d ? x? ? 2Rg 2g Therefore, the force acting on the plunger is F? ? Rg Ni ?l 1 2 dL ? x ? 2 i ? ? o ? Ni ? 2 dx 4gThe minus sign of the force indicates that the direction of the force is to reduce the displacement so as to reduce the reluctance of the air gaps. Since this force is caused by the variation of magnetic reluctance of the magnetic circuit, it is known as the reluctance force. Rg The singly excited linear actuator becomes a singly excited rotating actuator if the linearly movable plunger is repla ced by a rotor. Through a derivation similar to that for a singly excited linear actuator, one can readily obtain that the torque acting on the rotor can be expressed as the negative partial derivative of the energy stored in the agnetic field against the angular displacement or as the positive partial derivative of the coenergy against the angular displacement. Force and Torque Solution b) Voltage induced – Example †¢ The magnetically-linear electro-mechanical circuit breaker as shown is singly-excited via a N-turn coil. Its magnetic reluctance varies with the angle ? as R ? Rm? ? R0 , where Rm and R0 are constant. †¢ Derive the torque developed by the field from the system co-energy. †¢ When the device is excited with a direct current i=I, the angular displacement increases quadratically as ? ?t ? ? 1 ? t 2 ? ?t ? ? 0 , 2 where ? ? and ? 0 are constant. Find the voltage induced in the coil . Singly Excited Rotating Actuator Total turns, N = N1 + N2 Frame relu ctance Rf ? rf 2 Gap reluctance Rg ? 2rg ? ? lf 2? 0 ? r wd 2lg ?0rd (2? ? ? ) , 2? ? 760 ? 1. 33 rad Rg(? ) Rcore ?g Rarmature Fm=Ni e(t ) ? ? N 2 IRm (? t ? ? ) [ R0 ? Rm 1 ? t 2 ? ?t ? ? 0 ]2 2 ? Singly Excited Rotating Actuator ? Singly Excited Rotating Actuator airgap length, lg = 0. 001 m airgap radius, r = 0. 0745 m airgap depth, d = 0. 0255 m frame length lf = 0. 496 m limb width w = 0. 024 m Singly Excited Rotating Actuator ? (? ) ? T? ? NI R f ? Rg (? ) lf Rf ? 2 ? ? r wd Magnetic flux at equilibrium : ? NI ?0 ? ? ? R (? ) ? R f ?g ? ? ?0 NI lf 2 ? 0 ? r wd ? lg ?0rd? ? , Rg ? 2l g ?W f? ? ? ? N2 ? ?, ? R (? ) ? R ? f? ?g dRg dRg 2l g sign(? ) , where ? d? d? ?0 rd (2? ? ? )2 1 2 ? L(? ) 1 2 ? I ?I 2 2 122 ?1 IN 2 ?Rg (? ) ? R f ? 2 2l Rr sign(? ) 1 ? ? I 2N 2 , where Rr ? g 2 2 ?0 rd 4 ?Rg (? ) ? R f ? (2? ? ? ) ?0 rd (2? ? ? ) Restoring Torque ?1, x ? 0 sign ( x ) ? ? 1, x ? 0 NI? 0d lf l ?g 2 ? r w r? Force and Torque Singly Excited Rotating Actuator – Sing ly Excited Rotating Actuator (Cont. ) Torque Nm Flux mWb Flux, Torque for 2-pole motorEnergy In g eneral, 1. 5 Coenergy dW f ? id? ? Td ? dW f ‘ ? ? di ? Td ? ? i W f ? ? , ? ? ? ? i ? ? , ? ?d ? W f ‘ ? i , ? ? ? ? ? ?i , ? ?di ?W f ? ? , ? ? i? ?W f ? ? , ? ? T ?W f ‘ ? i , ? ? ?i ?W f ‘ ? i , ? ? T? 0 1. 0 mWb, Nm 0. 5 0 If the permeability is a constant, W f , ? ? ? 0. 0 0 5 10 15 20 25 30 35 40 45 rotor angle 50 55 60 65 70 75 80 1 ? 2 2 L ? 1 ? ? ? dL ? 1 2 dL ? ?i 2 ? L ? ? d ? 2 d? ? ? W f ‘ ? i , ? ? ? 2 T? T? 12 i L ? 2 1 2 dL ? i 2 d? Force and Torque Force and Torque – Doubly Excited Rotating Actuator – Doubly Excited Rotating Actuator (Cont. If a second winding is placed on the rotor, the singly excited actuator becomes a doubly excited actuator. The general principle for force and torque calculation discussed here is equally applicable to multi-excited systems. The differential energy and coenergy functions can be derived as dW f ? dWe ? dWm where dWe ? e1i1dt ? e2 i2 dt , e1 ? d? 1 dt , e2 ? d ? 