A free body diagram is a sketch that shows an isolated body and all the external forces acting on it. It does not show internal forces or the body’s environment. Forces are drawn as vectors at the point where they are applied. Common forces shown include weight, normal force, friction, and tension. Free body diagrams are used to write force balance equations for mechanical systems. Examples of free body diagrams include a block on a ramp, a book on a table, an object in projectile motion, and an object slowing down due to friction.
The document discusses isometric projection, which is a method for visually representing three-dimensional objects in two dimensions in technical drawings. It defines key terms like isometric axes and lines. The steps for constructing an isometric projection are outlined, including defining the axes and adding details to blocks. Various types of objects that can be drawn using isometric projection are described, such as those with normal, oblique, or curved surfaces. Circles are approximated as ellipses, while curved lines use a series of offset points.
This document provides an overview of engineering drawing standards and concepts. It discusses drawing sheets, scales, lettering, and line types. Drawing standards are sets of rules that govern technical drawings to ensure consistency. Common international standards include ISO, ANSI, JIS, BS, and AS. Key elements covered include appropriate sheet sizes, title blocks, scale designation, text styles, stroke sequences, word spacing, and basic line types. Engineering drawings use defined graphics and text to precisely depict an object’s shape, size, and specifications.
This document discusses various topics in mechanics including: – Mechanics deals with forces and their effects on bodies at rest or in motion. It includes statics, dynamics, and the mechanics of rigid and deformable bodies. – Forces can be analyzed using concepts such as free body diagrams, components, resultants, and equilibrium conditions. Friction and trusses are also analyzed. – Kinematics examines the motion of particles and rigid bodies without considering forces. It relates time, position, velocity, and acceleration. Dynamics analyzes forces and acceleration using concepts like work, energy, impulse, and momentum.
This document discusses Lami’s theorem and provides an example. It begins by introducing the topic of mechanics of solids and listing the group members and their enrollment numbers. It then defines different types of force systems including coplanar, non-coplanar, concurrent, parallel, and general systems of forces. The document explains the triangle and polygonal laws for graphical conditions of equilibrium. It states the conditions of equilibrium for concurrent forces as the sum of forces in the x and y directions equaling zero, or the sum of moments equaling zero. Lami’s theorem is then introduced as stating that if a particle is in equilibrium under three forces, each force bears the same proportionality to the sine of the angle between the
The document discusses shear stresses in beams. It defines shear stress as being due to shear force and perpendicular to the cross-sectional area. Shear stress is derived as τ = F/A, where F is the shear force and A is the cross-sectional area. Shear stress varies across standard beam cross sections like rectangular, circular, and triangular. Shear stress is maximum at the neutral axis for rectangular and circular beams, and at half the depth for triangular beams. Sample problems are included to demonstrate calculating and graphing the variation of shear stress across specific beam cross sections.
The document discusses beams, which are horizontal structural members that support applied loads. It defines applied and reactive forces, and describes different types of supports including roller, hinge, and fixed supports. It then defines and describes different types of beams, including cantilever, simply supported, overhanging, fixed, and continuous beams. It also discusses types of loads, including concentrated and distributed loads, and how beams experience both bending and shear forces from loads.
The document provides an overview of mechanics and engineering mechanics. It discusses key topics including types of mechanics, units of measurement, fundamental concepts like forces and moments. It also summarizes various types of force systems and the laws and methods for analyzing coplanar forces, including the parallelogram law, Varignon’s theorem, and analytical and graphical methods for determining the resultant of coplanar concurrent forces.
The document discusses frames and trusses, which are structures consisting of bars, rods, angles, and channels pinned or fastened together to support loads and transmit them to supports. Trusses contain only two-force members that experience either tension or compression, while frames can contain multi-force members and experience transverse forces as well. Common truss configurations include pinned, gusset plate, and bolted or welded joints. Trusses are analyzed using methods of joints or sections to determine member forces.
