Gravitational Potential Energy

Chapter 8 Potential Energy and Conservation of Energy In this chapter we will introduce the following concepts: Potential Energy Conservative and non-conservative forces Mechanical Energy Conservation of Mechanical Energy The conservation of energy theorem will be used to solve a variety of problems As was done in Chapter 7 we use scalars such as work ,kinetic energy, and mechanical energy rather than vectors. Therefore the approach is mathematically simpler. (8-1) A B g v o h v o Work and Potential Energy: Consider the tomato of mass m shown in the figure. The tomato is taken together with the earth as the system we wish to study. The tomato is thrown upwards with initial speed v o at point A. Under the action of the gravitational force it slows down and stops completely at point B. Then the tomato falls back and by the time it reaches point A its speed has reached the original value v o . Below we analyze in detail what happens to the tomato-earth system. During the trip from A to B the gravitational force F g does negative work W 1 = -mgh. Energy is transferred by F g from the kinetic energy of the tomato to the gravitational potential energy U of the tomato-earth system. During the trip from B to A the transfer is reversed. The work W 2 done by F g is positive ( W 2 = mgh ). The gravitational force transfers energy from the gravitational potential energy U of the tomato-earth system to the kinetic energy of the tomato. The change in the potential energy U is defined as: U W ∆ = − (8-2) A A B B k m Consider the mass m attached to a spring of spring constant k as shown in the figure. The mass is taken together with the spring as the system we wish to study. The mass is given an initial speed v o at point A. Under the action of the spring force it slows down and stops completely at point B which corresponds to a spring compression x. Then the mass reverses the direction of its motion and by the time it reaches point A its speed has reached the original value v o . As in the previous example we analyze in detail what happens to the mass- spring system . During the trip from A to B the spring force F s does negative work W 1 = -kx 2 /2 . Energy is transferred by F s from the kinetic energy of the mass to the potential energy U of the mass-spring system. During the trip from B to A the transfer is reversed. The work W 2 done by F s is positive ( W 2 = kx 2 /2 ). The spring force transfers energy from the potential energy U of the mass-spring system to the kinetic energy of the mass. The change in the potential energy U is defined as: U W ∆ = − (8-3) m m A B v o f k f k x d Conservative and non-conservative forces. The gravitational force as the spring force are called “conservative” because the can transfer energy from the kinetic energy of part of the system to potential energy and vice versa. Frictional and drag forces on the other hand are called “non-conservative” for reasons that are explained below. Consider a system that consists of a block of mass m and the floor on which it rests. The block starts to move on a horizontal floor with initial speed v o at point A. The coefficient of kinetic friction between the floor and the block is μ k . The block will slow down by the kinetic friction f k and will stop at point B after it has traveled a distance d. During the trip from point A to point B the frictional force has done work W f = - μ k mgd. The frictional force transfers energy from the Gravitational Potential Energy Gravitational Potential Energy Bởi: OpenStaxCollege Work Done Against Gravity Climbing stairs and lifting objects is work in both the scientific and everyday sense—it is work done against the gravitational force When there is work, there is a transformation of energy The work done against the gravitational force goes into an important form of stored energy that we will explore in this section Let us calculate the work done in lifting an object of mass m through a height h, such as in [link] If the object is lifted straight up at constant speed, then the force needed to lift it is equal to its weight mg The work done on the mass is then W = Fd = mgh We define this to be the gravitational potential energy (PEg) put into (or gained by) the object-Earth system This energy is associated with the state of separation between two objects that attract each other by the gravitational force For convenience, we refer to this as the PEg gained by the object, recognizing