2 dt , and dWm ? Td ? Hence, dW f 1 , ? 2 , ? ? ? i1d ? 1 ? i2 d ? 2 ? Td ? ? and ? W f 1 , ? 2 , ? ? ? W f 1 , ? 2 , ? ? ? W f 1 , ? 2 , ? ? d ? 1 ? d ? 2 ? d? 1 2 ? ? dW f ‘ ? i1 , i 2 , ? ? ? d i1 ? 1 ? i 2 ? 2 ? W f ? 1 , ? 2 , ? ? ? ?1 di1 ? ?2 di 2 ? T d ? ? ? W f ‘ ? i1 , i 2 , ? ? Therefore, T ? i1 di1 ? ? W f ‘ ? i1 , i 2 , ? ? ?Wf 1 , ? 2 , ? ? ? i2 or di 2 ? T? ? W f ‘ ? i1 , i 2 , ? ? Force and Torque – Doubly Excited Rotating Actuator (Cont. ) – Example 3 ? ? L? 1 For magnetically linear systems, ? ? 1 ? ? L11 ? ? ? L ? 2? ? 21 L 1 2 ? ? i1 ? L 22 ? ?i2 ? ? ? i1 ? ? ? 11 ?i ? ? ? ? ? 2? ? 21 or ? 1 2 ? ? ? 1 ? ? 22 ? ? ? 2 ? ? The magnetic energy and coenergy can then be expressed as W f ? ?1 , ? 2 , ? ? ? Therefore, d? ? W f ‘ ? i1 , i2 , ? ? Force and Torque and 1 1 2 ? 1 1 ? 12 ? 2 2 ? 2 ? ? 1 2 ? 1 ? 2 2 2 W f ‘ ? i 1 , i 2 , ? 1 1 L 1 1 i 12 ? L i 2 ? L 1 2 i1i 2 2 2 22 2 ? W f ‘ ? i 1 , i 2 , ? ? 1 2 d L 1 1 ? 1 2 d L 2 2 ? d L 1 2 ? ? i1 ? i2 ? i1i 2 2 2 T ?W f 1 , ? 2 , ? ? ? A magnetically-linear doubly-fed electromechanical actuator has two windings and a mechanical output with spatial rotary displacement ?. The self and mutual inductances of the windings are respectively L11 ? ? 5 ? cos(2? ) mH, L22 ? ? 50 ? 10 cos(2? ) mH, and L12 ? ? L21 ? ? 100 cos? mH. Brushless doubly-fed machine The first winding is supplied with i1 = 1. A while the second winding draws i2 = 20 mA. Determine: a) The general electromagnetic torque of the actuator as a function of ? . b) The maximum torque that the actuator can develop. Solution to Example 3 (a) Solution to Example 3 (cont. ) The  energy  stored  at  the  doubly? fed  actuator  is, 1 1 2 2 W f ? L11i1 ? L12 i1i2 ? L22 i2 2 2 1 1 ?3 2 ?3 2 ? (5 ? cos 2? ) ? 10 i1 ? (0. 1cos? )i1i2 ? (50 ? 10 cos 2? ) ? 10 i2 2 2 The  ex pression  of  electromagnetic  torque  is  obtained  as  follows:   ? ?W f (i1 , i2 ,? ) T ? i1 ? 1. 5, i2 ? 0. 02 ? 2 2 1 ? (i1 L11 ) ? (i1i2 L12 ) 1 ? (i2 L22 ) ? ? ? 2 2 1 1 (1. 5) 2 ( ? 2 sin 2? ) ? 10 ? 3 ? (1. 5)(0. 02)(? 0. 1sin ? ) ? (0. 02) 2 ( ? 20 sin 2? ) ? 10 ? 3 2 2 ?3 ? ? ( 2. 25 sin 2? ? 3 sin ? ) ? 10 Why Magnetic Field? Ratio of Electric and Magnetic Energy Densities in the air gap we ? 0 ? 0 E 2 1 ? ? wm B2 3. 6 ? 10 5 †¢ Saturation Flux Density Bs = 2T in commonlyused magnetic materials †¢ Air breakdown voltage Ebd=1,000,000 V/m b) At  maximum  torque, dT ?0 d? Differentiating  T  from  part  (a), 4. 5 cos 2? ? 3 cos ? ? 0 ? 1. 5 cos 2? ? cos ? ? 0 or               1. 5( 2 cos 2 ? ? 1) ? cos? ? 0 Solving  for  ? by  the  quadratic  formula, ?  =  55. 94 °Ã‚  and  153. 25 °Ã‚  (extraneous)Substituting  the  value  of  ? into  the  torque  expression  yields, T(max) ? ?(2. 25 s in 2(55. 94) ? 3 sin(55. 94)) ? 10 ? 3 ? ?4. 57 ? 10 ? 3 Nm Electric Machines †¢ Electric motor converts electrical energy into mechanical motion. †¢ The reverse task, that of converting mechanical motion into electrical energy, is accomplished by a generator or dynamo. †¢ In many cases the two devices differ only in their application and minor construction details, and some applications use a single device to fill both roles. For example, traction motors used on locomotive often perform both tasks if the locomotive is equipped with ynamic brakes. Introduction Electric Motors Electric Machine Insulation Class DC Motors Universal (DC/AC) AC