This document contains lecture notes on engineering dynamics. It begins with an outline of topics to be covered, including a review of statics concepts and an introduction to dynamics, kinematics, and kinetics. Dynamics is defined as the study of objects in motion as opposed to statics, which is the study of objects at rest. Kinematics deals with the geometry of motion, describing displacement, velocity, and acceleration over time without regard to forces. Kinetics uses Newton's laws of motion to analyze the forces that cause acceleration. Examples are provided to demonstrate applying concepts like Newton's second law to solve for acceleration given mass and net force, and using kinematic equations to solve for position, velocity, and acceleration over time.
This document contains lecture materials on engineering dynamics. It discusses kinematics concepts such as position, velocity, acceleration and their relationships. Rectilinear particle motion is analyzed using graphical and analytical methods. An example problem demonstrates applying kinematics equations to determine the velocity and time taken for a particle to travel between two points under varying acceleration. The document also discusses using graphical methods to analyze erratic or non-uniform particle motion by constructing velocity-time and acceleration-time graphs from a given position-time graph.
Thermodynamics Assignment 02 contains calculations for various cycles of a steam power plant operating between 40 bar and 0.04 bar:
1) Carnot, simple Rankine, and modified Rankine cycles are analyzed. The modified Rankine cycle with superheat has the highest efficiency of 40.86% and lowest SSC of 2.4820 kg/kWh.
2) "Metallurgical limit" refers to the maximum safe pressures and temperatures a power plant's components can withstand without damage.
3) Implementing reheating in the Rankine cycle increases efficiency to 41.05% and lowers SSC to 2.4663 kg/kWh by utilizing the steam's initial high temperature again
lab report structure deflection of cantileverYASMINE HASLAN
1. This experiment examines the deflection of cantilever beams made of aluminum, brass, and steel when subjected to increasing point loads.
2. The experiment measured the actual deflection of each beam for loads from 0-500g and calculated the theoretical deflection based on the beam's material properties.
3. The results showed aluminum had the largest deflection, brass was intermediate, and steel had the smallest deflection, as expected based on their moduli of elasticity. The actual deflection was always greater than the theoretical deflection.
This project report summarizes work done by a student team to apply homework calculations to measurements taken from a 2004 Mitsubishi Galant.
The team measured vehicle specifications, completed three homework problems involving calculations of engine speed, torque, fuel consumption, effective mass, acceleration, and brake performance.
Calculations were shown for static and dynamic load conditions, effects of passengers and a trailer, and comparisons of wheel loads with and without a load-equalizing hitch. Braking forces and times to accelerate to 300 mph in a quarter mile were also estimated.
This experiment examines how shear forces vary with increasing point loads applied to a beam. Theoretical calculations of shear force are compared to experimental measurements. As the applied load increases, both the theoretical and experimental shear forces increase linearly. The experimental shear forces are slightly lower than theoretical values. This shows that the equation used to calculate shear force theoretically accurately predicts the beam's behavior under different loading conditions. The results demonstrate the importance of understanding shear forces in structural engineering design.
The document discusses structural analysis and engineering design of structures. It provides background on structural analysis, including determining effects of loads, stresses, and stability. Structural analysis employs mechanics, materials science, and mathematics. Results are used to verify fitness and safety. The key is designing structures to support loads while meeting economic, aesthetic, and regulatory constraints. Structural systems combine elements and materials. Loads acting on structures must be specified to design them properly according to building codes.
This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.
Liza anna jj309 fluid mechanics (buku kerjalizaannaseri
The document is a student workbook on fluid mechanics. It contains 11 units that cover topics like fluid properties, fluid statics, fluid dynamics, energy loss in pipelines, and nozzles. Example problems are provided throughout to demonstrate concepts like pressure measurements, fluid characteristics, buoyancy, hydraulic systems, and manometers. The objectives are to explain fluid mechanics concepts, solve related problems correctly, and explain their applications in engineering.
This document contains lecture materials on engineering dynamics. It discusses kinematics concepts such as position, velocity, acceleration and their relationships. Rectilinear particle motion is analyzed using graphical and analytical methods. An example problem demonstrates applying kinematics equations to determine the velocity and time taken for a particle to travel between two points under varying acceleration. The document also discusses using graphical methods to analyze erratic or non-uniform particle motion by constructing velocity-time and acceleration-time graphs from a given position-time graph.
Thermodynamics Assignment 02 contains calculations for various cycles of a steam power plant operating between 40 bar and 0.04 bar:
1) Carnot, simple Rankine, and modified Rankine cycles are analyzed. The modified Rankine cycle with superheat has the highest efficiency of 40.86% and lowest SSC of 2.4820 kg/kWh.
2) "Metallurgical limit" refers to the maximum safe pressures and temperatures a power plant's components can withstand without damage.
3) Implementing reheating in the Rankine cycle increases efficiency to 41.05% and lowers SSC to 2.4663 kg/kWh by utilizing the steam's initial high temperature again
lab report structure deflection of cantileverYASMINE HASLAN
1. This experiment examines the deflection of cantilever beams made of aluminum, brass, and steel when subjected to increasing point loads.
