The document summarizes the problems and solutions from the 7th International Physics Olympiad held in 1974 in Warsaw, Poland. It includes 3 theoretical problems and 1 experimental problem prepared specifically for the competition. Problem 1 involves calculating the minimum velocity for an elastic collision between hydrogen atoms using the Bohr model. Problem 2 involves calculating refraction indices and trajectory of a light beam passing through a transparent plate with a refractive index that varies linearly. Problem 3 shows that there is no theoretical limit to the power of an ideal engine that uses gas and selective membranes as described.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
I. Cotaescu - "Canonical quantization of the covariant fields: the Dirac fiel...SEENET-MTP
The document discusses the canonical quantization of covariant fields on curved spacetimes, specifically the de Sitter spacetime. It introduces covariant fields that transform under representations of the spin group SL(2,C) and have covariant derivatives ensuring gauge invariance. Isometries of the spacetime generate Killing vectors and induce representations of the external symmetry group, which is the universal covering group of isometries and combines isometries with gauge transformations. Generators of these representations provide conserved observables that allow canonical quantization analogous to special relativity. The paper focuses on applying this framework to the Dirac field on de Sitter spacetime.
The document provides instructions for a 5-hour theoretical physics competition with 3 questions. It details formatting requirements for working out the questions, including labeling pages with question number, page number, and total pages used. It also provides instructions for arranging the completed pages in proper order at the end. The first theoretical question is about vibrational modes in a linear crystal lattice model and includes parts on deriving the equation of motion, solving for mode frequencies and wave numbers, calculating average phonon energy, determining total crystal energy, and relating heat capacity to temperature. The second question considers a "rail gun" device constructed by a young man to launch himself across a strait to reach his love within 11 seconds. It involves deriving acceleration, calculating
Jee advanced 2015 paper 1 code 1 final Pradeep Kumar
1. The document provides information about JEE Advanced 2015 paper 1, including 8 multiple choice questions in Section 1 and 10 multiple choice questions in Section 2.
2. Section 3 contains 2 matching questions matching concepts in Column I to statements in Column II.
3. The questions cover topics in physics including electromagnetism, quantum mechanics, thermodynamics, and nuclear physics.
This document contains information about JEE Advanced 2015 Paper 2 Code 3 for Physics. It includes 10 multiple choice questions testing concepts in physics. The questions cover topics such as optics, circuits, quantum mechanics, mechanics, thermodynamics and electromagnetism. For each question, students had to select the single correct answer ranging from 0 to 9. The document also provides two additional sections with more complex multi-concept questions, some requiring selecting one or more answers. The questions test a range of fundamental physics principles and problem solving abilities.
"When the top is not single: a theory overview from monotop to multitops" to...Rene Kotze
This document discusses potential deviations from the standard model in top quark pair production (ttbar) due to beyond standard model (BSM) physics. It summarizes that ttbar production is well measured but sensitive to BSM effects like resonant contributions from new particles that decay to top quark pairs. Non-resonant effects are also possible and can be parameterized using effective field theory operators. The document provides examples of limits set on specific BSM models like Z' bosons by the CMS experiment through analyses of the ttbar invariant mass spectrum and other observables.
N. Bilic - "Hamiltonian Method in the Braneworld" 2/3SEENET-MTP
This document discusses braneworld models and the Randall-Sundrum model. It begins by introducing the relativistic particle and string actions used to describe dynamics in higher dimensions. It then summarizes the two Randall-Sundrum models: RS I contains two branes separated in a fifth dimension to address the hierarchy problem, while RS II has the negative tension brane sent to infinity and observers on a single positive tension brane. Finally, it derives the RS II model solution, using Gaussian normal coordinates and imposing junction conditions at the brane.
This document is a solution to a physics problem set composed and formatted by E.A. Baltz and M. Strovink. It contains solutions to 6 problems using vector algebra and trigonometry. The document uses concepts like the law of cosines, dot products, cross products, and vector identities to break vectors into components and calculate angles between vectors. It also applies these concepts to problems involving vectors representing locations on a sphere and wind resistance problems for airplanes.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
I. Cotaescu - "Canonical quantization of the covariant fields: the Dirac fiel...SEENET-MTP
The document discusses the canonical quantization of covariant fields on curved spacetimes, specifically the de Sitter spacetime. It introduces covariant fields that transform under representations of the spin group SL(2,C) and have covariant derivatives ensuring gauge invariance. Isometries of the spacetime generate Killing vectors and induce representations of the external symmetry group, which is the universal covering group of isometries and combines isometries with gauge transformations. Generators of these representations provide conserved observables that allow canonical quantization analogous to special relativity. The paper focuses on applying this framework to the Dirac field on de Sitter spacetime.
The document provides instructions for a 5-hour theoretical physics competition with 3 questions. It details formatting requirements for working out the questions, including labeling pages with question number, page number, and total pages used. It also provides instructions for arranging the completed pages in proper order at the end. The first theoretical question is about vibrational modes in a linear crystal lattice model and includes parts on deriving the equation of motion, solving for mode frequencies and wave numbers, calculating average phonon energy, determining total crystal energy, and relating heat capacity to temperature. The second question considers a "rail gun" device constructed by a young man to launch himself across a strait to reach his love within 11 seconds. It involves deriving acceleration, calculating
Jee advanced 2015 paper 1 code 1 final Pradeep Kumar
1. The document provides information about JEE Advanced 2015 paper 1, including 8 multiple choice questions in Section 1 and 10 multiple choice questions in Section 2.
2. Section 3 contains 2 matching questions matching concepts in Column I to statements in Column II.
3. The questions cover topics in physics including electromagnetism, quantum mechanics, thermodynamics, and nuclear physics.
This document contains information about JEE Advanced 2015 Paper 2 Code 3 for Physics. It includes 10 multiple choice questions testing concepts in physics. The questions cover topics such as optics, circuits, quantum mechanics, mechanics, thermodynamics and electromagnetism. For each question, students had to select the single correct answer ranging from 0 to 9. The document also provides two additional sections with more complex multi-concept questions, some requiring selecting one or more answers. The questions test a range of fundamental physics principles and problem solving abilities.
"When the top is not single: a theory overview from monotop to multitops" to...Rene Kotze
This document discusses potential deviations from the standard model in top quark pair production (ttbar) due to beyond standard model (BSM) physics. It summarizes that ttbar production is well measured but sensitive to BSM effects like resonant contributions from new particles that decay to top quark pairs. Non-resonant effects are also possible and can be parameterized using effective field theory operators. The document provides examples of limits set on specific BSM models like Z' bosons by the CMS experiment through analyses of the ttbar invariant mass spectrum and other observables.
N. Bilic - "Hamiltonian Method in the Braneworld" 2/3SEENET-MTP
This document discusses braneworld models and the Randall-Sundrum model. It begins by introducing the relativistic particle and string actions used to describe dynamics in higher dimensions. It then summarizes the two Randall-Sundrum models: RS I contains two branes separated in a fifth dimension to address the hierarchy problem, while RS II has the negative tension brane sent to infinity and observers on a single positive tension brane. Finally, it derives the RS II model solution, using Gaussian normal coordinates and imposing junction conditions at the brane.
