...RULES OF MIXTURES FOR ELASTIC PROPERTIES The paper is about the rules of mixtures which are used to express the dependencies of the physical properties and mechanical properties which depend on type, form, quality and arrangement of its constituents, but they are based on various assumptions so one should with caution, especially if they are used anything more than preliminary design. The paper mainly concentrates on expressions for elastic properties which are as follows: Unidirectional Ply- longitudinal modulus: The Figure 1 clearly shows the orthogonal axes and fiber direction, the fiber directions. The first approximation made is E3= E4. And also for deriving the rules of mixtures the following assumptions are made: Fibers are uniform, parallel and continuous. Perfect bonding exists between fibers and matrix. A longitudinal load produces equal strain in fiber and matrix. Using the above assumptions and approximations two rules of mixtures are derived which are E1 = EfVf + EmVm = EfVf + Em (1- Vf) V12= vfVf+vm+Vm These two rules of mixtures are generally accepted as it goes well with experimental data. Unidirectional Ply- Transverse modulus: In this the rules of mixtures are less reliable than those for longitudinal properties as they are based on assumptions of stress distribution. In this the poisson’s contraction is ignored and the stress is assumed to be the same...
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...NC 27708-0305 rgb@phy.duke.edu Copyright Notice Copyright Robert G. Brown 1993, 2007, 2013 Notice This physics textbook is designed to support my personal teaching activities at Duke University, in particular teaching its Physics 141/142, 151/152, or 161/162 series (Introductory Physics for life science majors, engineers, or potential physics majors, respectively). It is freely available in its entirety in a downloadable PDF form or to be read online at: http://www.phy.duke.edu/∼rgb/Class/intro physics 1.php It is also available in an inexpensive (really!) print version via Lulu press here: http://www.lulu.com/shop/product-21186588.html where readers/users can voluntarily help support or reward the author by purchasing either this paper copy or one of the even more inexpensive electronic copies. By making the book available in these various media at a cost ranging from free to cheap, I enable the text can be used by students all over the world where each student can pay (or not) according to their means. Nevertheless, I am hoping that students who truly find this work useful will purchase a copy through Lulu or a bookseller (when the latter option becomes available), if only to help subsidize me while I continue to write inexpensive textbooks in physics or other subjects. This textbook is organized for ease of presentation and ease of learning. In particular, they are hierarchically organized in a way that directly supports efficient learning. They are also remarkably complete...
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...By partaking in three unique scenarios of both elastic and inelastic collisions, I was able to conclude that speed and velocity are both conserved. This conclusion was made through the change in velocity of a cart relative to its "crasher". For example: throughout the different-mass elastic collisions, the speed that which the cart started and ended were equivalent - indicating that there was conservation of speed, in addition to the complete transfer of velocity. However, in the different-mass elastic collisions, the transfer of the speed of the cart was not complete, but instead, the lighter cart moved quicker than the heavier cart. This shows us that although force may be the same, the transfer of momentum shows us why the lighter cart moves more quickly than the slower. Throughout our previous unit, we described the constant velocity of objects in motion. That laid the basis for this next unit, where we will be studying why and how the object moves the way it does, specifically the "push" or "pull" of force. The heavier cart in a same-direction elastic collision seems to push the lighter cart, which causes an increase in speed for the lighter cart. Although we may have brushed on the surface of movement, this unit will pave the path for further investigation on velocity as well as momentum. According to today's lab, it is possible to measure the mass of the carts and then multiple the mass by the velocity to determine momentum. These two things will be related to almost...
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...by the equation: * PTotali =PTotalf * m1v1i+m2v2i=m1v1f+m2v2f * When working with a complete inelastic collision, the two objects stick together after the collision, and the momentum conservation equation becomes: * PTotali =PTotalf * m1v1i+m2v2i=(m1+m2)vf * During this experiment, photogates will measure the motion of two carts before and after elastic collision. The cart masses can be measured by using a simple mass scale. * Then, total momentum of the two carts before collision will be compared to the total momentum of the two carts after collision. Equipment: 850 Universal | Dynamic Track | Two dynamic carts | Two picket fences | Mounting brackets | Mass Balance | Mass Bar | Two Photogates | Data: Part A – Elastic Collision with approx. equal masses: Trial | V1 i (m/s) | V2 i (m/s) | V1 f (m/s) | V2 f (m/s) | 1 | .310 | 0 | 0 | .287 | 2 | .468 | 0 | 0 | .439 | 3 | .486 | 0 | 0 | .435 | 4 | .274 | 0 | 0 | .254 | 5 | .468 | 0 | 0 | .441 | * m1 = mass of cart 1 = .510 kg * m2 = mass of cart 2 = .529 kg | Part B – Elastic Collision with Unequal Masses: Trial | V1 i (m/s) | V2 i (m/s) | V1 f (m/s) | V2 f (m/s) | 1 | .404 | 0 | -.113 | .245 | 2 | .417 | 0 | -.117 | .253 |...