This document discusses different types of projections used in engineering drawings. It describes parallel projections where lines never intersect and perspective projections where lines converge at a point. The main types of projections discussed are: – Orthographic projections where lines are perpendicular to the view plane. Multiview drawings use multiple orthographic projections. – Axonometric projections including isometric, dimetric, and trimetric which rotate the object along axes. – Oblique projections draw faces at arbitrary angles rather than 90 degrees. Specific types are cavalier and cabinet. – Perspective projections make distant objects look smaller to provide a realistic view, with one-point, two-point, and three-point varieties.
This document discusses different types of vibrations including free vibrations, forced vibrations, and forced-damped vibrations. It provides examples of each type and notes that forced vibrations can be created by step input forcing, harmonic forcing, or periodic forcing. Methods to isolate vibrations transmitted to machine foundations using springs and dampers are also covered, along with the concept of transmissibility to determine the amount of vibrations transmitted. Key equations for forced-damped vibrations and transmissibility are presented.
Download link: https://www.researchgate.net/publication/318852873_Engineering_Drawing_-_I DOI: 10.13140/RG.2.2.22512.56328 An engineering drawing is a type of technical drawing, used to fully and clearly define requirements for engineered items, and is usually created in accordance with standardized conventions for layout, nomenclature, interpretation, appearance size, etc. Its purpose is to accurately and unambiguously capture all the geometric features of a product or a component. The end goal of an engineering drawing is to convey all the required information that will allow a manufacturer to produce that component.
This document outlines force systems, including two-dimensional (2D) and three-dimensional (3D) force systems. It discusses 2D force resolution into rectangular components using the parallelogram rule. Examples show resolving forces into x and y scalar components using unit vectors. Exercises provide practice calculating resultant forces and moments, including moments about a point and combined moments. Couples are also introduced, along with examples of replacing force systems with equivalent couples and resultants.
The document discusses basic principles of statics and structural design. It covers: 1) Statics deals with forces on bodies at rest, while dynamics deals with moving bodies. Statics is used to analyze structural systems and ensure strength, stiffness, and stability. 2) Structural design involves preliminary design stages using experience and intuition, followed by detailed analysis and load estimations based on statics principles. 3) Static equilibrium equations must be satisfied for coplanar forces. Systems can be determinate, allowing determination of specific unknowns, or indeterminate.
This document provides an overview of forces and force systems in engineering. It introduces the concept of a force vector and its components. Key points covered include: – A force vector depends on both magnitude and direction. Most bodies are treated as rigid. – Any system of forces on a rigid body can be replaced by a single force and couple. The principle of transmissibility allows treating forces as “sliding vectors”. – Forces are classified as contact or body forces, and as concentrated or distributed. Weight is treated as a concentrated force through the center of gravity. – Methods for adding concurrent forces include the parallelogram and triangle laws. Forces can be resolved into rectangular components.
This document provides an overview of engineering mechanics. It defines mechanics as the branch of physics dealing with rest and motion. Mechanics can be divided into classical mechanics, relativistic mechanics, and wave mechanics. Engineering mechanics is further divided into solid mechanics and fluid mechanics. Solid mechanics includes rigid body mechanics and deformable body mechanics. Rigid body mechanics contains statics and dynamics. Dynamics contains kinematics and kinetics. The document also outlines Newton’s laws of motion, the law of universal gravitation, and other fundamental laws and concepts of mechanics. Finally, it discusses common units used in mechanics like the MKS, CGS, and FPS systems.
This document provides an introduction to statics and static equilibrium for particles. It defines key terms like particles, equilibrium, and free-body diagrams. It explains that a particle is in equilibrium if the net force acting on it is zero. Free-body diagrams show all forces acting on a particle and are used to apply the equations of equilibrium to solve problems. Examples are provided of drawing free-body diagrams and using them to determine unknown forces on mechanical components in static equilibrium.
The document uses a box named Billy and a table named Terry to explain free body diagrams. It provides an example of drawing a free body diagram for Billy, who has a mass of 5 kg and is pushed to the right by a 12 N force. Terry explains that the diagram would show Billy’s weight as a 49 N force down, a normal force of 49 N up from the table, the 12 N applied force to the right, and a 12 N frictional force to the left to balance the forces since Billy is moving at a constant speed. The document then provides another example where Billy accelerates to the right due to forces.
