# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

11 Pages

### 0930

Course: PHY 2048, Fall 2009
School: Fayetteville State...
Rating:

Word Count: 858

#### Document Preview

Momentum Conservation (Tipler-Mosca Chapter 8) The Center of Mass (CM): The CM rcm moves as if all the external foces acting on the system were acting on the total mass M of the system located at this point. In particular, it moves with constant velocity, if the external forces acting on the system add to zero. Definition: M rcm = n n mi ri i=1 where M= i=1 mi . Here the sum is over the particles of the system, mi...

Register Now

#### Unformatted Document Excerpt

Coursehero >> North Carolina >> Fayetteville State University >> PHY 2048

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Momentum Conservation (Tipler-Mosca Chapter 8) The Center of Mass (CM): The CM rcm moves as if all the external foces acting on the system were acting on the total mass M of the system located at this point. In particular, it moves with constant velocity, if the external forces acting on the system add to zero. Definition: M rcm = n n mi ri i=1 where M= i=1 mi . Here the sum is over the particles of the system, mi are the masses and ri are the position vectors of the particles. In case of a continuous object, this becomes M rcm = r dm where dm is the position element of mass located at position r, see figure 8-4 of Tipler-Mosca. 1 Example: Figures 8-1, 8-2 and 8-3 of Tipler-Mosca. Two masses a placed on the x-axis and xcm is defined by M xcm = m1 x1 + m2 x2 where M = m1 + m2 . If the masses are equal (8-1), the CM is midway between them. If the masses are unequal (8-2), the CM is closer to the heavier mass. Let us choose (8-3) x1 = 0. Then xcm m2 m2 = x2 = x2 . M m1 + m2 PRS: Assume a 8-kg mass is at the origin and a 4-kg mass at x=0.6 m. The CM is then at (pick one): 1. 7.2 m 2. 0.3 m 3. 0.2 m 4. 0.4 m 5. 0.1 m 6. 1.8 m 2 Gravitational Potential Energy and CM The gravitational potential energy of a system of particles is given by n n U= i=1 mi g hi = g i=1 mi hi Therefore, by definition of the CM n U = g M hcm with M hcm = i=1 mi hi We can use this result to locate the CM experimentally: If we suspend an irregular object from a pivot, the object will rotate until the CM reaches its lowest point and the CM lies somewhere on the vertical line drawn directly downward from the pivot. By repeating this for several pivots, we find the CM. Demonstration: CM of Florida (compare figure 8-11 of Tipler-Mosca). 3 For the mathematicaly ambitious: Finding the CM by Integration Example 1: Uniform Stick Figure 8-12 of Tipler-Mosca. dm = M M x dm = L xcm dx M = dx L L M 2 x dx = x 2L 0 L = . 2 L L M xcm = = 0 ML 2 Example 2: Semicircular Hoop Figure 8-13 of Tipler-Mosca. dm = M ds M = R d R R 4 x coordinate: xcm = 0 M xcm = M x dm = R 0 0 M x R d = R R cos() R d 0 y coordinate: ycm MR = = 2 R/ MR cos() d = sin() =0. 0 M ycm = 2M R = M y dm = R /2 0 0 M y R d = R R sin() R d 0 /2 2M R sin() d = - cos() = 0 2M R 5 Motion of the CM Velocity of the CM: drcm dr1 dr2 = m1 + m2 + ... = M dt dt dt Differentiating again give the acceleration of the CM: n dri mi . dt i=1 n M acm = m1 a1 + m2 a2 + . . . = i=1 mi ai The acceleration of each particle is due to internal and external forces: mi ai = Fi = Fi,int + Fi,ext 6 According to Newton's third law the internal forces come in pairs which cancel and we find: n M acm = i=1 Fi,ext = Fnet,ext i mi The CM moves like a particle of mass M = external force acting on the system. under the influence of the net Example: Tipler-Mosca figure 8-18. 80 kg and 120 kg sit on a 60 kg rowboat 2 m apart. The boat is at rest on a calm lake and 80 kg sits at the center of the boat. 80 g and 120 kg switch places. How far does the boat move? 7 Solution: As there are no external forces, the CM does not change. Therefore, the difference in the CM position before and after the move is how far the boat moves. We choose the center of the boat as the coordinate origin and find: Before the move xcm After the move xcm = (120 kg) (0) + (60 kg) (0) + (80 kg) (2 m) = 0.615 m 80 kg + 60 kg + 120 kg (80 kg) (0) + (60 kg) (0) + (120 kg) (2 m) = = 0.923 m 80 kg + 60 kg + 120 kg Therefore, the boat moves x = xcm - xcm = 0.923 m - 0.615 m = 0.308 m . 8 Momentum Conservation Definition: The mass of a particle times it velocity is called momentum p = mv . Newton's second law can be written as Fnet = dp d(mv) dv = =m = ...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Fayetteville State University - PHY - 2048