2. The experiment measured the actual deflection of each beam for loads from 0-500g and calculated the theoretical deflection based on the beam's material properties.
3. The results showed aluminum had the largest deflection, brass was intermediate, and steel had the smallest deflection, as expected based on their moduli of elasticity. The actual deflection was always greater than the theoretical deflection.
This project report summarizes work done by a student team to apply homework calculations to measurements taken from a 2004 Mitsubishi Galant.
The team measured vehicle specifications, completed three homework problems involving calculations of engine speed, torque, fuel consumption, effective mass, acceleration, and brake performance.
Calculations were shown for static and dynamic load conditions, effects of passengers and a trailer, and comparisons of wheel loads with and without a load-equalizing hitch. Braking forces and times to accelerate to 300 mph in a quarter mile were also estimated.
This experiment examines how shear forces vary with increasing point loads applied to a beam. Theoretical calculations of shear force are compared to experimental measurements. As the applied load increases, both the theoretical and experimental shear forces increase linearly. The experimental shear forces are slightly lower than theoretical values. This shows that the equation used to calculate shear force theoretically accurately predicts the beam's behavior under different loading conditions. The results demonstrate the importance of understanding shear forces in structural engineering design.
The document discusses structural analysis and engineering design of structures. It provides background on structural analysis, including determining effects of loads, stresses, and stability. Structural analysis employs mechanics, materials science, and mathematics. Results are used to verify fitness and safety. The key is designing structures to support loads while meeting economic, aesthetic, and regulatory constraints. Structural systems combine elements and materials. Loads acting on structures must be specified to design them properly according to building codes.
This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.
Liza anna jj309 fluid mechanics (buku kerjalizaannaseri
The document is a student workbook on fluid mechanics. It contains 11 units that cover topics like fluid properties, fluid statics, fluid dynamics, energy loss in pipelines, and nozzles. Example problems are provided throughout to demonstrate concepts like pressure measurements, fluid characteristics, buoyancy, hydraulic systems, and manometers. The objectives are to explain fluid mechanics concepts, solve related problems correctly, and explain their applications in engineering.
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
This document provides a mid-term review covering three topics: 1) energy analysis of closed systems, 2) mass and energy analysis of control volumes, and 3) the second law of thermodynamics. For the first topic, it provides examples of energy balance calculations for constant pressure processes in closed systems. For the second topic, it discusses the energy balance equation for control volumes and provides examples of its application to turbines, compressors, and throttling valves. For the third topic, it defines thermal efficiency and the coefficient of performance and discusses heat engines, refrigerators, and heat pumps.
Fluid tutorial 2_ans dr.waleed. 01004444149 dr walid
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Detailed calculations are shown to determine values like mass, pressure, shear stress, drag force, velocity, and viscosity based on given variables like temperature, volume, pressure, velocity, dimensions, torque, and fluid properties.
In the material testing laboratory, Tensile test was done on a mild steel specimen as figure 4 to identify the young’s modulus, ultimate tensile strength, yield strength and percentage elongation. The results were as table 1
Lateral or transverse vibration of thin beamM. Ahmad
This document summarizes concepts related to continuous systems and the lateral vibration of simply supported thin beams. It discusses free vibration, which occurs without external forces, and forced vibration, which is caused by external forces. It also outlines the Euler-Bernoulli beam theory used to model thin beam vibration and provides the equations of motion. The document solves examples of determining natural frequencies of beams and the steady-state response of a pinned-pinned beam to a harmonic force.
Deflection of simply supported beam and cantileveryashdeep nimje
This document describes experiments to measure the deflection of simply supported beams and cantilever beams under different loading conditions. For simply supported beams, deflection increases linearly with applied load and decreases with beam length. Deflection measurements match theoretical calculations. For cantilever beams, deflection increases linearly with both applied load and distance from the fixed end. The experiments demonstrate linear relationships between load/position and deflection as predicted by theory.
1. The document discusses concepts related to kinetics of particles including work, kinetic energy, and their relationship as described by the principle of work and energy. It provides equations and examples to calculate work, kinetic energy, and velocity using this principle.
2. Sample problems are presented to demonstrate applications of the principle to problems involving forces like gravity, springs, friction, and combinations of forces. The principle is used to determine velocities, distances, and other quantities without directly calculating acceleration.
3. Key concepts covered include work of constant and variable forces, work-energy theorem, power, efficiency, and applications to problems like blocks on an incline, springs, and motion down tracks. Diagrams and step-by-step solutions
This document summarizes a numerical study of airflow over an Ahmed body using RANS turbulence models. It finds that the k-ε-v2 model more accurately predicts separation and reattachment compared to other models. The study simulates flow over an Ahmed body with a 35 degree rear angle using various turbulence models and investigates the effects of grid layout and differencing schemes on the results. Numerical results agree well with experimental data on the wake structure and turbulent kinetic energy distribution behind the body.
This document discusses kinematics of rigid bodies, including:
- Types of rigid body motion such as translation, rotation about a fixed axis, and general plane motion.
- Translation motion is further divided into rectilinear and curvilinear types.
