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Transcription
You"re watching FreeSchool! Hi everyone! Today we"re going to talk about simple machines. A simple machine is a device that makes work easier by magnifying or changing the direction of a force. That means that simple machines allow someone to do the same work with less effort! Simple machines have been known since prehistoric times and were used to help build the amazing structures left behind by ancient cultures. The Greek philosopher Archimedes identified three simple machines more than 2,000 years ago: the lever, the pulley, and the screw. He discovered that a lever would create a mechanical advantage, which means that using a lever would allow a person to move something that would normally be too heavy for them to shift. Archimedes said that with a long enough lever and a place to rest it, a person could move the world. Over the next few centuries more simple machines were recognized but it was less than 450 years ago that the last of the simple machines, the inclined plane, was identified. There are six types of simple machines: the Lever, the Wheel and Axle, the Pulley, the Inclined plane, the Wedge, and the Screw. Pulleys and Wheel and Axles are both a type of Lever. Wedges and Screws are both types of Inclined Planes. Each type of Simple Machine has a specific purpose and way they help do work. When speaking of simple machines, "work" means using energy to move an object across a distance. The further you have to move the object, the more energy it takes to move it. Let's see how each type of simple machine helps do work. A LEVER is a tool like a bar or rod that sits and turns on a fixed support called a fulcrum. When you use a lever, you apply a small force over a long distance, and the lever converts it to a larger force over a shorter distance. Some examples of levers are seesaws, crowbars, and tweezers. A Wheel and Axle is easy to recognize. It consists of a wheel with a rod in the middle. You probably already know that it"s easier to move something heavy if you can put it in something with wheels, but you might not know why. For one thing, using wheels reduces the friction - or resistance between surfaces - between the load and the ground. Secondly, much like the lever, a smaller force applied to the rim of the wheel is converted to a larger force traveling a smaller distance at the axle. Wheel and axles are used for machines such as cars, bicycles, and scooters, but they are also used in other ways, like doorknobs and pencil sharpeners. A Pulley is a machine that uses a wheel with a rope wrapped around it. The wheel often has a groove in it, which the rope fits into. One end of the rope goes around the load, and the other end is where you apply the force. Pulleys can be used to move loads or change the direction of the force you are using, and help make work easier by allowing you to spread a weaker force out along a longer path to accomplish a job. By linking multiple pulleys together, you can do the same job with even less force, because you are applying the force along a much longer distance. Pulleys may be used to raise and lower flags, blinds, or sails, and are used to help raise and lower elevators. An Inclined Plane is a flat surface with one end higher than the other. Inclined planes allow loads to slide up to a higher level instead of being lifted, which allows the work to be accomplished with a smaller force spread over a longer distance. You may recognize an inclined plane as the simple machine used in ramps and slides. A Wedge is simply two inclined planes placed back to back. It is used to push two objects apart. A smaller force applied to the back of the wedge is converted to a greater force in a small area at the tip of the wedge. Examples of wedges are axes, knives, and chisels. A Screw is basically an inclined plane wrapped around a pole. Screws can be used to hold things together or to lift things. Just like the inclined plane, the longer the path the force takes, the less force is required to do the work. Screws with more threads take less force to do a job since the force has to travel a longer distance. Examples of screws are screws, nuts, bolts, jar lids, and lightbulbs. These six simple machines can be combined to form compound or complex machines, and are considered by some to be the foundation of all machinery. For example, a wheelbarrow is made of levers combined with a wheel and axle. A pair of scissors is another complex machine: the two blades are wedges, but they are connected by a lever that allows them to come together and cut. We use simple machines to help us do work every day. Every time you open a door or a bottle, cut up your food, or even just climb stairs, you are using simple machines. Take a look and see if you can identify the simple machines around you and figure out how they make it easier to do work.
Contents
History
The idea of a simple machine originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the Archimedean simple machines: lever, pulley, and screw. He discovered the principle of mechanical advantage in the lever. Archimedes" famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth." (Greek: δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ) expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to roughly calculate their mechanical advantage. For example, Heron of Alexandria (ca. 10–75 AD) in his work Mechanics lists five mechanisms that can "set a load in motion"; lever , windlass , pulley , wedge , and screw , and describes their fabrication and uses. However the Greeks" understanding was limited to the statics of simple machines (the balance of forces), and did not include dynamics, the tradeoff between force and distance, or the concept of work.
Ideal simple machine
If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions.
Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force F in (\displaystyle F_(\text(in))\,) is applied to the device at one point, and it does work moving a load, F out (\displaystyle F_(\text(out))\,) at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage
M A = F out / F in (\displaystyle \mathrm (MA) =F_(\text(out))/F_(\text(in))\,)that can be calculated from the machine"s geometry and friction.
v out v in = d out d in (\displaystyle (v_(\text(out)) \over v_(\text(in)))=(d_(\text(out)) \over d_(\text(in )))\,)Therefore the mechanical advantage of an ideal machine is also equal to the distance ratio, the ratio of input distance moved to output distance moved
M A ideal = F out F in = d in d out (\displaystyle \mathrm (MA)_(\text(ideal))=(F_(\text(out)) \over F_(\text(in)))= (d_(\text(in)) \over d_(\text(out)))\,)
This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the lever is equal to the ratio of its lever arms.
The mechanical advantage can be greater or less than one:
- The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards.
- In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
- A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block.
A machine will be self-locking if and only if its efficiency η is below 50%:
η ≡ F o u t / F i n d i n / d o u t< 0.50 {\displaystyle \eta \equiv {\frac {F_{out}/F_{in}}{d_{in}/d_{out}}}<0.50\,}Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio d in /d out(ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.
Proof
When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work W 1,2 (\displaystyle W_(\text(1,2))\,) is equal to the sum of the work done on the load force W load (\displaystyle W_(\text(load))\,) and the work lost to friction
W 1,2 = W load + W fric (1) (\displaystyle W_(\text(1,2))=W_(\text(load))+W_(\text(fric))\qquad \qquad (1 )\,)If the efficiency is below 50% η = W load / W 1.2< 1 / 2 {\displaystyle \eta =W_{\text{load}}/W_{\text{1,2}}<1/2\,}
2 W load< W 1,2 {\displaystyle 2W_{\text{load}}When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction W fric (\displaystyle W_(\text(fric))\,) is the same
W load = W 2,1 + W fric (\displaystyle W_(\text(load))=W_(\text(2,1))+W_(\text(fric))\,)So the output work is
W 2.1 = W load − W fric< 0 {\displaystyle W_{\text{2,1}}=W_{\text{load}}-W_{\text{fric}}<0\,}the machine self-locks, because the work dissipated in friction is greater than the work done by the load force Thus moving it backwards even with no input force
Modern machine theory
Kinematic chains
Classification of machines
The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines.
However, a more successful strategy was identified by Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface.
This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the revolute joint , sliding joint , cam joint and gear joint , and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints.
See also
References
- Chambers, Ephraim (1728), "Table of Mechanics", Cyclopædia, A Useful Dictionary of Arts and Sciences, London, England, Volume 2, p. 528, Plate 11.
- Paul, Akshoy; Roy, Pijush; Mukherjee, Sanchayan (2005), Mechanical sciences: engineering mechanics and strength of materials, Prentice Hall of India, p. 215, ISBN.
- ^ Asimov, Isaac (1988), Understanding Physics, New York, New York, USA: Barnes & Noble, p. 88, ISBN.
- Anderson, William Ballantyne (1914). Physics for Technical Students: Mechanics and Heat. New York, USA: McGraw Hill. pp. 112–122. Retrieved 2008-05-11 .
- ^ Compound machines, University of Virginia Physics Department, retrieved 2010-06-11 .
- ^ Usher, Abbott Payson (1988). A History of Mechanical Inventions. USA: Courier Dover Publications. p. 98.ISBN.
- Wallenstein, Andrew (June 2002). . Proceedings of the 9th Annual Workshop on the Design, Specification, and Verification of Interactive Systems. Springer. p. 136. Retrieved 2008-05-21 .
- ^ Prater, Edward L. (1994), Basic machines(PDF), U.S. Navy Naval Education and Training Professional Development and Technology Center, NAVEDTRA 14037.
- U.S. Navy Bureau of Naval Personnel (1971), Basic machines and how they work(PDF), Dover Publications.
- Reuleaux, F. (1963) The kinematics of machinery (translated and annotated by A.B.W. Kennedy), New York, New York, USA: reprinted by Dover.
- Cornell University, Reuleaux Collection of Mechanisms and Machines at Cornell University, Cornell University.
- ^ Chiu, Y. C. (2010), An introduction to the History of Project Management, Delft: Eburon Academic Publishers, p. 42, ISBN
- Ostdiek, Vern; Bord, Donald (2005). Inquiry into Physics. Thompson Brooks/Cole. p. 123. ISBN. Retrieved 2008-05-22 .
- Quoted by Pappus of Alexandria in Synagogue, Book VIII
Engineering Connection
Why do engineers care about simple machines? How do such devices help engineers improve society? Simple machines are important and common in our world today in the form of everyday devices (crowbars, wheelbarrows, highway ramps, etc.) that individuals, and especially engineers, use on a daily basis. The same physical principles and mechanical advantages of simple machines used by ancient engineers to build pyramids are employed by today's engineers to construct modern structures such as houses, bridges and skyscrapers. Simple machines give engineers added tools for solving everyday challenges.