Here are the free body diagrams for the given systems: 1. Axle of bicycle wheel: F_app R_1 R_2 2. Propped cantilever: W_1 W_2 R 3. Neoprene pad bearing functions like a roller support. 4. Circled part of building: W R_1 R_2 R_3 5. Dam: W_water R
Free body diagrams show the relative magnitude and direction of all forces acting upon an object by isolating it from its surroundings. The document provides examples of free body diagrams for the Statue of Liberty, a sitting gorilla, a wooden swing, a bungee jumper’s bucket, a traffic light, and the pin at point A of a truss bridge. Forces are shown as vectors with arrows indicating direction and labels providing magnitudes. Diagrams for static systems will sum the vertical and horizontal forces to zero, indicating equilibrium.
This document discusses two-force and three-force members in mechanical equilibrium. It defines a two-force member as one subjected to forces at only two points, requiring the forces to be equal in magnitude and opposite in direction. A three-force member requires the three forces to be concurrent or parallel. Examples of two-force members include a bucket link and hydraulic cylinder. An example problem solves for the force on a lever that is a three-force member.
1) A free body diagram shows all the forces acting on an object. 2) To draw a free body diagram, isolate the object, choose a coordinate system, sketch the forces with arrows representing magnitude and direction, resolve forces if at an angle, and find the net force. 3) For an example of a book at rest on a table, the free body diagram shows the force of gravity pulling down equal and opposite to the normal force of the table pushing up, resulting in no net force and no acceleration.
Presentation on free body diagram 10.01.03.119Safa Rahman
This document provides information about free body diagrams and internal/external forces. It includes: 1) A definition of a free body diagram as a pictorial device used to analyze forces and moments acting on a body. 2) The purpose of a free body diagram is to help determine unknown forces and equations of motion to analyze problems in statics or dynamics. 3) External forces act on an object from outside sources, while internal forces are introduced inside an object due to external forces and balance them to satisfy equilibrium.
1) Equations of equilibrium for a rigid body involve summing forces in x and y directions and moments about a point to equal zero. 2) Alternative equilibrium equations can use resultant forces and moments instead of individual forces and moments. 3) Analyzing equilibrium involves creating a free body diagram and applying the appropriate equilibrium equations. 4) Examples show calculating reactions at supports using the equilibrium approach.
The document covers various topics in mechanics including statics, dynamics, kinematics, kinetics, scalars, vectors, trigonometry functions, geometry, and Newton’s laws of motion. It defines concepts like particles, rigid bodies, and non-rigid bodies. It also explains the parallelogram law for adding vectors and how to use trigonometric functions and rules to solve problems involving forces and motion.
The instructor’s manual provides concise solutions to problems to allow instructors to check their work. It requests that the solutions not be used for classroom teaching. Additionally, it contains approximately 40 solved transparency problems that instructors can reproduce for classroom use to illustrate applications of the textbook concepts.
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
The document discusses internal forces in structural members and how to determine them using the method of sections. It outlines how to draw free body diagrams of structural members, determine support reactions, and use equilibrium equations to calculate shear forces and bending moments. Sample problems are worked through step-by-step to demonstrate how to analyze beams and shafts and draw the corresponding shear and moment diagrams.
This document provides an overview of the fluid mechanics course, including objectives, content, assessment, resources, and relevance to civil engineering. It will introduce fundamental fluid mechanics principles and demonstrate their application to simple hydraulic components. The course consists of lectures, two laboratory sessions, homework and example sheets, and will be assessed through one exam, two multiple choice tests, and one problem sheet. The document emphasizes that fluid mechanics is important to many areas of civil engineering and establishes the SI system of units to avoid confusion.
This document contains 13 multi-step solutions to mechanics problems involving blocks on inclined planes with tensions in cords or cables. The solutions include free body diagrams, identification of relevant forces, and setup and solution of the static equilibrium equations to determine minimum tensions, angles of impending motion, or other requested values. Key values or relationships are determined numerically in some cases.
this is my presentation of theory of machine subject. the topic of this presentation is static force analysis. In gujarat technological university mechanical engineering third year syllabus topic. there are many types of forces described in this ppt. and examples and domestic use.