that this is energy stored in the gravitational field of Earth Why we use the word “system”? Potential energy is a property of a system rather than of a single object—due to its physical position An object’s gravitational potential is due to its position relative to the surroundings within the Earth-object system The force applied to the object is an external force, from outside the system When it does positive work it increases the gravitational potential energy of the system Because gravitational potential energy depends on relative position, we need a reference level at which to set the potential energy equal to We usually choose this point to be Earth’s surface, but this point is arbitrary; what is important is the difference in gravitational potential energy, because this difference is what relates to the work done The difference in gravitational potential energy of an object (in the Earth-object system) between two rungs of a ladder will be the same for the first two rungs as for the last two rungs Converting Between Potential Energy and Kinetic Energy Gravitational potential energy may be converted to other forms of energy, such as kinetic energy If we release the mass, gravitational force will an amount of work 1/10 Gravitational Potential Energy equal to mgh on it, thereby increasing its kinetic energy by that same amount (by the work-energy theorem) We will find it more useful to consider just the conversion of PEg to KE without explicitly considering the intermediate step of work (See [link].) This shortcut makes it is easier to solve problems using energy (if possible) rather than explicitly using forces (a) The work done to lift the weight is stored in the mass-Earth system as gravitational potential energy (b) As the weight moves downward, this gravitational potential energy is transferred to the cuckoo clock More precisely, we define the change in gravitational potential energy ΔPEg to be ΔPEg = mgh, where, for simplicity, we denote the change in height by h rather than the usual Δh Note that h is positive when the final height is greater than the initial height, and vice versa For example, if a 0.500-kg mass from a cuckoo clock is raised 1.00 m, then its change in gravitational potential energy is mgh = (0.500 kg)(9.80 m/s2)(1.00 m) = 4.90 kg ⋅ m2/s2= 4.90 J 2/10 Gravitational Potential Energy Note that the units of gravitational potential energy turn out to be joules, the same as for work and other forms of energy As the clock runs, the mass is lowered We can think of the mass as gradually giving up its 4.90 J of gravitational potential energy, without directly considering the force of gravity that does the work Using Potential Energy to Simplify Calculations The equation ΔPEg = mgh applies for any path that has a change in height of h, not just when the mass is lifted straight up (See [link].) It is much easier to calculate mgh (a simple multiplication) than it is to calculate the work done along a complicated path The idea of gravitational potential energy has the double advantage that it is very broadly applicable and it makes calculations easier From now on, we will consider that any change in vertical position h of a mass m is accompanied by a change in gravitational potential energy mgh, and we will avoid the equivalent but more difficult task of calculating work done by or against the gravitational force The change in gravitational potential energy (ΔPEg) between points A and B is independent of the path ΔPEg = mgh for any path between the two points Gravity is one of a small class of forces where the work done by or against the force depends only on the starting and ending points, not on the path between them The Force to Stop Falling A 60.0-kg person jumps onto the floor from a height of 3.00 m If he lands stiffly (with his knee joints compressing by 0.500 cm), calculate the force on the knee joints Strategy 3/10 Gravitational Potential Energy This person’s energy is brought to zero in this ...J. Sci. Dev. 2009, 7 (Eng.Iss.1): 70 - 78 HA NOI UNIVERSITY OF AGRICULTURE 70 Energy recovery potential from landfill and environmental evaluation of landfill gas power generation system at nam son landfill, Vietnam Tiềm năng thu hồi năng lượng từ bãi rác và đánh giá lợi ích môi trường của hệ thống phát điện sử dụng khí từ bãi rác tại bãi rác Nam Sơn, Việt Nam Pham Chau Thuy 1 , Sohei Shimada 2 1 Department of Environmental Technology, Faculty of Natural Resource and Environment, Hanoi