MEEN 363. EXAMPLE of ANALYSIS (1 DOF) Luis San Andrés
|
|
- Buck Lawrence
- 5 years ago
- Views:
Transcription
1 MEEN 363. EAMPLE of ANALYSIS (1 DOF) Luis San Anrés Objectives: a) To erive EOM for a 1-DOF (one egree of freeom) system b) To unerstan concept of static equilibrium c) To learn the correct usage of physical units (US system) ) To calculate natural frequency an amping ratio e) To preict the time response (steay state an full transient) of a system f) To learn how to combine mathematical statements with explanatory sentences. Problem statement A pulley an cable system are assemble to pull a heavy block stuck in a hollow mining shaft. A motorcar imposes the known motion Z(t) require to pull the block. The stiffness K represents a flexible connection to the rive motorcar. The amping coefficient (C) represents the viscous rag between the block an shaft walls. Z K Y In the figure, YZ enote the static equilibrium position (SEP) of the system. a) Draw free boy iagrams for the block, label all forces an show their constitutive relation in terms of the motion coorinates, if applicable. b) Ientify the kinematical constraint relating motions Y an. The cable oes NOT slip on the pulley. c) Fin the static eflection ( ) of the spring element. ) Derive a single EOM for the block motion in terms of coorinate. θ M C For items (e) - (h) use K 1 5 lb/in, Mg5 lb, an C15 lb.s/in e) Fin the system natural frequency [Hz] an viscous amping ratio (ζ). f) The motorcar moves with Z(t)v t, where v 1 ft/. What is the terminal or final velocity of the block (M) in (ft/)? g) Fin the complete solution to the problem. That is fin (t) STATIC EQUILIBRIUM POSITION (SEP) SEP means no motion of block or external agent holing spring - cable. Thus, at the SEP spring K is alreay eflecte since it must support 5% of the block weight (W) as easily seen from the cable & pulley constraint. This knowlege is BASIC, oes not require of elaborate thinking or eriving lengthy equations. Important: Z(t) is KNOWN for all times, i.e. a function of time impose on the system by an external agent (motorcar)
2 FREE BODY iagrams an kinematic constraints Definitions: T Tension from cable connecting block to spring. Cable is NOT extensible F s force in spring connecting external DRIVE agent to inextensible cable F D viscous rag force static eflection for spring To raw FBDs, assume a state of motion >, (Z-Y)>. These mathematical statements mean: block moves UP, an spring is transmitting a force also upwars an to the left, see iagrams where F rive F spring T K + K (Z-Y) Note that (K W/ ) is the static force in the spring. This the static force necessary to hol the system statically, i.e. without motion. Hence.5 W/K
3 W : 5 lb K 1 5 lb in : C 15 lb (a) Assume a state of motion with Z-Y>, > ie. motorcar pulls block : in Z M : W g Y Drive force From the FBD iagram, assume >, an apply Newton's n law to obtain: M t W F Damper + T (1) where F Damper C t T K ( Z Y) + K F Drive () is the viscous rag force (3) T is the cable tension. (Z-Y)>, an δs is the spring static eflection (b) kinematic constraint - inextensible cable K W T M T FD C /t T The cable length is constant, thus an the kinematic constraint follows as (c) Static eflection of spring l c l c + Y Y (4) By efinition of SEP (Static equilibrium position), i.e. when ZY an at rest (without motion): W + K (5) (K δs ) is the static force neee to HOLD the block w/o motion Static eflection of the spring is: : W K.5 in (c) Derive single EOM for block motion Substituting (), (3) an (4) into EOM (1) reners Note: EOM cannot contain internal forces (Tension for example). The tension is DETERMINED by the motion. M t W C + K ( Z ) + K δ t s (6)
4 an thus the final EOM is: + C + 4 K K Zt () Ft () t t M (7) Note K Zt ()"appears" as a (ynamic) external force riving the block into motion. (e) Calculate natural frequency an viscous amping ratio: ω n : 4K W g.5 ω n f n : ω n π f n Hz ω : ω n 1 ζ 1 The amping ratio is rather large - motion will be oscillatory but quickly ampe! T : f The ampe natural frequency an perio of motion are: f ζ C 1 : T n :.5 f W ζ.33 n 4 K g ( ).5 ω ra 6.49 Hz T.38 f : ω π