Learning Objectives
After this lesson, students should be able to:
- Understand what a simple machine is and how it would help an engineer to build something.
- Identify six types of simple machines.
- Understand how the same physical principles used by engineers today to build skyscrapers were employed in ancient times by engineers to build pyramids.
- Generate and compare multiple possible solutions to creating a simple lever machine based on how well each met the constraints of the challenge.
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L(www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
NGSS: Next Generation Science Standards - Science
| NGSS Performance Expectation | ||
|---|---|---|
|
3-PS2-2. Make observations and/or measurements of an object's motion to provide evidence that a pattern can be used to predict future motion. (Grade 3) Do you agree with this alignment? Thanks for your feedback! |
||
| This lesson focuses on the following Three Dimensional Learning aspects of NGSS: | ||
| Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts |
| Make observations and/or measurements to produce data to serve as the basis for evidence for an explanation of a phenomenon or test a design solution. Alignment agreement: Thanks for your feedback! Science findings are based on recognizing patterns.Alignment agreement: Thanks for your feedback! | The patterns of an object's motion in various situations can be observed and measured; when that past motion exhibits a regular pattern, future motion can be predicted from it. (Boundary: Technical terms, such as magnitude, velocity, momentum, and vector quantity, are not introduced at this level, but the concept that some quantities need both size and direction to be described is developed.) Alignment agreement: Thanks for your feedback! | Patterns of change can be used to make predictions. Alignment agreement: Thanks for your feedback! |
International Technology and Engineering Educators Association - Technology
Lesson Closure
Today, we have discussed six simple machines. Who can name them for me? (Answer: Wedge, wheel and axle, lever, inclined plane, screw, and pulley.) How do simple machines make work easier? (Answer: Mechanical advantage enables us to use less force to move an object, but we have to move it a longer distance.) Why do engineers use simple machines? (Possible answers: Engineers creatively use their knowledge of science and math to make our lives better, often using simple machines. They invent tools that make work easier. They accomplish huge tasks that could not be done without the mechanical advantage of simple machines. They design structures and tools to use our environmental resources better and more efficiently.) Tonight, at home, think about everyday examples of the six simple machines. See how many you can find around your house!
Complete the KWL Assessment Chart (see the Assessment section). Gauge students" understanding of the lesson by assigning the Simple Machines Worksheet as a take-home quiz. As an extension, use the attached to conduct a simple machines scavenger hunt in which students find examples of simple machines used in the classroom and at home.
In other lessons of this unit, students study each simple machine in more detail and see how each could be used as a tool to build a pyramid or a modern building.
Vocabulary/Definitions
Design:
Engineering:
Force:
Inclined plane: A simple machine that raises an object to greater height. Usually a straight slanted surface and no moving parts, such as a ramp, sloping road or stairs.
Lever: A simple machine that increases or decreases the force to lift something. Usually a bar pivoted on a fixed point (fulcrum) to which force is applied to do work.
Mechanical advantage: An advantage gained by using simple machines to accomplish work with less effort. Making the task easier (which means it requires less force), but may require more time or room to work (more distance, rope, etc.). For example, applying a smaller force over a longer distance to achieve the same effect as applying a large force over a small distance. The ratio of the output force exerted by a machine to the input force applied to it.
Pulley: A simple machine that changes the direction of a force, often to lift a load. Usually consists of a grooved wheel in which a pulled rope or chain runs.
Pyramid: A massive structure of ancient Egypt and Mesoamerica used for a crypt or tomb. The typical shape is a square or rectangular base at the ground with sides (faces) in the form of four triangles that meet in a point at the top. Mesoamerican temples have stepped sides and a flat top surmounted by chambers.
Screw: A simple machine that lifts or holds materials together. Often a cylindrical rod incised with a spiral thread.
Simple machine: A machine with few or no moving parts that is used to make work easier (provides a mechanical advantage). For example, a wedge, wheel and axle, lever, inclined plane, screw, or pulley.
Spiral: A curve that winds around a fixed center point (or axis) at a continuously increasing or decreasing distance from that point.
Tool: A device used to do work.
Wedge: A simple machine that forces materials apart. Used for splitting, tightening, securing or levering. It is thick at one end and tapered to a thin edge at the other.
Wheel and axle: A simple machine that reduces the friction of moving by rolling. A wheel is a disk designed to turn around an axle passed through the center of the wheel. An axle is a supporting cylinder on which a wheel or a set of wheels revolves.
Work: Force on an object multiplied by the distance it moves. W = F x d (force multiplied by distance).