This document is a solution to a physics problem set composed and formatted by E.A. Baltz and M. Strovink. It contains solutions to 6 problems using vector algebra and trigonometry. The document uses concepts like the law of cosines, dot products, cross products, and vector identities to break vectors into components and calculate angles between vectors. It also applies these concepts to problems involving vectors representing locations on a sphere and wind resistance problems for airplanes.
1. Two stones are thrown up simultaneously from a cliff with different initial speeds. A graph showing the relative position of the second stone with respect to the first over time would be a curve that increases until the first stone hits the ground, then decreases until the second stone hits the ground.
2. The accuracy of determining the gravitational acceleration, g, from measurements of the period of a pendulum is calculated to be approximately 3%.
3. If two blocks of different weights are being pressed against a wall by a force, the frictional force applied by the wall on the heavier block is 120 N, which is enough to balance the total weight of 120 N of the two-block system.
The document contains the problems and solutions from the theoretical competition of the 27th International Physics Olympiad held in Oslo, Norway in 1996. It includes 7 problems covering various topics in physics like circuits, mechanics, thermodynamics, electromagnetism, and astrophysics. The problems are presented in English, with translations to other languages. Example student solutions and exam materials like photos from the grading process are also included.
conceptual-problems-in-physics-for-iit-jee (1)APEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
The document describes the problems presented at the 13th International Physics Olympiad held in Malente, Germany in 1982. It includes the five problems given to students, which covered both theoretical and experimental classical physics topics. It provides the solutions and explanations to each problem. The problems tested students on topics like electric circuits, oscillatory motion, optics, and spectroscopy. They varied in difficulty, with the oscillating coat hanger problem being the most challenging. The experimental problems required both theoretical understanding and experimental skills to solve.
This document provides information about the 18th International Physics Olympiad held in 1987 in Jena, Germany. It describes the four problems presented to competitors - three theoretical and one experimental. The theoretical problems were quite difficult, with only the first problem having medium difficulty. About half the competitors did not find adequate solutions to the other two theoretical problems. The experimental problem was much easier. The document then provides the full problems and their step-by-step solutions. It analyzes the challenges faced by competitors and explains the reasoning and physics concepts underlying each problem.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
The document provides the question paper and solutions for the Indian National Physics Olympiad held in 2014. It contains 7 multi-part physics questions related to topics like electromagnetism, mechanics, thermodynamics, and nuclear physics. For each question, the relevant concepts and formulas are provided along with step-by-step calculations to arrive at the final solutions. Diagrams and graphs are used to illustrate concepts where needed.
I. Antoniadis - "Introduction to Supersymmetry" 1/2SEENET-MTP
Supersymmetry (SUSY) is a symmetry that relates bosonic and fermionic degrees of freedom. It extends the Poincaré algebra by including spinorial generators (supercharges) that transform bosonic fields into fermionic fields and vice versa. SUSY provides motivations like natural elementary scalars, gauge coupling unification, and a dark matter candidate. SUSY is formulated using superspace, which extends spacetime by Grassmann coordinates. Chiral and vector superfields contain the bosonic and fermionic components of supermultiplets and allow constructing SUSY invariant actions.
(1) The document discusses fluid dynamics concepts including density, pressure, buoyancy, continuity, and Bernoulli's equation. It provides conceptual explanations and sample calculations for comparing volumes and densities of objects, calculating buoyant forces, and relating pressure, velocity, and flow rates in pipes.
(2) One example calculates the force needed to lift a car using a hydraulic lift, where the pressure applied must be the same at both the large and small pistons.
(3) Another example uses continuity and Bernoulli's equations to relate the velocity and pressure of water flowing at different diameters in a pipe. It finds the velocity and pressure change when the pipe narrows.
Outgoing ingoingkleingordon spvmforminit_proceedfrom12dec18foxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
Outgoing ingoingkleingordon spvmforminit_proceedfromfoxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
This document provides information about the dynamics of machinery course for several mechanical engineering students. It includes the learning objectives, symbols and definitions, response of a damped system under harmonic motion, an example problem, and key concepts about magnification factor, phase angle, and total response of a system. The example calculates the total response of a single-degree-of-freedom system subjected to an external harmonic force and free vibration.
Describes the mathematics of the Calculus of Variations.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website on http://www.solohermelin.com
The use of Calculus is very important in every aspects of engineering.
The use of Differential equation is very much applied in the concept of Elastic beams.
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of black holes. It first presents the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. Near the event horizon, the radial equation is approximated in the Regge-Wheeler coordinate, leading to oscillatory solutions. The time and radial solutions are then expressed in outgoing and ingoing coordinates, resulting in outgoing and ingoing waves with different analytic properties in the future and past event horizons.
1. The document discusses static equilibrium of coplanar force systems. It covers drawing free-body diagrams, identifying reaction forces, and applying the three equations of equilibrium.
2. Key steps for solving problems include drawing the free-body diagram, identifying known and reaction forces, and setting the sum of forces and moments equal to zero.
3. Examples show calculating unknown forces and reactions for beams, rods, and pulley systems in static equilibrium. Forces and moments are analyzed to determine the magnitude and direction of reaction forces.
The document is an unsolved physics paper from 2008 for IITJEE (Indian Institute of Technology Joint Entrance Examination). It contains multiple choice and reasoning questions about physics concepts. The questions cover topics like mechanics, electromagnetism, thermodynamics, and waves. There are four sections with different question types including objective, reasoning, comprehension, and matrix-match questions. The document provides figures and diagrams to accompany some of the physics problems.
Obtaining three-dimensional velocity information directly from reflection sei...Arthur Weglein
This paper present a formalism for obtaining the subsurface
velocity configuration directly from reflection seismic data.
Our approach is to apply the results obtained for inverse
problems in quantum scattering theory to the reflection
seismic problem. In particular, we extend the results of
Moses (1956) for inverse quantum scattering and Razavy
(1975) for the one-dimensional (1-D) identification of the
acoustic wave equation to the problem of identifying the
velocity in the three-dimensional (3-D) acoustic wave equation
from boundary value measurements. No a priori knowledge
of the subsurface velocity is assumed and all refraction,
diffraction, and multiple reflection phenomena are
taken into account. In addition, we explain how the idea of
slant stack in processing seismic data is an important part
of the proposed 3-D inverse scattering formalism.