Agricultural University, Trau Quy, Gia Lam, Hanoi 2 Graduate School of Frontier Sciences, Institute of Environmental Studies, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JAPAN TÓM TẮT Khí từ bãi rác là nguồn năng lượng xanh, sạch, có thể tái tạo được và có thể sử dụng để tạo ra điện, hay sử dụng trong công nghiệp năng lượng. Bài báo này đánh giá tiềm năng thu hồi năng lượng từ khí bãi chôn lấp chất thải rắn đô thị, mục đích làm giảm lượng phát thải methan nói riêng và giảm phát thải khí nhà kính nói chung. Ngoài ra, bài báo cung cấp cách sử dụng mô hình đánh giá lượng khí methan tạo ra từ bãi chôn lấp chất thải rắn đô thị và tiềm năng tạo ra năng lượng từ khí đã thu hồi. Đặc biệt, bài báo sử dụng phương pháp đánh giá vòng đời để đánh giá việc giảm phát thải khí nhà kính của hệ thống phát điện sử dụng khí từ bãi rác. Kết quả nghiên cứu chỉ ra rằng, bãi rác Nam Sơn là một bãi rác có tiềm năng lương lượng lớn cần thu hồi và sử dụng, góp phần đáng kể vào việc làm giảm phát thải khí nhà kính, hướng tới sự phát triển bền vững. Bài báo cung cấp một cách nhìn mới về công nghệ năng lượng sử dụng khí từ bãi rác cho Viêt Nam: hệ thống phát điên sử dụng động cơ khí và tuabin khí. Kết quả còn chỉ ra rằng, hệ thống phát điện bằng động cơ khí tỏ ra hiệu quả hơn về lợi ích về môi trường so với hệ thống phát điện bằng tuabin khí. Hệ thống này có thể ứng dụng cho bãi rác Nam Sơn và ứng dụng cho các bãi rác khác của Việt Nam trong tương lai. Từ khóa: Đánh giá vòng đời, giảm phát thải khí nhà kính, khí từ bãi rác, mô hình phát thải khí bãi rác. SUMMARY Landfill gas (LFG), a green, clean, and renewable energy source can be used for electricity generation or fuel industries. This research presents an attempt to assess the energy recovery potential from the Municipal Solid Waste (MSW) landfill, targeting at gas recovery and gas utilization, in mitigating methane emission in particular and green house gas (GHG) emission in general. Our research provides the using of landfill gas emission model (LFGEM) to quantify the methane generation volume for MSW landfill. We then evaluate of energy generation potential from recovered gas. Especially, this research conducted the Life Cycle Inventory to evaluate GHG emission mitigation of power generation system using LFG. The results show that the methane gas flow at Nam Son landfill can provide a considerable energy potential. LFG recovery and utilization could contribute remarkable to GHG emission mitigation, toward to sustainability. The research supplies a new vision of energy technology from LFG for Viet Nam: Gas Engine and Gas Turbine. The research found that Gas Engine is more attractive in term of environmental benefit, which can be applied primarily for Nam Son landfill and continue applied for other landfill in Vietnam for the future. Journal of Science and Development 2009: Tập VI, No 6: 69-77 HA NOI UNIVERSITY OF AGRICULTURE 71 Key words: Green House Gas emission mitigation, landfill gas, landfill gas emission model, life cycle Inventory. 1. INTRODUCTION Climbing LFG is considered as the largest anthropogenic emission source in the developed countries and also as a considerable emission source in developing countries up to now. Landfill gas (LFG) is produced from anaerobic biodegradable decomposition of organic content of landfilled waste. Release of LFG is one of the dangerous contaminations due to high methane content contributing to GHG J. Sci. Dev. 2009, 7 (Eng.Iss.1): 70 - 78 HA NOI UNIVERSITY OF AGRICULTURE 70 Energy recovery potential from landfill and environmental evaluation of landfill gas power generation system at nam son landfill, Vietnam Tiềm năng thu hồi năng lượng từ bãi rác và đánh giá lợi ích môi trường của hệ thống phát điện sử dụng khí từ bãi rác tại bãi rác Nam Sơn, Việt Nam Pham Chau Thuy 1 , Sohei Shimada 2 1 Department of Environmental Technology, Faculty of Natural Resource and Environment, Hanoi Agricultural University, Trau Quy, Gia Lam, Hanoi 2 Graduate School of Frontier Sciences, Institute of Environmental Studies, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JAPAN TÓM TẮT Khí từ bãi rác là nguồn năng lượng xanh, sạch, có thể tái tạo được và có thể sử dụng để tạo ra điện, hay sử dụng trong công nghiệp năng lượng. Bài báo này đánh giá tiềm năng thu hồi năng lượng từ khí bãi chôn lấp chất thải rắn đô thị, mục đích làm giảm lượng phát thải methan nói riêng và giảm phát thải khí nhà kính nói chung. Ngoài ra, bài báo cung cấp cách sử dụng mô