This document contains an examination for Applied Mechanics from the I B.Tech Supplimentary Examinations held in August/September 2008. It consists of 8 questions related to topics in applied mechanics, including forces, friction, belts, moments of inertia, and kinematics. Students were instructed to answer any 5 of the 8 questions, with all questions carrying equal marks. The questions involve calculations related to mechanical systems, structures, and motion.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
This document discusses methods for determining areas, volumes, centroids, and moments of inertia of basic geometric shapes. It begins by introducing the method of integration for calculating areas and volumes. Standard formulas are provided for areas of rectangles, triangles, circles, sectors, and parabolic spandrels. Formulas are also provided for volumes of parallelepipeds, cones, spheres, and solids of revolution. The concepts of center of gravity, centroid, and center of mass are defined. Equations are given for calculating the centroids of uniform bodies, plates, wires, and line segments. Methods for finding centroids of straight lines, arcs, semicircles, and quarter circles are illustrated.
This document discusses moments of inertia, which are a measure of an object's resistance to rotational acceleration about an axis. It defines the moment of inertia of an area and introduces key concepts like the parallel axis theorem, radius of gyration, and calculating moments of inertia through integration or for composite areas. Examples are provided to demonstrate calculating moments of inertia for various shapes, including rectangles, triangles, L-shapes, and composite profiles, about different axes. The document also covers determining moments of inertia at the centroidal axes versus other axes using the parallel axis theorem.
The document discusses key concepts related to the section properties of structural members including:
- The center of gravity is the point where the total weight of a system can be considered to be concentrated.
- The center of mass is calculated similarly using the total mass of a system rather than total weight.
- The centroid is the geometric center of an object, independent of forces or weights, and depends only on the object's shape.
- Moments of inertia measure the resistance of an area to bending and twisting forces, and are calculated based on the area properties and distance from specific axes.
The document discusses moments of inertia, which are integrals related to the distribution of mass of an object and how it resists rotational changes. It provides formulas for calculating the moment of inertia for basic shapes like rectangles and circles, and explains techniques like using differential area elements and the parallel axis theorem. Sample problems demonstrate calculating moments of inertia for composite shapes.
This document presents information on moments of inertia based on a course titled "pre-stressed concrete". It introduces moments of inertia and how they are calculated based on the distribution of mass or area relative to a given axis. Formulas are provided for calculating the moments of inertia of basic shapes like rectangles and circles through integration. The parallel axis theorem is also described, which relates the moments of inertia about different axes passing through an object. Examples are worked through, such as finding the moment of inertia of a triangle with respect to its base.
This document discusses axial members and includes two example problems. Axial members experience forces along their longitudinal axis. The key points are:
1) Axial members include cables, columns, rods, and other structural elements where forces act along the axis.
2) Internal forces in axial members can be represented by an equivalent axial force calculated through integration of stresses over the cross-sectional area.
3) Strains are uniform across axial members but stresses may vary depending on material properties and cross-sectional geometry.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
This document discusses methods for determining areas, volumes, centroids, and moments of inertia of basic geometric shapes. It begins by introducing the method of integration for calculating areas and volumes. Standard formulas are provided for areas of rectangles, triangles, circles, sectors, and parabolic spandrels. Formulas are also provided for volumes of parallelepipeds, cones, spheres, and solids of revolution. The concepts of center of gravity, centroid, and center of mass are defined. Equations are given for calculating the centroids of uniform bodies, plates, wires, and line segments. Methods for finding centroids of straight lines, arcs, semicircles, and quarter circles are illustrated.
This document discusses moments of inertia, which are a measure of an object's resistance to rotational acceleration about an axis. It defines the moment of inertia of an area and introduces key concepts like the parallel axis theorem, radius of gyration, and calculating moments of inertia through integration or for composite areas. Examples are provided to demonstrate calculating moments of inertia for various shapes, including rectangles, triangles, L-shapes, and composite profiles, about different axes. The document also covers determining moments of inertia at the centroidal axes versus other axes using the parallel axis theorem.
The document discusses key concepts related to the section properties of structural members including:
- The center of gravity is the point where the total weight of a system can be considered to be concentrated.
- The center of mass is calculated similarly using the total mass of a system rather than total weight.
- The centroid is the geometric center of an object, independent of forces or weights, and depends only on the object's shape.
- Moments of inertia measure the resistance of an area to bending and twisting forces, and are calculated based on the area properties and distance from specific axes.
The document discusses moments of inertia, which are integrals related to the distribution of mass of an object and how it resists rotational changes. It provides formulas for calculating the moment of inertia for basic shapes like rectangles and circles, and explains techniques like using differential area elements and the parallel axis theorem. Sample problems demonstrate calculating moments of inertia for composite shapes.
This document presents information on moments of inertia based on a course titled "pre-stressed concrete". It introduces moments of inertia and how they are calculated based on the distribution of mass or area relative to a given axis. Formulas are provided for calculating the moments of inertia of basic shapes like rectangles and circles through integration. The parallel axis theorem is also described, which relates the moments of inertia about different axes passing through an object. Examples are worked through, such as finding the moment of inertia of a triangle with respect to its base.
This document discusses axial members and includes two example problems. Axial members experience forces along their longitudinal axis. The key points are:
1) Axial members include cables, columns, rods, and other structural elements where forces act along the axis.
2) Internal forces in axial members can be represented by an equivalent axial force calculated through integration of stresses over the cross-sectional area.
3) Strains are uniform across axial members but stresses may vary depending on material properties and cross-sectional geometry.
This document discusses calculating the moment of inertia for composite cross-sections made up of multiple simple geometric shapes. It introduces the parallel axis theorem, which allows calculating the moment of inertia of each individual shape about a common reference axis so that the individual values can be added to determine the total moment of inertia of the composite cross-section. Several examples are provided to demonstrate calculating moments of inertia for composite areas using this approach.
Chapter 6: Pure Bending and Bending with Axial ForcesMonark Sutariya
This summary provides the key points about pure bending and bending with axial forces from the document:
1. Pure bending occurs when a beam segment is in equilibrium under bending moments alone, with examples being a cantilever loaded at the end or a beam segment between concentrated forces.
2. For beams with symmetric cross-sections, plane sections remain plane after bending according to the fundamental flexure theory. The elastic flexure formula gives the normal stress as proportional to the bending moment and the distance from the neutral axis.