- Key terms related to rotation about a fixed axis like angular position, displacement, velocity, and acceleration.
- Relations between linear and angular velocity and acceleration.
- Two special cases involving rotation of pulleys - a pulley connected to a rotating block, and two coupled pulleys rotating without slip.
- Five sample problems calculating values like angular velocity and acceleration, revolutions, linear velocity and acceleration for rotating bodies.
I. The document describes an engineering laboratory experiment conducted at Universiti Tun Hussein Onn Malaysia to analyze a rectilinear control system and compare the dynamics using springs of different stiffness.
II. The objectives are to analyze the control system through simulation, compare results for different system parameters like spring position and stiffness, and study the effect of adding a damper.
III. Procedures are outlined to collect data on the system using various configurations and calculate values like natural frequency and damping ratio to characterize the system dynamics.
This document provides an overview of planar kinematics of rigid body motion. It describes three types of planar rigid body motion: translation, rotation about a fixed axis, and general plane motion. Translation can be rectilinear or curvilinear. Rotation about a fixed axis involves angular position, velocity, acceleration, and the motion of a point on the rotating body. General plane motion is a combination of translation and rotation. Formulas are provided for analyzing velocity and acceleration during these different types of motion. Examples are also given to demonstrate how to apply the kinematic equations.
1) The document discusses water passing through a pressure-reducing valve and separating tank, including its state and amount that leaves as vapor.
2) It also discusses heat transfer calculations for air heated in an exchanger and flow rate measurement using a venturi meter.
3) Heat transfer principles and equations are reviewed for various processes, including perfect gas behavior, convection coefficients, radiation from a human body, and insensible evaporation heat loss.
Sekularisme dan Kesannya terhadap masyarakat dan negaraSiti Nur Ain
Ringkasan dokumen tersebut adalah:
Sekularisme merupakan fahaman yang memisahkan agama dari kehidupan bernegara. Ia mula muncul di Eropah akibat penindasan gereja terhadap kebebasan berfikir. Fahaman ini kemudiannya menyebar ke negara-negara Islam melalui penjajahan Barat. Sekularisme memberi kesan negatif terhadap masyarakat dan negara Islam dengan melemahkan akidah dan menggalak
This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).
Vibration refers to any motion that repeats itself periodically, such as a pendulum swinging back and forth or a plucked string oscillating. There are several types of vibration including free vibration where a system vibrates on its own after an initial disturbance, forced vibration where an external repeating force causes the vibration, and damped vibration where energy is lost during oscillations. Vibrations can also be classified as longitudinal, transverse, or torsional depending on the direction of motion of the vibrating particles. Proper vibration analysis is important for machine maintenance to identify faults and prevent damage.
The document summarizes key concepts from Chapter 2 of a Physics textbook on kinematics of linear motion. It discusses the following in 3 sentences:
Linear motion can be one-dimensional or two-dimensional projectile motion. Equations of motion include relationships between displacement, velocity, acceleration, and time. Uniformly accelerated motion follows equations that relate the initial and final velocity, acceleration, and time to determine displacement and distance traveled.
This document discusses base excitation in vibration analysis and provides examples. It begins by introducing base excitation as an important class of vibration analysis that involves preventing vibrations from passing through a vibrating base into a structure. Examples of base excitation include vibrations in cars, satellites, and buildings during earthquakes. The document then provides mathematical models and equations to analyze single degree of freedom base excitation systems. Graphs of transmissibility ratios are presented and examples are worked through, such as calculating car vibration amplitude at different speeds. Rotating unbalance is also covered as another source of vibration excitation.
This document provides an overview of pulley systems and example problems involving pulley kinetics. It begins with examples of simple pulley systems and their free body diagrams. Equations relating the accelerations and tensions in pulley systems are developed. Two example problems are then solved in detail. They involve drawing free body diagrams, establishing equations of motion, and relating accelerations based on kinematics. The accelerations of blocks and tension in ropes are calculated for each example problem.
This document outlines a lecture on engineering dynamics that covers:
1) The difference between treating an object as a particle versus a rigid body in dynamics problems.
2) Reviewing Newton's second law and how to relate real-world forces to theoretical free body diagrams.
3) The various forces that must be considered in dynamics problems, including gravity, normal forces, friction, spring stiffness, and damping.
4) How to draw free body diagrams to isolate the forces on individual objects in order to apply Newton's second law.
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
This document provides a mid-term review covering three topics: 1) energy analysis of closed systems, 2) mass and energy analysis of control volumes, and 3) the second law of thermodynamics. For the first topic, it provides examples of energy balance calculations for constant pressure processes in closed systems. For the second topic, it discusses the energy balance equation for control volumes and provides examples of its application to turbines, compressors, and throttling valves. For the third topic, it defines thermal efficiency and the coefficient of performance and discusses heat engines, refrigerators, and heat pumps.
Fluid tutorial 2_ans dr.waleed. 01004444149 dr walid
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Detailed calculations are shown to determine values like mass, pressure, shear stress, drag force, velocity, and viscosity based on given variables like temperature, volume, pressure, velocity, dimensions, torque, and fluid properties.