Announcement 1. Dr. Baba Jain will be holding a help session on Friday, Oct. 10, at 3:30 pm in UPL 110. 2. Look up your mini scores on the CAPA system and compare with your records! 3. Dr. Frawley is responsible for mini 3. Results were not good (7.9
Fayetteville State University - PHY - 5846
PHY5846C: INTRODUCTION TO EXPERIMENTAL TECHNIQUESPARTICLE DETECTION 1. Consider an particle of 5 MeV kinetic energy moving in silicon; a what is its range i.e. the distance travelled before it stops? b make a rough estimate of the time required for
Fayetteville State University - PHY - 98
PHY5846C: INTRODUCTION TO EXPERIMENTAL TECHNIQUESPARTICLE DETECTION 1. Consider an particle of 5 MeV kinetic energy moving in silicon; a what is its range i.e. the distance travelled before it stops? b make a rough estimate of the time required for
Fayetteville State University - PHY - 5846
PHY5846C: INTRODUCTION TO EXPERIMENTAL TECHNIQUES1. The luminosity of a colliding beam machine is de ned by N= ; where N interactions occur per second for cross section . For a machine with n1; n2 particles per bunch in the two beams with nB bunches
Fayetteville State University - PHY - 98
PHY5846C: INTRODUCTION TO EXPERIMENTAL TECHNIQUES1. The luminosity of a colliding beam machine is de ned by N= ; where N interactions occur per second for cross section . For a machine with n1; n2 particles per bunch in the two beams with nB bunches
Fayetteville State University - PHY - 3802
Fayetteville State University - PHY - 3802
percent, since the ratio5/540 reduces to 0.0093 (rounded off) in decimal form.Significant DigitsThe accuracy of a measurement is often described in t e r m s of the number of significant digits used in expressing it. If the digits of a number resu
Fayetteville State University - PHY - 3802
Fayetteville State University - PHY - 3802
Fayetteville State University - PHY - 3802
ELEC 3700 Spring 2001Page 1 of 4Anatomy of a Data Sheet LF155 Series Op-AmpsOverviewThis is a dissection of the data sheet for the LF155 series op-amps. The first four pages of the Dec. 1994 version of this data sheet are published in the text
Fayetteville State University - PHY - 3802
IM.3. The Geiger-Mller Counter1. Purpose: Some measurements in nuclear decay, notions of statistics 2. Apparatus: Scaler-Timer (The Nucleus model 550),Geiger-Mller tube, oscilloscope, radioactive sources.3. Introduction:A typical Geiger-Mller (G
Fayetteville State University - PHY - 3802
IM.1. Franck-Hertz Experiment1. Purpose:Perform the historic Franck-Hertz experiment to demonstrate the existence of discrete energy levels in mercury, and to determine the minimum kinetic energy needed by an electron in order to collide inelastica
Fayetteville State University - PHY - 3802
July 23, 2001Massachusetts Institute of Technology Physics Department8.13/8.14 Junior Physics Laboratory Experiment #7 2001/2002The Franck-Hertz Experiment and the Ramsauer-Townsend EectElastic and Inelastic Scattering of Electrons by AtomsPU
Fayetteville State University - PHY - 3802
The e/m ratioObjective To measure the electronic charge-to-mass ratio e/m, by injecting electrons into a magnetic field and examining their trajectories. We also estimate the magnitude of the earth's magnetic field. Introduction This experiment demo
Fayetteville State University - PHY - 3802
Fayetteville State University - EML - 3015
GROUP 3 ! Human Cooling SystemGroup Members: Brian Hammond Darren Fancher Chris Batsch Charles Coleman04/13/091OverviewDesign Proposal Objective Applications Material Selection &amp; Specifications Similar Products Actual System Design Calculatio
Fayetteville State University - EML - 3016
Basic Fluid Properties and Governing EquationsDensity (): mass per unit volume (kg/m3 or slug/ft3) Specific Volume (v=1/): volume per unit mass Temperature (T): thermodynamic property that measures the molecular activity of an object. It is used to