A2 k in the age of intellectual propertyberat celik
This document is the preface to the book "Access to Knowledge in the Age of Intellectual Property". It introduces the emerging field of activism known as the "access to knowledge" or A2K movement, which advocates for more open access to information and knowledge. The preface outlines the book's goals of making this new political movement understandable to outsiders and providing space for movement participants to analyze its evolution. It describes the book's structure, with sections on the conceptual foundations of A2K, historical case studies of A2K activism, conceptual frameworks for understanding A2K, and analyses of A2K strategies and tactics. The preface aims to provide context around this growing global debate over intellectual property without prescribing
Land Grabbing - A Mexican Presidium Under Threatberat celik
Around the world, huge tracts of fertile land are being sold or
rented for extremely low prices. Tens of millions of hectares
have been surrendered in recent years to produce food crops
for export or biofuels, to extract resources or to resell the land
on the financial market, like any other commodity.
This so-called land grabbing is severely threatening the
environment, the food sovereignty and the very lives of local
communities.
Robert Wenn has over 30 years of experience in teaching English and other subjects. He has worked as an English instructor for various institutes in Abu Dhabi since 2001. Prior to that, he held positions in sales, financial services, and law enforcement in the UK and UAE. He has qualifications in teaching English, management studies, and health and safety.
What is the the real cost of capital? Most individuals looking to purchase an asset do so from the wrong position. This presentation will explain the true cost of capital and interest rates. Before you make a considerable purchase, review this presentation and save yourself time, energy and money.
1. Two stones are thrown up simultaneously from a cliff with different initial speeds. A graph showing the relative position of the second stone with respect to the first over time would be a curve that increases until the first stone hits the ground, then decreases until the second stone hits the ground.
2. The accuracy of determining the gravitational acceleration, g, from measurements of the period of a pendulum is calculated to be approximately 3%.
3. If two blocks of different weights are being pressed against a wall by a force, the frictional force applied by the wall on the heavier block is 120 N, which is enough to balance the total weight of 120 N of the two-block system.
The document contains the problems and solutions from the theoretical competition of the 27th International Physics Olympiad held in Oslo, Norway in 1996. It includes 7 problems covering various topics in physics like circuits, mechanics, thermodynamics, electromagnetism, and astrophysics. The problems are presented in English, with translations to other languages. Example student solutions and exam materials like photos from the grading process are also included.
conceptual-problems-in-physics-for-iit-jee (1)APEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
The document describes the problems presented at the 13th International Physics Olympiad held in Malente, Germany in 1982. It includes the five problems given to students, which covered both theoretical and experimental classical physics topics. It provides the solutions and explanations to each problem. The problems tested students on topics like electric circuits, oscillatory motion, optics, and spectroscopy. They varied in difficulty, with the oscillating coat hanger problem being the most challenging. The experimental problems required both theoretical understanding and experimental skills to solve.
This document provides information about the 18th International Physics Olympiad held in 1987 in Jena, Germany. It describes the four problems presented to competitors - three theoretical and one experimental. The theoretical problems were quite difficult, with only the first problem having medium difficulty. About half the competitors did not find adequate solutions to the other two theoretical problems. The experimental problem was much easier. The document then provides the full problems and their step-by-step solutions. It analyzes the challenges faced by competitors and explains the reasoning and physics concepts underlying each problem.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
The document provides the question paper and solutions for the Indian National Physics Olympiad held in 2014. It contains 7 multi-part physics questions related to topics like electromagnetism, mechanics, thermodynamics, and nuclear physics. For each question, the relevant concepts and formulas are provided along with step-by-step calculations to arrive at the final solutions. Diagrams and graphs are used to illustrate concepts where needed.
I. Antoniadis - "Introduction to Supersymmetry" 1/2SEENET-MTP
Supersymmetry (SUSY) is a symmetry that relates bosonic and fermionic degrees of freedom. It extends the Poincaré algebra by including spinorial generators (supercharges) that transform bosonic fields into fermionic fields and vice versa. SUSY provides motivations like natural elementary scalars, gauge coupling unification, and a dark matter candidate. SUSY is formulated using superspace, which extends spacetime by Grassmann coordinates. Chiral and vector superfields contain the bosonic and fermionic components of supermultiplets and allow constructing SUSY invariant actions.
(1) The document discusses fluid dynamics concepts including density, pressure, buoyancy, continuity, and Bernoulli's equation. It provides conceptual explanations and sample calculations for comparing volumes and densities of objects, calculating buoyant forces, and relating pressure, velocity, and flow rates in pipes.
(2) One example calculates the force needed to lift a car using a hydraulic lift, where the pressure applied must be the same at both the large and small pistons.
(3) Another example uses continuity and Bernoulli's equations to relate the velocity and pressure of water flowing at different diameters in a pipe. It finds the velocity and pressure change when the pipe narrows.
Outgoing ingoingkleingordon spvmforminit_proceedfrom12dec18foxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
Outgoing ingoingkleingordon spvmforminit_proceedfromfoxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
This document provides information about the dynamics of machinery course for several mechanical engineering students. It includes the learning objectives, symbols and definitions, response of a damped system under harmonic motion, an example problem, and key concepts about magnification factor, phase angle, and total response of a system. The example calculates the total response of a single-degree-of-freedom system subjected to an external harmonic force and free vibration.
Describes the mathematics of the Calculus of Variations.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website on http://www.solohermelin.com
The use of Calculus is very important in every aspects of engineering.
The use of Differential equation is very much applied in the concept of Elastic beams.
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of black holes. It first presents the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. Near the event horizon, the radial equation is approximated in the Regge-Wheeler coordinate, leading to oscillatory solutions. The time and radial solutions are then expressed in outgoing and ingoing coordinates, resulting in outgoing and ingoing waves with different analytic properties in the future and past event horizons.
1. The document discusses static equilibrium of coplanar force systems. It covers drawing free-body diagrams, identifying reaction forces, and applying the three equations of equilibrium.
2. Key steps for solving problems include drawing the free-body diagram, identifying known and reaction forces, and setting the sum of forces and moments equal to zero.
3. Examples show calculating unknown forces and reactions for beams, rods, and pulley systems in static equilibrium. Forces and moments are analyzed to determine the magnitude and direction of reaction forces.
The document is an unsolved physics paper from 2008 for IITJEE (Indian Institute of Technology Joint Entrance Examination). It contains multiple choice and reasoning questions about physics concepts. The questions cover topics like mechanics, electromagnetism, thermodynamics, and waves. There are four sections with different question types including objective, reasoning, comprehension, and matrix-match questions. The document provides figures and diagrams to accompany some of the physics problems.
Obtaining three-dimensional velocity information directly from reflection sei...Arthur Weglein
This paper present a formalism for obtaining the subsurface
velocity configuration directly from reflection seismic data.
Our approach is to apply the results obtained for inverse
problems in quantum scattering theory to the reflection
seismic problem. In particular, we extend the results of
Moses (1956) for inverse quantum scattering and Razavy
(1975) for the one-dimensional (1-D) identification of the
acoustic wave equation to the problem of identifying the
velocity in the three-dimensional (3-D) acoustic wave equation
from boundary value measurements. No a priori knowledge
of the subsurface velocity is assumed and all refraction,
diffraction, and multiple reflection phenomena are
taken into account. In addition, we explain how the idea of
slant stack in processing seismic data is an important part
of the proposed 3-D inverse scattering formalism.