Motors †¢ Induction †¢ Synchronous Stepping Motors Brushless DC Motors Coreless DC Motors Linear Motors MEMS Nano Motors †¢ A critical factor in the reduced life of electrical equipment is heat. The type of insulation used in a motor depends on the operating temperature that the motor will experience. †¢ Average insulation life decreases rapidly with increases in motor internal operating temperatures. †¢ Electric motor converts electrical energy into mechanical motion: Lorentz force on any wire when it is onducting electricity while contained within a magnetic field †¢ Rotor: rotating part †¢ Stator: stationary part †¢ Armature: part of the motor across which the voltage is supplied MaglevMagnetic Levitation Three phase AC induction motors rated 1 Hp (750 W) and 25 W with small motors from CD player, toy and CD/DVD drive reader head traverse DC Generators / Dynamos AC Generators / Alternators As the first electrical generator capable of delivering power for industry, the dynamo uses electromagnetic principles to convert mechanical rotation into a pulsing direct electric current through the use of a commutator.Without a commutator, the dynamo is an example of an alternator, which is a synchronous singly-fed generator. With an electromechanical commutator, the dynamo is a classical direct current (DC) generator. The DC generator can operate at any speed within mechanical limits but always outputs a direct current waveform. Mechanical energy is used to rotate the coil (N turns, area A) at uniform angular velocity ? in the magnetic field B, it will produce a sinusoidal emf in the coil: Permanent Magnet DC Generators d? d ? ? ( NBA cos ? ) dt dt ? NBA? sin ? t e(t ) ? ? http://micro. magnet. fsu. edu/electromag/java/generator/dc. tml Automotive alternator Rotor emf and current are induced by rotating magnetic field http://micro. magnet. fsu. edu/electromag/java/generator/ac. html Mechanical Components Mechanical Components – Mass and Inertia The mechanical component which stores kinetic energy is a mass in a translational system, and a moment of inertia in a rotational system. – Mass and Inertia (Cont. ) The kinetic energy stored by a mass moving at a velocity v, or a moment of inertia rotating at an angular speed ?. can be calculated by ? x M T F J Wk ? 1 Mv2 2 d? d 2? T? J 2 ? J dt dt dv d 2x F? M ?M dt 2 dt 1 J? 2 2 (translational system) rotational system) Comparing with the relationships of voltage, current, and magnetic energy in an inductor: V? L By the Newton’s second law, we have Wk ? or di dt and WL ? 1 Li2 2 we may regard a mass or a moment of inertia as an inductor which stores magnetic energy, if we let J? L M? L or Mechanical Components Mechanical Components – Springs An ideal spring is a device with negligible mass and mechanical losses, whose deformation is a single-valued function of the applied force or torque. A linear ideal spring has deformation proportional to force or ? 1 torque. – Springs (Cont. ) For a given distortion of x and ? the potential energy stored in a spring is 1 1 W p ? ? Td ? ? K ? 2 W p ? ? Fdx ? Kx 2 T x1 F ? K ? x 1 ? x o ? ? Kx (linear spring) (torsional spring) Comparing with the relationships of electric charge, voltage and electric energy in a capacito r: Q V? C F 2 2 WC ? and 1 1 Q2 VQ ? 