Fayetteville State University - EML - 3016
Unsteady Heat Transfer in Semi-infinite SolidsSolidification process of the coating layer during a thermal spray operation is an unsteady heat transfer problem. As we discuss earlier, thermal spray process deposits thin layer of coating materials on
Fayetteville State University - EML - 3013
EML 3013 Dynamic Systems I Lab-1 Turn in these problems with your homework set #2Spring 2007Part A. A vehicle is moving along a straight line with its instantaneous velocity recorded in the attached spreadsheet: velocity as a function of time, v=
Fayetteville State University - EML - 3013
EML 3013HW-4Spring 200712185. If the end A of the cable is moving upwards at vA = 14 m/s, determine the speed of block B.12187. The cord is attached to the pin at C and passes over the two pulleys at A and D. The pulley at A is attached to th
Fayetteville State University - EML - 3013
EML 3013 Dynamic Systems I Lab-2 Spring 2007 (Turn in parts 2-A &amp; 2-B next Friday; turn in part 2-C with your lab report-experiment 2) Lab-2A. (also 13-96 from the textbook) The forked rod is used to move the smooth 2-lb particle around the horizonta
Fayetteville State University - EML - 3013
Homework 1 1218. A car is to be hoisted by elevator to the fourth floor of a parking garage, which is 48 ft above the ground. If the elevator can accelerate at 0.6 ft/s2, decelerate at 0.3 ft/s2, and reach a maximum speed of 8 ft/s, determine the sho
Fayetteville State University - EEL - 4746
68HC11 TimerHC11 or HC12: Chapter 10168HC11 Timer Subsystem Several timing functions: Basic timing Real time interrupts Output compare Input capture Computer Operating Properly Pulse Accumulator Pulse Width Modulation Based on a central
Fayetteville State University - EEL - 4746
68HC11 TimerChapter 10168HC11 Timer SubsystemSeveral timing functions: Basic timing Real time interrupts Output compare Input capture Computer Operating Properly Pulse Accumulator Pulse Width Modulation Based on a central timer Overflow
Fayetteville State University - EEL - 4746
Assembler ProgrammingChapter 6EEL-4746 Best PracticesEEL-4746 Best Practices1. All programs must begin with the following comment * * EEL-4746 Spring 2004 Semester * Homework #N Due (Due Date) * Problem #M * Name of Partner A * Name o
Fayetteville State University - EEL - 4746
68HC11 Serial I/OChapter 111Parallel I/OData_in Data_outNExt DeviceReady6811STRBMultiple I/O lines to transfer data from 6811 to Ext Device2Serial I/Oxmit rcvrExt Device6811Minimum of two lines needed to transfer data from 6
Fayetteville State University - EEL - 4746
68HC11 Parallel I/OChapter 7Microcontroller-Based SystemI/O Interface To I/OMemoryCPUBUS CPU: Central Processor Unit Microcontroller I/O: Input/Output e.g. M68HC11 Memory: Program and Data Bus: Address signals, Control signals, and Dat
Fayetteville State University - EEL - 4746
Number SystemsDecimal, Binary, and Hexadecimal1Base-N Number System Base N N Digits: 0, 1, 2, 3, 4, 5, ., N-1 Example: 1045N Positional Number SystemN LN N N N N d n -1 L d 4 d3 d 2 d1 d 0n -143210 Digit do is the least sign
Fayetteville State University - EEL - 4746
EEL 4746L Microprocessor Based System Design Lab Fall 2004Lab #4 InstructionsIn this lab, you will learn how to use THRSIM11 to simulate HC11 programs at home for purposes of homework assignments, projects, and lab assignments, in such a way that
Fayetteville State University - EEL - 4746
Experiment 1 Overview of the CME11E9-EVBU Development board &amp; Familiarization with running simple programsREFERENCES CME11e9-EVBU Development Board Instruction Manual (pdf file at the following link www.axman.com) EQUIPMENT &amp; MATERIALS CME11E9-EVBU
Fayetteville State University - EML - 4536
Beams and Framesbeam theory can be used to solve simple beams x complex beams with many cross section changes are solvable but lengthy x many 2-d and 3-d frame structures are better modeled by beam theoryxOne Dimensional ProblemsThe geometry of
Fayetteville State University - EML - 4536