3. The second moment of area, or moment of inertia, represents the beam's resistance to bending and is used to calculate maximum bending stresses. The elastic section modulus is a ratio of the moment
The document discusses bending and extension of beams. It defines stress resultants as the internal forces and moments acting on a beam cross section due to external loads. The stress resultants are defined as axial force P, shear forces Vy and Vz, and bending moments My and Mz. Linear differential equations are written relating the variation of stress resultants along the beam length to the applied loads. Stresses in the beam due to extension and bending are derived using Bernoulli-Euler beam theory assumptions. Methods to determine modulus weighted section properties of heterogeneous beams are also presented.
This chapter discusses stress and strain in materials subjected to tension or compression. It defines stress as the load applied over the cross-sectional area. Strain is defined as the change in length over the original length. Hooke's law states that stress is proportional to strain for elastic materials. Young's modulus is the constant of proportionality between stress and strain. The chapter also discusses stress and strain calculations for materials with non-uniform cross-sections, as well as examples of stress and strain problems.
This document presents a method for calculating the energy release rate (ERR) in Mode I delamination of angle ply laminated composites using a double cantilever beam (DCB) test specimen. The compliance equation is used to calculate the ERR based on a second order shear deformation beam theory (SSTDBT) model of the DCB specimen. Numerical examples show good agreement between the ERR calculated from the compliance equation and those obtained using J-integral calculations for glass/polyester DCB specimens with [±30°]5 and [±45°]5 layups.
This document presents the development of a state space equation approach to obtain the three-dimensional solution for thick orthotropic plates with symmetric clamped-free edges. The state space method allows for an exact solution that satisfies all equations of elasticity and accounts for all elastic constants. The system matrix, which is a key part of the state space solution, is derived for symmetric clamped-free boundary conditions. Modal expansions are used to develop sixth-order differential equations governing the transverse displacement, whose solutions provide the stresses and displacements across the plate thickness.
This document discusses centroids and centers of mass. It defines the centroid of a set of points as the point where the sum of first moments is equal to zero. The position vector of the centroid is given by the weighted average of the position vectors of the individual points. Similarly, the center of mass of a system of particles is the weighted average of their position vectors, where the weights are the particle masses. Methods for finding the centroid of curves, surfaces, solids and continuous bodies are presented using integrals. The first moment of an area is introduced and related to the area centroid. Properties of centroids and centers of mass, such as their dependence on reference frames and behavior under decomposition, are covered.
- The document discusses stress analysis of composite beams made of two materials like concrete and steel.
- It explains the concept of transforming the cross-section of the composite beam into an equivalent cross-section of one material using the modular ratio.
- The maximum stresses in each material can then be calculated from the transformed section and adjusted using the modular ratio to get the true stresses.
This document contains a multiple choice test with 27 questions related to physics concepts like forces, energy, momentum, collisions, and circular motion. The test includes questions that provide diagrams and ask students to choose the correct answer based on analyzing the physical situation described. It also includes some matching and true/false questions related to various physics terms and concepts.
1) Fracture mechanics is the study of crack propagation in materials under stress. It considers failure as cracks growing through a structure rather than simultaneous failure.
2) Linear elastic fracture mechanics describes crack growth in elastic materials, while elastic-plastic fracture mechanics describes ductile crack growth in metals.
3) Fracture mechanics models failure using energy and strength criteria, considering the energy required to form new crack surface area.
This document summarizes the mechanical properties of materials through stress-strain diagrams. It discusses the differences between stress-strain diagrams for ductile versus brittle materials. For ductile materials, the diagram shows elastic behavior, yielding, strain hardening, necking, and true stress-strain. Brittle materials exhibit no yielding and rupture occurs at a much smaller strain. The document also discusses Hooke's law, Poisson's ratio, axial loading of materials, and provides examples of calculating deformation based on applied loads and material properties.
This document contains a multiple choice quiz on concepts related to stress and strain in materials. There are 40 questions covering topics like:
- The relationships between elastic modulus, shear modulus, and Poisson's ratio for materials
- Calculating stresses and strains in loaded structures
- Principal stresses and maximum shear stress
- Mohr's circle representation of stresses
- Elastic properties like modulus of elasticity, modulus of resilience
- Stresses in loaded bars, beams, and other basic structural elements
The questions require applying stress/strain and material property equations to calculate values or identify correct statements regarding stresses and deformations in loaded materials and structures.
This document provides an overview of moment of inertia. It defines moment of inertia as the product of mass and the square of a distance, and discusses its units. The document then covers theorems of parallel and perpendicular axes, formulas for moment of inertia of common shapes, torque, angular acceleration, angular momentum, angular impulse, work done by a torque, and angular kinetic energy. Specific objectives are provided to define key terms and explain concepts related to moment of inertia.
Learning Geometric Algebra by Modeling Motions of the Earth and Shadows of Gn...James Smith
Because the shortage of worked-out examples at introductory levels is an obstacle to widespread adoption of Geometric Algebra (GA), we use GA to calculate Solar azimuths and altitudes as a function of time via the heliocentric model. We begin by representing the Earth's motions in GA terms. Our representation incorporates an estimate of the time at which the Earth would have reached perihelion in 2017 if not affected by the Moon's gravity. Using the geometry of the December 2016 solstice as a starting point, we then employ GA's capacities for handling rotations to determine the orientation of a gnomon at any given latitude and longitude during the period between the December solstices of 2016 and 2017. Subsequently, we derive equations for two angles: that between the Sun's rays and the gnomon's shaft, and that between the gnomon's shadow and the direction ``north" as traced on the ground at the gnomon's location. To validate our equations, we convert those angles to Solar azimuths and altitudes for comparison with simulations made by the program Stellarium. As further validation, we analyze our equations algebraically to predict (for example) the precise timings and locations of sunrises, sunsets, and Solar zeniths on the solstices and equinoxes. We emphasize that the accuracy of the results is only to be expected, given the high accuracy of the heliocentric model itself, and that the relevance of this work is the efficiency with which that model can be implemented via GA for teaching at the introductory level. On that point, comments and debate are encouraged and welcome.
1. The document contains a physics exam paper with multiple choice and numerical questions covering topics like work, power, energy, center of mass, collisions, kinematics, and Newton's laws of motion.
2. Sample questions include calculating the maximum value of mass m in an equilibrium system, finding the average velocity at different points for a particle with uniform acceleration, and determining the ratio of centripetal to normal force for a particle in a hemispherical bowl.
3. The document also provides the key/solutions to the exam questions. Sample solutions show calculating average velocities, using conservation of mechanical energy to relate potential and kinetic energy, and deriving an expression for the ratio of centripetal to normal force.