2 2C we may regard a spring as an electric capacitor which stores electric potential energy, if we let T ? K 1 ? ?o ? ? K ? K? 1 C Friction Friction Modelling Friction: force that opposes the relative motion or tendency of such motion of two surfaces in contact. Friction between the two objects converts kinetic energy into heat.Coefficient of friction (Frictional coefficient): dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together, needs not be less than 1 – under good conditions, a tire on concrete may have a coefficient of friction of 1. 7. Static friction (stiction) occurs when the two objects are not moving relative to each other: Rolling friction occuring when one object â€Å"rolls† on another (like a car's wheels on the ground), is stiction as the patch of the tire in contact with the ground, at any point while the tire spins, is stationary relati ve to the ground.Kinetic (or dynamic) friction occurs when two objects are moving relative to each other and rub together: – Sliding friction is when two objects are rubbing against each other. – Fluid friction is the friction between a solid object as it moves through a liquid or a gas. The drag of air on an airplane or of water on a swimmer are two examples of fluid friction. Lu-Gre Model (1995): ? 0 , ? 1 bristles’ stiffness and damping coefficient ?2 viscous friction FC , F S Coulomb and Stribeck friction ? F f ? ? 0 z ? ? 1z ? ? 2v ? z? v? v z g (v ) 2 1 g (v ) ? [ FC ? ( F S ? FC ) e ? v / v S ) ] ?0 Mechanical Components Mechanical Components – Damper The mechanical damper is analogous to electrical resistor in that it dissipates energy as heat. An ideal damper is a device that exhibits no mass or spring effect and exerts a force that is a function of the relative velocity between its two parts. A linear ideal damper has a force proportional to the relative velocity. In all cases a damper produces a force that opposes the relative motion of the two parts. Mechanical friction occurs in a variety of situations under many different physical conditions.Sometimes friction is unwanted but must be tolerated and accounted for analytically, as, for example, in bearings, sliding electrical contacts, and the aerodynamic drag on a moving body. In other cases friction is desired and is designed into equipment. Examples are vibration dampers and shock absorbers. d ? x2 ? x1 ? dt dx ?B dt F? B ? B? R d 2 ? ?1 ? dt d? ?B dt T? B – Damper (Cont. ) Mechanical Components Mechanical Components – Damper (Cont. ) The damping due to Coulomb friction, as shown by the characteristic, can be regarded as a nonlinear resistor, which can keep the voltage across it to be constant.The Coulomb friction force can be expressed as – Damper (Cont. ) There is another kind of damping caused by the drag of a viscous fluid in turbulent flow. 2 F ? ? Bs d x2 ? x1 dt F ? ?d Fn ? ? d Fn d ? x2 ? x1 ? dt ? ? ? Bs dx dt d ? x2 ? x1 ? dt ? 2 ? R ? B s dx dt dx dt ? dx dt or T ? ? Bs d 2 ? ?1 ? dt Comparing with V=RI, we may conclude that ?F R? d n dx dt ? ? ? Bs d? dt ? ? 2 2 ? R ? B s d ? dt MR Dampers as a semi-active device MR Damper New Models Non-symmetrical Model (2007) ? F ( x) ? c0 x ? ko ( x ? x0 ) ? ?z ? ? ? z ? (? ? ( ? ? ? sign( zx) z ) x n : hysteresis variable, ? , ? , ? , ? , n, c0 , k0 : model parameters Bouc-Wen Model: ? F ( x ) ? c0 x ? k o ( x ? x0 ) ? ? z ? ? ? ? z ? ? ? z | x || z | n ? 1 ? ? x | z | n ? ? x z: hysteresis variable , ? , ? , ? , ? , n , c 0 , k 0 : model parameters Static Hysteresis Model (2006) ? F ( x) ? cx ? kx ? ?z ? f 0 ? z ? tanh( ? x ? sign( x)) z : hysteresis variable, ? , ? , f 0 , c, k : model parameters Minimally-Parameterised Model (2007) ? F : G ( x ) ? D ( x ), F ( x) ? ? 1 ? F2 : G ( x ) ? D ( x ), b G ( x) ? a ? ? 1 ? exp ( cx ) ? D ( x ) ? rexp{? ( x / 2? ) 2 } ? 0 x ? 0, x