A2 k in the age of intellectual propertyberat celik
This document is the preface to the book "Access to Knowledge in the Age of Intellectual Property". It introduces the emerging field of activism known as the "access to knowledge" or A2K movement, which advocates for more open access to information and knowledge. The preface outlines the book's goals of making this new political movement understandable to outsiders and providing space for movement participants to analyze its evolution. It describes the book's structure, with sections on the conceptual foundations of A2K, historical case studies of A2K activism, conceptual frameworks for understanding A2K, and analyses of A2K strategies and tactics. The preface aims to provide context around this growing global debate over intellectual property without prescribing
Land Grabbing - A Mexican Presidium Under Threatberat celik
Around the world, huge tracts of fertile land are being sold or
rented for extremely low prices. Tens of millions of hectares
have been surrendered in recent years to produce food crops
for export or biofuels, to extract resources or to resell the land
on the financial market, like any other commodity.
This so-called land grabbing is severely threatening the
environment, the food sovereignty and the very lives of local
communities.
Robert Wenn has over 30 years of experience in teaching English and other subjects. He has worked as an English instructor for various institutes in Abu Dhabi since 2001. Prior to that, he held positions in sales, financial services, and law enforcement in the UK and UAE. He has qualifications in teaching English, management studies, and health and safety.
What is the the real cost of capital? Most individuals looking to purchase an asset do so from the wrong position. This presentation will explain the true cost of capital and interest rates. Before you make a considerable purchase, review this presentation and save yourself time, energy and money.
How the Culture of Economics Stops Economists from Studying Group Behavior an...berat celik
This document discusses how the culture of economics focuses analysis on individual behavior rather than group behavior and social influences. It argues that mainstream economics assumes humans act as isolated, rational individuals, ignoring evidence that people are social beings influenced by groups and culture. This prevents economists from studying important economic roles of organizations and the development of social phenomena. The paper draws on sociology, particularly Pierre Bourdieu's work, to explain how economics developed a culture of individualism that blinds practitioners from recognizing shortcomings in their approach and limits the scope of analysis. Overcoming this culture will be difficult as the culture itself prevents recognition of its limitations.
ARAN Kitchen World is a leading importer of modular kitchens from Italy. ARAN Kitchens are the most purchased modular kitchens in the world. We import a range of modern and high quality kitchens, which are customized to specifications and requirements of every client. We have dealers and showrooms across all major cities in India
This document describes Sparkless Bombay Tools, a leading supplier and manufacturer of non-sparking tools such as wrenches, hammers, spanners, pipe wrenches, and more for safe use in hazardous environments. They provide an unbeatable range of non-sparking tools including wrenches, hammers, pliers, pipe cutters, tool kits, torque wrenches, brushes, and chain hoist trolleys. Contact information is given for Sparkless Bombay Tools in Mumbai, India.
Breaking the silence: The hidden injuries of neo-liberal academiaberat celik
'Neoliberalism found fertile ground in academics whose predispositions to 'work hard'
and 'do well' meshed perfectly with it's demands for autonomous, self motivating,
responsibilised subjects. This is gendered, racialised and classed, too, to be sure, in
ways that merit urgent attention that I have been unable to give in this short piece. The
lack of resistance to the neoliberalisation of universities is partly a result of these
divisive, individualizing practices, of the silences around them, of the fact also that
people are too exhausted to resist and furthermore do not know what to resist or how to
do so. But it is also understandable, I suggest, in terms of the inherent pleasures and
fulfilment that many people derive from their work (when they find time to do it) or at
least the promise of/idea of it, as well as to the seductions of relatively autonomous
working lives -- though this autonomy is eroding fast, as universities import business
models which require for example that all e-mails be answered within 24 hours, or that
academics are present in the office five days a week. In reality, the much vaunted
autonomy often simply means that universities end up extracting even more labour from
us for free, as we participate in working lives in which there is often no boundary
between work and anything else (if indeed there is anything else).'
The Theory Of The Leisure Class - Thorstein Veblenberat celik
'..The substantial difference between the peaceable and the predatory phase
of culture, therefore, is a spiritual difference, not a mechanical one.
The change in spiritual attitude is the outgrowth of a change in the
material facts of the life of the group, and it comes on gradually as
the material circumstances favourable to a predatory attitude supervene.
The inferior limit of the predatory culture is an industrial limit.
Predation can not become the habitual, conventional resource of any
group or any class until industrial methods have been developed to such
a degree of efficiency as to leave a margin worth fighting for, above
the subsistence of those engaged in getting a living. The transition
from peace to predation therefore depends on the growth of technical
knowledge and the use of tools. A predatory culture is similarly
impracticable in early times, until weapons have been developed to such
a point as to make man a formidable animal. The early development of
tools and of weapons is of course the same fact seen from two different
points of view.'
---licensed under the terms of the Project Gutenberg License----
The Invention of Capitalism - Michael Perelmanberat celik
The Invention of Capitalism is novel in four major respects. First, it
addresses the question of what determines the social division of labor, the
division of society into independent firms and industries from the per-
spective of classical political economy. It also develops the theoretical
implications of primitive accumulation. Third, this book offers a signifi-
cantly different interpretation of classical political economy, demonstrat-
ing that this school of thought supported the process of primitive ac-
cumulation. Finally, it analyzes the role of primitive accumulation in the
work of Marx. All of these threads come together in helping us to under-
stand how modern capitalism developed and the role of classical political
economy in furthering this process.
URL: http://www.ejolt.org/2014/08/building-an-economy-on-quicksand/
'..Until recently sand was extracted in land quarries and riverbeds; however, these inland resources have nearly been depleted so that extraction has shifted to marine and coastal aggregates mining.'
Sand from deserts cannot be used for most purposes, as wind erosion over time forms round grains that do not bind well [4]. For most industrial uses, edged sand grains with a rough surface are needed, which stick together naturally. Desert sands, however, are usually fine- grained and of low shear strength –it does not even suit as material for the creation of artificial islands. Dubai, for example, used up all its suitable marine sand supplies for an artificial set of sand islands and, after these were exhausted, now has to import sand from Australia for continuing its building madness.
Most of the sand is by now extracted from the ocean floor – globally thousands of large boats are sucking up huge quantities of sand from the ocean floor in coastal areas like vacuum cleaners. As a result of currents, gravitation and movements of the waves, the gaps which were created by sand extraction are then filled by sand sliding in from surrounding areas and beaches. Due to this vicious cycle in Miami each year beaches have to be replenished with dredged-up sand to further provide tourists with its famous beaches.
In some extreme cases, the mining of marine aggregates has even changed international boundaries, such as through the disappearance of entire islands in Indonesia – since 2005 at least 24 small islands have disappeared as a result of erosion caused by illegal sand mining. Most of this sand is going to Singapore, which has expanded its surface area by 22% since the 1960s [5]. In response to this potentially heavy environmental toll many neighboring countries (Indonesia, Malaysia and Vietnam) have now banned exports of sand to Singapore, but this has only shifted the problem to countries such as Cambodia.