Chapter 1: Stress, Axial Loads and Safety ConceptsMonark Sutariya
This document provides an overview of stress, axial loads, and safety concepts in mechanics of solids. It discusses general concepts of stress including stress tensors and transformations. It also examines stresses in axially loaded bars, including normal and shear stresses. Finally, it covers deterministic and probabilistic design bases, discussing factors of safety, experimental data distributions, and theoretical probabilistic approaches to structural design and failure.
Kriging is a spatial prediction method that provides the "best linear unbiased estimator" (BLUE). It determines weights for a weighted linear combination of sample points that minimizes the prediction error variance. Ordinary kriging focuses on minimizing this error variance based on a variogram model that describes the spatial correlation between sample points. The kriging system is solved to determine the weights, and the predicted values and kriging variance can then be estimated at desired locations.
This document discusses the importance of quality in global business. It notes that quality helps firms increase sales and reduce costs in two key ways: through improved sales via factors like reputation, and reduced costs through increased productivity and lower rework costs. The document then outlines several tools for total quality management (TQM), including flowcharts, check sheets, scatter diagrams, cause-and-effect diagrams, and statistical process control charts. It emphasizes that quality is crucial for a firm's success through maintaining customer loyalty, a strong brand reputation, and the ability to attract and retain good staff.
This thesis proposal examines the opportunities, threats, problems and risks faced by Indian companies managing international operations and global projects. It will focus on institutional differences encountered in areas like regulations, norms and culture that can lead to project delays and cost overruns. The research will involve case studies of engineering and manufacturing companies working in countries like China and Australia. It will evaluate global project stakeholder management and how institutional knowledge of a country's regulatory, normative and cultural frameworks can help Indian firms better manage projects. The findings will help international project developers and manufacturing companies starting global operations to reduce impacts of institutional challenges.
This document discusses calculating the moment of inertia for composite cross-sections made up of multiple simple geometric shapes. It introduces the parallel axis theorem, which allows calculating the moment of inertia of each individual shape about a common reference axis so that the individual values can be added to determine the total moment of inertia of the composite cross-section. Several examples are provided to demonstrate calculating moments of inertia for composite areas using this approach.
Chapter 6: Pure Bending and Bending with Axial ForcesMonark Sutariya
This summary provides the key points about pure bending and bending with axial forces from the document:
1. Pure bending occurs when a beam segment is in equilibrium under bending moments alone, with examples being a cantilever loaded at the end or a beam segment between concentrated forces.
2. For beams with symmetric cross-sections, plane sections remain plane after bending according to the fundamental flexure theory. The elastic flexure formula gives the normal stress as proportional to the bending moment and the distance from the neutral axis.
3. The second moment of area, or moment of inertia, represents the beam's resistance to bending and is used to calculate maximum bending stresses. The elastic section modulus is a ratio of the moment
The document discusses bending and extension of beams. It defines stress resultants as the internal forces and moments acting on a beam cross section due to external loads. The stress resultants are defined as axial force P, shear forces Vy and Vz, and bending moments My and Mz. Linear differential equations are written relating the variation of stress resultants along the beam length to the applied loads. Stresses in the beam due to extension and bending are derived using Bernoulli-Euler beam theory assumptions. Methods to determine modulus weighted section properties of heterogeneous beams are also presented.
This chapter discusses stress and strain in materials subjected to tension or compression. It defines stress as the load applied over the cross-sectional area. Strain is defined as the change in length over the original length. Hooke's law states that stress is proportional to strain for elastic materials. Young's modulus is the constant of proportionality between stress and strain. The chapter also discusses stress and strain calculations for materials with non-uniform cross-sections, as well as examples of stress and strain problems.
This document presents a method for calculating the energy release rate (ERR) in Mode I delamination of angle ply laminated composites using a double cantilever beam (DCB) test specimen. The compliance equation is used to calculate the ERR based on a second order shear deformation beam theory (SSTDBT) model of the DCB specimen. Numerical examples show good agreement between the ERR calculated from the compliance equation and those obtained using J-integral calculations for glass/polyester DCB specimens with [±30°]5 and [±45°]5 layups.
This document presents the development of a state space equation approach to obtain the three-dimensional solution for thick orthotropic plates with symmetric clamped-free edges. The state space method allows for an exact solution that satisfies all equations of elasticity and accounts for all elastic constants. The system matrix, which is a key part of the state space solution, is derived for symmetric clamped-free boundary conditions. Modal expansions are used to develop sixth-order differential equations governing the transverse displacement, whose solutions provide the stresses and displacements across the plate thickness.
This document discusses centroids and centers of mass. It defines the centroid of a set of points as the point where the sum of first moments is equal to zero. The position vector of the centroid is given by the weighted average of the position vectors of the individual points. Similarly, the center of mass of a system of particles is the weighted average of their position vectors, where the weights are the particle masses. Methods for finding the centroid of curves, surfaces, solids and continuous bodies are presented using integrals. The first moment of an area is introduced and related to the area centroid. Properties of centroids and centers of mass, such as their dependence on reference frames and behavior under decomposition, are covered.
- The document discusses stress analysis of composite beams made of two materials like concrete and steel.
- It explains the concept of transforming the cross-section of the composite beam into an equivalent cross-section of one material using the modular ratio.
- The maximum stresses in each material can then be calculated from the transformed section and adjusted using the modular ratio to get the true stresses.
This document contains a multiple choice test with 27 questions related to physics concepts like forces, energy, momentum, collisions, and circular motion. The test includes questions that provide diagrams and ask students to choose the correct answer based on analyzing the physical situation described. It also includes some matching and true/false questions related to various physics terms and concepts.
1) Fracture mechanics is the study of crack propagation in materials under stress. It considers failure as cracks growing through a structure rather than simultaneous failure.
2) Linear elastic fracture mechanics describes crack growth in elastic materials, while elastic-plastic fracture mechanics describes ductile crack growth in metals.
3) Fracture mechanics models failure using energy and strength criteria, considering the energy required to form new crack surface area.
This document summarizes the mechanical properties of materials through stress-strain diagrams. It discusses the differences between stress-strain diagrams for ductile versus brittle materials. For ductile materials, the diagram shows elastic behavior, yielding, strain hardening, necking, and true stress-strain. Brittle materials exhibit no yielding and rupture occurs at a much smaller strain. The document also discusses Hooke's law, Poisson's ratio, axial loading of materials, and provides examples of calculating deformation based on applied loads and material properties.