1. This chapter discusses basic mechanics concepts including units of measurement, dimensions of physical quantities, and types of errors. 2. Dimensions relate physical quantities to base units like mass, length, and time, and are used to check the homogeneity of equations and derive new equations. 3. There are two types of errors: systematic errors due to instruments, observers, or surroundings, and random errors from mistakes or varying conditions that can be reduced by taking multiple readings.
University problems on Engineering Mechanics solved in differrent way part IIProf. S.Rajendiran
This short document discusses solutions to university problems in engineering mechanics provided by Prof. S. Rajendiran of Ashoka Institution. The problems are solved in a different way than the usual approach to engineering mechanics issues. Prof. Rajendiran presents alternative solutions to common university problems in the field of engineering mechanics.
This document contains a theory question bank related to mechanisms and kinematics. It includes 51 questions covering various topics such as definitions of terms like kinematic chain, degrees of freedom, types of constraints; inversions of mechanisms; calculation of degrees of freedom; explanations of mechanisms like steering gears, Whitworth quick return, Geneva, Oldham’s coupling, and elliptical trammel; Grashoff’s law; and more. It also contains 20 multiple choice questions testing knowledge of kinematic pairs, links, steering gears, inversions, and other topics.
This document provides an overview of key kinematic concepts in mechanics and IB Physics including: – Scalar and vector quantities as well as the differences between distance, displacement, speed, and velocity. – Definitions and equations for rest, motion, acceleration, and projectile motion. – Graphs showing relationships between position, velocity, and acceleration over time and how to calculate changes in position from these graphs. – Key equations of motion including the SUVAT equations that can be used when acceleration is constant.
Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams that were discussed in an earlier unit.
This document discusses engineering statics and vectors. It introduces scalars as physical quantities defined by magnitude alone, while vectors require both magnitude and direction. It then covers vector operations including multiplication and division by scalars, and addition using the parallelogram law, triangle rule, and for collinear vectors. Vector subtraction and addition of forces are discussed. Finally, the importance of free-body diagrams is explained as isolating the body of interest to account for all external forces acting on it.
This document discusses the concepts of equilibrium for rigid bodies. It defines equilibrium as a state where the net force on an object is zero, resulting in zero acceleration. Static equilibrium refers to objects at rest. The document provides steps for drawing free-body diagrams to analyze forces acting on objects, resolving forces into components, and using equations of equilibrium to solve problems involving rigid bodies.
This document discusses the concepts of equilibrium for rigid bodies. It defines equilibrium as a state where the net force on an object is zero, resulting in zero acceleration. Static equilibrium refers to objects at rest. The document provides methods for analyzing equilibrium using free body diagrams, resolving forces into components, and applying equations like the sum of the forces and moments being equal to zero. It gives steps for drawing free body diagrams and solving equilibrium problems.
The document provides an introduction to basic mechanics and resolution of vectors. It discusses that mechanics deals with the effect of forces on bodies at rest or in motion. Mechanics is divided into mechanics of fluids, mechanics of materials, and analytical mechanics. Analytical mechanics includes statics, which deals with bodies at rest or moving at constant velocity, and dynamics, which deals with accelerated motion. The document also discusses the International System of Units (SI Units) used in mechanics. It defines scalar and vector quantities and describes how to add and subtract vectors. Methods for resolving vectors into their rectangular components and determining the resultant of forces are presented. Examples of problems involving forces and their components are provided.
Here are the key steps to solve this problem: 1. Resolve each force into horizontal and vertical components. 2. Take the algebraic sum of the horizontal components to get the horizontal component (Fx) of the resultant. 3. Take the algebraic sum of the vertical components to get the vertical component (Fy) of the resultant. 4. Use the equations: Resultant (R) = √(Fx)2 + (Fy)2 tan(θ) = Fy/Fx to find the magnitude and direction of the resultant. 5. Use Varignon’s theorem to locate the position of the resultant from point O. By going through these steps, we find
This document provides an introduction to basic mechanical engineering concepts including statics. It outlines key topics such as mechanics, scalars and vectors, forces, and two-dimensional force systems. Forces are classified as contact or body forces. Rectangular components, moments, couples, and resultants are discussed for analyzing two and three-dimensional force systems. Numerical problems are provided as examples and exercises.