5 (f) pulling motocar moves with constant spee v, FIND terminal spee of block Let Hence: v : 1 ft zt () vt : (8) + C + 4 K K zt () Ft () t t M (7) What is steay-state motion? Since z(t) is linear in time, the particular solution to eqn (7) is: i.e block ALSO moves with constant SPEED p a + b t t p (8) b t p To fin the en or terminal velocity, take the time erivative of (7) 3 M 3 P t + C P + 4 K t t P K v Using the knowlege from erivatives of p 4 K t P K v Terminal velocity of block: t P v v.5 ft A more elaborate way follows from fining the whole particular solution: Substitute (8) into EOM (7) to fin Cb + 4 Ka ( + bt ) K v t From: equating like-powers of t Cb 4 K + K a b K p () t : a+ bt terminal velocity at which block moves is b.5 ft v Hence: v b : b 6 in C b a : K a.45 in
6 (g) fin the full transient response - ynamic motion of block Particular solution: P + C P + K P A + B t t t p a + b t M 1 a A C B b K K Complete solution: t () H + P B K..15 p () t.1 zt () t t () e ζ ( ( ) ( )) ω n t C 1 cos ω t + C sin ω t + ( a + b t) (11) t e ζ ω n t ( D 1 cos( ω t) + D sin( ω t) ) + b (1) Where D 1 ζ ω n C 1 + C ω D ζ ω n C (13) C ω satisfy initial conitions at t: from (11) an (1) at time t an from (13) o : ft o C 1 + a V o D 1 + b D 1 + ζω n C 1 C : ω V o : ft D C 1 : o a D 1 : V o b : ζ ω n C motion starts from rest C ω C 1.45 in C. in D 1 6 in D in
7 Let's graph the response for time values up to 4 x ampe perio (my choice) t (): e ζ ω n t ( C 1 cos( ω t) + C sin( ω t) ) + ( a + b t) ( ( ) ( )) Vt () e ζ ω n t : D 1 cos ω t + D sin ω t + b T max : 4 T velocity (ft/) time (s) V(t) V final (ft) t () a+ b t t time (s) motion - relative to steay state.4 t () ( a+ bt ) t
8 Spring (cable) force (ynamic+static) F s () t : K ( zt () t ()) W lb + K K lb Spring force (lbf) ( ) F s T max lb time (s) at steay state, spring (cable) force approaches ( a).115 in since: is the final eflection of spring F SS () t : K vt ( a + b t) + v 1 ft b ( ) F SS : K a 1 ft F SS lb as the graph shows!
a) Identify the kinematical constraint relating motions Y and X. The cable does NOT slip on the pulley. For items (c) & (e-f-g) use
EAMPLE PROBLEM for MEEN 363 SPRING 6 Objectives: a) To erive EOMS of a DOF system b) To unerstan concept of static equilibrium c) To learn the correct usage of physical units (US system) ) To calculate
More informationCable holds system BUT at t=0 it breaks!! θ=20. Copyright Luis San Andrés (2010) 1
EAMPLE # for MEEN 363 SPRING 6 Objectives: a) To erive EOMS of a DOF system b) To unerstan concept of static equilibrium c) To learn the correct usage of physical units (US system) ) To calculate natural
More informationDeriving 1 DOF Equations of Motion Worked-Out Examples. MCE371: Vibrations. Prof. Richter. Department of Mechanical Engineering. Handout 3 Fall 2017
MCE371: Vibrations Prof. Richter Department of Mechanical Engineering Handout 3 Fall 2017 Masses with Rectilinear Motion Follow Palm, p.63, 67-72 and Sect.2.6. Refine your skill in drawing correct free
More informationFinal Exam April 30, 2013
Final Exam Instructions: You have 120 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic
More informationMEEN Cheat Sheet for SDOF motion
MEEN 67 - Cheat Sheet for SDOF motion EOM: Me yke yce yf() t Luis San Anres - January 03 Pages an (only) allowe in exams Given a mechanical system with equivalent parameters (Me) mass, (Ke) stiffness,
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle Chapter Objectives To introduce the concept of the free-body diagram for a particle To show how to solve particle equilibrium
More informationME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given:
PROBLEM No. 2 (20 pts.) Given: Blocks A and B (having masses of 2m and m, respectively) are connected by an inextensible cable, with the cable being pulled over a small pulley of negligible mass. Block
More informationDetermine the angle θ between the two position vectors.
