Conservation & Acct Princ
Conservation & Acct Princ ES 201
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This 7 page Class Notes was uploaded by Napoleon Turcotte II on Monday October 19, 2015. The Class Notes belongs to ES 201 at Rose-Hulman Institute of Technology taught by Donald Richards in Fall. Since its upload, it has received 17 views. For similar materials see /class/225122/es-201-rose-hulman-institute-of-technology in Engineering & Applied Science at Rose-Hulman Institute of Technology.
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Date Created: 10/19/15
Learning Objectives Page 1 of2 Chapter 5 Chapter 5 Conservation of Linear Momentum 1 Define explain compare and contrast the following terms and concepts Particle vs Extended Body Rigid body Kinematic Relationships position velocity and acceleration Linear Momentum linear momentum of a particle P mV specific linear momentum l units of linear momentum N 39s lbf39s vector nature of linear momentum inertial reference frame Application of Accounting Principle for Linear Momentum amount of linear momentum Within the system Psys I Vpd V 9 transport rate of linear momentum across the system boundaries external forces ZFE body forces surface contact forces normal stress vs shear stress myml mass transport of linear momentum 2 WV 2 thV2 m 011 generationconsumption rate of linear momentum Within the system Empirical result Linear momentum is conserved Conservation of Linear Momentum Equation zmmmlzmv mm 611 m out rate form t2 lmpulse I Ith a I 2At l lmpulsive Force FaVg J th At At 2 Conservation of Linear Momentum and Newton s Laws Center of mass Dry Friction A useful constitutive relation static friction coefficient kinetic sliding friction Relative velocity Learning Objectives Page 2 of 2 Chapter 5 2 Given a problem that can be solved using conservation of linear momentum you should be able to do the following 1 Select an appropriate system that can be used to find the requested unknowns using the information given in the problem Clearly identify the system and its boundaries on an appropriate drawing Carefully label transports of linear momentum with the surroundings This is commonly called a freebody diagram Indicate the time interval appropriate for the problem AA CON VV Clearly identify and count the number of unknowns you are trying to find Define and use a unique symbol for each unknown A q Develop a set of INDEPENDENT equations that are equal in number to the number of unknowns and are sufficient to solve for the unknowns These equations are developed using the conservation and accounting equations and the information given in the problem Carefully indicate how the given information plus your assumptions are used to develop the problemspecific equations from the general accounting and conservation principles Recognize that in a twodimensional problem application of conservation of linear and angular momentum to a system can contribute at most three independent equations 5 Solve for the unknown values Starting with the conservation of linear momentum equation show what assumptions are necessary to develop the traditional result for a rigid body F ma Given information about the acceleration of an object as a function of time use elementary calculus to develop an equation for the velocity and as a function of time Given information about the velocity of an object as a function of time use elementary calculus to develop an equation for the position as a function of time Use the concepts embodied in the conservation of momentum equation including transport and storage of linear momentum to explain the behavior of a device or system Given a problem that involves friction use both sliding and static friction forces where appropriate to explain the motion andor forces in the system Given a problem with impulsive forces or loads evaluate the impulse applied to the system and if the time interval is known determine the average value of the impulsive force over the time interval Given a problme where relative velocities are given or required cor39rectly convert relative velocities to absolute velocities for use in the conservation of linear momentum equation Learning Objectives Page 1 of 3 Chapter 7 Chapter 7 Conservation of Energy 1 Define illustrate and compare and contrast the following terms and concepts WorkEnergy Principle relation to conservation of linear momentum Energy internal energy specific internal energy u mechanical energy gravitational potential energy specific gravitational potential energy g2 kinetic energy specific kinetic energy V22 spring energy Work mechanism for transferring energy mechanical work vs thermodynamic work work W vs power path function reversible quasiequilibrium work vs irreversible work types compressionexpansion pdV work shaft work elastic spring work electric workpower dc power ac power effective vs maximum values power factor Heat transfer mechanism for transferring energy heat transfer Q vs heat transfer rate adiabatic surface or boundary path function types of heat transfer conduction convection Newton s law of cooling convection heat transfer coefficient thermal radiation Learning Objectives Page 2 of 3 Chapter 7 Application of Accounting Principle to Energy rate of accumulation of energy within the system amount of energy Em J 6 pdV V where the specific energy is defined as e u V22 gz transport rate of energy by heat