In the material testing laboratory, Tensile test was done on a mild steel specimen as figure 4 to identify the young’s modulus, ultimate tensile strength, yield strength and percentage elongation. The results were as table 1
Lateral or transverse vibration of thin beamM. Ahmad
This document summarizes concepts related to continuous systems and the lateral vibration of simply supported thin beams. It discusses free vibration, which occurs without external forces, and forced vibration, which is caused by external forces. It also outlines the Euler-Bernoulli beam theory used to model thin beam vibration and provides the equations of motion. The document solves examples of determining natural frequencies of beams and the steady-state response of a pinned-pinned beam to a harmonic force.
Deflection of simply supported beam and cantileveryashdeep nimje
This document describes experiments to measure the deflection of simply supported beams and cantilever beams under different loading conditions. For simply supported beams, deflection increases linearly with applied load and decreases with beam length. Deflection measurements match theoretical calculations. For cantilever beams, deflection increases linearly with both applied load and distance from the fixed end. The experiments demonstrate linear relationships between load/position and deflection as predicted by theory.
1. The document discusses concepts related to kinetics of particles including work, kinetic energy, and their relationship as described by the principle of work and energy. It provides equations and examples to calculate work, kinetic energy, and velocity using this principle.
2. Sample problems are presented to demonstrate applications of the principle to problems involving forces like gravity, springs, friction, and combinations of forces. The principle is used to determine velocities, distances, and other quantities without directly calculating acceleration.
3. Key concepts covered include work of constant and variable forces, work-energy theorem, power, efficiency, and applications to problems like blocks on an incline, springs, and motion down tracks. Diagrams and step-by-step solutions
This document summarizes a numerical study of airflow over an Ahmed body using RANS turbulence models. It finds that the k-ε-v2 model more accurately predicts separation and reattachment compared to other models. The study simulates flow over an Ahmed body with a 35 degree rear angle using various turbulence models and investigates the effects of grid layout and differencing schemes on the results. Numerical results agree well with experimental data on the wake structure and turbulent kinetic energy distribution behind the body.
This document discusses kinematics of rigid bodies, including:
- Types of rigid body motion such as translation, rotation about a fixed axis, and general plane motion.
- Translation motion is further divided into rectilinear and curvilinear types.
- Key terms related to rotation about a fixed axis like angular position, displacement, velocity, and acceleration.
- Relations between linear and angular velocity and acceleration.
- Two special cases involving rotation of pulleys - a pulley connected to a rotating block, and two coupled pulleys rotating without slip.
- Five sample problems calculating values like angular velocity and acceleration, revolutions, linear velocity and acceleration for rotating bodies.
I. The document describes an engineering laboratory experiment conducted at Universiti Tun Hussein Onn Malaysia to analyze a rectilinear control system and compare the dynamics using springs of different stiffness.
II. The objectives are to analyze the control system through simulation, compare results for different system parameters like spring position and stiffness, and study the effect of adding a damper.
III. Procedures are outlined to collect data on the system using various configurations and calculate values like natural frequency and damping ratio to characterize the system dynamics.
This document provides an overview of planar kinematics of rigid body motion. It describes three types of planar rigid body motion: translation, rotation about a fixed axis, and general plane motion. Translation can be rectilinear or curvilinear. Rotation about a fixed axis involves angular position, velocity, acceleration, and the motion of a point on the rotating body. General plane motion is a combination of translation and rotation. Formulas are provided for analyzing velocity and acceleration during these different types of motion. Examples are also given to demonstrate how to apply the kinematic equations.
1) The document discusses water passing through a pressure-reducing valve and separating tank, including its state and amount that leaves as vapor.
2) It also discusses heat transfer calculations for air heated in an exchanger and flow rate measurement using a venturi meter.
3) Heat transfer principles and equations are reviewed for various processes, including perfect gas behavior, convection coefficients, radiation from a human body, and insensible evaporation heat loss.
Sekularisme dan Kesannya terhadap masyarakat dan negaraSiti Nur Ain
Ringkasan dokumen tersebut adalah:
Sekularisme merupakan fahaman yang memisahkan agama dari kehidupan bernegara. Ia mula muncul di Eropah akibat penindasan gereja terhadap kebebasan berfikir. Fahaman ini kemudiannya menyebar ke negara-negara Islam melalui penjajahan Barat. Sekularisme memberi kesan negatif terhadap masyarakat dan negara Islam dengan melemahkan akidah dan menggalak
This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).
Vibration refers to any motion that repeats itself periodically, such as a pendulum swinging back and forth or a plucked string oscillating. There are several types of vibration including free vibration where a system vibrates on its own after an initial disturbance, forced vibration where an external repeating force causes the vibration, and damped vibration where energy is lost during oscillations. Vibrations can also be classified as longitudinal, transverse, or torsional depending on the direction of motion of the vibrating particles. Proper vibration analysis is important for machine maintenance to identify faults and prevent damage.
