PY241 Solutions Set 9 (Dated: November 7, 2002)
|
|
- Corey Simpson
- 6 years ago
- Views:
Transcription
1 PY241 Solutions Set 9 (Dated: Noveber 7, 2002) 9-9 At what displaceent of an object undergoing siple haronic otion is the agnitude greatest for the... (a) velocity? The velocity is greatest at x = 0, the equilibriu position. At any other position, there is both inetic energy and spring energy, but at the equilibriu, all of the energy is inetic. Maxiu inetic energy axiu velocity (b) acceleration? Newton s law applied to a spring tells us: F = a = x a = x, thus acceleration is greatest when the spring is copressed/stretched the greatest. For an oscillation with aplitude A, the greatest acceleration is at x = ±A 9-15 When a 30 N ass is applied to a spring, it stretches 0.2. (a) If a 5 g ass is hung fro the spring and reains at rest, how uch is the string stretched fro its original length? Knowing that the spring stretches 0.2 with 30 N applied to it, we can solve for the spring constant. F = x 30 N = (0.2 ) = 150 N 1 (1) Now that we have, we can solve for the distance any force will stretch the spring. For a 5 g ass hanging on the spring, the resulting stretching is: g = x (5 g)(9.8 s 2 ) = (150 N 1 )(x) x =.326 (2) (b) What is the period of oscillation of the ass and the spring? The period is defined as: T = 1 ( 1 f = 2π T = (2π) ) 1 = (2π) 5 g = 1.15 s (3) 150 N A 50 g boy rides on a Pogo stic, a pole with a spring on its botto. lands on the ground, copressing the spring.05. He jups into the air 0.3 and (a) How uch energy is stored in the spring? By the conservation of energy, all of the gravitational potential energy at the pea of the jup ust be converted to spring potential energy when the boy hits the ground. U spring = GP E = gh = (50 g)(9.8 s 2 )(0.3 ) = 147 J (4)
2 2 (b) What is the spring constant? U spring = 1 2 x2 = 147 J 1 2 (0.05 )2 = 147 J = (2)(147 J) (0.05 ) 2 = 117, 600 N 1 (5) (c) What is the characteristic frequency of oscillation? 2π = 1 117, 600 N 1 = 7.72 Hz (6) 2π 50 g 9-42 The otolith in a fish has a ass of.022 g = g, and the effective spring constant is 3 N 1. (a) What is the characteristic frequency of the otolith? We can calculate the frequency using the sae procedure as before: 2π = 1 3 N 1 2π = Hz (7) g This oscillation is a daped. This eans that over tie the aplitude will decrease, as will the frequency. Therefore this frequency will only be correct very shortly after the onset of oscillation. (b) Is the frequency consistent with the idea that the otolith should respond rapidly to changes in orientation? The period corresponding to this frequency is T = 1/f =.017 s. This is a very short aount of tie, which agrees with the idea that the otolith responds rapidly to changes in orientation The huan leg can be approxiated by a cylinder. (a) Estiate the characteristic frequency of your legs, when swung fro the hip with the nee loced. In this proble we are treating the huan leg as a physical pendulu. physical pendulu is: gd 2π I The frequency associated with a (8) Where I is the oent of inertia for the object that is oscillating. If we approxiate waling otion as a rod (the leg) rotating about its end, we can then directly apply the forula above. The oent of inertia of a rod or cylinder rotating about its end it I = 1 3 l2. d is the distance fro the rotation axis to the center of gravity of the object. For
3 3 siplicity let us tae d = l/2. Plugging in to (8) gd 2π I g l 2 2π 1 3 l2 3g 2π 2l For the length of a leg, lets use l = 1. The frequency can now be calculated: 3(9.8 s 2 ) =.61 Hz (10) 2π 2(1.25 ) (9) (b) If noral waling were perfored with the legs swinging at their natural frequency, how far could you wal in 1 hour? The period corresponding to the frequency calculated above is T = 1/.61 = 1.64 s. This is how long it taes to coplete one stride. In order to calculate the distance travelled in an hour we need the distance covered in a single stride. Waling brisly, each stride is 2. Therefore: ( 1 stride )( 2 )( 3600 s ) = 4400 = 4.4 (11) 1.64 s 1 stride 1 hr 9-69 The siple haronic oscillator provides a good odel for sall oscillations about equilibriu in any systes, including olecules. In the H 2 olecule, the two hydrogen