Assessment
Pre-Lesson Assessment
Know / Want to Know / Learn (KWL) Chart: Create a classroom KWL chart to help organize learning about a new topic. On a large sheet of paper or on the classroom board, draw a chart with the title "Building with Simple Machines." Draw three columns titled, K, W and L, representing what students !} know about simple machines, what they want to know about simple machines and what they learned about simple machines. Fill out the K and W sections during the lesson introduction as facts and questions emerge. Fill out the L section at the end of the lesson.
Post-Introduction Assessment
Reference Sheet: Hand out the attached Simple Machines Reference Sheet. Review the information and answer any questions. Suggest the students keep the sheet handy in their desks, folders or journals.
Lesson Summary Assessment
Closing Discussion: Conduct an informal class discussion, asking the students what they learned from the activities. Ask the students:
- Who can name the different types of simple machines? (Answer: Wedge, wheel and axle, lever, inclined plane, screw, and pulley.)
- How do simple machines make work easier? (Answer: Mechanical advantage enables us to use less force to move an object, but we have to move it a longer distance.)
- Why do engineers use simple machines? (Possible answers: Engineers creatively use their knowledge of science and math to make our lives better, often using simple machines. They invent tools that make work easier. They accomplish huge tasks that could not be done without the mechanical advantage of simple machines. They design structures and tools to use our environmental resources better and more efficiently.)
Remind students that engineers consider many factors when they plan, design and create something. Ask the students:
- What are the considerations an engineer must keep in mind when designing a new structure? (Possible answers: Size and shape (design) of the structure, available construction materials, calculation of materials needed, comparing materials and costs, making drawings, etc.)
- What are the considerations an engineer must keep in mind when choosing a site to build a new structure? (Possible answers: Site physical characteristics, distance to construction resources, suitability for the structure's purpose.)
KWL Chart (Conclusion): As a class, finish column L of the KWL Chart as described in the Pre-Lesson Assessment section. List all of the things they learned about simple machines. Were all of the W questions answered? What new things did they learn?
Take-Home Quiz: Gauge students" understanding of the lesson by assigning the Simple Machines Worksheet as a take-home quiz.
Lesson Extension Activities
Use the attached Simple Machines Scavenger Hunt! Worksheet to conduct a fun scavenger hunt. Have the students find examples of all the simple machines used in the classroom and their homes.
Bring in everyday examples of simple machines and demonstrate how they work.
Illustrate the power of simple machines by asking students to do a task without using a simple machine, and then with one. For example, create a lever demonstration by hammering a nail into a piece of wood. Have students try to pull the nail out, first using only their hands
Bring in a variety of everyday examples of simple machines. Hand out one out to each student and have them think about what type of simple machine it is. Next, have students place the items into categories by simple machines and explain why they chose to place their item there. Ask students what life would be like without this item. Emphasize that simple machines make our life easier.
See the Edheads website for an interactive game on simple machines: http://edheads.org.
Engineering Design Fun with Levers: Give each pair of students a paint stirrer, 3 small plastic cups, a piece of duct tape and a wooden block or spool (or anything similar). Challenge the students to design a simple machine lever that will throw a ping pong ball (or any other type of small ball) as high as possible. In the re-design phase, allow the students to request materials to add on to their design. Have a small competition to see which group was able to send the ping pong ball flying high. Discuss with the class why that particular design was successful versus other variations seen during the competition.
Additional Multimedia Support
See http://edheads.org for a good simple machines website with curricular materials including educational games and activities.
References
Dictionary.com. Lexico Publishing Group, LLC. Accessed January 11, 2006. (Source of some vocabulary definitions, with some adaptation) http://www.dictionary.com
Simple Machines. inQuiry Almanack, The Franklin Institute Online, Unisys and Drexel eLearning. Accessed January 11, 2006. http://sln.fi.edu/qa97/spotlight3/spotlight3.html
Contributors
Greg Ramsey; Glen Sirakavit; Lawrence E. Carlson; Jacquelyn Sullivan; Malinda Schaefer Zarske; Denise Carlson, with design input from the students in the spring 2005 K-12 Engineering Outreach Corps courseCopyright
© 2005 by Regents of the University of Colorado.Supporting Program
Integrated Teaching and Learning Program, College of Engineering, University of Colorado BoulderAcknowledgments
The contents of these digital library curriculum were developed by the Integrated Teaching and Learning Program under National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.
Last modified: December 4, 2019
Topics: Simple machine, Mechanical advantage, Force Pages: 5 (856 words) Published: September 22, 2013
Activity 1.1.2 Simple Machines Practice Problems Answer Key
Procedure
Answer the following questions regarding simple machine systems. Each question requires proper illustration and annotation, including labeling of forces, distances, direction, and unknown values. Illustrations should consist of basic simple machine functional sketches rather than realistic pictorials. Be sure to document all solution steps and proper units.