-100. Determine the angle θ between the two position vectors. -105. A force of 80 N is applied to the handle of the wrench. Determine the magnitudes of the components of the force acting along the axis
More informationENGINEERING MECHANICS BAA1113
ENGINEERING MECHANICS BAA1113 Chapter 3: Equilibrium of a Particle (Static) by Pn Rokiah Bt Othman Faculty of Civil Engineering & Earth Resources rokiah@ump.edu.my Chapter Description Aims To explain the
More informationTutorial Test 5 2D welding robot
Tutorial Test 5 D weling robot Phys 70: Planar rigi boy ynamics The problem statement is appene at the en of the reference solution. June 19, 015 Begin: 10:00 am En: 11:30 am Duration: 90 min Solution.
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle 1 Chapter Objectives Concept of the free-body diagram for a particle Solve particle equilibrium problems using the equations
More informationTOPIC E: OSCILLATIONS EXAMPLES SPRING Q1. Find general solutions for the following differential equations:
TOPIC E: OSCILLATIONS EXAMPLES SPRING 2019 Mathematics of Oscillating Systems Q1. Find general solutions for the following differential equations: Undamped Free Vibration Q2. A 4 g mass is suspended by
More informationEQUATIONS OF MOTION: RECTANGULAR COORDINATES
EQUATIONS OF MOTION: RECTANGULAR COORDINATES Today s Objectives: Students will be able to: 1. Apply Newton s second law to determine forces and accelerations for particles in rectilinear motion. In-Class
More informationMechatronics. MANE 4490 Fall 2002 Assignment # 1
Mechatronics MANE 4490 Fall 2002 Assignment # 1 1. For each of the physical models shown in Figure 1, derive the mathematical model (equation of motion). All displacements are measured from the static
More informationPhysics 170 Week 7, Lecture 2
Physics 170 Week 7, Lecture 2 http://www.phas.ubc.ca/ goronws/170 Physics 170 203 Week 7, Lecture 2 1 Textbook Chapter 12:Section 12.2-3 Physics 170 203 Week 7, Lecture 2 2 Learning Goals: Learn about
More informationGiven: We are given the drawing above and the assumptions associated with the schematic diagram.
PROBLEM 1: (30%) The schematic shown below represents a pulley-driven machine with a flexible support. The three coordinates shown are absolute coordinates drawn with respect to the static equilibrium
More information3.7 Implicit Differentiation -- A Brief Introduction -- Student Notes
Fin these erivatives of these functions: y.7 Implicit Differentiation -- A Brief Introuction -- Stuent Notes tan y sin tan = sin y e = e = Write the inverses of these functions: y tan y sin How woul we
More informationIf the solution does not follow a logical thought process, it will be assumed in error.
Please indicate your group number (If applicable) Circle Your Instructor s Name and Section: MWF 8:30-9:20 AM Prof. Kai Ming Li MWF 2:30-3:20 PM Prof. Fabio Semperlotti MWF 9:30-10:20 AM Prof. Jim Jones
More informationarxiv:physics/ v2 [physics.ed-ph] 23 Sep 2003
Mass reistribution in variable mass systems Célia A. e Sousa an Vítor H. Rorigues Departamento e Física a Universiae e Coimbra, P-3004-516 Coimbra, Portugal arxiv:physics/0211075v2 [physics.e-ph] 23 Sep
More informationLecture 2 Lagrangian formulation of classical mechanics Mechanics
Lecture Lagrangian formulation of classical mechanics 70.00 Mechanics Principle of stationary action MATH-GA To specify a motion uniquely in classical mechanics, it suffices to give, at some time t 0,
More informationAnnouncements. Equilibrium of a Particle in 2-D
nnouncements Equilibrium of a Particle in 2-D Today s Objectives Draw a free body diagram (FBD) pply equations of equilibrium to solve a 2-D problem Class ctivities pplications What, why, and how of a
More informationLecture 3: Development of the Truss Equations.
