Kinetic Energy and the Work Energy Theorem

Kinetic Energy and the Work Energy Theorem tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất c...

Chapter 7 Kinetic Energy and Work In this chapter we will introduce the following concepts: Kinetic energy of a moving object Work done by a force Power In addition we will develop the work-kinetic energy theorem and apply it to solve a variety of problems This approach is alternative approach to mechanics. It uses scalars such as work and kinetic energy rather than vectors such as velocity and acceleration. Therefore it simpler to apply. (7-1) m m Kinetic Energy: We define a new physical parameter to describe the state of motion of an object of mass m and speed v We define its kinetic energy K as: 2 2 mv K = We can use the equation above to define the SI unit for work (the joule, symbol: J ). An object of mass m = 1kg that moves with speed v = 1 m/s has a kinetic energy K = 1J Work: (symbol W) If a force F is applied to an object of mass m it can accelerate it and increase its speed v and kinetic energy K. Similarly F can decelerate m and decrease its kinetic energy. We account for these changes in K by saying that F has transferred energy W to or from the object. If energy it transferred to m (its K increases) we say that work was done by F on the object (W > 0). If on the other hand. If on the other hand energy its transferred from the object (its K decreases) we say that work was done by m (W < 0) (7-2) m m Consider a bead of mass that can move without friction along a straight wire along the x-axis. A constant force applied at an angle Finding an expression for Work to the wire is acting on th b : e m F φ r ead 2 We apply Newton's second law: We assume that the bead had an initial velocity and after it has travelled a distance its velocity is . We apply the third equation of kinematics: x x o F ma v d v v v = − r r r 2 2 2 2 2 2 We multiply both sides by / 2 2 2 cos 2 2 2 2 2 The change in kinetic energy cos 2 Thus the work done the force the beby on o x x o x x i o f f i a d m F m m m m m v v a d d F d F d K v m m K v K K Fd W φ ϕ = → − = = = = = = → − = ad is given by: cos x W F d Fd ϕ = = cosW Fd ϕ = W F d= × r r (7-3) A F r B F r C F r m m The unit of is the same as that of i.e. The expressions for work we have developed apply when is constant We have made the implicit assumption that the m Note 1: Note oving objec t jo i ule s p2 - s : oint W K F like 0 if 0 90 , 0 if 90 180 If we have several forces acting on a body (say three as in the picture) there are two methods that can be used to calculate the Note 3: Net Wor : n k et W W φ φ > < < ° < ° < < ° work First calculate the work done by each force: by force , by force , and by force . Then determine C Method 1: Method 2: alculate first ; n net A A B B C C net B C C A et A B W W W F W F W F F F F W W F W = = + + + + r r r r r r r Then determine net W F d= × r r cosW Fd ϕ = W F d= × r r (7-4) m m We have seen earlier that: . We define the change in kinetic energy as: . The equation above becomes th work-kinetic energy te heorem f i net f i K K W K K K − = ∆ = − Work-Kinetic Energy Theorem f i net K K K W∆ = − = Change in the kinetic net work done on energy of a pareticle the particle     =         The work-kinetic energy theorem holds for both positive and negative values of If 0 0 If 0 0 net net f i f i net f i f i W W K K K K W K K K K > → − > → > < → − < → < (7-5) A B Consider a tomato of mass that is thrown upwards Kinetic Energy and the Work-Energy Theorem Kinetic Energy and the Work-Energy Theorem Bởi: OpenStaxCollege Work Transfers Energy What happens to the work done on a system? Energy is transferred into the system, but in what form? Does it remain in the system or move on? The answers depend on the situation For example, if the lawn mower in [link](a) is pushed just hard enough to keep it going at a constant speed, then energy put into the mower by the person is removed continuously by friction, and eventually leaves the system in the form of heat transfer In contrast, work done on the briefcase by the person carrying it up stairs in [link](d) is stored in the briefcase-Earth system and can be recovered at any time, as shown in [link](e) In fact, the building of the pyramids in ancient Egypt is an example of storing energy in a system by doing work on the system Some of the energy imparted to the stone blocks in lifting them during construction of the pyramids remains in the stoneEarth system and has the potential to work In this section we begin the study of various types of work and forms of energy We