Activity Guide Levers/Simple Machines Levers/Simple Structure Andstructure Function/Adaptations Ratios/Graphing
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Motion Projectile Motion,And Straight Linemotion, Differences Between the Similaritiesand 2 CHAPTER 2 Acceleration Make Thefollowing As Youreadthe ●
026_039_Ch02_RE_896315.qxd 3/23/10 5:08 PM Page 36 User-040 113:GO00492:GPS_Reading_Essentials_SE%0:XXXXXXXXXXXXX_SE:Application_File chapter 2 Motion section ●3 Acceleration What You’ll Learn Before You Read ■ how acceleration, time, and velocity are related Describe what happens to the speed of a bicycle as it goes ■ the different ways an uphill and downhill. object can accelerate ■ how to calculate acceleration ■ the similarities and differences between straight line motion, projectile motion, and circular motion Read to Learn Study Coach Outlining As you read the Velocity and Acceleration section, make an outline of the important information in A car sitting at a stoplight is not moving. When the light each paragraph. turns green, the driver presses the gas pedal and the car starts moving. The car moves faster and faster. Speed is the rate of change of position. Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. Remember that velocity is a measure that includes both speed and direction. Because of this, a change in velocity can be either a change in how fast something is moving or a change in the direction it is moving. Acceleration means that an object changes it speed, its direction, or both. How are speeding up and slowing down described? ●D Construct a Venn When you think of something accelerating, you probably Diagram Make the following trifold Foldable to compare and think of it as speeding up. But an object that is slowing down contrast the characteristics of is also accelerating. Remember that acceleration is a change in acceleration, speed, and velocity. -
Frames of Reference
Galilean Relativity 1 m/s 3 m/s Q. What is the women velocity? A. With respect to whom? Frames of Reference: A frame of reference is a set of coordinates (for example x, y & z axes) with respect to whom any physical quantity can be determined. Inertial Frames of Reference: - The inertia of a body is the resistance of changing its state of motion. - Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames. - Special relativity deals only with physics viewed from inertial reference frames. - If we can neglect the effect of the earth’s rotations, a frame of reference fixed in the earth is an inertial reference frame. Galilean Coordinate Transformations: For simplicity: - Let coordinates in both references equal at (t = 0 ). - Use Cartesian coordinate systems. t1 = t2 = 0 t1 = t2 At ( t1 = t2 ) Galilean Coordinate Transformations are: x2= x 1 − vt 1 x1= x 2+ vt 2 or y2= y 1 y1= y 2 z2= z 1 z1= z 2 Recall v is constant, differentiation of above equations gives Galilean velocity Transformations: dx dx dx dx 2 =1 − v 1 =2 − v dt 2 dt 1 dt 1 dt 2 dy dy dy dy 2 = 1 1 = 2 dt dt dt dt 2 1 1 2 dz dz dz dz 2 = 1 1 = 2 and dt2 dt 1 dt 1 dt 2 or v x1= v x 2 + v v x2 =v x1 − v and Similarly, Galilean acceleration Transformations: a2= a 1 Physics before Relativity Classical physics was developed between about 1650 and 1900 based on: * Idealized mechanical models that can be subjected to mathematical analysis and tested against observation. -
From Ancient Greece to Byzantium
Proceedings of the European Control Conference 2007 TuA07.4 Kos, Greece, July 2-5, 2007 Technology and Autonomous Mechanisms in the Mediterranean: From Ancient Greece to Byzantium K. P. Valavanis, G. J. Vachtsevanos, P. J. Antsaklis Abstract – The paper aims at presenting each period are then provided followed by technology and automation advances in the accomplishments in automatic control and the ancient Greek World, offering evidence that transition from the ancient Greek world to the Greco- feedback control as a discipline dates back more Roman era and the Byzantium. than twenty five centuries. II. CHRONOLOGICAL MAP OF SCIENCE & TECHNOLOGY I. INTRODUCTION It is worth noting that there was an initial phase of The paper objective is to present historical evidence imported influences in the development of ancient of achievements in science, technology and the Greek technology that reached the Greek states from making of automation in the ancient Greek world until the East (Persia, Babylon and Mesopotamia) and th the era of Byzantium and that the main driving force practiced by the Greeks up until the 6 century B.C. It behind Greek science [16] - [18] has been curiosity and was at the time of Thales of Miletus (circa 585 B.C.), desire for knowledge followed by the study of nature. when a very significant change occurred. A new and When focusing on the discipline of feedback control, exclusively Greek activity began to dominate any James Watt’s Flyball Governor (1769) may be inherited technology, called science. In subsequent considered as one of the earliest feedback control centuries, technology itself became more productive, devices of the modern era. -
The Impacts of Technological Invention on Economic Growth – a Review of the Literature Andrew Reamer1 February 28, 2014