This document contains a multiple choice quiz on concepts related to stress and strain in materials. There are 40 questions covering topics like:
- The relationships between elastic modulus, shear modulus, and Poisson's ratio for materials
- Calculating stresses and strains in loaded structures
- Principal stresses and maximum shear stress
- Mohr's circle representation of stresses
- Elastic properties like modulus of elasticity, modulus of resilience
- Stresses in loaded bars, beams, and other basic structural elements
The questions require applying stress/strain and material property equations to calculate values or identify correct statements regarding stresses and deformations in loaded materials and structures.
This document provides an overview of moment of inertia. It defines moment of inertia as the product of mass and the square of a distance, and discusses its units. The document then covers theorems of parallel and perpendicular axes, formulas for moment of inertia of common shapes, torque, angular acceleration, angular momentum, angular impulse, work done by a torque, and angular kinetic energy. Specific objectives are provided to define key terms and explain concepts related to moment of inertia.
Learning Geometric Algebra by Modeling Motions of the Earth and Shadows of Gn...James Smith
Because the shortage of worked-out examples at introductory levels is an obstacle to widespread adoption of Geometric Algebra (GA), we use GA to calculate Solar azimuths and altitudes as a function of time via the heliocentric model. We begin by representing the Earth's motions in GA terms. Our representation incorporates an estimate of the time at which the Earth would have reached perihelion in 2017 if not affected by the Moon's gravity. Using the geometry of the December 2016 solstice as a starting point, we then employ GA's capacities for handling rotations to determine the orientation of a gnomon at any given latitude and longitude during the period between the December solstices of 2016 and 2017. Subsequently, we derive equations for two angles: that between the Sun's rays and the gnomon's shaft, and that between the gnomon's shadow and the direction ``north" as traced on the ground at the gnomon's location. To validate our equations, we convert those angles to Solar azimuths and altitudes for comparison with simulations made by the program Stellarium. As further validation, we analyze our equations algebraically to predict (for example) the precise timings and locations of sunrises, sunsets, and Solar zeniths on the solstices and equinoxes. We emphasize that the accuracy of the results is only to be expected, given the high accuracy of the heliocentric model itself, and that the relevance of this work is the efficiency with which that model can be implemented via GA for teaching at the introductory level. On that point, comments and debate are encouraged and welcome.
1. The document contains a physics exam paper with multiple choice and numerical questions covering topics like work, power, energy, center of mass, collisions, kinematics, and Newton's laws of motion.
2. Sample questions include calculating the maximum value of mass m in an equilibrium system, finding the average velocity at different points for a particle with uniform acceleration, and determining the ratio of centripetal to normal force for a particle in a hemispherical bowl.
3. The document also provides the key/solutions to the exam questions. Sample solutions show calculating average velocities, using conservation of mechanical energy to relate potential and kinetic energy, and deriving an expression for the ratio of centripetal to normal force.
Chapter 1: Stress, Axial Loads and Safety ConceptsMonark Sutariya
This document provides an overview of stress, axial loads, and safety concepts in mechanics of solids. It discusses general concepts of stress including stress tensors and transformations. It also examines stresses in axially loaded bars, including normal and shear stresses. Finally, it covers deterministic and probabilistic design bases, discussing factors of safety, experimental data distributions, and theoretical probabilistic approaches to structural design and failure.
Kriging is a spatial prediction method that provides the "best linear unbiased estimator" (BLUE). It determines weights for a weighted linear combination of sample points that minimizes the prediction error variance. Ordinary kriging focuses on minimizing this error variance based on a variogram model that describes the spatial correlation between sample points. The kriging system is solved to determine the weights, and the predicted values and kriging variance can then be estimated at desired locations.
This document discusses the importance of quality in global business. It notes that quality helps firms increase sales and reduce costs in two key ways: through improved sales via factors like reputation, and reduced costs through increased productivity and lower rework costs. The document then outlines several tools for total quality management (TQM), including flowcharts, check sheets, scatter diagrams, cause-and-effect diagrams, and statistical process control charts. It emphasizes that quality is crucial for a firm's success through maintaining customer loyalty, a strong brand reputation, and the ability to attract and retain good staff.
This thesis proposal examines the opportunities, threats, problems and risks faced by Indian companies managing international operations and global projects. It will focus on institutional differences encountered in areas like regulations, norms and culture that can lead to project delays and cost overruns. The research will involve case studies of engineering and manufacturing companies working in countries like China and Australia. It will evaluate global project stakeholder management and how institutional knowledge of a country's regulatory, normative and cultural frameworks can help Indian firms better manage projects. The findings will help international project developers and manufacturing companies starting global operations to reduce impacts of institutional challenges.
The document provides information on the board of directors of Hindustan Petroleum Corporation Limited. It lists the Chairman and Managing Director, Mr. M.K. Surana, and provides details about his background and experience. It also lists and provides details on the Functional Directors, including Mr. P K Joshi, Director- Human Resources, Mr. B. K Namdeo, Director - Refineries, and Mr. Y K Gawali, Director - Marketing. Finally, it briefly introduces some other board members, including Mr. Ramaswamy, Director –Finance, Ms.Urvashi Sadhwani, and Shri.Ram Niwas Jain.
This document summarizes a summer internship report on the business impact of standard operating procedures (SOPs) in retail outlet operations for urban and highway dealers. The intern conducted research at Hindustan Petroleum Corporation Limited outlets in Noida, Meerut, and Muzaffarnagar. The objectives were to understand the impact of SOPs, compare SOP-enabled and non-enabled outlets, and inspect SOP adherence. Key findings included the percentage of SOP-enabled outlets in each city and maintenance levels for five SOP components. The intern concluded SOPs increase sales, productivity, and store image, meeting customer demand better. Recommendations to improve SOP implementation were provided.
This document provides an overview of key facts about South Korea, including its history, culture, economy, and technology adoption. It discusses historical periods like the Three Kingdoms period and Japanese colonial rule. It also outlines demographic characteristics, noting South Korea's highly educated and technologically connected population. The economy is characterized as innovative with major companies like Samsung and a focus on exports. Internet and mobile technology have been widely adopted. The document analyzes South Korea's culture, including traditions like Hanbok dresses and the importance of family and education. It also summarizes business etiquette and opportunities/threats around marketing to seniors.
Tata Steel is an Indian steel company and subsidiary of Tata Group. It has manufacturing operations in 26 countries and employs around 80,500 people. Some key points:
- Tata Steel was established in 1907 and is headquartered in Mumbai, India. It acquired UK steelmaker Corus in 2007 in its largest international acquisition.