will find that some types of work leave the energy of a system constant, for example, whereas others change the system in some way, such as making it move We will also develop definitions of important forms of energy, such as the energy of motion Net Work and the Work-Energy Theorem We know from the study of Newton’s laws in Dynamics: Force and Newton's Laws of Motion that net force causes acceleration We will see in this section that work done by the net force gives a system energy of motion, and in the process we will also find an expression for the energy of motion Let us start by considering the total, or net, work done on a system Net work is defined to be the sum of work done by all external forces—that is, net work is the work done by the net external force Fnet In equation form, this is Wnet = Fnetd cos θ where θ is the angle between the force vector and the displacement vector 1/10 d Kinetic Energy and the Work-Energy Theorem [link](a) shows a graph of force versus displacement for the component of the force in the direction of the displacement—that is, an F cos θ vs d graph In this case, F cos θ is constant You can see that the area under the graph is Fd cos θ, or the work done [link](b) shows a more general process where the force varies The area under the curve is divided into strips, each having an average force (F cos θ)i(ave) The work done is (F cos θ)i(ave)di for each strip, and the total work done is the sum of the Wi Thus the total work done is the total area under the curve, a useful property to which we shall refer later (a) A graph of F cos θ vs d, when F cos θ is constant The area under the curve represents the work done by the force (b) A graph of F cos θ vs d in which the force varies The work done for each interval is the area of each strip; thus, the total area under the curve equals the total work done Net work will be simpler to examine if we consider a one-dimensional situation where a force is used to accelerate an object in a direction parallel to its initial velocity Such a situation occurs for the package on the roller belt conveyor system shown in [link] A package on a roller belt is pushed horizontally through a distance 2/10 Kinetic Energy and the Work-Energy Theorem The force of gravity and the normal force acting on the package are perpendicular to the displacement and no work Moreover, they are also equal in magnitude and opposite in direction so they cancel in calculating the net force The net force arises solely from the horizontal applied force Fapp and the horizontal friction force f Thus, as expected, the net force is parallel to the displacement, so that θ = 0º and cos θ = 1, and the net work is given by Wnet = Fnetd The effect of the net force Fnet is to accelerate the package from v0 to v The kinetic energy of the package increases, indicating that the net work done on the system is positive (See [link].) By using Newton’s second law, and doing some algebra, we can reach an interesting conclusion Substituting Fnet = ma from Newton’s second law gives Wnet = mad To get a relationship between net work and the speed given to a system by the net force acting on it, we take d = x − x0 and use the equation studied in Motion Equations for Constant Acceleration in One Dimension for the change in speed over a distance d if the acceleration has the constant value a; namely, v2 = v02 + 2ad (note that a appears in the expression for the net work) Solving for acceleration gives a = substituted into the preceding expression for Wnet, we obtain Wnet = m ( v2 − v02 2d v2 − v02 2d When a is )d The d cancels, and we rearrange this to obtain W net = mv2 − mv02 This expression is called the work-energy theorem, and it actually applies in general (even for forces that vary in direction and magnitude), although we have derived it for the special case of a constant force parallel to the ...DNA strand exchange activity of rice recombinase OsDmc1 monitored by fluorescence resonance energy transfer and the role of ATP hydrolysis Chittela Rajanikant 1 , Manoj Kumbhakar 2 , Haridas Pal 2 , Basuthkar J. Rao 3 and Jayashree K. Sainis 1 1 Molecular Biology Division, Bhabha Atomic Research Center, Mumbai, India 2 Radiation Chemistry and Chemical Dynamics Division, Bhabha Atomic Research Center, Mumbai, India 3 Department of Biological Sciences, Tata Institute of Fundamental Research, Mumbai, India Homologous recombination is a fundamental process by which two DNA molecules physically interact with each other. This process is important for repairing the double strand breaks (DSBs) induced during mitosis, meiosis