Equilibrium & equation of equilibrium in 3Dimoinul007
This document provides information about equilibrium and related concepts in physics. It defines equilibrium as a state where opposing forces neutralize each other such that there is no net force acting on an object. Key points discussed include: – The definition of equilibrium is derived from Latin words meaning “equal balance”. – Equilibrium can be static, with zero net force and no movement, or dynamic, with zero net force but constant motion. – Newton’s first law relates to equilibrium, stating that an object at rest stays at rest unless a net force acts on it. – For an object to be in equilibrium, the net force and net torque on it must equal zero. – Free body diagrams are used to visualize all
The document provides instructions for modeling and simulating a simple pendulum using SimMechanics. It describes modeling the ground, body, and revolute joint that connects them. It also explains how to add a joint sensor to measure the pendulum’s angular motion and start the simulation. The goal is to create the simplest possible mechanical model of a pendulum swinging from a fixed point.
This document provides an introduction to applied mechanics. It discusses key topics including statics, dynamics, forces, moments, and equilibrium. Statics deals with bodies at rest under the influence of forces, while dynamics examines forces on moving bodies. Key concepts covered include rigid bodies, physical quantities, types of forces, characteristics of forces, force systems, methods of resolving forces, and laws of forces such as the triangle law and parallelogram law. The document also discusses free body diagrams, equilibrant forces, Lami’s theorem, moments of forces, and Varignon’s theorem.
1) Mechanics of materials is concerned with the relationship between external loads applied to a body and the internal stresses and strains caused within the body. 2) Basic definitions covered in the document include equilibrium, scalars, vectors, forces, moments, and couples. 3) The document provides procedures for determining internal forces in bodies, including drawing free body diagrams, applying equilibrium equations, and using the method of sections to isolate portions of bodies.
Forces can be described as any influence that causes an object to change its movement, direction or shape. A force is a vector quantity that has both magnitude and direction. The fundamental types of forces are gravity, electromagnetic forces, nuclear forces, and contact forces like normal force, friction, tension etc. Forces always occur in pairs as an action-reaction pair according to Newton’s third law. Equilibrium occurs when the vector sum of all forces acting on a body is zero. Forces can be resolved into orthogonal components to simplify the calculation of their resultant using trigonometric relationships.
This document contains lecture material from Dr. Devaprakasam Deivasagayam for the course ME202: Engineering Mechanics. It discusses key concepts related to 2D and 3D equilibrium conditions including: – Expressing the 2D and 3D equilibrium equations for particles based on Newton’s first law of motion. – The process for drawing accurate free body diagrams by identifying forces, establishing a coordinate system, isolating the body, and representing external forces. – Calculating the rectangular components of forces acting at angles in 3D space. – Examples of solving equilibrium problems by applying the 3D force component equations. – Homework being assigned on the topic of moment, which
1. The document outlines the structure and content of an introductory mechanics course, including topics, textbook, evaluation criteria, and course schedule. 2. It introduces fundamental concepts in mechanics like vectors, units, forces, and Newton’s laws of motion. 3. Five sample problems are presented at the end to help students practice concepts covered in the course.
Strength of materials is the study of stress and strain in solid bodies subjected to external loads. Stress is related to material strength while strain measures deformation. The subject also examines stability of loaded columns. Understanding mechanics of materials principles is important because engineering design codes are based on them. The field originated in the 17th century with Galileo’s experiments on loaded rods and beams. In the 18th century, improved testing methods led to important theoretical studies, primarily in France. Over time, advanced math and computing were needed to solve more complex problems, expanding mechanics into other areas like elasticity and plasticity. Research continues to meet engineering challenges.
State chart diagrams define the different states an object can be in during its lifetime, and how it transitions between states in response to events. They are useful for modeling reactive systems by describing the flow of control from one state to another. The key elements are initial and final states, states represented by rectangles, and transitions between states indicated by arrows. State chart diagrams are used to model the dynamic behavior and lifetime of objects in a system and identify the events that trigger state changes.