- It has an annual crude steel capacity of 25.3 million tonnes and is the 11th largest steel producer globally.
- The company's vision is to be a global benchmark in value creation and corporate citizenship through excellence of people, innovation, and conduct.
- Tata Steel has manufacturing facilities in India, Europe, Southeast Asia and produces a variety of
The document discusses various considerations for extending marketing internationally, including deciding whether to enter global markets, which specific markets to target, and how to enter those markets through options like exporting, licensing, joint ventures, or direct investment. It also covers adapting the marketing mix of product, price, promotion, and place for different cultural and economic environments in international markets.
Tata Steel is one of the largest steel producers in the world with a presence in over 50 countries. It has a crude steel production capacity of 30 million tonnes annually. The company has expanded significantly through acquisitions in recent years including Corus Group, which expanded its operations in Europe. It is focusing on increasing production capacity in India and securing raw materials globally through investments and joint ventures. The global economic slowdown has impacted steel demand and Tata Steel's financial performance. It is taking steps like cost reductions and production rationalization to address challenges in the current market environment.
This document outlines a dissertation proposal on the effectiveness of online advertising on social networking sites. The proposal discusses the purpose of studying this topic, relevant research questions, and objectives. It provides an extensive literature review on previous research regarding advertising on social media and the emergence of major social networking platforms. The proposed research methodology is also summarized, including the sampling approach, data collection methods, and proposed timeline.
Developing Your International Market StrategyStephen Davis
To succeed in global business, companies need to simplify their approach to export operations while unifying their international sales and marketing efforts.
This was a presentation as part of a panel where we disccused: strategy considerations before your first actions; how to approach the daunting task of positioning your business for international sales, marketing and distribution; how brand positioning and direct communications can have a multiplier effect on your success; and how to integrate cultural, language and marketing considerations so they are synergistic with your business strategy and execution plans.
International marketing refers to marketing activities that cross national borders. It involves identifying foreign markets, selecting market entry strategies, and developing marketing mixes tailored to compete abroad. The main approaches are exporting, joint ventures, and foreign direct investment like assembly or manufacturing plants. Effective international marketing requires understanding differences in cultures, laws, and economies between countries while maintaining a consistent global brand. It presents new opportunities but also challenges of adapting to varied international consumer behaviors and business environments.
This document is a dissertation report submitted by Ranjan Kumar to Acharya Institute of Management and Sciences in partial fulfillment of the requirements for a Master of Business Administration degree. The report studies customer satisfaction at Reliance Fresh retail outlets in Bangalore, India. It includes declarations by Ranjan Kumar and his advisor Prof. K. Ranganathan, as well as certificates of approval. Ranjan Kumar acknowledges and thanks those who supported the completion of his dissertation report.
The document is a project report on the marketing strategies of Coca Cola. It discusses Coca Cola's history in India, including withdrawing from the country in 1977 due to government demands and then returning in 1993 to a changed soft drink market dominated by competitors like Parle. To gain market share, Coca Cola decided to take over Parle, gaining access to their network of over 200,000 retailer outlets and 60 bottlers. The marketing strategies Coca Cola employed in the 1990s to win the "Cola war" in India were successful, increasing their market share to 48.3% by 1998.
The document provides an overview of value analysis and value engineering. It defines value analysis as identifying unnecessary costs to increase profitability. The value of a product is determined by its function relative to cost. The value analysis method involves defining the basic function of a product abstractly to allow for alternative ideas. It then describes the 8-step value analysis process including questioning techniques, creativity phases, analysis, development, presentation, implementation, and verification.
R05010302 E N G I N E E R I N G M E C H A N I C Sguestd436758
This document appears to be an exam paper for the subject of Engineering Mechanics. It contains 8 multi-part questions covering various topics in mechanics, including reactions at supports, forces on inclined planes, belt drives, moments of inertia, projectile motion, and vibrations. Students have to answer any 5 of the 8 questions in the 3 hour exam, which has a maximum score of 80 marks. The questions involve calculating values, deriving equations, distinguishing between concepts, and determining properties of mechanical systems and components.
The document is a set of problems from a Classical Mechanics exam for an engineering program. It contains 8 multi-part problems related to topics in classical mechanics, such as forces, centroids, moments of inertia, and oscillations. The problems include calculating results for systems of forces, nding properties of geometric shapes, determining member forces in trusses and frames, and analyzing linear and rotational motion. Diagrams supplement some of the problems to illustrate the systems under consideration.
R05010203 E L E C T R I C A L C I R C U I T Sguestd436758
This document contains an examination for an Electrical Circuits course. It consists of 8 questions covering various topics in electrical circuits, including ideal and practical sources, active and passive elements, network analysis techniques like source transformations, and three-phase systems. Students are required to answer any 5 of the 8 questions in the allotted 3 hours.
C L A S S I C A L M E C H A N I C S J N T U M O D E L P A P E R{Wwwguest3f9c6b
This document contains two sets of questions for a Classical Mechanics exam for engineering students. Set 1 contains 8 questions related to topics like forces, moments of inertia, centroids, and kinematics. Set 2 contains similar questions, involving calculating forces in trusses, centroids, moments of inertia, overtaking problems, and spring/mass systems. The questions involve applying concepts of classical mechanics to solve physics problems regarding structures, forces, motion, springs, and vibrations.
R05010401 N E T W O R K A N A L Y S I Sguestd436758
This document appears to be an exam for a network analysis course, as it contains multiple choice and numerical problems related to electrical networks. It begins by providing the course information and instructions for the exam, which allows students to answer any 5 of 8 questions. The questions cover various network analysis topics, including waveforms in RLC circuits, network matrices, resonance, network theorems, and filter design. Solutions are not provided. The document provides circuit diagrams and equations to accompany the analysis problems.
This model question paper contains questions from 5 modules on Calculus and Linear Algebra. The questions are of varying marks ranging from 4 to 8 marks each. They test a variety of concepts like derivatives, integrals, limits, Taylor series, maxima and minima of functions, matrices and determinants. Students are required to answer any 5 full questions with at least 1 question from each module. The questions can be solved using concepts of differentiation, integration, Taylor's series, maxima and minima, matrices and determinants.
The document is a past exam paper for a course on antennas and wave propagation. It contains 8 questions related to topics like directivity, power gain, radiation resistance, beamwidth, array patterns, propagation mechanisms, and more. Students were required to answer any 5 of the 8 questions in the 3 hour exam. The questions involve both theoretical derivations and calculations.