3.1 Derivation of the Stiffness Matrix for a Bar in Local Coorinates. In 3.1 we will perform Steps 1-4 of Logan s FEM. Derive the truss element equations. 1. Set the element type. 2. Select a isplacement
More informationProblem 1: Find the Equation of Motion from the static equilibrium position for the following systems: 1) Assumptions
Problem 1: Find the Equation of Motion from the static equilibrium position for the following systems: 1) Assumptions k 2 Wheels roll without friction k 1 Motion will not cause block to hit the supports
More informationChapter 5 Design. D. J. Inman 1/51 Mechanical Engineering at Virginia Tech
Chapter 5 Design Acceptable vibration levels (ISO) Vibration isolation Vibration absorbers Effects of damping in absorbers Optimization Viscoelastic damping treatments Critical Speeds Design for vibration
More informationFigure XP3.1 (a) Mass in equilibrium, (b) Freebody diagram, (c) Kinematic constraint relation Example Problem 3.1 Figure XP3.1 illustrates a mass m
LECTURE 7. MORE VIBRATIONS ` Figure XP3.1 (a) Mass in equilibrium, (b) Freebody diagram, (c) Kinematic constraint relation Example Problem 3.1 Figure XP3.1 illustrates a mass m that is in equilibrium and
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. In-Class
More informationUnit #6 - Families of Functions, Taylor Polynomials, l Hopital s Rule
Unit # - Families of Functions, Taylor Polynomials, l Hopital s Rule Some problems an solutions selecte or aapte from Hughes-Hallett Calculus. Critical Points. Consier the function f) = 54 +. b) a) Fin
More informationAN INTRODUCTION TO AIRCRAFT WING FLUTTER Revision A
AN INTRODUCTION TO AIRCRAFT WIN FLUTTER Revision A By Tom Irvine Email: tomirvine@aol.com January 8, 000 Introuction Certain aircraft wings have experience violent oscillations uring high spee flight.
More information6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads.
6.6 FRAMES AND MACHINES APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationCore Mathematics M1. Dynamics (Planes)
Edexcel GCE Core Mathematics M1 Dynamics (Planes) Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil Advice to Candidates You must ensure that your
More informationCHAPTER 2: EQUILIBRIUM OF RIGID BODIES
For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be zero Summation of all external forces. Equilibrium: Sum of moments of all external forces.
More informationLectures HD#14 Dynamic response of continuous systems. Date: April
ectures -3 Date: April 4 7 Toay: Vibrations of continuous systems HD#4 Dynamic response of continuous systems Free vibrations of elastic bars an beams. Properties of normal moe functions. Force response
More informationAssignment 1. g i (x 1,..., x n ) dx i = 0. i=1
Assignment 1 Golstein 1.4 The equations of motion for the rolling isk are special cases of general linear ifferential equations of constraint of the form g i (x 1,..., x n x i = 0. i=1 A constraint conition
More informationCIRCULAR MOTION AND SHM: Solutions to Higher Level Questions
CIRCULAR MOTION AND SHM: Solutions to Higher Level Questions ****ALL QUESTIONS-ANSWERS ARE HIGHER LEVEL*** Solutions 015 Question 6 (i) Explain what is meant by centripetal force. The force - acting in
More informationME 141. Engineering Mechanics
ME 141 Engineering Mechanics Lecture : Statics of particles Ahma Shahei Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.b, shakil6791@gmail.com Website: teacher.buet.ac.b/sshakil
More informationNumerical Integrator. Graphics
1 Introuction CS229 Dynamics Hanout The question of the week is how owe write a ynamic simulator for particles, rigi boies, or an articulate character such as a human figure?" In their SIGGRPH course notes,
More informationBohr Model of the Hydrogen Atom