The document summarizes key concepts from Chapter 2 of a Physics textbook on kinematics of linear motion. It discusses the following in 3 sentences:
Linear motion can be one-dimensional or two-dimensional projectile motion. Equations of motion include relationships between displacement, velocity, acceleration, and time. Uniformly accelerated motion follows equations that relate the initial and final velocity, acceleration, and time to determine displacement and distance traveled.
This document discusses base excitation in vibration analysis and provides examples. It begins by introducing base excitation as an important class of vibration analysis that involves preventing vibrations from passing through a vibrating base into a structure. Examples of base excitation include vibrations in cars, satellites, and buildings during earthquakes. The document then provides mathematical models and equations to analyze single degree of freedom base excitation systems. Graphs of transmissibility ratios are presented and examples are worked through, such as calculating car vibration amplitude at different speeds. Rotating unbalance is also covered as another source of vibration excitation.
This document provides an overview of pulley systems and example problems involving pulley kinetics. It begins with examples of simple pulley systems and their free body diagrams. Equations relating the accelerations and tensions in pulley systems are developed. Two example problems are then solved in detail. They involve drawing free body diagrams, establishing equations of motion, and relating accelerations based on kinematics. The accelerations of blocks and tension in ropes are calculated for each example problem.
This document outlines a lecture on engineering dynamics that covers:
1) The difference between treating an object as a particle versus a rigid body in dynamics problems.
2) Reviewing Newton's second law and how to relate real-world forces to theoretical free body diagrams.
3) The various forces that must be considered in dynamics problems, including gravity, normal forces, friction, spring stiffness, and damping.
4) How to draw free body diagrams to isolate the forces on individual objects in order to apply Newton's second law.
1) The document discusses dimensions and units in engineering dynamics, explaining that equations represent equality where the dimensions and units of both sides must match.
2) It covers dimensional analysis, defining common engineering quantities like force, pressure, work, and power in terms of mass, length, and time dimensions.
3) Rules for operating on dimensional quantities are presented, showing that derivatives and integrals retain the dimensions of the original terms.
4) An example exam question is provided to illustrate the application of dimensional analysis.
1) The document discusses dimensions and units in engineering dynamics, explaining that equations represent equality where the dimensions and units of both sides must match.
2) It covers dimensional analysis, defining common engineering quantities like force, pressure, work, and power in terms of mass, length, and time dimensions.
3) Rules for operating on dimensional quantities are presented, showing that derivatives and integrals retain the dimensions of the original terms.
This document is a lecture outline for an Engineering Dynamics course. It introduces the course, instructor, and topics to be covered, which include kinematics of particles and rigid bodies, forces and torques, energy, vibrations, and applications to mechanisms. Assessment will consist of practice classes, a lab, quizzes, a midterm, project work, and a final exam. Students are advised to spend 7 hours per week studying and are encouraged to attend office hours for help. Key concepts that will be covered are position, displacement, velocity, and acceleration.
Este documento describe los detalles de un proyecto de construcción de una carretera. Explica que la carretera tendrá 6 carriles y medirá 50 kilómetros de largo. También incluirá 3 intercambiadores y se espera que reduzca el tiempo de viaje entre las dos ciudades en una hora. El costo total del proyecto se estima en $200 millones.
Here are the steps to solve this problem:
1) Resolve each force into x and y components:
F1x = 40 cos 30° = 40(0.866) = 34.64 N
F1y = 40 sin 30° = 40(0.5) = 20 N
F2x = 30 cos 45° = 30(0.707) = 21.21 N
F2y = 30 sin 45° = 30(0.707) = 21.21 N
2) Sum the x and y components:
Rx = F1x + F2x = 34.64 + 21.21 = 55.85 N
Ry = F1y + F2y = 20 +
1) Los estudiantes midieron los coeficientes de fricción estática y cinética usando un riel como plano inclinado y luego en posición horizontal con una polea. 2) Los valores medidos de los coeficientes de fricción fueron consistentes con la teoría de que son independientes de la fuerza normal y que el coeficiente estático es mayor que el cinético. 3) La práctica cumplió con el objetivo de demostrar experimentalmente los coeficientes de fricción y comparar los valores obtenidos por diferentes métodos.
This document contains 12 solutions to physics problems related to dynamics and kinematics. The solutions calculate things like work, acceleration, forces, velocities, distances, and times using concepts like Newton's laws of motion, kinematics equations, coefficients of friction, and inclines. Equations are set up and solved to find the requested unknown variables.
Mecánica vectorial para ingenieros dinámica - 10ma edición - r. c. hibbelerKoka Mitre
El documento proporciona en repetidas ocasiones los enlaces http://libreria-universitaria.blogspot.com y www.FreeLibros.com, sugiriendo que se trata de recursos relacionados con libros universitarios y libros gratuitos.
Thermodynamic Chapter 2 Properties Of Pure SubstancesMuhammad Surahman
This document provides an overview of properties of pure substances and phase change processes. It defines a pure substance as having a fixed chemical composition throughout. Pure substances can exist in solid, liquid, or gas phases. Phase change processes like melting, boiling, and condensation occur at saturation conditions where two phases coexist in equilibrium. Properties like specific volume, internal energy, and enthalpy vary based on temperature, pressure, and quality (ratio of vapor mass to total mass) of mixtures. Property tables and interpolation are used to determine properties at given conditions for pure substances like water. Examples show how to apply these concepts to calculate properties like pressure, temperature, and enthalpy at different states.