The conflicts caused by sand mining were for the first time brought to the attention of the general public through the documentary Sand Wars. Among many other outreach victories, the documentary inspired the United Nations Environment Programme (UNEP) to publish a Global Environmental Alert in March 2014 titled “Sand, rarer than one thinks”. In it, the authors state that “Formed by erosive processes over thousands of years, they [sand and gravel] are now being extracted at a rate far greater than their renewal”.
Harvesting Justice - Transforming Food, Land, and Agricultural Systems in the...berat celik
“We are the food we eat, the water
we drink, the air we breathe. And
reclaiming democratic control
over our food and water and our
ecological survival is the neces-
sary project for our freedom.” 3
— Vandana Shiva, physicist and activist
Rape as torture in the DRC: Sexual violence beyond the conflict zoneberat celik
'This report is about the torture of women by state
security forces in the Democratic Republic of the
Congo (DRC). It is based on a study of 34 forensic
reports prepared for individual torture survivors by
the Medical Foundation Medico-Legal Report Ser-
vice at Freedom from Torture. The recommenda-
tions that follow have been informed by the views
of Congolese women who are survivors of torture
and former clients of Freedom from Torture.
The report provides evidence of the torture of
women by state security forces in the DRC, mainly
in non-conflict contexts. It indicates the exten-
sive use of rape and other forms of sexual tor-
ture against women detained mostly for political
reasons, and the use of a variety of other torture
methods including beating, burning and psycho-
logical and environmental forms of torture. It
highlights the lack of access to justice, including
due process, and appropriate services for women
victims of torture in the DRC; as well as the impu-
nity of suspected perpetrators.'
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help boost feelings of calmness, happiness and focus.
1. The document provides solutions to physics problems involving charged spheres and cubes, rotating wheels, friction on motorcycles, chasing foxes and rabbits, growing raindrops, and springs wrapped around poles.
2. It derives equations and ratios for potentials, field strengths, minimum distances, meeting points, accelerations, temperatures, spring constants, and more using principles of electrostatics, kinematics, dynamics, and thermodynamics.
3. The solutions are detailed and rigorous, employing techniques like Gauss' law, dimensional analysis, conservation of energy, and modeling circular and conical motions.
This document provides solutions to 15 problems related to magnetic materials and magnetism. It begins by deriving expressions for how the angular frequency and radius of a classical electron orbit change with the application of a magnetic field using the Lorentz force. It then calculates magnetic moments and susceptibilities for various systems. Other problems cover topics like Lenz's law, diamagnetism, paramagnetism, Bohr orbits, susceptibility measurements, and predicting magnetic behaviors in different materials. Detailed step-by-step workings are shown for each problem.
1) The document presents three theoretical physics problems involving spinning balls, charged particles in loops, and laser cooling of atoms.
2) Problem 1 considers a spinning ball falling and rebounding, calculating the rebound angle, horizontal distance traveled, and minimum spin rate. Problem 2 analyzes relativistic effects on charged particles in a moving loop in an electric field.
3) Problem 3 describes using lasers to cool atoms by resonant absorption. It calculates the laser frequency needed, velocity range absorbed, direction change upon emission, maximum velocity decrease, number of absorption events to slow to zero velocity, and distance traveled during cooling.
This document provides solutions to theoretical physics problems from the 1st Asian Physics Olympiad held in Karawaci, Indonesia in April 2000. The solutions include:
1) Deriving an expression for the relative angular velocity of Jupiter and Earth and calculating the relative velocity.
2) Calculating the detection limit of a radioactive source using an ionization chamber and determining the necessary voltage pulse amplifier gain.
3) Using Gauss' law to calculate the electric field and potential between the plates of a parallel plate capacitor and deriving an expression for the capacitance per unit length.
The document discusses the dual nature of matter and radiation. It provides answers to multiple choice and numerical questions related to photoelectric effect, de Broglie wavelength, and magnetic effect of current. Regarding photoelectric effect, it explains that electron emission from a zinc plate in ultraviolet light is due to the photoelectric effect. It also discusses how kinetic energy of photoelectrons varies with frequency of incident radiation. Regarding magnetic effect of current, it describes how to determine direction and magnitude of magnetic field around current carrying wires using the right hand grip rule. It also solves problems related to forces experienced by charged particles in magnetic fields.
The document summarizes the problems from the IV International Olympiad in Physics held in Moscow, USSR in 1970. Teams from 8 countries participated in theoretical and experimental competitions. The theoretical problems covered mechanics, crystal structure, electrostatics, and optics. The experimental problem involved determining focal lengths of lenses. The solutions provided the calculations and reasoning to solve each theoretical problem in under 3 sentences.
This document summarizes solutions to three theoretical questions:
1) Describes how to use measurements of gravitational redshift to determine the mass and radius of a star.
2) Explains Snell's law and how it can be used to determine the path of light rays through a medium with a linear change in refractive index.
3) Analyzes the motion of a floating cylindrical buoy, determining equations for its vertical and rotational oscillations and relating the periods.
This document provides information on the dual nature of matter and radiation, including photoelectric effect questions and answers. It discusses key concepts such as:
- The photoelectric effect and how an uncharged zinc plate becomes positively charged when irradiated by ultraviolet radiation.
- Graphs showing the relationship between photoelectric current and anode potential when frequency is kept constant.
- Questions regarding the wave-particle duality of matter and radiation, including the de Broglie wavelength equation.
- Multi-part questions analyzing graphs and equations related to the photoelectric effect and Einstein's photoelectric equation.
This document discusses the dual nature of matter and radiation, including photoelectric effect and de Broglie wavelength. It provides 5 one-mark questions and answers on topics like photoelectric effect and characteristics of incident radiation. It also gives 5 two-mark questions and answers exploring topics such as kinetic energy relationship between an electron and alpha particle with the same de-Broglie wavelength. Finally, it provides 5 three-mark questions and answers examining Einstein's photoelectric equation and variations in photoelectric experiments.
1) The document discusses the propagation of waves, including plane waves, cylindrical waves, and spherical waves. It describes how the amplitude of each type of wave decreases with distance from the source.
2) Huygens' principle is introduced, which models light propagation as secondary spherical wavelets emerging from each point on a propagating wavefront.
3) When light travels from one medium to another, it results in reflected and refracted waves at the interface between the media. Snell's law relates the angles of incidence and refraction.
The document discusses the history and development of models of the hydrogen atom. It begins by mentioning early observations of hydrogen. It then covers Thomson's "plum pudding" model, Rutherford's planetary model, Bohr's theory that electrons orbit the nucleus in distinct energy levels, and Schrodinger's wave equation solution that provides a more complete quantum mechanical description. The energy levels predicted by Bohr's theory and Schrodinger's equation match, both giving the ground state energy of the hydrogen atom as 13.6 electron volts.