All problem calculations should assume ideal conditions and no friction loss.
Simple Machines – Lever
A first class lever in static equilibrium has a 50lb resistance force and 15lb effort force. The lever's effort force is located 4 ft from the fulcrum.
1.Sketch and annotate the lever system described above.
2.What is the actual mechanical advantage of the system?
3.Using static equilibrium calculations, calculate the length from the fulcrum to the resistance force. FormulaSubstitute / SolveFinal Answer
A wheel barrow is used to lift a 200 lb load. The length from the wheel axle to the center of the load is 2 ft. The length from the wheel and axle to the effort is 5 ft.
4.Illustrate and annotate the lever system described above.
5.What is the ideal mechanical advantage of the system?
FormulaSubstitute / SolveFinal Answer
6.Using static equilibrium calculations, calculate the effort force needed to overcome the resistance force in the system. FormulaSubstitute / SolveFinal Answer
A medical technician uses a pair of four inch long tweeters to remove a wood sliver from a patient. The technician is applying 1 lb of squeezing force to the tweezers. If more than 1/5 lb of force is applied to the sliver, it will break and become difficult to remove.
7.Sketch and annotate the lever system described above.
8.What is the actual mechanical advantage of the system?
FormulaSubstitute / SolveFinal Answer
9.Using static equilibrium calculations, calculate how far from the fulcrum the tweezers must be held to avoid damaging the sliver FormulaSubstitute / SolveFinal Answer
Simple Machines – Wheel and Axle
10. What is the linear distance traveled in one revolution of a 36 in. diameter wheel? FormulaSubstitute / SolveFinal Answer
An industrial water shutoff valve is designed to operate with 30 lb of effort force. The valve will encounter 200 lb of resistance force applied to a 1.5 in. diameter axle.
11.Sketch and annotate the wheel and axle system described above.
12.What is the required actual mechanical advantage of the system? FormulaSubstitute / SolveFinal Answer
13.What is the required wheel diameter to overcome the resistance force? FormulaSubstitute / SolveFinal Answer
Simple Machines – Pulley System
A construction crew lifts approximately 560 lb of material several times during a day from a flatbed truck to a 32 ft rooftop. A block and tackle system with 50 lb of effort force is designed to lift the materials.
14.What is the required actual mechanical advantage?
FormulaSubstitute / SolveFinal Answer
15.How many supporting strands will be needed in the pulley system? FormulaSubstitute / SolveFinal Answer
A block and tackle system with nine supporting strands is used to lift a metal lathe in a manufacturing facility. The motor being used to wind the cable in the pulley system can provide 100 lb of force.
16.What is the mechanical advantage of the system?
FormulaSubstitute / SolveFinal Answer
17.What is the maximum weight of the lathe?
FormulaSubstitute / SolveFinal Answer
Simple Machines – Inclined Plane
A civil engineer...
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Chapter 4 Simple regression model Practice problems Use Chapter 4 Powerpoint question 4.1 to answer the following questions: 1. Report the Eveiw output for regression model . Please write down your fitted regression model. 2. Are the sign for consistent with your expectation, explain? 3. Hypothesize the sign of the coefficient and test your hypothesis at 5% significance level using t-table. 4. What percentage of variation in 30 year fixed mortgage rate is explained by this model? Why? Use Chapter 4 Powerpoint question 4.2 to answer the following questions: 5. Report the Eveiw output for regression model Based on the estimation period of 1986.01 – 1999.07. Please write down your fitted regression model. 6. Is Trend correlated with USPI? Set up the hypothesis testing at 5% significance level. 7. What percentage of variation in USPI is explained by this model? Why? 8. Based on your Eview model, report your forecast of USPI for the period of 1999.08-2000.07. Report RMSE. Use Chapter 4 Powerpoint question 4.3 to answer the following questions: 9. Report the Eveiw output for regression model USPIt = (USTBR)t + t based on the estimation period of 1986.01 – 1999.07. Please write down your fitted regression model. Dependent Variable: USPI | | | Method: Least Squares | | | Date: 01/24/11 Time: 16:46 | | | Sample:...