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...Report Results Summary Elastic Collision Initial Momentum = .414 N | Initial Momentum = 0 N | Initial Kinetic Energy = .084 J | Initial KE = 0 J | V1’ = .0596 m/s | V2’ = .462 m/s | Final Momentum = .061 N | Final Momentum = .354 N | Final KE = .00182 J | Final KE = 0.082 J | Inelastic Collision Initial Momentum = n/a | Initial Momentum = n/a | Initial Kinetic Energy = n/a | Initial KE = n/a | V1’ = n/a | V2’ = n/a | Final Momentum = n/a | Final Momentum = n/a | Final KE = n/a | Final KE = n/a | Discussion For the first part of our lab we were able to successfully show that both kinetic energy and momentum were conserved during the collision. As stated in the lab procedure, we kept one mass heavier than the other and made the heavier object collide with the lighter object at rest. Looking back, there wasn’t too much difference between the sizes of the mass. There was only a 300 gram difference in the system and that may have helped in keeping the collision elastic. The speed was recorded as .404 m/s and that also may have helped in causing the object at rest to bounce off the moving object. We were not able to complete the inelastic collision part of the lab because we were not able to make the objects stick together. We were not sure if the plane the objects were set on was level and this may have caused the objects to keep bouncing away from each other. We also kept the weight and velocity (roughly) the same from the elastic test, which could have...
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...employment, product and services, publicity and sales. Retail paper and plastic bags are common packaging tools in the market but due to environmental issues and the public’s awareness more people are decided to use retail paper bag instead of plastic. Paper bags are used for many things, to put up lunches for kids, to bring in the groceries, to take out the trash, to hold the things and help us stay organized. Many markets have switched from plastic bags to paper bags. Paper bags are less expensive. Cost Effectiveness is one of the reasons why they prefer paper bag other than plastic bag. Many vendors and consumers have complained about using plastic bags to put their goods. Some market and grocery stores now give a choice between paper bags or plastic bags. Some Smart shoppers choose to use paper bags instead of plastic assuming that it is an environmentally friendly and better alternative. Paper Bags are usually made up of plant fibers substance from fibrous cellulose materials as rags, woods, or barks. Paper bags were invented in the 1850’s. Paper bags are recyclable. Well known grocery stores, supermarkets, fast food chain, establishment and markets uses brown paper bags to hold their items since there are laws that are implemented to ban the usage of plastic bags in some provinces and cities in the Philippines. Paper bags can easily be disposed and not a harmful thing in the environment...
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...Assignment 5 (30 points) 1. (5 points) Compute the longitudinal and transverse stiffness E1, E2 of an S-glass epoxylamina for a fiber volume fraction Vf = 0.7, using the properties from attached Tables. 2. (5 points) Plot the longitudinal stiffness E1 of an E-glass/nylon unidirectionally reinforced composite, as a function of the volume fraction Vf of fiber. Use the properties from attached Tables. 3. (5 points) Plot the longitudinal tensile strength of an E-glass/epoxy unidirectionallyreinforced composite, as a function of the volume fraction of fiber, assuming tensile strength follows a volume rule of additivity. Use the properties from attached Tables. 4. (5 points) What is the maximum volume fraction of spherical fillers that could be obtained in the particle-reinforced composite assuming cubic packing? Please show the step. 5. (4 points) Using the Takayanagi model and assuming uniform strain in the matrix, derive a relationship for the transverse, tensile compliance of a unidirectionally-reinforced composite. 6. (6 points) Two test specimens have the same Young’s modulus in tension. However, one of the specimens is homogeneous while the other one has two layers with one layer stiffer than other layer. How will the flexural modulus of the two specimens differ? Explain. (Hint, use Parallel and Series model to calculate the modulus to compare them. Assume the modulus of stiff material is 1X109MPa as and the modulus of soft material is 1X108 , and the volume fraction of each...