The document discusses key concepts in thermodynamics including:
1. It defines systems, surroundings, boundaries, properties, states, paths, processes, cycles, and equilibrium.
2. It explains heat, work, temperature, and the different mechanisms of heat transfer.
3. It introduces the three laws of thermodynamics and their implications for engineering systems and processes.
This document provides an overview of momentum and collisions. It discusses linear momentum, impulse, the impulse-momentum theorem, conservation of momentum, and elastic and inelastic collisions. Key points include:
- Momentum is defined as mass times velocity.
- Impulse is the product of force and time. According to the impulse-momentum theorem, impulse causes a change in momentum.
- The total momentum of interacting objects before a collision equals the total momentum after (law of conservation of momentum).
- Collisions can be perfectly inelastic (objects stick together), elastic (momentum and kinetic energy conserved), or inelastic (kinetic energy not conserved).
1. Engineering mechanics deals with the behavior of bodies at rest or in motion. It is divided into statics (study of bodies at rest) and dynamics (study of bodies in motion). Dynamics is further divided into kinematics (motion without forces) and kinetics (motion with forces).
2. The document defines key terms like vector quantity (specified by magnitude and direction), scalar quantity (specified by magnitude only), and moment of a force (the tendency of a force to rotate or twist a body about a pivot point).
3. Examples are given to illustrate concepts like rigid bodies, moments, and systems of forces in real-life scenarios involving braking on a bike, balancing on a skateboard, and
This presentation provides instructions on how to view and navigate through a slideshow on momentum and collisions. It contains sections on momentum and impulse, conservation of momentum, and elastic and inelastic collisions. Sample problems are included with step-by-step worked solutions showing calculations and applying concepts like conservation of momentum and kinetic energy.
This presentation provides instructions on how to view and navigate through a slideshow on momentum and collisions. It contains sections on momentum and impulse, conservation of momentum, and elastic and inelastic collisions. Sample problems are included with step-by-step worked solutions showing calculations and applying concepts like conservation of momentum and kinetic energy.
This document provides an overview of moment of inertia for a Grade 12 Physics class. It defines moment of inertia as a measurement of a body's resistance to changes in rotational motion. The objectives are to explain moment of inertia, provide examples where it is observed, and how it can be used to improve work. Formulas for calculating moment of inertia for different shapes are presented, along with examples such as calculating it for a solid cylinder versus a hollow hoop. Applications of moment of inertia are discussed briefly, such as in car wheels and machines. The document ends with an assessment question and a prompt for students to discuss applications of moment of inertia in creating useful work materials.
This document provides information about an engineering dynamics course, including its synopsis, outcomes, topics, and teaching plan. The course applies principles of dynamics including kinetics, kinematics, energy and momentum methods to analyze motion. Key topics include particle and rigid body kinetics and kinematics in one and two dimensions. By the end of the course, students should be able to solve dynamics problems, explain energy and momentum methods, and conduct a dynamics experiment. The course runs over 15 weeks and covers topics such as particle kinematics and kinetics, systems of particles, and rigid body kinematics.
This document provides an overview of topics related to general physics concepts for the Cambridge iGCSE syllabus. It includes definitions, explanations, examples, and sample questions related to key concepts like length, time, speed, acceleration, distance-time graphs, speed-time graphs, density, forces, Newton's laws of motion, and moments. The document is intended to be a study guide and reference for students preparing for the Cambridge iGCSE physics exam. It covers the essential information about these foundational physics concepts in a concise yet comprehensive manner.
This chapter discusses the kinematics and motion analysis of particles. It introduces concepts like position, displacement, velocity, and acceleration. Methods for analyzing 1D continuous and erratic motion as well as 2D and 3D curved motion are presented. The chapter also covers dependent and relative motion analysis of multiple particles using both fixed and translating coordinate systems. The goal is to establish a foundation for studying the kinetics of particles subjected to various force systems.
Studynama.com provides free educational resources like lecture notes, presentations, guides and projects for engineering, medical, management and law students in India. Users can also discuss career prospects and other queries in a growing online community. All files are uploaded by users and Studynama.com is not responsible for their content. For feedback, email info@studynama.com.
The document then provides course material on Engineering Mechanics including an introduction covering pioneers in mechanics like Newton and Hooke. It discusses concepts like deformation, strain, stress and load and their mathematical representation using vectors and tensors. The objective is to formulate problems in mechanics by reducing complexity to appropriate mechanical and mathematical models.
The document continues by
Theory of machines_static and dynamic force analysisKiran Wakchaure
This document contains information about static and dynamic force analysis in machines. It discusses various topics including:
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3. Mechanics Roadmap
Thus the study of
FORCES
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Stationary
Moving
Statics
Dynamics
Kinematics
Kinetics
Our main interest
is in this area.
4. Statics
Lecture Outline
The study of bodies at rest stresses, loads, etc.