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FBE 421 Prof. Briggs Problem Set #1 Please print out this document and clearly handwrite your answers to each of the questions below in the space provided. Show all your work accordingly. A. Calculate LTM (a) Revenue and (b) Net Income for Costco Wholesale (COST) using their latest financial statements as of 3Q2011. 77946+60737-53821=84.862 MM Revenue 1303+984-871= 1.416 MM Net-income B. Calculate Costco’s LTM (a) EBIT and (b) EBITDA. 2077+1677-1389=2.365 MM EBIT (2077+795)+(1677+582)-(1389+549)= 3192 MM EBITDA Name: Student ID: 1. C. Calculate Costco's (a) Market Cap, (b) Total Debt and (c) Enterprise Value as of 3Q2011. a) 437,735,000 * 85.07 = 37.238 Bn b) 1+900+1,247=2.148 Bn c) 37.238+2.148+.578 (minority interest)-4.082= 35.882 Bn (35,882 MM) D. Calculate Costco's (a) EV/Revenue and (b) EV/EBIT multiples. a) 35,882/84,862=.42x b) 35,882/2,365=15.17x 2. Explain the differences between a firm’s (a) market value, (b) enterprise value, and (c) book value. a) Market value, otherwise known as market capitalization, is the current value of the firm’s common equity on the open market. This is the value necessary to buy the entire firm’s equity. b) Enterprise value is the value of all the claims on the firm’s capital structure less cash. This includes the value of equity, preferred stock, debt, and minority interest less cash. This is the value necessary to purchase the entire firm. c) Book value is the value of a firm’s equity...
Kinematics: Simple Machine and Prime Mover Essay
Pure motion - motion considered abstractly, without reference to force or mass. Engineers use kinematics in machine design. Although hidden in much of modern technology, kinematic mechanisms are important components of many technologies such as robots, automobiles, aircraft, satellites, and consumer electronics, as well as biomechanical prostheses. In physics, kinematics is part of the teaching of basic ideas of dynamics; in mathematics, it is a fundamental part of geometric thinking and concepts of motion. The development of high-speed computers and robotics, and the growth of design synthesis theory and mechatronics have recently revived interest in kinematics and early work in machine design. Working in the decades following Ampère"s death, Franz Reuleaux (1829-1905) is considered the founder of modern kinematics. Reuleaux called it "the study of the motion of bodies of every kind…and the study of the geometric representation of motion" (Kinematics of Machinery 56).Kinematics flourished in the 19th century as machine inventors learned to transmit information and forces (power) from one element in the machine to another. Steam- and water-based machines revolutionized the l9th century, but both of those energy sources generate circular motions, creating the need to convert these steady circular motions into nonsteady linear and curvilinear motion for machine applications....
A lever is a simple machine that allows you to gain a mechanical advantage in moving an object or in applying a force to an object. It is considered a "pure" simple machine because friction is usually so small that it is not considered a factor to overcome, as in other simple machines.
A lever consists of a rigid bar or beam that is allowed to rotate or pivot about a fulcrum. An applied force is then used to move a load. There are three common types or classes of levers, depending on where the fulcrum and applied force is located.
The mechanical advantage is that you can move a heavy object using less force than the weight of the object, you can propel an object faster by applying a force at a slower speed, or you can move an object further than the distance you apply to the lever.
Questions you may have include:
- What are the parts of a lever?
- What are the three types or classes of levers?
- What are the uses for a lever?
This lesson will answer those questions. Useful tool: Units Conversion
A typical lever consists of a solid board or rod that can pivot about a point or fulcrum. Since humans usually provide energy to levers, "effort" and "load" are often used instead of input and output.
An input force or effort is applied, resulting in moving or applying an output force to a load.
The distance from the applied force or effort force to the fulcrum is called the effort or input arm and the distance from the load to the fulcrum is called the load or output arm.
Since there is typically a very small amount of friction at the fulcrum, overcoming friction is not a factor in a lever as it might be in another simple machine like a ramp or wedge. Thus, we consider a lever a pure simple machine.
Lever configurations
There are three types or classes of levers, according to where the load and effort are located with respect to the fulcrum.
Class 1
A class 1 lever has the fulcrum placed between the effort and load. The movement of the load is in the opposite direction of the movement of the effort. This is the most typical lever configuration.
Class 2
A class 2 lever has the load between the effort and the fulcrum. In this type of lever, the movement of the load is in the same direction as that of the effort. Note that the length of the effort arm goes all the way to the fulcrum and is always greater than the length of the load arm in a class 2 lever.
Class 3
A class 3 lever has the effort between the load and the fulcrum. Both the effort and load are in the same direction. Because of the configuration, the fulcrum must prevent the lever beam from moving upward or downward. Often a bearing is used to allow the beam to pivot.
Note that the length of the load arm goes all the way to the fulcrum and is always greater than the length of the effort arm in a class 3 lever. The result is a force mechanical advantage less than 1.
Uses for a lever
The reason for a lever is that you can use it for a mechanical advantage in lifting heavy loads, moving things a greater distance or increasing the speed of an object.
Increase force
Increase distance moved
You can increase the applied force in order to lift heavier loads.
Increase speed
You can increase the speed that the load moves with Class 1 or Class 3 levers.
