Intro to Engineering
Intro to Engineering ENGR 107
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Date Created: 09/28/15
91 Mass as a Fundamental Dimension 39 Atoms are made up of even smaller parts electrons protons and neutrons 39 Atoms are combined to create molecules 39 At standard atmospheric pressure water exists in a solid form as long asthe temperature is kept un er 0C 39 Understandard atmospheric pressure at sea level water remains liquid up toatemperature C Mass moment of inertia a measure of how hard it is to rotate something with respect to center of rotation 92 Measurement of Mass 39 gram unit of mass in SI equal to mass of the international prototype of the kilo ram Mass ofan object is measured indirectly by using how much something weighs Mass moment of inertia I rzm 93 Density Speci c Volume 8 Speci c Gravity 39 D nsity o any substance is defined as the ratio of the mass to the volume that it occupies e sity density massvolume 39 Density provides a measure of how compact the material is for a given vo ume 39 The density of matter changes with temperature and could also change with pressure 39 SI unit for density is kgma 36 is slugsfta US is lbmft3 39 Specific volume inverse ofdensity volume m 39 Specific volume is used in the study of thermodynamics 39 Specific volume is SI units is mSkg 39 n mmon way to represent heaviness or lightness of some material is by comparing its density tothe density of water 9 comparison is called specific gravity 39 Specific gravity density of a material density of water at 4C 39 Specific weight is defined asthe ratio ofthe weight ofthe material by the volume that it occupies 39 Specific weight weight volume 39 Specific weight density acceleration due to gravity 94 Mass Flow Rate 39 Mass flow rate tells engineers how much material is being used or moved over a period of time so that they can replenish the supply of the material 39 Mass flow rate is simply defined bythe amount of mass that flows through something per unit of time Mass flow rate masstime 95 Mass Moment of Inertia 39 When it comes tothe rotation of objects the distribution of mass about the center of rotation plays a significant role T e farther away the mass is located from the centerof rotation the harder it is to rotate the mass about the given center of rotation 39 A measure of how hard it isto rotate something with respect to center of rotation is called mass moment of inertia 39 For a single mass particle m located at a distance rfrom the axis of rotation zz the mass moment of inertia is defined by I rzm 39 To include a system of mass particles mass moment of inertia forthe 171 2 2 system of masses shown about zz axis Is I r m r m rgzm 39 The mass moment of inertia for a body such as wheel or shaft In r dm 39 MASS MOMENT OF INERTIA 39 Disk amp Circular Cylinder9m V2 mrz Sphere9m 25mr2 Rectangular Plate9lm 112mw2 96 Momentum 39 Momentum is a physical variable that is defined asthe product of mass and velocit 39 Momentum L mV Lmomentum vector Vveocityvector 39 Because velocity has direction we assume a direction with momentum as well same direction asV 39 Momentum of an object or a person at rest is 0 39 Magnitude of linear momentum is mass times ve ocity 39 Kinetic energy is another quantity that is mass dependent and is used in engineering analysis and design Kinetic energy V2 mVZ 97 Conservation of Mass TL 1 destroy mass 39 The rate at which water comes to the tub is equal to the rate at which the water leaves the tub plus the time rate of accumulation of the mass of water within the tub The rate at which afluid enters a control volume minus the rate at which thefluid leaves the control volume should be equal to the rate of accumulation or depletion of the mass offluid within the given control volume ma nu ma 101What We Mean by Force The simplest form ofa force that represents the interaction of2 objects is a push ora 39 A forces whetherthey represent the interaction of 2 bodies in direct contact orthe interaction of 2 bodies at a distance gravitational force are defined by their magnitudes their directions and the points of application 39 Natural tendency of a force acting on an object if unbalanced will be to translate the object amp rotate 39 The amount by which the object will translate rotate elongate shorten bend ortwist will depend on its support conditions material and geometric properties 39 The newton N is the ujnit offorce in SI A newton is defined as the force that will accelerate 1kg of mass at a rate of 1 msz This relationship is based on Newton s law of motion 1 Newton 1kg1msz 1b 1 slug1 ftsz 1lbf4448N 39 Hooke s law states that overthe elastic range the deformation ofa spring is directly proportional to the applied force according to Fkx Fapplied force N or lb kspring constant Nmm or Ncm or bin xdeformation of the spring mm or cm or in use unitsthat are consistent wi h 39 Elastic range isthe range over which if the applied force is removed the internal spring force will return the spring to its original unstretched shape and size and do so with no permanent deformation Springforce is equal to the applied force 39 There are basically 2 types of frictional forces that are important In engineering design dwfrictional forces and viscous friction orthe fluid friction Friction force is not constant and reaches a maximum value which is given by szxuN N is normal force 1 is coefficient of static friction for the 2 surfaces involved 39 The magnitude ofthe friction force drops to a value called the dynamic or kinetic friction 102 Newton s Laws in Mechanics 39 Newton sfirst law9 If a