General Procedure for Finite Element MethodFEM is based on Direct Stiffness approach or Displacement approach. A broad procedural outline is listed below 1. Discretize and select element type.Skeletal structuresSkeletal structure gets discretized
Fayetteville State University - EGM - 5611
EML 5300 CONTINUUM MECHANICS Dr. N. Chandra Fall 1999345 Engineering Building Class Hours: Tuesday, Thursday 8:55 to 10:10 am Phone: 410-6331 Office Hours:Tuesday 2:00 to 4:00 pmCOURSE OBJECTIVE To introduce the concept of the mechanics of defor
Fayetteville State University - EGM - 5611
MOHRS CIRCLE IN THREE DIMENSIONS Consider the state of stress given byT11 T12 T13 o T = T21 T22 T23 T31 T32 T33 {e ,e ,e } o1 o2 o3I II T is symmetric. When we determine the principal value, let T , T and T III be the principal value. Let T
Fayetteville State University - EGM - 5611
EML 5611 CONTINUUM MECHANICS Course Outline 1. Introduction (2 Lectures) Continuum Theory Definition and Ramifications Solids and Fluids General Principles and Field Equations 2. Cartesian Tensor Theory (6 Lectures) Indicial Notation Scalars, Vectors
Fayetteville State University - EGM - 5611
Review to Section 3.12 to 3.17 1. Time rate of change of element is given by the velocity gradient v where the differential is with respect to the spatial coordinate system. This can be decomposed into% where D and respectively.% W are the rate o
Fayetteville State University - EGM - 5611
I Piola- Kirchoff Stress Tensor Let\$ df = to .dAo .t o is the fictitious traction, has a direction of n \$ t = T noo odA t dAo Since % \$ o = dA T n = T dAn \$ % \$ To n dAo dAo to dAo = tdA to =T \$ \$ Q dAn = dAo (det F ) ( F -1 ) e3 T \$ T o
Fayetteville State University - PORTUGAL - 04
Modeling of CNT based compositesN. Chandra and C. ShetFAMU-FSU College of Engineering, Florida State University, Tallahassee, FL 32310AMMLAnswer: Currently NO!Ep x tlRs a h r e e rc e M trix aV l% N o C TC lc la n a u tio Pra l a lle96 .
Fayetteville State University - EML - 3
EML 3004CCHAPTER 3Engineers and the Real World?Namas Chandra Introduction to Mechanical engineeringChapter 3-1EML 3004CObjectivesExamine Society's View of Engineering Learn about the Role of Failure in Engineering Design Discuss Classic D
Fayetteville State University - EML - 3004
EML 3004CCHAPTER 3Engineers and the Real World?Namas Chandra Introduction to Mechanical engineeringChapter 3-1EML 3004CObjectivesExamine Society's View of Engineering Learn about the Role of Failure in Engineering Design Discuss Classic D
Fayetteville State University - EML - 3004
EML 3004CMechanical Engineering as A ProfessionDepartment of MEAACMIBQ0FAMU-FSU College of EngineeringNamas Chandra Mechanical engineering- a great professionME generalEML 3004CMechanical EngineeringMechanical engineers design, analyze
Fayetteville State University - EML - 3004
EML 3004CChapter 3: Force System ResultantsNamas Chandra Introduction to Mechanical engineeringHibbeler Chapter 3-1EML 3004CCross ProductThe Cross product of two vectors A and B C = A BMagnitude:C=AB sinDirection: C is perpend
Fayetteville State University - EML - 11
EML 3004CCHAPTER 11Materials and Mechanical EngineeirngNamas Chandra Introduction to Mechanical engineeringChapter 11-1EML 3004CRelative Mechanical Properties of Materials at Room TemperatureT A B L E 2 . 1 S t r e n g t hH a r d n e s s
Fayetteville State University - EML - 3004
EML 3004CCHAPTER 11Materials and Mechanical EngineeirngNamas Chandra Introduction to Mechanical engineeringChapter 11-1EML 3004CRelative Mechanical Properties of Materials at Room TemperatureT A B L E 2 . 1 S t r e n g t hH a r d n e s s
Fayetteville State University - EML - 3004
Chapter 9-Statics, Dynamics and Mechanical EngineeringObjectives and what should you Know: What are statics and Dynamics? What are the Newtons's three laws of motion? What is the difference between a scalar and a vector? How do you compute the c
Fayetteville State University - EML - 3004
EML 3004CCHAPTER 5Engineering Design ToolsNamas Chandra Introduction to Mechanical engineeringChapter 4-1EML 3004CObjectivesExamine the role of computer in engineering design Learn when and when not to use the computer. Examples of comput
Fayetteville State University - EML - 5