Summary
A lever is a simple machine that allows you to gain a mechanical advantage. It consists of a consists of a rigid bar or beam that is allowed to rotate or pivot about a fulcrum, along with an applied force and load. The three types or classes of levers, depend on where the fulcrum and applied force is located.
Uses for a lever are that you can move a heavy object using less force than the weight of the object, propel an object faster by applying a force at a slower speed, or move an object further than the distance you apply to the lever.
Leveraging gives you an advantage
And began to be called YaBB SE.
As YaBB SE developed, it became more and more, and by that time there were some aspects that required reworking and improving the project. It was decided that it was best to separate from YaBB SE, because it was something different than YaBB. The most correct decision was to abandon everything that had been developed and start all over again. This is where development began SMF.
The first version was released on September 29, 2003 SMF 1.0 beta1, which was distributed only to the group Charter Member. This was a big disadvantage, since the forum could only be used by a limited circle of people who were part of this group. The first public release was released on March 10, 2004 SMF. Web forums based on SMF 1.1: ami.lv and no less popular iratbildes.lv.
SMF was created as a replacement for an online forum YaBB SE, which has gained a bad reputation due to the problems of its counterpart developed in Perl with a similar name - YaBB.
First versions YaBB were known for performance issues and were resource intensive. YaBB SE was written as an example PHP-port YaBB, but at the same time it was less demanding on resources and even free of security problems.
SMF started as a small project of one of the developers YaBB SE, and in order to expand the capabilities of templates YaBB SE. Since then, the project has gradually expanded: adding general functionality “ordered” by users, solving performance problems and security issues.
Version 2.0 of the forum was announced on April 8, 2007. A public beta release was released on March 17, 2008. The main innovations include:
- Database abstraction: support planned PostgreSQL And SQLite.
- Moderation Center, which combines all moderation functions for all moderators, and also allows pre-moderation of topics, messages and attachments, if necessary.
- User warning system
- Additional management of user groups such as moderators, as well as free and on-demand groups.
- Support OpenID. Possibility to use OpenID-account for registering and logging into the forum.
- Additional fields in user profiles.
- WYSIWYG-editor to provide an intuitive user interface.
- Task Manager and Message Queuing System
The project's source code is available in the public repository at GitHub github.com/SimpleMachines/SMF2.1
License
SMF 1.0 and 1.1 are published under a proprietary license. While open source, redistribution and/or distribution of modified components is limited to authorized entities.
Simple Machines Forum versions 2.0 and 2.1 under the BSD 3-p license. It is also open source with modified code redistributed based on BSD requirements.
Localization
SMF Team
More than 50 people work on SMF, including:
- 3 managers
- 6 developers
- 3 documenters
Team motto: “Small, proud, passionate!” (The few, the proud, the geeky! (English))
see also
Write a review about the article "Simple Machines Forum"
Notes
Literature
- Phil Hughes(English) // Linux Journal. - 2008. - March 4.
Links
- - official website of Simple Machines Forum (English)
- (Russian)
- (Russian)
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An excerpt characterizing the Simple Machines Forum
On guardianship matters of the Ryazan estate, Prince Andrei had to see the district leader. The leader was Count Ilya Andreich Rostov, and Prince Andrei went to see him in mid-May.It was already a hot period of spring. The forest was already completely dressed, there was dust and it was so hot that driving past the water, I wanted to swim.
Prince Andrei, gloomy and preoccupied with considerations about what and what he needed to ask the leader about matters, drove up the garden alley to the Rostovs’ Otradnensky house. To the right, from behind the trees, he heard a woman's cheerful cry, and saw a crowd of girls running towards his stroller. Ahead of the others, a black-haired, very thin, strangely thin, black-eyed girl in a yellow cotton dress, tied with a white handkerchief, from under which strands of combed hair were escaping, ran up to the carriage. The girl screamed something, but recognizing the stranger, without looking at him, she ran back laughing.
Prince Andrei suddenly felt pain from something. The day was so good, the sun was so bright, everything around was so cheerful; and this thin and pretty girl did not know and did not want to know about his existence and was content and happy with some kind of separate, certainly stupid, but cheerful and happy life. “Why is she so happy? what is she thinking about! Not about the military regulations, not about the structure of the Ryazan quitrents. What is she thinking about? And what makes her happy?” Prince Andrei involuntarily asked himself with curiosity.
Count Ilya Andreich in 1809 lived in Otradnoye still as before, that is, hosting almost the entire province, with hunts, theaters, dinners and musicians. He, like any new guest, was glad to see Prince Andrei, and almost forcibly left him to spend the night.
Throughout the boring day, during which Prince Andrei was occupied by the senior hosts and the most honorable of the guests, with whom the old count's house was full on the occasion of the approaching name day, Bolkonsky, looking several times at Natasha, who was laughing and having fun among the other young half of the company, kept asking himself: “What is she thinking about? Why is she so happy!”