Quantum Theory. Wave Particle Duality. Particle in a Box. Schrodinger wave equation. Quantum Numbers and Electron Orbitals. Principal Shells and Subshells. A Fourth Quantum Number. Effective nuclear charge
The document describes an experiment to measure the refractive index of HCl gas using a Michelson interferometer. A HeNe laser beam is split into two paths, with one path passing through an evacuated glass cell. As the cell is pumped out, the interference fringes shift due to the changing optical path length. Counting the number of fringe shifts allows calculating the refractive index from the changing wavelength of light in the gas versus vacuum. The experiment is performed at varying HCl pressures and temperatures, with results corrected to standard temperature and pressure for comparison to literature values of the molar refractivity and effective molecular radius of HCl.
1. A particle moving perpendicular to a magnetic field will follow a circular path. The radius of the path is determined by the particle's mass, charge, speed, and the magnetic field strength.
2. A velocity selector uses uniform, perpendicular electric and magnetic fields. Particles pass through undeflected if their speed equals the ratio of the field strengths.
3. A mass spectrometer accelerates ions and uses a magnetic field to cause circular orbits. Heavier ions have smaller orbit radii allowing separation based on mass.
This document contains solved problems related to Bohr's atomic model and quantum mechanics. Problem 1 explains that Bohr's model can only be applied to systems with one electron. Problem 3 gives the ratio of photon energies as 2 for wavelengths of 2000Å and 4000Å. Problem 5 gives the wave number of the first line of the Balmer series for hydrogen as 15,200 cm-1.
This document discusses problems from the 9th International Physics Olympiad held in Budapest, Hungary in 1976. It presents three theoretical problems and one experimental problem. The first theoretical problem involves calculating the minimum coefficient of friction needed to prevent a block from slipping inside a rotating hollow sphere. The second problem calculates the work done on a piston by compressing gas in an insulated cylinder. The third problem describes methods for determining the diameter of an air bubble inside a glass sphere without damaging it. The experimental problem involves using heating and time-temperature graphs to determine unknown thermal properties of a crystalline substance.
Lecture34e - EM Wave Propopagation.pptssuser88da4c
1) Maxwell's equations describe light waves and are used to derive the wave equation. Light waves are transverse electromagnetic waves with perpendicular electric and magnetic fields.
2) Light waves can constructively or destructively interfere depending on their relative phase and polarization. Waves of different frequencies do not interfere.
3) At low light levels, light behaves as particles called photons with energy proportional to frequency. Photon counting reveals the particle nature of light.
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The document discusses the Robertson-Walker metric and its application to cosmological redshifts. It contains the following key points:
1. The Robertson-Walker metric describes a homogeneous and isotropic universe and can account for the observed redshift of distant galaxies by considering the expansion of the universe over time.
2. The metric allows for spaces with positive, negative, or zero curvature, corresponding to closed, open, or flat geometries for the universe.
3. Application of the metric successfully explains Hubble's observation of redshift proportional to distance as being due to the Doppler effect from the receding motion of galaxies caused by the expansion of the universe.
1. Problems of the 7th International Physics Olympiad1
(Warsaw, 1974)
Waldemar Gorzkowski
Institute of Physics, Polish Academy of Sciences, Warsaw, Poland 2
Abstract
The article contains the competition problems given at the 7th International Physics
Olympiad (Warsaw, 1974) and their solutions.
Introduction
The 7th
International Physics Olympiad (Warsaw, 1974) was the second one organized
in Poland. It took place after a one-year organizational gap, as no country was able to
organize the competition in 1973.
The original English version of the problems of the 7th
IPhO has not been preserved.
We would like to remind that the permanent Secretariat of the IPhOs was established only in
1983; previously the Olympic materials had been collected by individual people in their
private archives and, in general, are not complete. English texts of the problems and
simplified solutions are available in the book by R. Kunfalvi [1]. Unfortunately, they are
somewhat deformed as compared to the originals. Fortunately, we have very precise Polish
texts. Also the full solutions in Polish are available. This article is based on the books [2, 3]
and article [4].
The competition problems were prepared especially for the 7th
IPhO by Andrzej
Szymacha (theoretical problems) and Jerzy Langer (experimental problem).
THEORETICAL PROBLEMS
Problem 1
A hydrogen atom in the ground state, moving with velocity v , collides with another
hydrogen atom in the ground state at rest. Using the Bohr model find the smallest velocity 0v
of the atom below which the collision must be elastic.
At velocity 0v the collision may be inelastic and the colliding atoms may emit
electromagnetic radiation. Estimate the difference of frequencies of the radiation emitted in
the direction of the initial velocity of the hydrogen atom and in the opposite direction as a
fraction (expressed in percents) of their arithmetic mean value.
Data:
J182.18eV6.13
2
18-
2
4
⋅===
me
Ei ; (ionization energy of hydrogen atom)
kg1067.1 27−
⋅=Hm ; (mass of hydrogen atom)
1
This article has been sent for publication in Physics Competitions in September 2003
2
e-mail: gorzk@ifpan.edu.pl
2. ( m - mass of electron; e - electric charge of electron; - Planck constant;
numerical values of these quantities are not necessary.)
Solution
According to the Bohr model the energy levels of the hydrogen atom are given by the
formula:
2
n
E
E i
n −= ,
where n = 1, 2, 3, … The ground state corresponds to 1=n , while the lowest excited state
corresponds to 2=n . Thus, the smallest energy necessary for excitation of the hydrogen
atom is:
ii EEEEE 4
3
4
1
12 )1( =−=−=∆ .
During an inelastic collision a part of kinetic energy of the colliding particles is
converted into their internal energy. The internal energy of the system of two hydrogen atoms
considered in the problem cannot be changed by less than E∆ . It means that if the kinetic
energy of the colliding atoms with respect to their center of mass is less than E∆ , then the
collision must be an elastic one. The value of 0v can be found by considering the critical
case, when the kinetic energy of the colliding atoms is equal to the smallest energy of
excitation. With respect to the center of mass the atoms move in opposite direction with
velocities 02
1
v . Thus
( ) ( ) iHH Evmvm 4
32
02
12
02
1
2
1
2
1
=+
and
H
i
m
E
v
3
0 = ( 4
1026.6 ⋅≈ m/s).
Consider the case when 0vv = . The collision may be elastic or inelastic. When the
collision is elastic the atoms remain in their ground states and do not emit radiation. Radiation
is possible only when the collision is inelastic. Of course, only the atom excited in the
collision can emit the radiation. In principle, the radiation can be emitted in any direction, but
according to the text of the problem we have to consider radiation emitted in the direction of
the initial velocity and in the opposite direction only. After the inelastic collision both atom
are moving (in the laboratory system) with the same velocities equal to 02
1
v . Let f denotes
the frequency of radiation emitted by the hydrogen atom in the mass center (i.e. at rest).