Beowulf Essay

Beowulf Essay Beowulf Essay Picking up the Pieces What is a nation to do when everything they stand for is gone? This is the unfolding story in the poem Beowulf. Beowulf is a Geat warrior who sacrifices his own safety to battle the evil that presents itself against the Danes in the form of the fierce monster Grendel. King Hrothgar and the Danes exemplify pride, happiness, and power before Grendel steals everything from them when he attacks what is dearest to King Hrothgar's heart: Herot, the glorious palace built for celebration. Once Grendel makes his initial appearance, it takes a miracle to bring celebration back into the hearts of the Danes. Before Grendel begins his reign of terror, Herot is a place of pride. People everywhere can see its beauty and stature as it reaches â€Å"higher toward Heaven than anything that had ever been known to the sons of men" (Beowulf 25). With golden pillars and remarkable architecture, Herot symbolizes hope and joy. Shame replaces pride when the Danes cannot stand ag ainst Grendel. This horrifying monster overpowers the Danes on every front. Nothing they can do will stop Grendel and his vindictive nature. Beowulf's journey begins here when he does something no mortal man can do; he defeats Grendel. By the grace of God, Beowulf restores the Danes' pride and then some. A characteristic of a hero is humility and Beowulf does not possess this trait in the slightest. Though this seems negative, it benefits the Danes as Beowulf's conceit brings pride back to these countrymen. Grendel may have originally stole away their pride, but Beowulf brings it back. Herot used to be the epitome of happiness and joy. Anybody who came near to Herot instantly became blanketed by peace because supposedly nothing could ever harm it. That is until Grendel decides to intercede. Grendel hears the happiness and euphoria erupting from Herot while in his cave. Jealousy ensues and he can no longer stand hearing the joy when he is miserable and alone. Instead of c reating his own happiness, Grendel steals the Danes’. By Grendel killing people and stealing their bodies, Herot becomes a house of sorrow. When Grendel is finally defeated, the Danes rejoice for Beowulf has come through triumphant. In all this happiness, though, there is still someone who the joy cannot touch. Grendel’s mother is heartbroken over the death of her son and she is seeking vengeance. As Grendel did before, his mother takes the life of a noble soldier, snatching away the happiness just as it is returned. Beowulf dives back into a fierce battle that goes back and forth until the brave warrior is able to win the battle, but he does not do it for the Danes’ per se. During a time when Beowulf is struggling, the poet writes â€Å"but Beowulf longed only for fame, leaped back into battle† (Beowulf 71). Even though Beowulf yearns only for the notoriety of the victory, this minor indiscretion does not faze the Danes’ as they are the o nes benefitting. The joy is returned and they are finally jubilant again. Having power is something the Danes and many others respect. Not only do they respect it, they deem power a necessity. Without it, others will assume they can obliterate and overthrow the Danes with ease. The Danes grew accustomed to putting angst into the eyes of those around them, but Grendel changed that by putting dread into theirs. Power is transferred through the