given object is at rest and if there are no unbalanced forces acting on it the object will then remain at rest If the object is moving with a constant speed in a certain direction and if there are no unbalanced forces acting on it the object will continue to move with its constant speed and in the same direction 39 Newton s second law9 Newton obsened that as he increased the Moon916ms2 Mars937ms2 103 Moment Torque Force Acting at a Distance 39 Tendency of force is measured in terms of a moment of a force about an axis or a point Moment has both direction and magnitude 39 When an object is subjected to an external force internal forces are created inside the material to hold the material and the components together neauiun 39 39 39 39 39 39 to keep the object held in position as planned 104 WorkForce Acting Over a Distance 39 Mechanical work is defined as the component ofthe force that moves the object times the distance the object moves The work done bythe pushing force movingthe carfrom position 1 to position 2 is given by W Fcose d 105 Pressure and StressForce Acting Over an Ar 39 Pressure provides a measure of intensity of a force acting over an area It can be defined as the ratio offorce overthe contact surface area pressure force re 39 Pressure in SI units are expressed in pascal N m2 Pressure in US units are expressed in psi pound per square inch Pbin2Pbft21ft2144in2 39 Pascal39s law9 states that for a fluid at rest pressure at a point is the same in all directions Ppgh Pfluid pressure at point B in Pa or lbftz pdensity of he fluid in kgm3 orslugsfta gacceleration due to gravity98ms2 or 322fts2 hheight of fluid column in m orft 39 Buoyancy is the force that a fluid exerts on a submerged object FBpVg F is buoyancyforceN pdensity of the fluid kgm3 gacceleration due to gravity98ms2 Vvolumem3 39 Standard atmosphere at sea level has a value of 101325 kPa 39 1atm101325Pa1013kPa 1atm1469 lbinz 1atm760mmHg 1atm2992inH Pabsolute Pgauge Patmosphmc 39 The ratio of the normal vertical component ofthe force to the area is called the normal stress and the ratio ofthe horizontal component of the force the component ofthe force that is parallel to the place surface to the area is called shear stress Normal stress component is often called pressure 106 Modulus of Elasticity Modulus of Rigidity and Bulk Modulus of Compressibility 39 modulus ofelasticity is a measure of how easily a material will stretch when pulled subject to a tensile force or how well the material will shorten when pushed subject to a compressive force 5 whe e onormal stress Nm2 or lbinz Emodulus of elasticityNm2 or lbinz 2normal strain the ratio of change in length to original length dimensionless 39 Modulus of rigidity or shear modulus measure of how easily a material can be twisted or she red 39 Tensile strength or ultimate strength of a material is expressed as the maximum tensile force per unit of the original crosssectional area of the specimen 39 Compressive strength of a material is expressed asthe maximum c mpressive force per unit ofthe crosssectional area ofthe specimen 107 Linear mpuseForce Acting OverTime 39 Linear impulse representsthe net effect of a force acting over a period 1Pa1 RF45967 RF45967 oftime 131Work Mechanical Energy Thermal Energy v2 Kinetic energy 12 m AKE V2 mV22 Vlmv12 The work required to lift an object with a mass m by a vertical distance is called gravitational potential energy Change in PE APE h g gacceleration due to gravity 981ms2 Ahchange in elevation m When a spring is stretched or compressed from its unstreched position elastic energy is stored in spring energy that will be released when the spring is allowed to return to its unstretched position Elastic energy V2 kx2kspring constant Nm xdeflection of spring from unstretched position m Consenation of mechanical energy states that the total mechanical energy ofa system is constant The change in the kinetic energy of the object plus the change in the elastic energy plus the change in the potentialenergyisO AKEAPEAEE0 1joule1Nm1kgm2s2 lBtu778bft 15m 10551 Conservation DfEaEivgy Law ofThermodynamics The first law ofthermodynamics states that energy is conserved It cannot be created or destroyed energy can only change forms Aftera system having a fixed mass the net heartransferto the system minus the work done bythe system is equal tothe change in total energy of the system QWAE Qnet heat transfer intothe system in J Wnet work done bythe system in J AEchange in energy Understanding WhatWe Mean by Power Power is defined as the time rate of doing work orthe required work orenergy divided by the time required to perform the task work Power worktime forcedistance time or powerenergytime Watts and Horsepower Unitof powerin SI isWatts NmsJsW Unit of power in US is hp and lbrfts 1hp 550lbrfts 1lbrfts 13558W 1hp745 69W 1kW 1000 W 100015 36000001 36 MJ 1 Btu 1055 W 1055 kW Btuh 1kWh 100015 3600s 1 ton of refrigeration 12000 Ef ciency Efficiency actual output actual input Power plant efficiency energy generated energy input from fuel Thermal efficiency power output heat power input asfuel is burned Elec motorefficiencypower input to device being driven by motorelectric power input by motor Efficiency of pump power input to fluid bythe pump power input to the pump bythe motor eva poratorenergy input to the compressor Energy efficiency ratioEERheat removal from evaporator Btuenergy input to compressor Wh 1 x 10396 meter m Nllcrometermlcron H Olnt prlnter s I 39 eter p Nlllllm c 59 P32 F 959 32 K 59R R 95K 10936 yard 11 yard Meter Kllometer yd Mlle 1000 meter m 16093 Kllometer km 5280 ft