Burj Khalifa:
828m tall
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Millennium Bridge
World’s lowest-profile suspension bridge
6. Dynamics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
• Statics: Analysis of a body at rest
• E.g., dams, buildings, etc.
• Dynamics If the body is moving:
• Provided motion not approaching speed of light,
we can rely on Newtonian mechanics (Sir Isaac
Newton)
• This study named “DYNAMICS”, and comprises
sub-classes
• Kinematics
• Kinetics
7. Kinematics & Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
• Kinetics:
• Deals with forces causing the motion
• Kinematics:
• Deals with geometry of motion (s, v, a, t)
8. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
In this unit, we will use Newton’s Laws as a
model governing the motion of mechanical
devices.
He deduced three laws of motion.
The First Law
A particle originally at rest,
or moving in a straight line
with a constant velocity, will
remain in this state provided
the particle is not subjected
to an unbalanced force.
9. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
In this unit, we will use Newton’s Laws as a
model governing the motion of mechanical
devices.
He deduced three laws of motion.
The Third Law
The mutual forces of
action and reaction
between two
particles are equal,
opposite and
collinear.
10. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
In this unit, we will use Newton’s Laws as a
model governing the motion of mechanical
devices.
He deduced three laws of motion.
The Second Law
A particle acted upon by an
unbalanced force F
experiences an acceleration
a that has the same direction
as the force and a magnitude
that is directly proportional to
the force.
11. Kinetics
Lecture Outline
Topic Context
• Isaac Newton proposed the following to model
objects moving in a straight line (the 2nd law):
Statics Review
Dynamics:
Kinematics &
Kinetics
F
m a
An important feature of
this equation, is that we
must know either all the
forces acting on, or the
acceleration of, the mass
m to be able to solve our
problem.
11
12. Kinetics
Lecture Outline
Topic Context
• Often we know two terms of this equation, and
need to calculate the third.
Statics Review
Dynamics:
Kinematics &
Kinetics
F
m a
Example:
A crate, of mass 80kg is
being hoisted with a
force of 90kN. What is its
acceleration?
12
13. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example:
This crate, of mass 80kg
is being hoisted upward
with a force of 90kN.
What is its acceleration?
First step : Define a coordinate system. Which way is positive?
13
14. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example:
This crate, of mass 80kg
is being hoisted upward
with a force of 90kN.
What is its acceleration?
Second step : Draw a free body diagram. Do we know all the
forces acting on the crate?
14
15. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example:
This crate, of mass 80kg
is being hoisted upward
with a force of 90kN.
What is its acceleration?
Third step : Substitute our known forces into the general
equation – we don’t change the RHS of the equation...
F
m a
15
16. Kinetics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example:
This crate, of mass 80kg
is being hoisted upward
with a force of 90kN.
What is its acceleration?
Final step : Solve our equation for the unknown (acceleration)...
a
?
a = 1115.19 m/s2
What does the sign of a mean?
16
17. Kinetics
Lecture Outline
Topic Context
• Often, we have several forces acting on a body.
They may be pulling the body in different
directions.
Statics Review
Dynamics:
Kinematics &
Kinetics
• In this case, we write out the components of the
force in i,j,k format.
Fx
max
Fy
ma y
Fz
maz
17
18. Kinetics Example
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example 2
A 50 kg crate rests on a horizontal plane with coefficient
of kinetic friction μk = 0.3.
From rest, the crate is subjected to a 400 N towing force.
What is the acceleration of the crate along the ground?
19. Kinetics Example
Lecture Outline
Topic Context
Statics Review
Example 2
Analysis Procedure
• Establish a coordinate system
Dynamics:
Kinematics &
Kinetics
Consider a Cartesian coordinate system in the plane of
the tow rope, the weight, and friction forces, etc.
y
x
21. Kinetics Example
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example 2
Analysis Procedure
3. Establish known & unknown quantities
We know the weight and towing force
We need to work out the normal reaction of the floor on
the crate. This will reveal the friction, which then allows
us to uncover any force imbalances
22. Kinetics Example
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Example 2
Analysis Procedure
4. Apply Equation(s) of Motion in each direction
Fx
Fy
max ;
ma y ;
Solving gives…
NC
290.5N
a 5.19m / s 2
Which is our answer...
23. Kinetics – a brief summary
Lecture Outline
Topic Context
• There are many examples where Newton’s laws
are used to solve engineering problems...
Statics Review
Dynamics:
Kinematics &
Kinetics
• But remember they are only a
model. They can’t be used for
all situations...
23
24. Kinetics Example
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
Notice with both examples we have followed
the same steps.
In both cases we needed to know the
acceleration...
25. Kinematics
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
• Notice that Newton’s Second Law only provides
information about the mass, force and
acceleration.
F
m a
Often we want to
know the exact
position and velocity
of an object as well.
Enter kinematics...
25
27. Kinematics
Lecture Outline
• Therefore finding the velocity or displacement
requires integration...
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
• If we have an equation for the velocity (or
displacement), we can find the derivative to find
the acceleration...
• Notice that kinematics does not require us to
know what the forces are, only what the motion
is.