Facts About Eohippus

Facts About Eohippus In paleontology, correctly naming a new genus of extinct animal can often be a long, tortured affair. Eohippus, aka Hyracotherium, is a good case study: this prehistoric horse was first described by the famous 19th-century paleontologist Richard Owen, who mistook it for an ancestor of the hyrax (hence the name he bestowed on it in 1876, Greek for hyrax-like mammal). A few decades later, another eminent paleontologist, Othniel C. Marsh, gave a similar skeleton discovered in North America the more memorable name Eohippus (dawn horse). Since for a long time Hyracotherium and Eohippus were considered to be identical, the rules of paleontology dictated that we call this mammal by its original name, the one bestowed by Owen. Never mind that Eohippus was the name used in countless encyclopedias, childrens books, and TV shows. Now, the weight of opinion is that Hyracotherium and Eohippus were closely related, but not quite identical, the result is that its once again kosher to refer to the American specimen, at least, as Eohippus. Amusingly, the late evolutionary scientist Stephen Jay Gould railed against the depiction of Eohippus in the popular media as a fox-sized mammal, when in fact it was the size of a deer. An Ancestor of Modern Horses Theres a similar amount of confusion about whether Eohippus and/or Hyracotherium actually deserve to be called the first horse. When you go back in the fossil record 50 million years or so, it can be difficult, verging on impossible, to identify the ancestral forms of any given extant species. Today, most paleontologists classify Hyracotherium as a palaeothere, that is, a perissodactyl (odd-toed ungulate) ancestral to both horses and the giant plant-eating mammals known as brontotheres (typified by Brontotherium, the thunder beast). Its close cousin Eohippus, on the other hand, seems to deserve a place more firmly in the equid than the palaeothere family tree, though of course, this is still up for debate! Whatever you choose to call it, Eohippus was clearly at least partly ancestral to all modern-day horses, as well as to the numerous species of prehistoric horse (like Epihippus and Merychippus) that roamed the North American and Eurasian plains of the Tertiary and Quaternary periods. As with many such evolutionary precursors, Eohippus didnt look much like a horse, with its slender, deerlike, 50-pound body and three- and four-toed feet; also, to judge by the shape of its teeth, Eohippus munched on low-lying leaves rather than grass. (In the early Eocene epoch, when Eohippus lived, grasses had yet to spread across the North American plains, which spurred the evolution of grass-eating equids.) Facts About Eohippus Eohippus (Greek for dawn horse), pronounced EE-oh-HIP-us; also known as Hyracotherium (Greek for hyrax-like beast), pronounced HIGH-rack-oh-THEE-ree-um Habitat: Woodlands of North America and Western Europe Historical Epoch: Early-Middle Eocene (55-45 million years ago) Size and Weight: About two feet high and 50 pounds Diet: Plants Distinguishing Characteristics: Small size; four-toed front and three-toed back feet

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