Kinematics Of Machinery Jntu Model Paper{Www.Studentyogi.Com}guest3f9c6b
The document contains information about an exam for a course on Kinematics of Machinery. It lists 8 questions that students could answer, all worth equal marks. The questions cover various topics in kinematics including mechanisms that generate straight-line motion, velocity and acceleration analysis of linkages, gear trains, cam profiles, steering mechanisms, and transmission of motion through belts and pulleys. Diagrams are provided to illustrate some of the mechanisms discussed in the questions. The exam is worth a total of 80 marks and students must answer any 5 questions.
This document provides an overview of friction and circular motion topics. It discusses frictional force, types of friction, angle of friction, minimum friction angle, and direction of friction. It also covers circular motion topics like centripetal acceleration, kinematics of circular motion including angular velocity and centripetal force, dynamics of circular motion. Non-uniform circular motion, banking of roads, vehicles taking turns, and vertical circular motion are also summarized. Sample problems related to these topics are included for practice. The document promotes Unacademy subscription plans for access to live classes, study material and tests for JEE preparation.
12302 Basic Electrical And Electronics Engineeringguestac67362
This document contains information about an exam for a Basic Electrical and Electronics Engineering course for Bio-Technology students. It provides 8 questions that students can answer, each with multiple parts. The questions cover topics like RMS values, DC machines, semiconductor physics, rectifiers, transistors, amplifiers, oscillators, and binary conversions. Students must answer 5 of the 8 questions and have 3 hours to complete the exam, which is out of a maximum of 80 marks.
12302 Basic Electrical And Electronics Engineeringguestd436758
This document contains questions from an exam on basic electrical and electronics engineering. It is divided into 8 sections, each containing 2-3 questions on topics like:
- Calculating RMS values, current, resistance and power in DC circuits
- Components, principles and comparisons of DC motors and transformers
- Operation of PN junction diodes and their dynamic resistance
- Half wave and full wave rectifiers including calculations of output values
- Input/output characteristics and operating points of transistor circuits
- Classifications and workings of amplifiers including push-pull configurations
- Applications and effects of operational amplifiers
- Boolean logic expressions and implementations using gates
The document describes an experiment to determine the Young's modulus of brass, bronze, and titanium beams using deflection analysis. Beams made of each material were loaded with incremental masses in a simulator, and the deflection was measured. Deflection vs. force graphs were plotted, and linear regression was used to calculate the Young's modulus for each material. The calculated values were compared to literature values to determine percent error. Titanium had the lowest percent error of 1.90% while brass and bronze experiments were also described.
R05010204 E L E C T R O N I C D E V I C E S A N D C I R C U I T Sguestd436758
This document contains an exam for an electronics course, with 8 questions covering various topics:
1. Deriving expressions for electron trajectory in a magnetic field and CRT deflection sensitivity.
2. Explaining pn-junction energy band diagrams and calculating diode current from voltage.
3. Comparing filter circuits, determining ripple factor for an L-type filter.
4. Analyzing a transistor switching circuit and explaining MOSFET structure.
5. Discussing thermal runaway and resistance, calculating voltages in a circuit.
6. Deriving relations for current/voltage gain and input resistance for a CE amplifier.
7. Explaining feedback factors and calculating gains for a
R05010501 B A S I C E L E C T R I C A L E N G I N E E R I N Gguestd436758
The document is a study guide for an exam on basic electrical engineering. It contains 8 questions related to topics like Ampere's law, Faraday's law of induction, capacitors, magnetic circuits, alternating current, transformers, DC generators, induction motors, and electrical instruments. Students are instructed to answer any 5 of the 8 questions in the 3 hour exam.
This document provides instructions for using the conjugate beam method to solve for slope angles and deflections at various points along 6 beams. For each beam, students are asked to determine vertical deflections and rotations at specific points, as well as draw the elastic curve of the beam. The beams vary in their dimensions, loads, and points of interest along the length.
- This document contains an exam for Engineering Mechanics from Jawaharlal Nehru Technological University.
- It consists of 8 multiple choice questions covering topics like forces, moments, centroids, area moments of inertia, and virtual work.
- Detailed figures and calculations are provided for parts of questions involving determination of forces, reactions, distances, and other mechanical properties.
The document discusses various methods for analyzing beam deflection and deformation under loading, including:
1) Deriving the differential equation for the elastic curve of a beam and applying boundary conditions to determine the curve and maximum deflection.
2) Using the method of superposition to analyze beams subjected to multiple loadings by combining the effects of individual loads.
3) Applying moment-area theorems which relate the bending moment diagram to slope and deflection, allowing deflection calculations for beams with various support conditions.
This document discusses kinematics concepts related to linkages and mechanisms. It includes the following:
1) Definitions for kinematic chain, machine, structure, self closed pair, and force closed pair.
2) Explanations and sketches of the Whitworth quick return mechanism, ratchet and pawl mechanism, and toggle mechanism.
3) Calculation of angular velocities and accelerations for a four bar linkage given link lengths and angular velocity of one link.
The document discusses influence lines, which graphically depict the variation of structural quantities (bending moment, shear force, etc.) due to a moving unit load. It provides examples of drawing influence line diagrams for bending moment and shear force at specific points on simply supported beams. The maximum value of a structural quantity occurs when the moving load is located at the point of maximum ordinate on the influence line diagram. Uniformly distributed loads produce the greatest effect when placed over regions where the ordinates have the same sign.
1. Newton's law of universal gravitation relates the gravitational force between two masses to the masses and the distance between them. The proportionality constant G has SI units of m3/kg∙s2.
2. The passage provides definitions, conversions, and calculations regarding speed, distance, displacement, time, velocity, acceleration, forces, and other physics concepts. Problems involve vectors, forces, work, energy, and motion.
3. Chapter excerpts are provided from physics textbooks involving technical measurement, forces, equilibrium, torque, rotational motion, uniform acceleration, projectile motion, work, energy, and power. Multiple problems follow each section requiring calculations, graphing, and applying physics principles.
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R05010105 A P P L I E D M E C H A N I C S
1. www.studentyogi.com www.studentyogi.com
Code No: R05010105
Set No. 1
I B.Tech Supplimentary Examinations, Aug/Sep 2008
APPLIED MECHANICS
(Civil Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Calculate the magnitude of the force supported by the pin at B for the bell crank
loaded and supported as shown in Figure 1. [16]
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i.c
Figure 1
g
2. (a) Explain the types of friction with examples.