hình đánh giá lượng khí methan tạo ra từ bãi chôn lấp chất thải rắn đô thị và tiềm năng tạo ra năng lượng từ khí đã thu hồi. Đặc biệt, bài báo sử dụng phương pháp đánh giá vòng đời để đánh giá việc giảm phát thải khí nhà kính của hệ thống phát điện sử dụng khí từ bãi rác. Kết quả nghiên cứu chỉ ra rằng, bãi rác Nam Sơn là một bãi rác có tiềm năng lương lượng lớn cần thu hồi và sử dụng, góp phần đáng kể vào việc làm giảm phát thải khí nhà kính, hướng tới sự phát triển bền vững. Bài báo cung cấp một cách nhìn mới về công nghệ năng lượng sử dụng khí từ bãi rác cho Viêt Nam: hệ thống phát điên sử dụng động cơ khí và tuabin khí. Kết quả còn chỉ ra rằng, hệ thống phát điện bằng động cơ khí tỏ ra hiệu quả hơn về lợi ích về môi trường so với hệ thống phát điện bằng tuabin khí. Hệ thống này có thể ứng dụng cho bãi rác Nam Sơn và ứng dụng cho các bãi rác khác của Việt Nam trong tương lai. Từ khóa: Đánh giá vòng đời, giảm phát thải khí nhà kính, khí từ bãi rác, mô hình phát thải khí bãi rác. SUMMARY Landfill gas (LFG), a green, clean, and renewable energy source can be used for electricity generation or fuel industries. This research presents an attempt to assess the energy recovery potential from the Municipal Solid Waste (MSW) landfill, targeting at gas recovery and gas utilization, in mitigating methane emission in particular and green house gas (GHG) emission in general. Our research provides the using of landfill gas emission model (LFGEM) to quantify the methane generation volume for MSW landfill. We then evaluate of energy generation potential from recovered gas. Especially, this research conducted the Life Cycle Inventory to evaluate GHG emission mitigation of power generation system using LFG. The results show that the methane gas flow at Nam Son landfill can provide a considerable energy potential. LFG recovery and utilization could contribute remarkable to GHG emission mitigation, toward to sustainability. The research supplies a new vision of energy technology from LFG for Viet Nam: Gas Engine and Gas Turbine. The research found that Gas Engine is more attractive in term of environmental benefit, which can be applied primarily for Nam Son landfill and continue applied for other landfill in Vietnam for the future. Journal of Science and Development 2009: Tập VI, No 6: 69-77 HA NOI UNIVERSITY OF AGRICULTURE 71 Key words: Green House Gas emission mitigation, landfill gas, landfill gas emission model, life cycle Inventory. 1. INTRODUCTION Climbing LFG is considered as the largest anthropogenic emission source in the developed countries and also as a considerable emission source in developing countries up to now. Landfill gas (LFG) is produced from anaerobic biodegradable decomposition of organic content of landfilled waste. Release of LFG is one of the dangerous contaminations due to high methane content contributing to GHG INTERIOR-POINT METHODS FOR MINIMIZATION OF POTENTIAL ENERGY FUNCTIONS OF POLYPEPTIDES MUTHU SOLAYAPPAN (M.S., University of Florida) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. MUTHU SOLAYAPPAN 11 April 2013 ii Acknowledgements First and foremost, I would like to thank my supervisors, Dr. Ng Kien Ming and Professor Poh Kim Leng for accepting me as their student and giving me an opportunity to pursue my research under their guidance. I am thankful to both of them for having spent time with me discussing research, which often helps me to gain a better perspective of the research problem. I appreciate the freedom that they gave me in my research work and I’ll always be indebted to them for that. I also thank my supervisors for providing me an opportunity to work on other research projects. Apart from providing financial support, the experience also helped me to gain some knowledge in other areas of research as well. I would also like to thank the Department of Industrial and Systems Engineering (ISE) for supporting my research financially. Special thanks to the administrative staff at ISE, especially Ms. Ow Lai Chun for helping me with the administrative work during my candidature at the University. The computing lab has always provided me with an excellent working atmosphere and I am thankful to my colleagues who made it possible. I have always enjoyed my conversations with Pan Jie, Zhu Zhecheng, and Aldy Gunawan. I couldn’t have enjoyed my stay in Singapore more if it wasn’t for the friends that I made whilst my stay here. In particular, I appreciate my friendship with Manohar, Murali, Pradeep, Satish and Malik for they always have been a source iii of support and encouragement during my stay in Singapore. My wife and my son has always been a source of emotional support for me over the past years and I thank both of them for their patience, love and care that they continue to shower on me. Lastly, my parents love and support have played a great role in motivating me. I thank them for their patience and the belief they had in me. iv C ontents Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Current Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 B ackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.1 Amino Acids . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.2 Types of Protein Structure . . . . . . . . . . . . . . . . . . 8 1.4.3 Protein Structure Prediction . . . . . . . . . . . . . . . . . 11 1.4.3.1 H omology Modeling . . . . . . . . . . . . . . . . 12 1.4.3.2 Protein Threading . . . . . . . . . . . . . . . . . 13 1.4.3.3 Ab Initio Folding . . . . . . . . . . . . . . . . . . 14 v 1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . 2 Literature S urvey 16 17 2.1 Introductory R eferences . . INTERIOR-POINT METHODS FOR MINIMIZATION OF POTENTIAL ENERGY FUNCTIONS OF POLYPEPTIDES MUTHU SOLAYAPPAN (M.S., University of Florida) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis This thesis has also not been submitted for any degree in any university previously MUTHU SOLAYAPPAN 11 April 2013 ii Acknowledgements First and foremost, I would like to thank my supervisors, Dr Ng Kien Ming and Professor Poh Kim Leng for accepting me as their student and giving me an opportunity to pursue my research under their guidance I am thankful to both of them for having spent time with me discussing research, which often helps me to gain a better perspective of the research problem I appreciate the freedom that they gave me in my research work and I’ll always be indebted to them for that I also thank my supervisors for providing me an opportunity to work on other research projects Apart from providing financial support, the experience also helped me to gain some knowledge in other areas of research as well I would also like to thank the Department of Industrial and Systems Engineering (ISE) for supporting my research financially Special thanks to the administrative staff at ISE, especially Ms Ow Lai Chun for helping me with the administrative work during my candidature at the University The computing lab has always provided me with an excellent working atmosphere and I am thankful to my colleagues who made it possible I have always enjoyed my conversations with Pan Jie, Zhu Zhecheng, and Aldy Gunawan I couldn’t have enjoyed my stay in Singapore more if it wasn’t for the friends that I made whilst my stay here In particular, I appreciate my friendship with Manohar, Murali, Pradeep, Satish and Malik for they always have been a source iii of support and encouragement during my stay in Singapore My wife and my son has always been a source of emotional support for me over the past years and I thank both of them for their patience, love and care that they continue to shower on me Lastly, my parents love and support have played a great role in motivating me I thank them for their patience and the belief they had in me iv C ontents Declaration i Acknowledgements ii Abstract viii List of Tables x List of Figures xii Introduction 1.1 Motivation 1.2 Current Scenario 1.3 Challenges 1.4 B ackground 1.4.1 Amino Acids 1.4.2 Types of Protein Structure 1.4.3 Protein Structure Prediction 11 1.4.3.1 H omology Modeling 12 1.4.3.2 Protein Threading 13 1.4.3.3 Ab Initio Folding 14 v 1.5 Organization of Thesis Literature S urvey 16 17 2.1 Introductory R eferences 18 2.2 Existing R esearch on Prediction Methods 18 2.2.1 H omology Modeling 19 2.2.2 Protein Threading 21 2.2.3 Ab Initio Folding 24 2.3 Optimization ... change in gravitational potential energy is mgh = (0.500 kg)(9.80 m/s2)(1.00 m) = 4.90 kg ⋅ m2/s2= 4.90 J 2/10 Gravitational Potential Energy Note that the units of gravitational potential energy. .. conservation of energy Making Connections: Take-Home Investigation—Converting Potential to Kinetic Energy One can study the conversion of gravitational potential energy into kinetic energy in this... power facility (see [link]) converts the gravitational potential energy of water behind a dam to electric energy (a) What is the gravitational potential energy relative to the generators of a lake