Class 2 page 1 Bohr Moel of the Hyrogen Atom The Bohr Moel of the hyrogen atom assumes that the atom consists of one electron orbiting a positively charge nucleus. Although it oes NOT o a goo job of escribing
More informationFRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a
FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations
More informationCHAPTER 4 NEWTON S LAWS OF MOTION
62 CHAPTER 4 NEWTON S LAWS O MOTION CHAPTER 4 NEWTON S LAWS O MOTION 63 Up to now we have described the motion of particles using quantities like displacement, velocity and acceleration. These quantities
More informationMath 115 Section 018 Course Note
Course Note 1 General Functions Definition 1.1. A function is a rule that takes certain numbers as inputs an assigns to each a efinite output number. The set of all input numbers is calle the omain of
More informationMath Notes on differentials, the Chain Rule, gradients, directional derivative, and normal vectors
Math 18.02 Notes on ifferentials, the Chain Rule, graients, irectional erivative, an normal vectors Tangent plane an linear approximation We efine the partial erivatives of f( xy, ) as follows: f f( x+
More information16.30/31, Fall 2010 Recitation # 1
6./, Fall Recitation # September, In this recitation we consiere the following problem. Given a plant with open-loop transfer function.569s +.5 G p (s) = s +.7s +.97, esign a feeback control system such
More informationChapter 2 Lagrangian Modeling
Chapter 2 Lagrangian Moeling The basic laws of physics are use to moel every system whether it is electrical, mechanical, hyraulic, or any other energy omain. In mechanics, Newton s laws of motion provie
More informationChapter 5. The Laws of Motion
Chapter 5 The Laws of Motion The Laws of Motion The description of an object in motion included its position, velocity, and acceleration. There was no consideration of what might influence that motion.
More informationThe Principle of Least Action
Chapter 7. The Principle of Least Action 7.1 Force Methos vs. Energy Methos We have so far stuie two istinct ways of analyzing physics problems: force methos, basically consisting of the application of
More informationME 563 Mechanical Vibrations Lecture #1. Derivation of equations of motion (Newton-Euler Laws)
ME 563 Mechanical Vibrations Lecture #1 Derivation of equations of motion (Newton-Euler Laws) Derivation of Equation of Motion 1 Define the vibrations of interest - Degrees of freedom (translational, rotational,
More information:= 0.75 Ns m K N m. := 0.05 kg. K N m. (a.1) FBD and forces. (a.2) derive EOM From the FBD diagram, Newton's 2nd law states:
P FA - Derive EO for simple mechanical system L San Andres (c) For the system shown in the figure, Z (t) Z o cos( t) is a periodic displacement input (known). Perform the following tasks: a) Set X(t) as
More information2.003 Engineering Dynamics Problem Set 4 (Solutions)
.003 Engineering Dynamics Problem Set 4 (Solutions) Problem 1: 1. Determine the velocity of point A on the outer rim of the spool at the instant shown when the cable is pulled to the right with a velocity
More informationEQUILIBRIUM OF A PARTICLE, THE FREE-BODY DIAGRAM & COPLANAR FORCE SYSTEMS
EQUILIBRIUM OF PRTICLE, THE FREE-BODY DIGRM & COPLNR FORCE SYSTEMS Today s Objectives: Students will be able to : a) Draw a free body diagram (FBD), and, b) pply equations of equilibrium to solve a 2-D
More informationWorksheet 4: Energy. 1 Mechanical Energy
Name: 3DigitCoe: Worksheet 4: Energy 1 Mechanical Energy ##$%$ A) B) C) D) ##$)$ ##$($ ##$'$ ##$&$ (left) Threeballsarefiresimultaneouslywithequal spees from the same height above the groun. Ball 1 is
More informationFigure 5.28 (a) Spring-restrained cylinder, (b) Kinematic variables, (c) Free-body diagram