transfer Heat transfer rate transport rate of energy by work at non ow boundaries Power transport rate of energy by work at flow boundaries 2 pvmm Z pvmgm Flow Power 2 2 2m V7gzm me V7gztm transport rate of energy mass flow Rate form of Conservation of Energy dEW dt s V2 V2 QNztw WNztw 2 h 7 gzmm Z 17 7 gzm0ul where h u pv is a new property called enthalpy Substance models ldeal gas with roomtemperature specific heats p atuie specific heats LWWW rum k with A Thermodynamic cycles Definition three parts Classifications Working uid single vs twophase Structure Closed periodic vs Closedloop steadystate Purpose Power vs Refrigeration vs Heat Pump cycles Measures of Performance General definition Power cycles 9 Thermal efficiency 7 n Refrigeration cycle 9 Coefficient of Performance 7 COPref Heat pump cycles 9 Coefficient of Performance 7 COPhp 2 Given a mechanical system consisting of particles apply the WorkEnergy Principle where appropriate to solve problems where changes in mechanical energy kinetic potential and spring can be balanced with mechanical work done on the system 3 Given a closed or open system and sufficient information about the properties of the system apply conservation of energy to determine changes in energy rates of change within the system and heat transfers heat transfer rates and work transfers of energy power with the surroundings Learning Objectives Page 3 of3 Chapter 7 r 01 E7 1 90 Given sufficient information determine the change in specific internal energy Au and the change in Ah for a substance that can be modeled using one of the following substance models ldeal gas with roomtemperature specific heats 3911 L4 1 with t p atuie specific heats and use this information in conjunction to meet Objective 3 above Given the indicated information calculate the magnitude and the direction of the associated work transfer of energy or power for the system I Given a relation between system pressure and system volume calculate the compressionexpansion work for the system I Given a torque and a rotational speed for a shaft calculate the shaft power transmitted by the shaft I Given an electric current and the corresponding voltage difference across the terminals calculate the electric power supplied to or by the system You should be able to perform this calculation for both DC and AC systems Given a numerical value for a typical energy or power quantity make the appropriate unit conversions to change the units to the requested values eg convert fth2 to Btulbm Given a device that operates in a closedperiodic cycle or a closedloop steadystate cycle I determine whether the device operates as a power cycle heat engine or a refrigerator or heat pump and I calculate the appropriate measure of performance for the specific device ie a thermal efficiency for a power cycle and a coefficient of performance COP for a refrigerator or heat pump List the appropriate assumptions to recover the mechanical energy balance from the general conservation of energy equation Learning Objectives Page 1 of2 Chapter 6 Chapter 6 Conservation of Angular Momentum 1 Define explain compare and contrast the following terms and concepts Motion of a rigid body Rectilinear translation vs Curvilinear translation Rotation about a fixed axis General motion Rotational motion Angular position 9 radians Angular velocity a radianssecond Angular acceleration a radiansseconds2 Angular momentum about origin 0 angular momentum about the origin 0 for a particle L7 I X mV specific angular momentum about the origin 0 lo r gtltV Where r is the position vector With respect to the origin 0 righthand rule sign convention vector nature of angular momentum units of angular momentum N 39m 39s lbf ft 39s Application of Accounting Principle for Angular Momentum rate of accumulation of angular momentum With the system amount of angular momentum about origin 0 Laws IltrgtltVgtpdV 9 s E mass moment of inertia about a single axis 39 relation between mass moment of inertia angular momentum and angular velocity transport rate of angular momentum across system boundaries transport With forces torques or moments of an external force about origin 0 Zr X Fm torque or moment of a couple ML7 mass transport of angular momentum about the 0 2m xv 7 2m xVgtm Learning Objectives Page 2 of 2 Chapter 6 generationconsumption of angular momentum Within the system Empirical Result gt Angular momentum is conserved Conservation of Angular Momentum about the origin 0 dL rate form d Z Mammal Z r X Fm Z rquot r X V Z rquot r X V t z I m an Due to couples Due to forces Due to mass transport Angular lmpulse SPECIAL CASE Plane Translational Motion of a Closed Rigid System angular momentum about origin 0 L7 w 1 6 X mVG Where rs the position vector of the center of mass With respect to the origin VG the velocity of the center of mass Conservation of Angular Momentum Liz zerzM rG meG ZrXFm ZZM7 dV Mrsxm altsZrgtltFmZZM7 since VGXVG 0 dV rGgtltm d Z1 gtltFMZM7 Where 139 the position vector With respect to the origin I39G the position vector of the center of mass With respect to the origin 2 Apply conservation of angular momentum to solve problems involving 1 steadystate open or closed systems 2 static stationary closed system 3 closed stationary rigidbody systems 4 translating closed rigid body systems ie systems with 30 and oc0 See item number 2 on the linear momentum objective page to see necessary steps