EML 3004CCHAPTER 5Engineering Design ToolsNamas Chandra Introduction to Mechanical engineeringChapter 4-1EML 3004CObjectivesExamine the role of computer in engineering design Learn when and when not to use the computer. Examples of comput
Fayetteville State University - EML - 3004
Find the integrals of the following problem. f ( y ) = y ln( y )dy Select one of the following: A) y 2 ln( y ) F ( y) = +C 2 F ( y) = y 2 ln( y ) - 1+ C 2 y 2 ln( y ) y 2 - +C 2 4B)C) D) E)F ( y) =F ( y ) = y 2 ln( y) - y 2 + C None of the A
Fayetteville State University - EML - 3004
Find the inverse of the function below p (t ) = 1.04t Select one of the following: p (t ) -1 = ln(1.04 * t ) p (t ) -1 = ln( 1.t04 ) p (t ) -1 = ln(t ) + ln(1.04) p (t ) -1 = ln(t ) * ln(1.04) None of the AboveA) B) C) D) E)To Solve: x = 1.04t in
Fayetteville State University - EML - 3004
Estimate the following limit. (3 + h) 3 - 27 lim =X h 0 h Select one of the following: A) B) C) D) E) X=0 X = 27 X=3 X=6 None of the AboveTo Solve: Approach from left and right side. h = 0.1 27.91 h = -0.1 26.11 lim (3 + h) 3 - 27 = 27 h 0 hAns
Fayetteville State University - EML - 2
EML3004C Introduction to Mechanical Engineering Fall 2002 Test #2 Time 65 minutes Name _ Student ID _Part AChoose only one of the following by marking a cross in the space. All questions carry equal points There are no negative points 1. A civil e
Fayetteville State University - EML - 3004
EML3004C Introduction to Mechanical Engineering Fall 2002 Test #2 Time 65 minutes Name _ Student ID _Part AChoose only one of the following by marking a cross in the space. All questions carry equal points There are no negative points 1. A civil e
Fayetteville State University - EML - 3004
EML 3004C Introduction to Mechanical Engineering Fall 2002Quiz # _ Date _Professor Namas Chandra Fall 2002
Fayetteville State University - EML - 3004
Introduction to Mechanical Engineering EML3004C-Fall 2002 Home work #2 Posted: 5September 02 Due: 12 September 02 1.Write a synopsis of the engineering disasters listed below. Make a comprehensive analysis of the disaster. a. Ford-Pinto case. b. Thre
Fayetteville State University - EML - 3004
Introduction to Mechanical Engineering EML3004C-Fall 2002 Group Project #1 Posted: 3 September 02 Due: 20 September 02 Points: 25 As a group, you need to come up with a comprehensive report on the historical, engineering, social aspects of the follow
Fayetteville State University - ECH - 4824
Without consulting the periodic table, classify the electronic configurations below as that of an inert gas, a halogen, an alkali metal, an alkaline earth metal or a transition metal:(a) 1s^2 2s^2 2p^6 3s^2 3p^5(b) 1s^2 2s^2 2p^6 3s^2 3p^6 3d^7 4
Fayetteville State University - EML - 3015
EML 3015C Description of Thermal-Fluids Design ProjectFall 2002As discussed in the Course Outline handed out at the beginning of the semester, each group will be responsible for proposing, designing and building a thermo-fluid `device' that illus
Fayetteville State University - EML - 3015
EML 3015C Thermal Fluids I Lab Exercise 1Fall 2002 September 4, 2002A solar collector plate is receiving solar irradiation from the sun at a rate of G=500 W/m2 outside a space station. It is known that this &quot;opaque&quot; collector has a reflectivity =
Fayetteville State University - EML - 3015
EML 3015C Thermal Fluids I Lab Assignment # 3 (Sept. 18, 2002)Fall 20021. Water is draining from a large tank with a cross-sectional area of 1 m2 through a small hole with an exit area of 0.01 m2 (a) Determine the velocity and mass flow rate of t
Fayetteville State University - EML - 3015
EML 3015C Fall 2002 Homework No. 2, Due Sept. 20, 2002 (Individual Assignment) In addition to the 2 problems below, please do the following from Fox and McDonald, FOURTH EDITION (the edition in the library): 3.15, 3.31, 3.34, 3.37 1. One side of the
Fayetteville State University - EML - 3016
Lab-1,Week 1, EML 3016 C- Spring 2003 Electronic Device CoolingA thin (assume zero thickness) electronic chip has a square shape of an area 5x5 cm2, is mounted on a PCB as shown. The outer surface of the chip is exposed to an air stream with a conve