Lecture 30. MORE GENERAL-MOTION/ROLLING- WITHOUT-SLIPPING EXAMPLES A Cylinder, Restrained by a Spring and Rolling on a Plane Figure 5.28 (a) Spring-restrained cylinder, (b) Kinematic variables, (c) Free-body
More informationVector and scalar quantities
Vector and scalar quantities A scalar quantity is defined only by its magnitude (or size) for example: distance, speed, time. It is easy to combine two or more scalar quantities e.g. 2 metres + 3 metres
More informationRead textbook CHAPTER 1.4, Apps B&D
Lecture 2 Read textbook CHAPTER 1.4, Apps B&D Today: Derive EOMs & Linearization undamental equation of motion for mass-springdamper system (1DO). Linear and nonlinear system. Examples of derivation of
More information+ ] B A BA / t BA / n. B G BG / t BG / n. a = (5)(4) = 80 in./s. A G AG / t AG / n. ] + [48 in./s ]
PROLEM 15.113 3-in.-radius drum is rigidly attached to a 5-in.-radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that
More informationDynamical Systems. Mechanical Systems
EE/ME/AE324: Dynamical Systems Chapter 2: Modeling Translational Mechanical Systems Common Variables Used Assumes 1 DoF per mass, i.e., all motion scalar Displacement: x ()[ t [m] Velocity: dx() t vt ()
More informationDifferentiability, Computing Derivatives, Trig Review
Unit #3 : Differentiability, Computing Derivatives, Trig Review Goals: Determine when a function is ifferentiable at a point Relate the erivative graph to the the graph of an original function Compute
More informationIsaac Newton ( ) 1687 Published Principia Invented Calculus 3 Laws of Motion Universal Law of Gravity
Isaac Newton (1642-1727) 1687 Published Principia Invented Calculus 3 Laws of Motion Universal Law of Gravity Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of
More informationCheck Homework. Reading Quiz Applications Equations of Equilibrium Example Problems Concept Questions Group Problem Solving Attention Quiz
THREE-DIMENSIONAL FORCE SYSTEMS Today s Objectives: Students will be able to solve 3-D particle equilibrium problems by a) Drawing a 3-D free body diagram, and, b) Applying the three scalar equations (based
More informationG4003 Advanced Mechanics 1. We already saw that if q is a cyclic variable, the associated conjugate momentum is conserved, L = const.
G4003 Avance Mechanics 1 The Noether theorem We alreay saw that if q is a cyclic variable, the associate conjugate momentum is conserve, q = 0 p q = const. (1) This is the simplest incarnation of Noether
More informationAnnouncements. Equilibrium of a Rigid Body
Announcements Equilibrium of a Rigid Body Today s Objectives Identify support reactions Draw a free body diagram Class Activities Applications Support reactions Free body diagrams Examples Engr221 Chapter
More informationNewton s 3 Laws of Motion
Newton s 3 Laws of Motion 1. If F = 0 No change in motion 2. = ma Change in motion Fnet 3. F = F 1 on 2 2 on 1 Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of
More informationWelcome back to Physics 211
Welcome back to Physics 211 Today s agenda: Weight Friction Tension 07-1 1 Current assignments Thursday prelecture assignment. HW#7 due this Friday at 5 pm. 07-1 2 Summary To solve problems in mechanics,
More information7.6 Journal Bearings
7.6 Journal Bearings 7.6 Journal Bearings Procedures and Strategies, page 1 of 2 Procedures and Strategies for Solving Problems Involving Frictional Forces on Journal Bearings For problems involving a
More informationChapter 4: Newton s Second Law F = m a. F = m a (4.2)
Lecture 7: Newton s Laws and Their Applications 1 Chapter 4: Newton s Second Law F = m a First Law: The Law of Inertia An object at rest will remain at rest unless, until acted upon by an external force.