and other stages where chromosomal break- ages ensue. There are several sequential biochemical Keywords Dmc1; FRET; renaturation; rice; strand exchange Correspondence J. K. Sainis, Molecular Biology Division, Bhabha Atomic Research Centre, Mumbai 400 085, India Fax: +91 22 25505326 Tel : +91 22 25595079 E-mail: jksainis@magnum.barc.ernet.in (Received 18 October 2005, revised 2 February 2006, accepted 8 February 2006) doi:10.1111/j.1742-4658.2006.05170.x Rad51 and disrupted meiotic cDNA1 (Dmc1) are the two eukaryotic DNA recombinases that participate in homology search and strand exchange reactions during homologous recombination mediated DNA repair. Rad51 expresses in both mitotic and meiotic tissues whereas Dmc1 is confined to meiosis. DNA binding and pairing activities of Oryza sativa disrupted mei- otic cDNA1 (OsDmc1) from rice have been reported earlier. In the present study, DNA renaturation and strand exchange activities of OsDmc1 have been studied, in real time and without the steps of deproteinization, using fluorescence resonance energy transfer (FRET). The extent as well as the rate of renaturation is the highest in conditions that contain ATP, but sig- nificantly less when ATP is replaced by slowly hydrolysable analogues of ATP, namely adenosine 5¢-(b,c-imido) triphosphate (AMP-PNP) or adeno- sine 5¢-O-(3-thio triphosphate) (ATP-c-S), where the former was substan- tially poorer than the latter in facilitating the renaturation function. FRET assay results also revealed OsDmc1 protein concentration dependent strand exchange function, where the activity was the fastest in the presence of ATP, whereas in the absence of a nucleotide cofactor it was several fold ( 15-fold) slower. Interestingly, strand exchange, in reactions where ATP was replaced with AMP-PNP or ATP-c-S, was somewhat slower than that of even minus nucleotide cofactor control. Notwithstanding the slow rates, the reactions with no nucleotide cofactor or with ATP-analogues did reach the same steady state level as seen in ATP reaction. FRET changes were unaffected by the steps of deproteinization following OsDmc1 reaction, suggesting that the assay results reflected stable events involving exchanges of homologous DNA strands. All these results, put together, suggest that OsDmc1 catalyses homologous renaturation as well as strand exchange events where ATP hydrolysis seems to critically decide the rates of the reac- tion system. These studies open up new facets of a plant recombinase func- tion in relation to the role of ATP hydrolysis. Abbreviations AMP-PNP, adenosine 5¢-(b,c-imido) triphosphate; ATP-c-S, adenosine 5¢-O-(3-thio triphosphate); Dmc1, disrupted meiotic cDNA1; DS, double stranded; DSBs, Copyright © National Academy of Sciences. All rights reserved. Implementing the New Biology: Decadal Challenges Linking Food, Energy, and the Environment: Summary of a Workshop, June 3-4, 2010 http://www.nap.edu/catalog/13018.html Paula Tarnapol Whitacre, Adam P. Fagen, Jo L. Husbands, and Frances E. Sharples Planning Committee on Achieving Research Synergies for Food/Energy/ Environment Challenges: A Workshop to Explore the Potential of the “New Biology” Board on Life Sciences Division on Earth and Life Studies IMPLEMENTING THE NEW BIOLOGY Decadal Challenges Linking Food, Energy, and the Environment SU M MARY OF A WORKS HOP JUN E 3- 4 , 2010 Copyright © National Academy of Sciences. All rights reserved. Implementing the New Biology: Decadal Challenges Linking Food, Energy, and the Environment: Summary of a Workshop, June 3-4, 2010 http://www.nap.edu/catalog/13018.html THE NATIONAL ACADEMIES PRESS 500 Fifth Street, N.W. Washington, DC 20001 NOTICE: The project that is the subject of this report was approved by the Gov- erning Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engi- neering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This study was supported by the United States Department of Energy, the United States Department of Agriculture, the National Institutes of Health, the National Science Foundation, the Gordon and Betty Moore Foundation, and the Howard Hughes Medical Institute. Any opinions, findings, conclusions, or recommenda- tions expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project. International Standard Book Number-13: 978-0-309-16194-7 International Standard Book Number-10: 0-309-16194-0 Additional copies of this report are available from the National Academies Press, 500 Fifth Street, N.W., Lockbox 285, Washington, DC 20055; (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area); Internet, http://www.nap.edu. Copyright 