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Lecture 1,2 Engineering Mechanics CE - 101 Lt Col Syed Mohsin Ali [email protected] 0334-5231553 Introduction Introduction Lt Col Syed Mohsin Ali 1997 – 2000 BE Mechanical Engineering (EME College) Gold Medal in Final Year Project 2004 – 2006 and 2009 – 2010 OIC Design Centre – Military Vehicles Research & Development Establishment 2011 – 2012 MSc in Art & Science of Warfare (Staff Course) 2013 – 2015 MSc in Mechanized Mining Systems (South Africa) 2015 – 2016 Instructor Class-B at MCE (EM, FCP, CACE) Class Introduction Course Outline Course Outline Credit Hours Total = 3 Theory = 2.5 Practical = 0.5 Number of Contact hours Total = 64 Theory = 40 Practical = 24 Course Learning Outcomes • Understand the basic terms used throughout the course, geometrical properties of plane areas and basic concepts about virtual work and dynamics. • Resolution of forces, moments, couples, two dimensional force system and frictional forces; and finding reaction and member forces in simple beams and plane trusses. • Verify some of the concepts through practical in the laboratory. Course Plan Do’s and Don'ts Introduction to Engineering Mechanics -What is Mechanics? Mechanics is the science which describes and predicts the conditions of rest or motion of bodies under the action of forces -Categories of Mechanics? - Rigid bodies A Rigid Body does not deform under load! - Statics - Dynamics - Deformable bodies - Fluids Branches of Engineering Mechanics Introduction to Engineering Mechanics Mechanics is the foundation of most engineering sciences and is an indispensable prerequisite to their study Introduction to Engineering Mechanics - Rigid Body Mechanics • Statics: deals with equilibrium of bodies under action of forces (bodies may be either at rest or move with a constant velocity). Designing structures (Mechanical & Civil). Introduction to Engineering Mechanics - Rigid Body Mechanics • Dynamics: deals with motion of bodies (accelerated motion). Analyze responses of buildings to earthquakes (Civil) & determine trajectories of satellites (Aerospace). Introduction to Engineering Mechanics • Engineering Applications – Describes how mechanics is applied in various fields of engineering – Emphasis on 2 essential aspects of engineering: • Design – to choose parameters values to satisfy stated design criteria • Safety – to evaluate the safety of devices and choose parameter values to satisfy stated safety requirements Fundamental Concepts • Space & Time – Space: • 3-dimensional space & locations/positions of points in space • Distance between 2 points in space = length of the straight line joining them • SI unit of length: meter (m) • U.S. Customary unit: foot (ft) Fundamental Concepts • Space & Time – Time: • Measured by the intervals between the events • SI unit & U.S. Customary unit of time: second (s) Fundamental Concepts • Position of a point in space relative to some reference point changes with time: – Rate of change of position = velocity • SI unit: meters per second (m/s) • U.S. Customary unit: feet per second (ft/s) – Rate of change of velocity = acceleration • SI unit: meters per second squared (m/s2) • U.S. Customary unit: feet per second squared (ft/s2) Fundamental Concepts • Mass: Quantity of matter in a body measure of inertia of a body (its resistance to change in velocity) Fundamental Concepts • Force: The ‘push’ or ‘pull’ exerted by one body on another Characterized by its magnitude, direction of its action, and its point of application. Force is a Vector quantity. Fundamental Concepts • Force: Force acting on a body is related to the mass of the body and the variation of its velocity with time. Force can also occur between bodies that are physically separated (Examples: gravitational, electrical, and magnetic forces) Fundamental Concepts • Remember: - Mass is a property of matter that does not change from one location to another - Weight refers to the gravitational attraction of the earth on a body or quantity of mass. Its magnitude depends upon the elevation at which the mass is located - Weight of a body is the gravitational force acting on it Units and Dimensions Quantity Unit Area m2 Volume m3 Velocity m/s Acceleration m/s2 Mechanics - Idealization • Particle: A body with mass but with dimensions that can be neglected Mechanics - Idealization • Particle: A body with mass but with dimensions that can be neglected Three forces act on the hook at A. All forces met at point A. → Hook can be assumed as a Particle A Mechanics - Idealization • Rigid Body: - A combination of large number of particles in which all particles remain at a fixed distance (practically) from one another before and after applying a load - Material properties of rigid body are not required to be considered when analyzing the forces acting on the body - In most cases, actual deformations occurring in structures, machines, mechanisms, etc. are relatively small, and rigid body assumption is suitable for analysis Newton’s Three Laws of Motion Newton’s 1st Law of Motion A particle originally at rest, or moving in a straight line with constant velocity will remain in this state provided particle is not subjected to an unbalanced force Newton’s Three Laws of Motion Newton’s 1st Law of Motion First Law contains the principle of the equilibrium of forces main topic of concern in Statics Newton’s Three Laws of Motion Newton’s 2nd Law of Motion 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 F=m.a Newton’s Three Laws of Motion Newton’s 3rd Law of Motion The mutual forces exerted by 2 particles on each other are equal in magnitude & opposite in direction. The particles remains in state of equilibrium only if exerted forces on them are collinear Newtonian Gravitation • Gravitational force between 2 particles of mass m1 & m2 that are separated by a distance ‘r’ is: Gm1m2 F 2 r where G = universal gravitational constant G = 6.673 × 10–11 Nm2/kg2 D Newtonian Gravitation • Weight of an object of mass m due to the gravitational attraction of the earth is approximated by: GmmE W 2 r where mE = mass of earth, r = distance from the center of earth to the object Newtonian Gravitation • Weight of an object at sea level (r = RE): W mg • The value of g varies from location to location on the surface of the earth. – g = 9.81 m/s2 (SI units) – g= 32.2 ft/s² Newtonian Gravitation Systems of units - Very important for Engineers - SI (System international) is used in Europe - FPS ( Foot pound System) is used In USA - Be careful when switching from one system to the other Units • U.S. Customary Units: – Base units: • Length: feet (ft) • Force: pounds (lb) • Time: second (s) – Derived Unit: • Mass: slug (the mass of material accelerated at 1 ft/s2 by a force of 1 lb) • Newton’s 2nd law: 1 lb 1 slug 1 ft/s 2 1 slug 1 lb s 2 /ft C Systems of units – Force & mass are defined by the 2nd law 1 slug = Amount of matter accelerated at 1 ft/s2 when acted upon by a force of 1 lb (slug = lb· s2/ft). 1 Newton = Force required to give 1 kg of mass an acceleration 1 m/s2 (N= 1kg· m/s2) Systems of units Newton 1 Newton is the force required to give a mass of 1 kg an acceleration of 1 m/ s². Weight is a force. The weight of 1 kg Mass is: W = mg W = (1 kg)(9.81 m/ s²) W = 9.81 N Conversion of Units Values must be expressed in terms of one system of units before they are substituted into the equation Conversion of Units Example: To express 1 mi/h in terms of ft/s: 5280 ft 1 mi/h 1.47 ft/s 3600 s Conversion of Units Convert: (a) 60 miles/h to ft/sec (b) 100 lb.ft/s2 to kg.m/s2 2 2 (c) 20 slug/ft to kg/m Units - Prefixes • E.g. 1 kg = 1000 g, 1 Mg = 106 g = 1000 kg