More informationLecture 6 mechanical system modeling equivalent mass gears
M2794.25 Mechanical System Analysis 기계시스템해석 lecture 6,7,8 Dongjun Lee ( 이동준 ) Department of Mechanical & Aerospace Engineering Seoul National University Dongjun Lee Lecture 6 mechanical system modeling
More informationDSC HW 3: Assigned 6/25/11, Due 7/2/12 Page 1
DSC HW 3: Assigned 6/25/11, Due 7/2/12 Page 1 Problem 1 (Motor-Fan): A motor and fan are to be connected as shown in Figure 1. The torque-speed characteristics of the motor and fan are plotted on the same
More informationVector Mechanics: Statics
PDHOnline Course G492 (4 PDH) Vector Mechanics: Statics Mark A. Strain, P.E. 2014 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088 www.pdhonline.org www.pdhcenter.com
More informationAnswers without work shown will not be given any credit.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 2012 Problem 1 of 4 (25 points) Exam 1 Solutions with Grading Scheme Answers without work shown will not be given any
More informationMechanisms Simple Machines. Lever, Wheel and Axle, & Pulley
Mechanisms Simple Machines Lever, Wheel and Axle, & Pulley Simple Machines Mechanisms that manipulate magnitude of force and distance. The Six Simple Machines Lever Wheel and Axle Pulley The Six Simple
More informationA. B. C. D. E. v x. ΣF x
Q4.3 The graph to the right shows the velocity of an object as a function of time. Which of the graphs below best shows the net force versus time for this object? 0 v x t ΣF x ΣF x ΣF x ΣF x ΣF x 0 t 0
More informationThe Principle of Least Action and Designing Fiber Optics
University of Southampton Department of Physics & Astronomy Year 2 Theory Labs The Principle of Least Action an Designing Fiber Optics 1 Purpose of this Moule We will be intereste in esigning fiber optic
More informationNewton s Laws.
Newton s Laws http://mathsforeurope.digibel.be/images Forces and Equilibrium If the net force on a body is zero, it is in equilibrium. dynamic equilibrium: moving relative to us static equilibrium: appears
More informationDifferentiability, Computing Derivatives, Trig Review. Goals:
Secants vs. Derivatives - Unit #3 : Goals: Differentiability, Computing Derivatives, Trig Review Determine when a function is ifferentiable at a point Relate the erivative graph to the the graph of an
More informationPhysics 2211 ABC Quiz #3 Solutions Spring 2017
Physics 2211 ABC Quiz #3 Solutions Spring 2017 I. (16 points) A block of mass m b is suspended vertically on a ideal cord that then passes through a frictionless hole and is attached to a sphere of mass
More informationEng Sample Test 4
1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by
More informationME 375 EXAM #1 Friday, March 13, 2015 SOLUTION
ME 375 EXAM #1 Friday, March 13, 2015 SOLUTION PROBLEM 1 A system is made up of a homogeneous disk (of mass m and outer radius R), particle A (of mass m) and particle B (of mass m). The disk is pinned
More informationSpring 2016 Network Science
Spring 206 Network Science Sample Problems for Quiz I Problem [The Application of An one-imensional Poisson Process] Suppose that the number of typographical errors in a new text is Poisson istribute with
More informationFALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing 2.
More informationApplications of First Order Equations
Applications of First Orer Equations Viscous Friction Consier a small mass that has been roppe into a thin vertical tube of viscous flui lie oil. The mass falls, ue to the force of gravity, but falls more
More informationMEM202 Engineering Mechanics - Statics MEM
E Engineering echanics - Statics E hapter 6 Equilibrium of Rigid odies k j i k j i R z z r r r r r r r r z z E Engineering echanics - Statics Equilibrium of Rigid odies E Pin Support N w N/m 5 N m 6 m
More informationSection 2.1 The Derivative and the Tangent Line Problem
Chapter 2 Differentiation Course Number Section 2.1 The Derivative an the Tangent Line Problem Objective: In this lesson you learne how to fin the erivative of a function using the limit efinition an unerstan
More information05 The Continuum Limit and the Wave Equation
Utah State University DigitalCommons@USU Founations of Wave Phenomena Physics, Department of 1-1-2004 05 The Continuum Limit an the Wave Equation Charles G. Torre Department of Physics, Utah State University,
More informationPhysics 2514 Lecture 13
Physics 2514 Lecture 13 P. Gutierrez Department of Physics & Astronomy University of Oklahoma Physics 2514 p. 1/18 Goals We will discuss some examples that involve equilibrium. We then move on to a discussion
More informationCalculus in the AP Physics C Course The Derivative
Limits an Derivatives Calculus in the AP Physics C Course The Derivative In physics, the ieas of the rate change of a quantity (along with the slope of a tangent line) an the area uner a curve are essential.