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... Conclusions 1. It is necessary that they glide on a cushion of air, so that they can avoid any friction which would slow down their movement and could possibly keep them from colliding. The friction would differ for each mass, and would change all the predicted values. If the masses were not on an air cushion, it is impossible to predict that the two masses would ever collide because of the differing frictions for each mass. 2.If the masses were doubled, the before and after collision velocities would both decrease by a factor of two. Because the gliders would take double the time to get to the same distance for collision as if they were not doubled.(newton’s law) 3.The original assumption of this experiment was that it was an elastic collision because there was no visible deformation or heat loss. After further calculations it...
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...writing. In fact, the three universities that I have attended in the past have all required me to use the APA style of writing. As I recall my high school years, the APA style of writing also seemed to be a favorite amongst my high school teachers. They all required that term papers be written in APA style as well. This type of writing actually does not differ much from the ones included in the text reading. The text mentioned the APA style of writing several times. In my opinion, it appears to be the most popular style of writing, especially amongst college students. Based on the results of the quizzes, my grammar skills were actually a little better than average. I actually had expected to do better, but I guess my grammar skills are not as good as I thought they were. In any event I feel very confident when it comes to spelling, as I have always been a great speller. Even in grade school, I was a good speller. I learned at a very young age to challenge myself when it comes to spelling. Challenging my-self in that area really paid off as I became older, as I’ve never had a problem with spelling. However, I feel that I need more help with run on sentences and with thought patterns. Though I proof read my paper several times, it’s hard for me to see that I have several run on sentences until after I get my grade back. In general, I feel that my writing is just mediocre. However, I also believe that when it comes to writing, I am my own worst critic. Reason being, I am never...
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...computer and communications equipment (owned by MIS) magnetic media (owned by Manager) power supplies and plant, such as air-conditioning units (owned by MIS) Software assets (owned by MIS) • • • • application software system software development tools utilities Information assets (owned by Manager or MIS) ‘Information’ means information held by the Company on its own behalf and that entrusted to it by others. The following are examples of the media which may contain or comprise information assets. • • • • • • • • • • databases and data files system documentation user manuals training material operational or support procedures continuity plans and fallback arrangements back-up media on-line magnetic media off-line magnetic media paper Services • • computing and communications services (owned by MIS) heating, lighting and power (owned by Manager or Building Services Manager) 1 17/01/03 First•Base Technologies Town Hall Chambers High Street Shoreham-by-Sea West Sussex BN43 5DD UK Tel: +44 (01273 454 525 Fax: +44 (0)1273 454 526 info@firstbase.co.uk Guidance on Information Classification Categories for classifying document security Category 1 : Routine (non-confidential) documents Description: All documents of a routine nature. Effects of disclosure: No measurable damage to the company or a department. Examples: Normal memos, routine reports, circulars. Estimated occurrence of this classification: More than 80% of all documents would be within this class...
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...TO: FROM: SUBJECT: DATE: CC: [CLICK HERE AND TYPE NAME] SAMUEL NEWMAN-BREMANG [CLICK HERE AND TYPE SUBJECT] OCTOBER 22, 2013 [CLICK HERE AND TYPE NAME] C R E A T I N G W A T E R M A R KS I N M I C R O S O F T W O R D [Note: Some steps may vary in Word 97. For additional help, search for “watermark” in the product help or on the Microsoft support site at http://support.microsoft.com.] A watermark is any text or graphic image (such as the “Draft” in the background of this document) that is printed to overlap existing text in a document. A logo printed lightly behind a letter or the word "Confidential" printed lightly on a contract are other examples of watermarks. The rotated “Draft” watermark on this page was created using the Word Art feature. You can insert pictures (such as a logo) from a file or using Clip Art. All three features can be found by clicking on Picture in the Insert menu. To view a watermark as it will appear on the printed page, click Print Layout on the View menu or click Print Preview on the File menu. The watermark will print on every page of this document, just like headers and footers. To edit the watermark or insert a new one, you need to click Header and Footer on the View menu. TO FORMAT A WORDART WATERMARK (LIKE THIS “DRAFT” EXAMPLE): Use the WordArt… command on the Format menu to choose your desired settings for your watermark. There are multiple tabs in that dialog. Use the “Colors and Lines” tab to set the color and transparency. (This “draft”...