2010 by the National Academies. All rights reserved. Printed in the United States of America. Copyright © National Academy of Sciences. All rights reserved. Implementing the New Biology: Decadal Challenges Linking Food, Energy, and the Environment: Summary of a Workshop, June 3-4, 2010 http://www.nap.edu/catalog/13018.html The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal govern- ment on scientific and technical matters. Dr. Ralph J. Cicerone is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its mem- bers, sharing with the National Academy of Sciences the responsibility for advis- ing Managing “always on” Mobility and the work-life balance in organisations* Written by the Economist Intelligence Unit personal lives by obliging them to bring work home”.2 Discussions about “always on” can stir emotions, as demonstrated in a lengthy debate running recently in the The Financial Times about how accessible employees should be while on holiday.3 Concerns about the side effects of 24/7 connectivity are by no means a reason to curtail mobility, but organisations looking to maximise its benefits to the business should be considering how to help employees to manage the inevitable stresses A degree of culture change is certainly in order in many firms to foster effective mobile working; helping employees and managers understand how to “switch off” should be part of this Time to think T he era of the always-on workforce is upon us Mobile technologies have created an environment of ubiquitous connectivity in which employees can be accessible at any time of the day, any day of the week According to a 2011 study, 91% of employees using mobile devices in their jobs said they regularly checked their devices for messages outside of working hours.1 The benefits that such connectivity brings to employees and the business are indisputable Greater productivity, better responsiveness to customers, colleagues and managers, faster decision-making, and the ability to work flexibly (untethered from the office desk) are the most prominent, and the list is longer For employees looking to balance workplace demands with personal challenges such as childcare, mobility is an enormous boon Such levels of accessibility can be intrusive, however, as the boundaries blur between work and home In an August 2013 study published by the consultancy Deloitte, the majority of surveyed British employees said that mobile technology has helped them to improve their worklife balance At the same time, 45% complained that “it impacts their *This and other articles about the challenges and opportunities of mobility, sponsored by EE, can be found at http://eefutureconnections.economist.com/ The iPass Global Mobile Workforce Report, Q3 2011 Deloitte, “Upwardly Mobile: Redefining business mobility in Britain”, August 2013 Lucy Kellaway, “Must I check emails on holiday?”, FT.com, August 13, 2013, and “The email refuseniks have been gaining ground”, FT.com, August 28, 2013 Mobile technology is not the only driver of always-on connectivity According to Lynda Gratton, professor of management practice at London Business School and author of The Shift: The Future of Work is Already Here, the international dimension also needs to be considered “Globalisation means that many people are now working in situations where colleagues, suppliers and clients are in another time zone The consequence is, even if you don’t want to work outside normal working hours, somebody you work with will be doing so.” Nonetheless, humans need time to process the information they receive Clear thinking requires time and space, which can be limited if people are constantly having to respond to each other And given that numerous studies illustrate the health benefits of time away from the office, taking the office everywhere is not ideal As a consequence, working practices and operational models need to be adjusted (necessary for bringing about cultural change) to reap the improvements in productivity, responsiveness and employee flexibility, while ensuring that people can switch off when not at work This is not an easy balance to strike, not least because traditional organisational models often reward people who are more visibly productive Based on her Future of Work research, Ms Gratton recommends responding at the levels of the corporation, the team and the individual “24/7 working crept up on people; it is demanding in both time and effort Corporations large and small have been built for stability, but they need to think about how to manage [this new type of working environment],” she