Because of the Doppler effect, in the laboratory system this frequency is observed as (c
denotes the velocity of light):
a) f
c
v
f
+= 02
1
1 1 - for radiation emitted in the direction of the initial velocity of the
hydrogen atom,
3. b) f
c
v
f
−= 02
1
2 1 - for radiation emitted in opposite direction.
The arithmetic mean value of these frequencies is equal to f . Thus the required ratio
is
c
v
f
ff
f
f 021
=
−
=
∆
( %102 2−
⋅≈ ).
In the above solution we took into account that cv <<0 . Otherwise it would be
necessary to use relativistic formulae for the Doppler effect. Also we neglected the recoil of
atom(s) in the emission process. One should notice that for the visible radiation or radiation
not too far from the visible range the recoil cannot change significantly the numerical results
for the critical velocity 0v and the ratio
f
f∆
. The recoil is important for high-energy quanta,
but it is not this case.
The solutions were marked according to the following scheme (draft):
1. Energy of excitation up to 3 points
2. Correct description of the physical processes up to 4 points
3. Doppler effect up to 3 points
Problem 2
Consider a parallel, transparent plate of thickness d – Fig. 1. Its refraction index varies
as
R
x
n
n
−
=
1
0
.
Fig. 1
A light beam enters from the air perpendicularly to the plate at the point A (xA = 0) and
emerges from it at the point B at an angle α .
1. Find the refraction index Bn at the point B.
y
xBA x
d
B
α
4. 2. Find Bx (i.e. value of x at the point B)
3. Find the thickness d of the plate.
Data:
2.10 =n ; 13=R cm; °=30α .
Solution
Fig. 2
Consider a light ray passing through a system of parallel plates with different
refractive indexes – Fig. 2. From the Snell law we have
2
1
1
2
sin
sin
n
n
=
β
β
i.e.
1122 sinsin ββ nn = .
In the same way we get
2233 sinsin ββ nn = , etc.
Thus, in general:
=iin βsin const.
This relation does not involve plates thickness nor their number. So, we may make use
of it also in case of continuous dependence of the refractive index in one direction (in our case
in the x direction).
Consider the situation shown in Fig. 3.
β2
n1
n2
n3
β1
β2
β3
β3
α
5. Fig. 3
At the point A the angle °=90Aβ . The refractive index at this point is 0n . Thus, we have
BBAA nn ββ sinsin = ,
BBnn βsin0 = .
Additionally, from the Snell law applied to the refraction at the point B, we have
B
B
n=
−° )90sin(
sin
β
α
.
Therefore
2
0
2222
)sin(sin1cossin nnnnnn BBBBBBBB −=−=−== βββα
and finally
α22
0 sin+= nnB .
Numerically
3.1
10
5
10
12
22
=
+
=Bn
The value of Bx can be found from the dependence )(xn given in the text of the
problem. We have
R
x
n
xnn
B
BB
−
==
1
)( 0
,
−=
B
B
n
n
Rx 0
1 ,
Numerically
1=Bx cm.
xB
A
BβB
6. The answer to the third question requires determination of the trajectory of the light
ray. According to considerations described at the beginning of the solution we may write (see
Fig. 4):
0)(sin)( nxxn =β .
Thus
R
xR
xn
n
x
−
==
)(
)(sin 0
β .
Fig. 4
Consider the direction of the ray crossing a point C on the circle with radius R and
center in point O as shown in Fig. 4. We see that
∠sin COC' )(sin x
R
xR
β=
−
= .
Therefore, the angle ∠ COC' must be equal to the angle )(xβ formed at the point C by the
light ray and CC'. It means that at the point C the ray must be tangent to the circle. Moreover,
the ray that is tangent to the circle at some point must be tangent also at farther points.
Therefore, the ray cannot leave the circle (as long as it is inside the plate)! But at the
beginning the ray (at the point A) is tangent to the circle. Thus, the ray must propagate along
the circle shown in Fig. 4 until reaching point B where it leaves the plate.
Already we know that A'B = 1 cm. Thus, B'B = 12 cm and from the rectangular
triangle BB'O we get
22
1213OB' −==d cm = 5 cm.
The shape of the trajectory )(xy can be determined also by using more sophisticated
calculations. Knowing )(xβ we find )(tg xβ :
22
)(
)(tg
xRR
xR
x
−−
−
=β .
A’
A
B
O
R
d
C C’
R
R - x
B’
β(x)
7. But )(tg xβ is the derivative of )(xy . So, we have
( )22
22
)(
)(
xRR
dx
d
xrR
xR
dx
dy
−−=
−−
−
= .
Thus
constxRRy +−−= 22
)(
Value of const can be found from the condition
0)0( =y .
Finally:
22
)( xRRy −−= .
It means that the ray moves in the plate along to the circle as found previously.
Fig. 5
Now we will present yet another, already the third, method of proving that the light in
the plate must move along the circle.
We draw a number of straight lines (inside the plate) close to each other and passing
trough the point (R,0) - Fig. 5. From the formula given in the text of the problem it follows
that the refraction index on each of these lines is inversely proportional to the distance to the
point (R,0). Now we draw several arcs with the center at (R,0). It is obvious that the geometric
length of each arc between two lines is proportional to the distance to the point (R,0).
It follows from the above that the optical path (a product of geometric length and
refractive index) along each arc between the two lines (close to each other) is the same for all
the arcs.
Assume that at +-certain moment t the wave front reached one of the lines, e.g. the
line marked with a black dot in Fig. 5. According to the Huygens principle, the secondary
sources on this line emit secondary waves. Their envelope forms the wave front of the real
wave at some time tt ∆+ . The wave fronts of secondary waves, shown in Fig. 5, have
different geometric radii, but - in view of our previous considerations - their optical radii are
(R,0)
y
x
8. exactly the same. It means that at the time tt ∆+ the new wave front will correspond to one
of the lines passing trough (R,0). At the beginning the wave front of the light coincided with
the x axis, it means that inside the plate the light will move along the circle with center at the
point (R,0).
The solutions were marked according to the following scheme (draft):
1. Proof of the relation =βsinn const up to 2 points
2. Correct description of refraction at points A and B up to 2 points
3. Calculation of Bx up to 1 point
4. Calculation of d up to 5 points
Problem 3
A scientific expedition stayed on an uninhabited island. The members of the
expedition had had some sources of energy, but after some time these sources exhausted.
Then they decided to construct an alternative energy source. Unfortunately, the island was
very quiet: there were no winds, clouds uniformly covered the sky, the air pressure was
constant and the temperatures of air and water in the sea were the same during day and night.
Fortunately, they found a source of chemically neutral gas outgoing very slowly from a
cavity. The pressure and temperature of the gas are exactly the same as the pressure and
temperature of the atmosphere.
The expedition had, however, certain membranes in its equipment. One of them was
ideally transparent for gas and ideally non-transparent for air. Another one had an opposite
property: it was ideally transparent for air and ideally non-transparent for gas. The members
of the expedition had materials and tools that allowed them to make different mechanical
devices such as cylinders with pistons, valves etc. They decided to construct an engine by
using the gas from the cavity.