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...How to Write a Good Academic Paper? That is a question which most students ask and most of them are new to academic writing. Academic writing if taken as a whole, then it would help you figure its significance and what is more important is, it would help you understand the purpose of it. Any good academic writer’s quality is his/her mind is loaded with creative set of ideas that help him navigate through the whole topic of academic paper. Ideas lead you to somewhere and only a few good students are gifted by nature and if you are not then you can also build up a good rhythm of academic writing. Secondly, you should also have a good sense of your audience; you should know what element of your academic writing would entice them and also create some space for your write-up for reading in their schedule. You then research for resources and data that would be of great use to enlighten your readers. Knowing what you audience wants, should be in your priority because readers enjoy what they seek in your writing. Usually what they look out for is something that could either bring them a smile or get them to think over the subject. Having creative ideas doesn’t guarantee a good and well-researched academic writing. You need to able to figure out ways of putting your research in a proper format so that readers don’t feel deviated from the focal point of your write-up. You should use your sources with proper attentiveness else it would completely ruin your efforts from top to bottom....
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...Hey Jessica, I’m glad your interested in attending the University of Phoenix let me tell you about some of the great resources that are available. First of all they have all kinds of hands on workshops that you can sign up for. They have ones for writing, math, computer skills, exam prep and plenty more. Some other resources are the Center for writing excellence and the Center for mathematics, there are grammar tutorials and plagiarism tutorials and a plagiarism checker as well to help make sure your papers have the proper grammar and the plagiarism checker reviews your paper and tells you how much similarities there is with your paper and other papers so you don’t accidentally plagiarize your paper. Riverpoint writer is a tool to help make sure you are citing your papers properly. In the center for mathematics center they have running start which gives you a review of math concepts to help you brush up on your skills, build math confidence gives you tips to deal with math anxiety it also has study tips, test tips, worksheets and videos. They also have live online math coaching which is only available two weeks before your math class starts through the end of your class. Hope reading about all these resources makes you want to come to the University even more. gotta go talk later. Hello Everyone, I want to review some of the great resources available here at the University of Phoenix. First off I want to go over the workshops that are available to you. There are all...
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...Joe Polce English 015 Mrs. Wickman How To Roll Your Own Cigarette Is anyone in your life a cigarette smoker? Do you often notice that they are always complaining about their ever-rising price? According to the U.S Census Bureau, out of the 6.7 billion people in the world, 2 billion are smokers of cigarettes or some other form of tobacco. Almost 75% of these 2 billion spend between $1000 - $1500 yearly on their favorite packs and cartons that they just cannot resist. We know its a habit, right? Its also an expensive habit. I am going to show you a quick and easy way to not only cut the cost of cigarettes in half, but also save you hundred of dollars. A select few smokers of the modern world have been fortunate enough to find the solution to the climbing prices of cigarettes. This solution is actually very simple. Why don’t we, instead of spending the $6 plus on an already produced pack of Marlboro Lights, make and produce our own pack of very similar cigarettes? Herein lies the solution; roll your own cigarettes. Most people shy away from such an idea claiming that they would never know where to start, or have no idea where they would buy the equipment, but on contrary the first steps to this new lifestyle are very easy, and the tools needed are readily available. The benefits of rolling your own cigarettes are numerous. First off, its inexpensive. GS Hammack, a man who writes for a website called AssociatedContact.com, said that “smokers that are looking for...
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...go fuck urself Paper is a thin material mainly used for writing upon, printing upon, drawing or for packaging. It is produced by pressing together moist fibers, typically cellulose pulp derived from wood, rags or grasses, and drying them into flexible sheets. Paper is a versatile material with many uses. Whilst the most common is for writing and printing upon, it is also widely used as a packaging material, in many cleaning products, in a number of industrial and construction processes, and even as a food ingredient – particularly in Asian cultures. Contents [hide] 1 History 2 Papermaking 2.1 Chemical pulping 2.2 Mechanical pulping 2.3 Deinked pulp 2.4 Additives 2.5 Producing paper 2.6 Finishing 3 Applications 4 Types, thickness and weight 5 Paper stability 6 The future of paper 7 See also 8 References and notes 9 External links History Main article: History of paper Further information: Science and technology of the Han Dynasty and List of Chinese inventions Hemp wrapping paper, China, circa 100 BCE.The oldest known archeological fragments of paper date to 2nd century BC China. Papermaking is considered one of the Four Great Inventions of Ancient China, and the pulp papermaking process is ascribed to Cai Lun, a 2nd century AD Han court eunuch.[1] With paper an effective substitute for silk in many applications, China could export silk in greater quantity, contributing to a Golden Age. Paper spread from China through the Islamic...
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