Free body diagrams are used to visualize forces acting on an object. They show the magnitude and direction of all forces using vectors. To make a free body diagram: 1. Identify the object of interest 2. Identify all direct forces on the object 3. Draw the object as a dot 4. Draw vectors for each force labeled with the force type and objects 5. Vectors should sum to zero for stationary objects or the acceleration vector for moving objects.
Here are the steps to solve this example: 1) Draw a parallelogram with V1 and V2 as two adjacent sides. The diagonal of the parallelogram gives the vector sum S. 2) Use the law of cosines to find the magnitude of S: S = √(V12 + V22 – 2V1V2cosα) 3) Use trigonometry to find the angle α between S and the x-axis. 4) Write S in terms of its components: S = Scosα i + Ssinα j 5) Write a unit vector along S as: u = cosα i + sinα j 6) To find the difference D
The document discusses concepts related to mechanical engineering including: – Equilibrium, which is when the resultant forces and moments on a body are zero. – A free body diagram isolates a system by showing only the external forces acting on it. – There are four categories of force systems that can exist in two-dimensional equilibrium. – An example problem is presented involving finding tensions in ropes connecting multiple pulleys where free body diagrams are drawn for each pulley and the equilibrium equations are set up and solved.
1) A free body diagram is used to represent all external forces and torques acting on a system. It is an important step in solving kinetics problems. 2) The document provides guidance on constructing free body diagrams including identifying the system, drawing external forces and torques, and specifying the point of application and direction. 3) Lever systems use an effort force to move a load force. There are three classes of levers that vary based on the relative positions of the effort, load, and fulcrum. Mechanical advantage determines the trade off between force and distance of movement.
Similar to Free body diagram Concept in Mechanics (20)
This document provides a tutorial on probability problems with examples and solutions. It contains two questions: 1) A coin is tossed 1000 times with 499 heads and 501 tails. The empirical probability of heads is 0.499 and tails is 0.501. The sum of the two probabilities equals 1. 2) In a cricket match, a batswoman hits a boundary 6 times out of 30 balls. The probability that she did not hit a boundary is calculated as 24/30 = 4/5. The document explains how to calculate empirical probabilities from sample data and find the probability of complementary events. It provides the full worked out solutions and explanations.
This document provides an overview of key concepts in probability. It defines probability as a measure of likelihood between 0 and 1, and discusses how probability is used in various fields. Key terms are explained, such as randomness, trial, independent trial, experiment, event, and sample space. Randomness refers to experiments with unpredictable outcomes, like rolling a die. Trials are the individual occurrences of an experiment, like each coin toss. The document also discusses empirical probability, which is the probability of an event calculated based on the frequency of outcomes from experiments. Empirical probability depends on the specific experiment and can take on different values.
This document discusses capacitors connected in parallel and series circuits. When capacitors are in parallel, the equivalent capacitance is the sum of the individual capacitances and the voltage is the same across each capacitor. When capacitors are in series, the equivalent capacitance is calculated by taking the reciprocal of the sum of the reciprocals of the individual capacitances and the charge is the same across each capacitor. An example problem is worked out where three equal-valued capacitors are connected in a combination of parallel and series connections to find the equivalent capacitance of the overall circuit and the charge on one of the capacitors.
This document provides an overview of polynomials. It defines polynomials as expressions with multiple terms where the exponents are whole numbers. Monomials have one term, binomials have two terms, and trinomials have three terms. Polynomials can have variables, constants, and exponents of whole numbers. Expressions with non-whole number exponents or fractions are not polynomials. The document also notes that polynomials of one variable can be written as a sum of terms with coefficients and descending exponents, and the highest exponent indicates the degree of the polynomial.
This document provides solutions to two problems about finding rational numbers between given values. For the first problem, it finds the three rational numbers between 1 and 2 using an average method and a number line method. For the second problem, it finds the three rational numbers between 1/3 and 7/2 again using an average method and a method of converting the fractions to a common denominator. The document explains each step of the solutions in detail.
Rational numbers can be expressed as fractions p/q where p and q are integers and q is not zero. All integers, natural numbers, and whole numbers are rational numbers. There are an infinite number of rational numbers between any two rational numbers. Rational numbers either terminate as decimals or repeat as non-terminating decimals. The sum, difference, product, and quotient of rational numbers are also rational numbers, meaning rational numbers are closed under the operations of addition, subtraction, multiplication, and division.