says 1 www.victoria.ac.nz/atp/ Link to this article: http://www.victoria.ac.nz/atp/articles/pdf/ElOjeili-2011.pdf Citation: El Ojeili, Chamsy, “After Post-Socialism: Social Theory, Utopia, and the Work of Castoriadis in a Global Age”, in AntePodium, Victoria University Wellington, 2011 This article will also be available in a forthcoming volume published by the Society for Philosophy and Culture, cf www.philosophyandculture.org After Post-Socialism: Social Theory, Utopia, and the Work of Castoriadis in a Global Age Chamsy el-Ojeili A widespread feature of contemporary social theoretical commentary has been to note the post-1970s troubles faced by social theory, utopia, Marxism, and socialism, often linked to the proliferating “posts” and “ends of” that have marked discussion in the human sciences over the past three-four decades Thus, Peter Wagner notes the doubts that have ‘arisen during the closing decades of the twentieth century as to whether the social science’s way of observing, interpreting and explaining the world really brought superior insights into the social life of human beings;’1 thus, Perry Anderson argues that ‘the utopian itself has been in general suspension since the mid-seventies,’ bringing a ‘remorseless closure of space;’2 thus, we find a variety of lamentations and celebrations of the death of Marxism and socialism – as either evidence of a dispiriting conformism, end to contestation, disorientation, and political-intellectual stasis, or a welcome move beyond the totalitarian imaginary, beyond the abstract, unrealistic schemes pushed by disreputable intellectuals I want to explore some of these notions, here – first and foremost, by examining post-Marxism as an intellectual formation, and, in particular, the concentrating on the work of Cornelius Castoriadis Castoriadis remains a somewhat neglected figure, even though a number of his books have now appeared in English translation, and his work has not yet found a place in the canon of political and social theory This is unfortunate, because Castoriadis is, I believe, an important thinker whose work has central links to more prominent contributors to theoretical debates Born in Constantinople in 1922, Castoriadis was philosophically literate and politically active by his teenage years Hunted down in Greece in the early 1940s by both Stalinists and fascists, he left to take up a never-completed doctoral thesis in France, where he worked as an economist for the OECD, then as a psychoanalyst, and finally as an academic in the school for advanced studies in the social sciences He died in France in 1997.4 Perhaps Castoriadis is best known for his tutelage of the now-legendary group Socialism or Barbarism, which split from the Trotskyist Fourth International in 1949, and whose ranks included psychoanalyst Jean Laplanche, philosopher Claude Lefort, Jean-Francois Lyotard, and Guy Debord, author of The Society of the Spectacle Socialism or Barbarism belongs within that rather neglected political current of what might be labelled “left communism”, a strand of socialism that contested the socialist orthodoxies of both social democracy and Leninism, that interpreted the regimes of “really existing socialism” as forms of capitalism, and that posited the possibility of a different type of socialism, often a directly democratic socialism of workers’ councils This left communist strand is of interest today, I shall argue towards the close of this essay, but, for the most part, I am interested in Castoriadis as arguably the earliest representative of that contemporary intellectual formation of “postMarxism”.5 In the following pages, I want, first, to explore the “co-ordinates of unity”6 of this intellectual formation, illustrating them primarily with reference to Castoriadis’ work I then want to turn back to suggest that, today, the post-Marxist, post-socialist contentions found in this work are more problematic than they once might have appeared, troubled by the troubles of ... of energy The Work -Energy Theorem The net work on a system equals the change in the quantity mv2 1 Wnet = mv2 − mv02 3/10 Kinetic Energy and the Work -Energy Theorem The quantity mv2 in the work -energy. .. by either approach Determining Speed from Work and Energy 6/10 Kinetic Energy and the Work -Energy Theorem Find the speed of the package in [link] at the end of the push, using work and energy. .. mv2 • The work -energy theorem states that the net work Wnet on a system changes its 1 kinetic energy, Wnet = mv2 − mv02 8/10 Kinetic Energy and the Work -Energy Theorem Conceptual Questions The