More informationTruss Analysis Method of Joints. Steven Vukazich San Jose State University
Truss nalysis Method of Joints Steven Vukazich San Jose State University General Procedure for the nalysis of Simple Trusses using the Method of Joints 1. raw a Free Body iagram (FB) of the entire truss
More informationShort Intro to Coordinate Transformation
Short Intro to Coorinate Transformation 1 A Vector A vector can basically be seen as an arrow in space pointing in a specific irection with a specific length. The following problem arises: How o we represent
More informationWhen a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero.
When a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero. 0 0 0 0 k M j M i M M k R j R i R F R z y x z y x Forces and moments acting on a rigid body could be
More informationEquilibrium of a Particle
ME 108 - Statics Equilibrium of a Particle Chapter 3 Applications For a spool of given weight, what are the forces in cables AB and AC? Applications For a given weight of the lights, what are the forces
More information1. Draw a FBD of the toy plane if it is suspended from a string while you hold the string and move across the room at a constant velocity.
1. Draw a FBD of the toy plane if it is suspended from a string while you hold the string and move across the room at a constant velocity. 2. A 15 kg bag of bananas hangs from a taunt line strung between
More informationIB Math High Level Year 2 Calc Differentiation Practice IB Practice - Calculus - Differentiation (V2 Legacy)
IB Math High Level Year Calc Differentiation Practice IB Practice - Calculus - Differentiation (V Legac). If =, fin the two values of when = 5. Answer:.. (Total marks). Differentiate = arccos ( ) with
More informationWeek 9 solutions. k = mg/l = /5 = 3920 g/s 2. 20u + 400u u = 0,
Week 9 solutions ASSIGNMENT 20. (Assignment 19 had no hand-graded component.) 3.7.9. A mass of 20 g stretches a spring 5 cm. Suppose that the mass is also attached to a viscous damper with a damping constant
More informationThe Laws of Motion. Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples
The Laws of Motion Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples Gravitational Force Gravitational force is a vector Expressed by Newton s Law of Universal
More informationPhysics 12 January 2000 Provincial Examination
Physics 12 January 2000 Provincial Examination ANSWER KEY / SCORING GUIDE Organizers CURRICULUM: Sub-Organizers 1. Vector Kinematics in Two Dimensions A, B and Dynamics and Vector Dynamics C, D 2. Work,
More informationPhysics 111 Lecture 4 Newton`s Laws
Physics 111 Lecture 4 Newton`s Laws Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com he Laws of Motion q Newton s first law q Force q Mass q Newton s second law q Newton s third law q Examples Isaac
More informationChapter 5. The Laws of Motion
Chapter 5 The Laws of Motion The Laws of Motion The description of an object in There was no consideration of what might influence that motion. Two main factors need to be addressed to answer questions
More informationAutomobile manual transmission
Design of Shaft A shaft is a rotating member usually of circular crosssection (soli or hollow), which is use to transmit power an rotational motion. Axles are non rotating member. Elements such as gears,
More informationQ2. A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book.
AP Physics 1- Dynamics Practice Problems FACT: Inertia is the tendency of an object to resist a change in state of motion. A change in state of motion means a change in an object s velocity, therefore
More informationARCH 614 Note Set 5 S2012abn. Moments & Supports
RCH 614 Note Set 5 S2012abn Moments & Supports Notation: = perpenicular istance to a force from a point = name for force vectors or magnitue of a force, as is P, Q, R x = force component in the x irection
More informationGAYAZA HIGH SCHOOL MATHS SEMINAR 2016 APPLIED MATHS
GAYAZA HIGH SCHOOL MATHS SEMINAR 06 APPLIED MATHS STATISTICS AND PROBABILITY. (a) The probability that Moses wins a game is /. If he plays 6 games, what is (i) the epecte number of games won? (ii) the
More information