This document provides instructions on how to solve momentum problems in physics. It defines momentum as mass times velocity (p=mv) and explains that the total momentum of a system is equal to the vector sum of the momentum of objects within it. It also states that the change in momentum of an object is equal to the applied force times the time over which it acts (p2-p1=Ft). The document then works through an example problem involving calculating the average force and final momentum of a golf ball hit by a club to demonstrate how to apply these momentum equations.
The document discusses the concept of center of mass and how to solve center of mass problems. It defines center of mass as the point where the total mass of a system can be considered to be concentrated. The velocity and acceleration of the center of mass can be calculated using the formulas provided. In the absence of external forces, the velocity of the center of mass remains constant. Examples are provided to demonstrate how to calculate the position of the center of mass for a system of particles and how the center of mass will continue along the original path after a rocket explodes into parts due to no change in external forces.
1) Capacitance is a measure of the ability of a system to store electric charge. It consists of two non-touching plates that store equal but opposite charges. 2) The capacitance C of a system is defined as the ratio of the stored charge Q to the potential difference V between the plates. 3) For a parallel plate capacitor, the capacitance is given by C=ε0A/d, where ε0 is the permittivity of free space, A is the area of each plate, and d is the distance between the plates.
The document discusses the first law of thermodynamics and different thermodynamic processes. The first law states that the energy put into a system equals the sum of the work done by the system and the change in internal energy. An isothermal process occurs at constant temperature, with heat equal to work. An adiabatic process involves no heat transfer, so a change in internal energy is equal and opposite to work, causing temperature to increase or decrease depending on the work’s direction.
Moment of inertia is a measure of an object’s resistance to changes in its angular acceleration due to an applied torque. It depends on how the object’s mass is distributed relative to its pivot point. The moment of inertia of a rigid body can be calculated by imagining it divided into particles, multiplying each particle’s mass by the square of its distance from the axis of rotation, and summing these values. Important theorems for calculating moment of inertia include the perpendicular axis theorem and parallel axis theorem. Examples are given for calculating the moment of inertia of a solid disk and sphere about their central axes.
This document provides instructions for solving force problems in physics: 1. Draw a diagram showing all forces and choose a coordinate system. 2. Make free body diagrams for each object showing all forces. 3. Resolve all forces into components using the coordinate system and apply Newton’s Second Law. 4. Identify known and unknown values and solve the equations, ensuring the same number of equations as unknowns. Check units. It then works through an example problem involving three connected objects to find accelerations and contact forces. The example solves the problem by drawing free body diagrams, applying Newton’s Second Law to each object, and combining the equations.
This document discusses how to calculate the electric field due to continuous distributions of charge. It explains that charges can be modeled as continuously distributed along a line, over a surface, or throughout a volume. The electric field is then calculated through an integral performed over the entire charge distribution.
This document discusses how to apply Gauss’s law to find the electric field through a surface. It explains that Gauss’s law can be used when the distribution of electric charge inside the surface and the electric field through the surface are known. The document also notes that the Gaussian surface should be selected based on the symmetry of the charge distribution, such as a cylindrical surface for an infinitely long line of uniform charge.
Apply Gauss’s law to find electric field due to linear distribution of chargesphysicscatalyst
Gauss’s law can be used to find the electric field due to a long, straight wire with a uniform charge distribution. At points far from the ends of the wire, the electric field lines will be radial and perpendicular to the wire. The electric field only depends on the linear charge density and not on the length of the wire.
Gauss’s law can be used to derive Coulomb’s law, which describes the electrostatic force between two point charges. An isolated positive charge will produce a radial electric field of equal magnitude at all points the same distance r from the charge. Taking advantage of the symmetry, Gauss’s law relates the electric flux through a Gaussian surface enclosing the charge to the enclosed charge, allowing the derivation of the inverse square relationship in Coulomb’s law.