THE GEORGE WASHINGTON INSTITUTE OF PUBLIC POLICY The Impacts of Technological Invention on Economic Growth – A Review of the Literature Andrew Reamer1 February 28, 2014 I. Introduction In their recently published book, The Second Machine Age, Erik Brynjolfsson and Andrew McAfee rely on economist Paul Krugman to explain the connection between invention and growth: Paul Krugman speaks for many, if not most, economists when he says, “Productivity isn’t everything, but in the long run it’s almost everything.” Why? Because, he explains, “A country’s ability to improve its standard of living over time depends almost entirely on its ability to raise its output per worker”—in other words, the number of hours of labor it takes to produce everything, from automobiles to zippers, that we produce. Most countries don’t have extensive mineral wealth or oil reserves, and thus can’t get rich by exporting them. So the only viable way for societies to become wealthier—to improve the standard of living available to its people—is for their companies and workers to keep getting more output from the same number of inputs, in other words more goods and services from the same number of people. Innovation is how this productivity growth happens.2 For decades, economists and economic historians have sought to improve their understanding of the role of technological invention in economic growth. As in many fields of inventive endeavor, their efforts required time to develop and mature. In the last five years, these efforts have reached a point where they are generating robust, substantive, and intellectually interesting findings, to the benefit of those interested in promoting growth-enhancing invention in the U.S. -
Chapter 8 Glossary
Technology: Engineering Our World © 2012 Chapter 8: Machines—Glossary friction. A force that acts like a brake on moving objects. gear. A rotating wheel-like object with teeth around its rim used to transmit force to other gears with matching teeth. hydraulics. The study and technology of the characteristics of liquids at rest and in motion. inclined plane. A simple machine in the form of a sloping surface or ramp, used to move a load from one level to another. lever. A simple machine that consists of a bar and fulcrum (pivot point). Levers are used to increase force or decrease the effort needed to move a load. linkage. A system of levers used to transmit motion. lubrication. The application of a smooth or slippery substance between two objects to reduce friction. machine. A device that does some kind of work by changing or transmitting energy. mechanical advantage. In a simple machine, the ability to move a large resistance by applying a small effort. mechanism. A way of changing one kind of effort into another kind of effort. moment. The turning force acting on a lever; effort times the distance of the effort from the fulcrum. pneumatics. The study and technology of the characteristics of gases. power. The rate at which work is done or the rate at which energy is converted from one form to another or transferred from one place to another. pressure. The effort applied to a given area; effort divided by area. pulley. A simple machine in the form of a wheel with a groove around its rim to accept a rope, chain, or belt; it is used to lift heavy objects. -
Chapter 3 Motion in Two and Three Dimensions
Chapter 3 Motion in Two and Three Dimensions 3.1 The Important Stuff 3.1.1 Position In three dimensions, the location of a particle is specified by its location vector, r: r = xi + yj + zk (3.1) If during a time interval ∆t the position vector of the particle changes from r1 to r2, the displacement ∆r for that time interval is ∆r = r1 − r2 (3.2) = (x2 − x1)i +(y2 − y1)j +(z2 − z1)k (3.3) 3.1.2 Velocity If a particle moves through a displacement ∆r in a time interval ∆t then its average velocity for that interval is ∆r ∆x ∆y ∆z v = = i + j + k (3.4) ∆t ∆t ∆t ∆t As before, a more interesting quantity is the instantaneous velocity v, which is the limit of the average velocity when we shrink the time interval ∆t to zero. It is the time derivative of the position vector r: dr v = (3.5) dt d = (xi + yj + zk) (3.6) dt dx dy dz = i + j + k (3.7) dt dt dt can be written: v = vxi + vyj + vzk (3.8) 51 52 CHAPTER 3. MOTION IN TWO AND THREE DIMENSIONS where dx dy dz v = v = v = (3.9) x dt y dt z dt The instantaneous velocity v of a particle is always tangent to the path of the particle. 3.1.3 Acceleration If a particle’s velocity changes by ∆v in a time period ∆t, the average acceleration a for that period is ∆v ∆v ∆v ∆v a = = x i + y j + z k (3.10) ∆t ∆t ∆t ∆t but a much more interesting quantity is the result of shrinking the period ∆t to zero, which gives us the instantaneous acceleration, a. -
Engineering Philosophy Louis L
Engineering Philosophy Louis L. Bucciarelli ISBN 90-407-2318-4 Copyright 2003 by Louis L. Bucciarelli Table of Contents Introduction 1 Designing, like language, is a social process. 9 What engineers don’t know & why they believe it. 23 Knowing that and how 43 Learning Engineering 77 Extrapolation 99 Index 103 1 Introduction “Let’s stop all this philosophizing and get back to business”1 Philosophy and engineering seem worlds apart. From their remarks, we might infer that engineers value little the problems philosophers address and the analyses they pursue. Ontological questions about the nature of existence and the categorial structure of reality – what one takes as real in the world – seem to be of scant inter- est. It would appear that engineers don’t need philosophy; they know the differ- ence between the concrete and the abstract, the particular and the universal – they work within both of these domains every day, building and theorizing, testing and modeling in the design and development of new products and systems. Possible worlds are not fictions but the business they are about. As Theodore Von Karman, an aerospace engineer and educator, reportedly claimed Scientists discover the world that exists; engineers create the world that never was. Epistemological questions about the source and status of engineering knowl- edge likewise rarely draw their attention.2 Engineers are pragmatic. If their pro- ductions function in accord with their designs, they consider their knowledge justified and true. Such knowledge, they will show you, is firmly rooted in the sci- entific explanation of phenomenon which, while dated according to physicists, may still provide fertile grounds for innovative extension of their understanding of how things work or might work better. -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