(b) Two equal bodies A and B of weight ‘W’ each are placed on a rough inclined
omyo
plane. The bodies are connected by a light string. If A = 1/2 and B = 1/3,
show that the bodies will be both on the point of motion when the plane is
inclined at tan-1 (5/12). [6+10]
t
3. (a) Distinguish between open and crossed belt drives.
i.cen
(b) A belt weighing 1000 3 has a maximum permissible stress of 2 5 2
Determine the maximum power that can be transmitted by a belt of 200 ×
12 if the ratio of the tight side to slack side tension is 2. [6+10]
otgud
4. (a) Di erentiate between ‘polar moment of inertia’ and ‘product of inertia’
(b) Find the moment of inertia and radius of gyration about the horizontal cen-
troidal axis. shown in Figure 4b. [6+10]
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Code No: R05010105
Set No. 1
Figure 4b
5. A rectangular parallelopiped has the following dimensions.
Length along x-axis = ‘ ’
Height along y-axis = ‘a’
om
Breadth along z-axis = ‘b’
Density of the material is ‘w’
Determine the mass moment of inertia of the parallelopiped about the centroidal
axes.
[16]
6. Cycle is travelling along a straight road with a velocity of 10m/s. Determine the
i.c
velocity of point A on the front wheel as shown in gure6 Radius of cycle wheel =
0.4m and distance of A from C=0.2m. [16]
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Figure 6
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7. (a) A homogeneous sphere of radius of a=100 mm and weight W=100 N can
rotate freely about a diameter. If it starts from rest and gains, with constant
angular acceleration, an angular speed n=180rpm, in 12 revolutions, nd the
acting moment. .
u
(b) A block starts from rest from‘A’. If the co e cient of friction between all sur-
.st
faces of contact is 0.3, nd the distance at which the block stop on the hori-
zontal plane. Assume the magnitude of velocity at the end of slope is same as
that at the beginning of the horizontal plane.
As shown in the Figure7b [8+8]
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Code No: R05010105
Set No. 1
Figure 7b
8. (a) A homogeneous circular disk of radius ‘r’ and weight ‘W’ hangs in a vertical
plane from a pin ‘O’ at its circumference. Find the period for small angles
of swing in the plane of the disk
om
(b) A slender wire 0.90 m long is bent in the form of a equilateral triangle and
hangs from a pin at ‘O’ as shown in the gure8b. Determine the period for
small amplitudes of swing in the plane of the gure. [16]
i.c
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Figure 8b
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w .st
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Code No: R05010105
Set No. 2
I B.Tech Supplimentary Examinations, Aug/Sep 2008
APPLIED MECHANICS
(Civil Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) A Prismatic bar AB of weight ‘W’ is resting against a smo oth vertical wall at
‘A’ and is supported on a small roller at the point ‘D’. If a vertical force F
is applied at the end ‘B’, Find the position of equilibrium as de ned by the
angle ‘ ’.{As shown in the Figure1a}.
om
i.c
ogFigure 1a
(b) Two rollers of weights P and Q are connected by a exible string DE and rest
on two mutually perpendicular planes AB and BC, as shown in gure 1b. Find
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the tension (‘T’) in the string and the ‘ ’ that it makes with the horizontal
when the system is in equilibrium. The following numerical data are given.
P= 270 N, Q = 450 N, = 300. Assume that the string is inextensible and
passes freely through slots in the smo oth inclined planes AB and BC. [6+10]
u de
w .st
Figure 1b
2. (a) Explain the principles of operation of a screw jack with a neat sketch.
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Code No: R05010105
Set No. 2
(b) Outside diameter of a square threaded spindle of a screw Jack is 40 mm. The
screw pitch is 10 mm. If the coe cient of friction between the screw and the
nut is 0.15, neglecting friction between the nut and collar, determine
i. Force required to be applied at the screw to raise a load of 2000N
ii. The e ciency of screw jack
iii. Force required to be applied at pitch radius to lower the same load of 2000
N and
iv. E ciency while lowering the load
v. What should be the pitch for the maximum e ciency of the screw? and
vi. What should be the value of the maximum e ciency? [6+10]
3. (a) Obtain the conditions for the maximum power transmitted by a belt from one
pulley to another.
(b) A shaft running at 100 r.p.m drives another shaft at 200 r.p.m and transmits
om
12 kW. The belt is 100 mm wide and 12 mm thick and = 0.25. The distance
between the shafts is 2.5 meters and the diameter of the smaller pulley is 500
mm.
Calculate the stress in
i. An open belt
i.c
ii. A crossed belt, connecting the two pulleys. [6+10]
4. (a) Di erentiate between centroid and center of gravity.
(b) Determine the product of inertia of shaded area as shown in Figure 4b about
the x-y axis.
og [6+10]
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Figure 4b
u
5. Derive the expression for the moment of inertia of a cylinder length ‘ ’, radius ‘r’ and
density ‘w’ about longitudinal centroidal axis and about the centroidal transverse
.st
axis. [16]
6. (a) A train is traveling at a speed of 60 km/hr. It has to slow down due to certain
repair work on the track. Hence, it moves with a constant retardation of 1
w
km/hr/second until its speed is reduced to 15 km/hr. It then travels at a
constant speed of for 0.25 km/hr and accelerates at 0.5 km/hr per second
until its speed once more reaches 60 km/hr. Find the delay caused.
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Code No: R05010105
Set No. 2
(b) The motion of a particle in rectilinear motion is de ned by the relation
= 2 3 - 9 2 + 12 - 10 where s is expressed in metres and t in seconds. Find
i. the acceleration of the particle when the velocity is zero
ii. the position and the total distance traveled when the acceleration is zero.
[8+8]
7. (a) A body weighing 20 N is projected up a 200 inclined plane with a velocity of
12 m/s, coe cient of friction is 0.15. Find
i. The maximum distance S, that the body will move up the inclined plane
ii. Velocity of the bo dy when it returns to its original position.