Show that there is no theoretical limit on the power of an ideal engine that uses the gas
and the membranes considered above.
Solution
Let us construct the device shown in Fig. 6. B1 denotes the membrane transparent for
the gas from the cavity, but non-transparent for the air, while B2 denotes the membrane with
opposite property: it is transparent for the air but non-transparent for the gas.
Initially the valve Z1 is open and the valve Z2 is closed. In the initial situation, when
we keep the piston at rest, the pressure under the piston is equal to 00 pp + due to the Dalton
law. Let 0V denotes an initial volume of the gas (at pressure 0p ).
Now we close the valve Z1 and allow the gas in the cylinder to expand. During
movement of the piston in the downwards direction we obtain certain work performed by
excess pressure inside the cylinder with respect to the atmospheric pressure 0p . The partial
pressure of the gas in the cylinder will be reduced according to the formula VVpp /00= ,
where V denotes volume closed by the piston (isothermal process). Due to the membrane B2
the partial pressure of the air in the cylinder all the time is 0p and balances the air pressure
outside the cylinder. It means that only the gas from the cavity effectively performs the work.
Cavity
9. Fig. 6
Consider the problem of limits for the work that can be performed during isothermal
expansion of an initial portion of the gas. Let us analyze the graph of the function VVp /00
versus V shown in Fig. 7.
It is obvious that the amount of work performed by the gas during isothermal
expansion from 0V to kV is represented by the area under the curve (shown in the graph)
from 0V to kV . Of course, the work is proportional to 0V . We shall prove that for large
enough kV the work can be arbitrarily large.
Consider ...,16,8,4,2, 00000 VVVVVV = It is clear that the rectangles I, II, III, …
(see Fig. 7) have the same area and that one may draw arbitrarily large number of such
rectangles under the considered curve. It means that during isothermal expansion of a given
portion of the gas we may obtain arbitrarily large work (at the cost of the heat taken from sthe
urrounding) – it is enough to take kV large enough.
After reaching kV we open the valve Z2 and move the piston to its initial position
without performing any work. The cycle can be repeated as many times as we want.
In the above considerations we focused our attention on the work obtained during one
cycle only. We entirely neglected dynamics of the process, while each cycle lasts some time.
One may think that - in principle - the length of the cycle increases very rapidly with the
effective work we obtain. This would limit the power of the device we consider.
Take, however, into account that, by proper choice of various parameters of the
device, the time taken by one cycle can be made small and the initial volume of the gas 0V
can be made arbitrarily large (we consider only theoretical possibilities – we neglect practical
difficulties entirely). E.g. by taking large size of the membrane B1 and large size of the piston
we may minimize the time of taking the initial portion of the gas 0V from the cavity and
make this portion very great.
In our analysis we neglected all losses, friction, etc. One should remark that there are
no theoretical limits for them. These losses, friction etc. can be made negligibly small.
Z1
B2
B1
Z2
p0
p
p0
p0
10. Fig. 7
The device we analyzed is very interesting: it produces work at cost of heat taken from
surrounding without any difference in temperatures. Does this contradict the second law of
thermodynamics? No! It is true that there is no temperature difference in the system, but the
work of the device makes irreversible changes in the system (mixing of the gas from the
cavity and the air).
The solutions were marked according to the following scheme (draft):
1. Model of an engine and its description up to 4 points
2. Proof that there is no theoretical limit for power up to 4 points
3. Remark on II law of thermodynamics up to 2 points
EXPERIMENTAL PROBLEM
In a "black box" there are two identical semiconducting diodes and one resistor
connected in some unknown way. By using instruments provided by the organizers find the
resistance of the resistor.
Remark: One may assume that the diode conducts current in one direction only.
List of instruments: two universal volt-ammeters (without ohmmeters), battery, wires
with endings, graph paper, resistor with regulated resistance.
Solution
At the beginning we perform preliminary measurements by using the circuit shown in
Fig. 8. For two values of voltage 1U and 2U , applied to the black box in both directions,
we measure four values of current: )( 1UI , )( 2UI , )( 1UI − and )( 2UI − . In this way
we find that:
II
III
I
p0
p
V
V
0
2V0 4V0 8V0
p0/2
p0/4
p0/8
Vk
11. 1. The black box conducts current in both directions;
2. There is an asymmetry with respect to the sign of the voltage;
3. In both directions current is a nonlinear function of voltage.
Fig. 8
The diodes and resistor can be connected in a limited number of ways shown in Fig. 9
(connections that differ from each other in a trivial way have been omitted).
Fig. 9
mV
mA
12. Only one of these connections has the properties mentioned at the beginning. It is:
Fig. 10
For absolute values of voltages we have
UUUU ABR ∆=−= ,
where RU denotes voltage on the resistor when a current I flows trough the branch B, AU
- voltage on the black box when the current I flows through the branch A, and BU -
voltage on the black box when the current I flows through the branch B.
Therefore
I
U
I
IUIU
I
IU
R ABR ∆
=
−
==
)()()(
.
It follows from the above that it is enough to take characteristics of the black box in
both directions: by subtraction of the corresponding points (graphically) we obtain a straight
line (example is shown in Fig. 11) whose slope allows to determine the value of R .
The solutions were marked according to the following scheme (draft):
Theoretical part:
1. Proper circuit and method allowing determination of connections
the elements in the black box up to 6 points
2. Determination of R (principle) up to 2 points
3. Remark that measurements at the same voltage in both
directions make the error smaller up to 1 point
4. Role of number of measurements (affect on errors) up to 1 point
Experimental part:
1. Proper use of regulated resistor as potentiometer up to 2 points
2. Practical determination of R (including error) up to 4 points
3. Proper use of measuring instruments up to 2 points
4. Taking into account that temperature of diodes increases during
measurements up to 1 point
5. Taking class of measuring instruments into account up to 1 point
B
20406080100150
200 I
[mA]
∆U
[mV]
0 5 10 15 20 25
B
A
13. Fig. 11
Acknowledgement
Author wishes to express many thanks to Prof. Jan Mostowski for reading the text and
for many valuable comments and remarks that allowed improving the final version.
Literature
[1] R. Kunfalvi, Collection of Competition Tasks from the Ist trough XVth International
Physics Olympiads, 1967 – 1984, Roland Eotvos Physical Society and UNESCO,
Budapest 1985
[2] W. Gorzkowski, Olimpiady Fizyczne – XXIII I XXIV, WSiP, Warszawa 1977
[3] W. Gorzkowski, Zadania z fizyki z całego świata (z rozwiązaniami) - 20 lat
Międzynarodowych Olimpiad Fizycznych, WNT, Warszawa 1994 [ISBN 83-204-1698-1]
[4] W. Gorzkowski, VII Międzynarodowa Olimpiada Fizyczna, Fizyka w Szkole, nr 3/75, pp.
23 – 28