Exploring Robotics Joel Kammet Supplemental Notes on Gear Ratios
CORC 3303 – Exploring Robotics Joel Kammet Supplemental notes on gear ratios, torque and speed Vocabulary SI (Système International d'Unités) – the metric system force torque axis moment arm acceleration gear ratio newton – Si unit of force meter – SI unit of distance newton-meter – SI unit of torque Torque Torque is a measure of the tendency of a force to rotate an object about some axis. A torque is meaningful only in relation to a particular axis, so we speak of the torque about the motor shaft, the torque about the axle, and so on. In order to produce torque, the force must act at some distance from the axis or pivot point. For example, a force applied at the end of a wrench handle to turn a nut around a screw located in the jaw at the other end of the wrench produces a torque about the screw. Similarly, a force applied at the circumference of a gear attached to an axle produces a torque about the axle. The perpendicular distance d from the line of force to the axis is called the moment arm. In the following diagram, the circle represents a gear of radius d. The dot in the center represents the axle (A). A force F is applied at the edge of the gear, tangentially. F d A Diagram 1 In this example, the radius of the gear is the moment arm. The force is acting along a tangent to the gear, so it is perpendicular to the radius. The amount of torque at A about the gear axle is defined as = F×d 1 We use the Greek letter Tau ( ) to represent torque. -
Levers and Gears: a Lot for a Little
Physics Levers and Gears: A lot for a little A surprising number of the tools and machines we rely on every day – from door handles and cricket bats to clocks and bikes – can be explained in terms of a few simple ideas. The same principles allowed ancient civilizations to build enormous pyramids and the mysterious astronomical device known as the Antikythera Mechanism. In this lesson you will investigate the following: • How do simple machines allow us to achieve a lot with little effort? • What is mechanical advantage and how does it apply to levers, wheels and gears? • How do gear systems work? So gear up for a look at how some of our most useful machines work. This is a print version of an interactive online lesson. To sign up for the real thing or for curriculum details about the lesson go to www.cosmosforschools.com Introduction: Levers and Gears A reconstruction of the Antikythera Mechanism. In 1900 a team of divers discovered a 2000-year-old shipwreck near the Greek island of Antikythera. Inside the wreck they found an incredible range of treasures including beautiful bronze statues and glass bowls. They also found a plain-looking lump of bronze no bigger than a shoebox. Closer examination revealed that the object had gear wheels embedded in it – as though it was some kind of ancient clock. It soon became known as the Antikythera Mechanism but its internal structure and purpose remained mysterious for decades. Later investigations using X-rays uncovered thirty interlocking gears and inscriptions of the ancient Greek words for “sphere” and “cosmos”. -
Lever Lifting
Lever Lifting Simple machines can help us accomplish a task by trading force and distance. As the distance we apply a force goes up, we need to put in less force to do the same thing. A lever is a type of simple machine, and in this activity, students will experiment with the connection between force and distance. Materials 12-inch ruler (optional) a second ruler for making measurements 2 small paper cups (Dixie cups would work) Tape Weights (such as marbles, steel nuts, or dead AA batteries) Dry erase marker, or some other cylinder to use as a fulcrum Table (Page 4) Making the Lever The students will be making a lever out of the ruler and thick marker. The marker will be the fulcrum, and the ruler will be the bar. Start off by placing the marker underneath the ruler at the 6‐inch line. The ruler should be able to easily tilt back and forth. In order to do tests with this lever, we will tape one paper cup on each end of the ruler (perhaps around 1‐inch and 11‐inches), facing up. Have them write the letter L (Load) on the cup near the 1‐inch mark. This will act as our load, what we are trying to lift. Mark the other cup with the letter E (Effort). Now to experiment with the lever, we can put some number of weights in the load cup and see how many weights we have to add to the effort cup to lift it up. By moving where the fulcrum is, the students can test out the effects of changing a lever. -
Rotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn that where the force is applied and how the force is applied is just as important as how much force is applied when we want to make something rotate. This tutorial discusses the dynamics of an object rotating about a fixed axis and introduces the concepts of torque and moment of inertia. These concepts allows us to get a better understanding of why pushing a door towards its hinges is not very a very effective way to make it open, why using a longer wrench makes it easier to loosen a tight bolt, etc. This module begins by looking at the kinetic energy of rotation and by defining a quantity known as the moment of inertia which is the rotational analog of mass. Then it proceeds to discuss the quantity called torque which is the rotational analog of force and is the physical quantity that is required to changed an object's state of rotational motion. Moment of Inertia Kinetic Energy of Rotation Consider a rigid object rotating about a fixed axis at a certain angular velocity. Since every particle in the object is moving, every particle has kinetic energy. To find the total kinetic energy related to the rotation of the body, the sum of the kinetic energy of every particle due to the rotational motion is taken. The total kinetic energy can be expressed as ..