Gauss’s law relates the electric flux through a closed surface to the net electric charge enclosed by the surface. It states that the total electric flux through any closed surface is equal to 1/ε0 times the net charge enclosed, divided by the permittivity of free space ε0. Gauss’s law provides an easier way to calculate electric fields than Coulomb’s law and can be used to find electric fields when you know the charge distribution inside the surface.
This is an introduction to Google Productivity Tools for office and personal use in a Your Skill Boost Masterclass by the Excellence Foundation for South Sudan on Saturday 13 and Sunday 14 July 2024. The PDF talks about various Google services like Google search, Google maps, Android OS, YouTube, and desktop applications.
In Odoo, Hooks are Python methods or functions that are invoked at specific points during the execution of Odoo’s processing cycle. The pre-init hook is a method provided by the Odoo framework to execute custom code before the initialization of the module’s data. ie, it works before the module installation.
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APM event held on 9 July in Bristol. Speaker: Roy Millard The SWWE Regional Network were very pleased to welcome back to Bristol Roy Millard, of APM’s Assurance Interest Group on 9 July 2024, to talk about project reviews and hopefully answer all your questions. Roy outlined his extensive career and his experience in setting up the APM’s Assurance Specific Interest Group, as they were known then. Using Mentimeter, he asked a number of questions of the audience about their experience of project reviews and what they wanted to know. Roy discussed what a project review was and examined a number of definitions, including APM’s Bok: “Project reviews take place throughout the project life cycle to check the likely or actual achievement of the objectives specified in the project management plan” Why do we do project reviews? Different stakeholders will have different views about this, but usually it is about providing confidence that the project will deliver the expected outputs and benefits, that it is under control. There are many types of project reviews, including peer reviews, internal audit, National Audit Office, IPA, etc. Roy discussed the principles behind the Three Lines of Defence Model:, First line looks at management controls, policies, procedures, Second line at compliance, such as Gate reviews, QA, to check that controls are being followed, and third Line is independent external reviews for the organisations Board, such as Internal Audit or NAO audit. Factors which affect project reviews include the scope, level of independence, customer of the review, team composition and time. Project Audits are a special type of project review. They are generally more independent, formal with clear processes and audit trails, with a greater emphasis on compliance. Project reviews are generally more flexible and informal, but should be evidence based and have some level of independence. Roy looked at 2 examples of where reviews went wrong, London Underground Sub-Surface Upgrade signalling contract, and London’s Garden Bridge. The former had poor 3 lines of defence, no internal audit and weak procurement skills, the latter was a Boris Johnson vanity project with no proper governance due to Johnson’s pressure and interference. Roy discussed the principles of assurance reviews from APM’s Guide to Integrated Assurance (Free to Members), which include: independence, accountability, risk based, and impact, etc Human factors are important in project reviews. The skills and knowledge of the review team, building trust with the project team to avoid defensiveness, body language, and team dynamics, which can only be assessed face to face, active listening, flexibility and objectively. Click here for further content: https://www.apm.org.uk/news/a-beginner-s-guide-to-project-reviews-everything-you-wanted-to-know-but-were-too-afraid-to-ask/
2. What is Free Body diagram • A free body diagram is a sketch of the body of interest and the forces acting on the body. • With the help of free body diagram you can the precisely define the body(or object under consideration) to which you are applying mechanical equations and the forces that are needed to be considered. PhysicsCatalyst.com
3. Free Body diagram Features • Free body diagram is the picture of body on which you would like to apply the balance of forces and such a diagram is isolated from its environment which means that we do not draw the things near the body or object under consideration • The forces and moments are shown in a free body diagram at the point where they are applied. • Free body diagrams shows all external forces acting on the body and they do not show any internal forces. • Free body diagrams shows nothing sbout the motion of the system. PhysicsCatalyst.com
4. How to draw it • First create a mental picture of the body for which you want to write Force balance equation. • Draw rough sketch of your system showing it to be isolated from its environment. • Place a dot in the center of the object and at this point all the forces are assumed to be acting upon. This is for force balance equation. If we are calculating moment, we need to draw the forces at the point where they are applied • For every force acting on that body , draw a vector which shows size and direction of the force. each vector should start at the dot. • Label each vector based on the type of force and remember not to include numbers and calculations. PhysicsCatalyst.com