27
28. Kinematics Examples
Lecture Outline
Topic Context
• Example 4
Statics Review
A car moves in a straight line. For a short time its velocity
is defined by v = (0.9t2 + 0.6t) m/s (t in seconds).
Dynamics:
Kinematics &
Kinetics
Determine its position and acceleration when t = 3 s.
When t = 0, s = 0.
29. Kinematics Examples
Lecture Outline
• Example 4
Topic Context
Solution:
Statics Review
Coordinate System:
Dynamics:
Kinematics &
Kinetics
The position coordinate extends from the fixed origin O
to the car, positive to the right.
Position:
Since v = f(t), the car’s position can be determined
from v = ds/dt, since this equation relates v, s and t.
Noting that s = 0 when t = 0, we have
v
ds
dt
0.9t 2 0.6t
Rearrange…
30. Kinematics Examples
Lecture Outline
• Example 4
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
s
0
t
ds
0
s
s
0.3t
0.9t
3
2
0.6t dt
0.3t
0
s
2
t
0
0.3t
3
0.3t
2
When t = 3 s,
s = 10.8 m
31. Kinematics Examples
Lecture Outline
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
• Example 4
Acceleration:
Since v = f(t), the car’s position can be determined
from a = dv/dt, since this equation relates v, s and t.
v
a
0.9t 2 0.6t
dv
1.8t 0.6
dt
When t = 3 s,
a = 6m/s2
32. Kinematics
Lecture Outline
Topic Context
• Occasionally we are lucky, and we can assume
constant acceleration...
Statics Review
Dynamics:
Kinematics &
Kinetics
• In this case, the integral equations simplify to:
s
1 2
at
2
v
at
v
2
v
2
0
v0 t
v0
2as
32
33. Kinematics Examples
Lecture Outline
• Example 5
Topic Context
A rocket travel upward at 75m/s.
Statics Review
When at altitude of 40 m, the engine
fails.
Dynamics:
Kinematics &
Kinetics
Determine:
• Max. height sB reached by the rocket,
• Speed just before it hits the ground.
34. Kinematics Examples
Lecture Outline
Topic Context
• Example 5
Solution:
Statics Review
Dynamics:
Kinematics &
Kinetics
Coordinate System:
• Origin O for the position coordinate at ground
level with positive upward.
Maximum Height:
• Rocket traveling upward, vA = +75m/s when t = 0.
• s = sB when vB = 0 at max height.
• For entire motion, acceleration aC = -9.81m/s2 (negative
since it act opposite sense to positive velocity or positive
displacement)
35. Kinematics Examples
Lecture Outline
Topic Context
• Example 5
Maximum Height:
Statics Review
Dynamics:
Kinematics &
Kinetics
Use
v
at v0
s
1 2
at
2
v
v2
v0 t
u 2 2as
2
u
2
2as
75 m/s
2
vB
0
2
vA
40 m
2aC ( s B
sA )
-9.81 m/s2
Solve for sB = 326.697… 327 m
36. Kinematics Examples
Lecture Outline
• Example 5
Topic Context
A rocket travel upward at 75m/s.
Statics Review
When at altitude of 40 m, the engine
fails.
Dynamics:
Kinematics &
Kinetics
Determine:
• Max. height sB reached by the rocket,
• Speed just before it hits the ground.
37. Kinematics Examples
Lecture Outline
Topic Context
• Example 5
Speed before impact:
Statics Review
0
Dynamics:
Kinematics &
Kinetics
Use
v
s
v
v2
v0 t
v
2
B
2aC ( sC
sB = 327 m
sB )
-9.81 m/s2
at v0
1 2
at
2
2
C
0
2
vC
6415 .74
u 2 2as
vC
80 .1 m/s down
The negative root was
chosen since the rocket
is moving downward
38. Constant acceleration problems
Lecture Outline
Topic Context
• To recap, kinetics and kinematics are interrelated:
Statics Review
Dynamics:
Kinematics &
Kinetics
• If acceleration is constant,
38
39. Constant acceleration problems
Lecture Outline
Topic Context
• Remember that constant acceleration implies a
constant force (and vice versa)...
Statics Review
Dynamics:
Kinematics &
Kinetics
F
m a
• If a problem specifies a constant force, you can
use the constant acceleration equations.
39
40. Kinetics/Kinematics problems...
Lecture Outline
Analysis procedure
Topic Context
Statics Review
1. Establish a coordinate system
Dynamics:
Kinematics &
Kinetics
2. Draw Free Body Diagram(s)
•
Graphical representation of all forces acting on
the system.
3. Establish known & unknown quantities
4. Apply Equation(s) of Motion in each direction
5. Evaluate kinematics to solve problem
41. Conclusions
Lecture Outline
• Statics – Deals with things which are stationary.
Topic Context
Statics Review
Dynamics:
Kinematics &
Kinetics
• Dynamics – Deals with things which move.
• Kinematics – Describes the motion of a body
• Kinetics – Describes the forces acting on a body
• Following the procedure discussed on the
previous slide, you should be able to tackle a
range of problems...
41