In the evening, left alone in a new place, he could not fall asleep for a long time. He read, then put out the candle and lit it again. It was hot in the room with the shutters closed from the inside. He was annoyed with this stupid old man (as he called Rostov), who detained him, assuring him that the necessary papers in the city had not yet been delivered, and he was annoyed with himself for staying.
Prince Andrei stood up and went to the window to open it. As soon as he opened the shutters, moonlight, as if he had been on guard at the window for a long time waiting for it, rushed into the room. He opened the window. The night was fresh and still bright. Just in front of the window there was a row of trimmed trees, black on one side and silvery lit on the other. Under the trees there was some kind of lush, wet, curly vegetation with silvery leaves and stems here and there. Further behind the black trees there was some kind of roof shining with dew, to the right a large curly tree, with a bright white trunk and branches, and above it was an almost full moon in a bright, almost starless spring sky. Prince Andrei leaned his elbows on the window and his eyes stopped at this sky.
Prince Andrei's room was on the middle floor; They also lived in the rooms above it and did not sleep. He heard a woman talking from above.
“Just one more time,” said a female voice from above, which Prince Andrei now recognized.
- When will you sleep? - answered another voice.
- I won’t, I can’t sleep, what should I do! Well, last time...
Two female voices sang some kind of musical phrase that constituted the end of something.
- Oh, how lovely! Well, now sleep, and that's the end.
“You sleep, but I can’t,” answered the first voice approaching the window. She apparently leaned out of the window completely, because the rustling of her dress and even her breathing could be heard. Everything became quiet and petrified, like the moon and its light and shadows. Prince Andrei was also afraid to move, so as not to betray his involuntary presence.
- Sonya! Sonya! – the first voice was heard again. - Well, how can you sleep! Look what a beauty it is! Oh, how lovely! “Wake up, Sonya,” she said almost with tears in her voice. - After all, such a lovely night has never, never happened.
Sonya reluctantly answered something.
- No, look what a moon it is!... Oh, how lovely! Come here. Darling, my dear, come here. Well, do you see? So I would squat down, like this, I would grab myself under the knees - tighter, as tight as possible - you have to strain. Like this!
- Come on, you'll fall.
There was a struggle and Sonya’s dissatisfied voice: “It’s two o’clock.”
- Oh, you're just ruining everything for me. Well, go, go.
Again everything fell silent, but Prince Andrei knew that she was still sitting here, he sometimes heard quiet movements, sometimes sighs.
- Oh my god! My God! what is this! – she suddenly screamed. - Sleep like that! – and slammed the window.
“And they don’t care about my existence!” thought Prince Andrei as he listened to her conversation, for some reason expecting and fearing that she would say something about him. - “And there she is again! And how on purpose!” he thought. In his soul suddenly arose such an unexpected confusion of young thoughts and hopes, contradicting his whole life, that he, feeling unable to understand his condition, immediately fell asleep.
The next day, having said goodbye to only one count, without waiting for the ladies to leave, Prince Andrei went home.
It was already the beginning of June when Prince Andrei, returning home, again drove into that birch grove in which this old, gnarled oak had struck him so strangely and memorably. The bells rang even more muffled in the forest than a month and a half ago; everything was full, shady and dense; and the young spruces, scattered throughout the forest, did not disturb the overall beauty and, imitating the general character, were tenderly green with fluffy young shoots.
It was hot all day, a thunderstorm was gathering somewhere, but only a small cloud splashed on the dust of the road and on the succulent leaves. The left side of the forest was dark, in shadow; the right one, wet and glossy, glistened in the sun, slightly swaying in the wind. Everything was in bloom; the nightingales chattered and rolled, now close, now far away.
“Yes, here, in this forest, there was this oak tree with which we agreed,” thought Prince Andrei. “Where is he,” Prince Andrei thought again, looking at the left side of the road and without knowing it, without recognizing him, he admired the oak tree that he was looking for. The old oak tree, completely transformed, spread out like a tent of lush, dark greenery, swayed slightly, swaying slightly in the rays of the evening sun. No gnarled fingers, no sores, no old mistrust and grief - nothing was visible. Juicy, young leaves broke through the tough, hundred-year-old bark without knots, so it was impossible to believe that this old man had produced them. “Yes, this is that same oak tree,” thought Prince Andrei, and suddenly an unreasonable, spring feeling of joy and renewal came over him. All the best moments of his life suddenly came back to him at the same time. And Austerlitz with the high sky, and the dead, reproachful face of his wife, and Pierre on the ferry, and the girl excited by the beauty of the night, and this night, and the moon - and all this suddenly came to his mind.