(b) Find the acceleration of the moving loads as shown in gure 7b. Take mass
of P=120 kg and that of Q=80 Kg and co e cient of friction between surfaces
of contact is 0.3. Also nd the tension in the connecting string. [8+8]
om
i.c
Figure 7b
8. In a mechanism, a cross-head moves in straight guide with simple harmonic motion.
At distances of 125 mm and 200 mm from its mean position, it has velo cities of 6
og
m/sec and 3 m/sec respectively. Find the amplitude, maximum velo city and perio d
of vibration. If the cross-head weighs 2N, calculate the maximum force on it in the
direction of motion. [16]
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w .st
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Code No: R05010105
Set No. 3
I B.Tech Supplimentary Examinations, Aug/Sep 2008
APPLIED MECHANICS
(Civil Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) A ball of weight ‘W’ rests upon a smo oth horizontal plane and has attached
to its center two strings AB and AC which pass over frictionless pulleys at B
and C and carry loads P and Q, respectively, as shown in Figure1a. If the
string AB is horizontal, nd the angle that the string AC makes with the
horizontal when the ball is in a position of equilibrium. Also nd the pressure
R between the ball and the plane.
om
i.c
Figure 1a
(b) Determine the forces S1 and S2 induced in the bars AC and BC in Figure1b.
together at C and to the foundation at A and B.
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due to the action of the horizontal applied load at C. The bars are hinged
[8+8]
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Figure 1b
de
2. (a) Explain the types of friction with examples.
(b) Two equal bodies A and B of weight ‘W’ each are placed on a rough inclined
plane. The bodies are connected by a light string. If A = 1/2 and B = 1/3,
u
show that the bodies will be both on the point of motion when the plane is
inclined at tan-1 (5/12). [6+10]
.st
3. A cross belt drive is to transmit 7.5 KW at 1000 r.p.m of the smaller pulley.
The diameter of the smallest pulley is 250mm and velocity ratio is 2. The centre
distance between the pulley is 1250mm. A at belt of thickness 6 mm and of
w
co e cient friction 0.3 is used over the pulleys. Determine the necessary width of
the belt if the maximum allowable stress in the belt is 1 75 2 and density of
the belt is 1000 3.
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Code No: R05010105
Set No. 3
4. (a) Di erentiate between centroid and center of gravity.
(b) Determine the product of inertia of shaded area as shown in Figure 4b about
the x-y axis. [6+10]
om
Figure 4b
5. (a) De ne mass moment of inertia and explain Transfer formula for mass moment
of inertia.
(b) Derive the expression for the moment of inertia of a homogeneous sphere of
i.c
radius ‘r’ and mass density ‘w’ with reference to its diameter. [8+8]
6. A roller of radius 0.1m rides between two horizontal bars moving in opposite direc-
tions as shown in gure6 Assuming no slip at the points of contact A and B, locate
the instantaneous center ‘I’ of the roller. Also locate the instantaneous center when
both the bars are moving in the same directions. og [16]
nty
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Figure 6
7. (a) A body weighing 20 N is projected up a 200 inclined plane with a velocity of
.st
12 m/s, coe cient of friction is 0.15. Find
i. The maximum distance S, that the body will move up the inclined plane
ii. Velocity of the bo dy when it returns to its original position.
w
(b) Find the acceleration of the moving loads as shown in gure 7b. Take mass
of P=120 kg and that of Q=80 Kg and co e cient of friction between surfaces
of contact is 0.3. Also nd the tension in the connecting string. [8+8]
ww
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Set No. 3
Figure 7b
8. (a) Explain how a simple pendulum di er from a compound pendulum brie y
with the help of di erential mathematical equations.
(b) Determine the sti ness in N/cm of a vertical spring to which a weight of
50 N is attached and is set vibrating vertically. The weight makes 4 oscillations
per second. [8+8]
om
i.c
og
nty
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w .st
ww
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Set No. 4
I B.Tech Supplimentary Examinations, Aug/Sep 2008
APPLIED MECHANICS
(Civil Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) State and prove Lame’s theorem.
(b) A prismatic bar AB of 7m long is hinged at A and supported at B as shown
in Figure 1b. Neglecting friction, determine the reaction Rb produced at B
owing to the weight of the bar. Q = 4000 N, Take = 250. [6+10]
om
i.c
Figure 1b
2. (a) Explain the types of friction with examples.
og
(b) Two equal bodies A and B of weight ‘W’ each are placed on a rough inclined
plane. The bodies are connected by a light string. If A = 1/2 and B = 1/3,
show that the bodies will be both on the point of motion when the plane is
inclined at tan-1 (5/12). [6+10]
nty
3. (a) Deduce an expression for centrifugal tension of belt drive.
(b) The maximum allowed tension in a belt is 1500 N. The angle of lap is 1700
and coe cient of friction between the belt and material of the pulley is 0.27.
Neglecting the e ect of centrifugal tension, calculate the net driving tension
and power transmitted if the belt speed is 2 m/s.
de
[6+10]
4. (a) Find the centroid of the ‘Z’ section shown in Figure 4a.
u
w .st
ww
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Set No. 4
Figure 4a
(b) Find the moment of inertia about the horizontal centroidal axis.shown in Fig-
ure 4b. [6+10]
om
i.c
og
Figure 4b
5. A thin plate of mass ‘m’ is cut in the shape of a parallelogram of thickness ‘t’ as
shown in gure5. Determine the mass moment of inertia of the plate about the
nty
x-axis. [16]
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.st
Figure 5
6. (a) A baloon is ascending with a velocity of 20 m/s above a lake. A stone is
w
dropped to fall from the balloon and the sound of the splash is heard 6 seconds
later. Find the height of the balloon when the stone was dropped. Velocity of
sound is 340 m/s.
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Set No. 4
(b) The acceleration of a particle in rectilinear motion is de ned by the relation
= 25 - 4 2 where ‘a’ is expressed in 2 and ‘s’ is position coordinate
in metres. The particle starts with no initial velocity at the position s = 0.
Determine
i. the velo city when s = 3metres
ii. the position where the velocity is again zero
iii. the position where the velocity is maximum. [8+8]
7. (a) A body weighing 20 N is projected up a 200 inclined plane with a velocity of
12 m/s, coe cient of friction is 0.15. Find
i. The maximum distance S, that the body will move up the inclined plane
ii. Velocity of the bo dy when it returns to its original position.
(b) Find the acceleration of the moving loads as shown in gure 7b. Take mass
of P=120 kg and that of Q=80 Kg and co e cient of friction between surfaces
om
of contact is 0.3. Also nd the tension in the connecting string. [8+8]
i.c
Figure 7b
og
8. A centrifugal pump rotating at 400 rpm is driven by an elastic motor at 1200
rpm through a single stage reduction gearing. The moment of inertia of the pump
impeller at the motor are 1500 kg.m2 and 450 kg.m2 respectively. The lengths of
the pump shaft and the motor shaft are 500 and 200 mm, and their diameters are
nty
100 and 50 mm respectively. Neglecting the inertia of the gears, nd the frequency
of torsional oscillations of the system. G = 85 GN/m2.
[16]
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