atos can oscillate toward and away fro each other, so that the center of ass reains stationary. Each oves as though connected to a spring with constant 1130 N 1. (a) Find the frequency of oscillation. Using H = g: 2π = 1 2π 1130 N g = Hz (12) (b) If the vibrational energy of the olecule is 1.23 ev, what is the aplitude of the oscillations for each ato? Each Hydrogen ato has half of the energy of the olecule. aplitude, all of the energy of the ato is stored in the spring : When the oscillations are at their axiu E ato E ato = P E spring =.5(1.23 ev ) =.615 ev = 1 2 A2.615 ev = J = 1 2 (1130 N 1 )A 2 A = Notice that we had to convert to Joules so that the units would end up correct 2( J) 1130 N 1 = (13)
4 4 (c)find the axiu velocity of the atos relative to the center of ass. Given an equation for SHM x(t) = A cos(ωt), the velocity as a function of tie is the tie derivative of the position. v(t) = ωa sin(ωt). The axiu value that v(t) can reach is v ax = ωa N v ax = ωa = g ( ) = s 1 (14) 9-73 Show that x(t) = A cos(ωt + φ) is a solution of the SHM equation a = x. a(t) = d2 x(t) d 2 t, so to test our function we ust tae two tie derivatives: d 2 d (A cos(ωt + φ)) = ωa sin(ωt + φ) dt dt 2 (A cos(ωt + φ)) = d dt ( ωa sin(ωt + φ)) = ω2 A cos(ωt + φ) = ω 2 x(t) (15) By definition, ω = ω2 = a(t) = ω 2 x(t) = x(t) (16) Our choice of x(t) = A cos(ωt + φ) as a solution to the SHM equation is correct. (b) What is the significance of φ. φ is a constant, nown as the phase. It describes the starting point of the oscillation. The equation x(t) = A cos(ωt) only describes an oscillation has x(0) = A. The introduction of φ allows us to describe an oscillation with any starting position Since various parts of the body have characteristic frequencies of vibration, we can thin of these parts as being connected by springs. The spring is fored by the flexible connections of these parts of the body. In Ch. 8 we learned that the spring constant is proportional to the cross sectional area divided by the length of the spring aterial. (a) Using scaling hypothesis of 8.6 l r 2/3, show that the spring constant 1/2. Fro Ch. 8 we now that = EA l. Using A r 2, and l r 2/3 r l 3/2 we can see how scales: r2 l (l 3/2 ) 2 l l 2 (17) The scaling law in 8.6 lead to the conclusion that l 4 l 1/4. Therefore: l 2 1/2 (18) (b) Show that the characteristic frequency should scale as f 1/4. f 1/2 1/2 1/4 (19)
5 The abdoen and thorax of a 60 g huan has a resonance at about 3 Hz. (a) Using the result of proble 9-82, what would you expect the corresponding characteristic frequency to be in a 20 g = 2 2 g ouse? Fro the previous proble, we now that f 1/4. We can write this relationship as = c 1/4, where c is a constant. We can solve for c using the nuerical values for the resonant frequency of a huan abdoen: f = c 1/4 c = f = 3 Hz 1/4 (60 g) = /4 g1/4 s (20) Applying the relationship to the ouse, with the correct value of c gives us the guess for the resonant frequency of a ouse abdoen: f ouse = c 1/4 ouse = (8.35 g 1/4 s)( g) 1/4 = 22 Hz (21) (b) Experientally the frequency in ice is between 18 and 25 Hz. How does this copare to the result in part (a)? The calculated value of 22 Hz is within the easured range. body parts is correct in this experient. The scaling law for resonant frequencies of
Periodic Motion is everywhere
Lecture 19 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand and use energy conservation
More informationPhysics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14
Physics 07, Lecture 18, Nov. 3 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand
More informationm A 1 m mgd k m v ( C) AP Physics Multiple Choice Practice Oscillations
P Physics Multiple Choice Practice Oscillations. ass, attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is.
More informationCHECKLIST. r r. Newton s Second Law. natural frequency ω o (rad.s -1 ) (Eq ) a03/p1/waves/waves doc 9:19 AM 29/03/05 1
PHYS12 Physics 1 FUNDAMENTALS Module 3 OSCILLATIONS & WAVES Text Physics by Hecht Chapter 1 OSCILLATIONS Sections: 1.5 1.6 Exaples: 1.6 1.7 1.8 1.9 CHECKLIST Haronic otion, periodic otion, siple haronic
More informationSimple Harmonic Motion
Reading: Chapter 15 Siple Haronic Motion Siple Haronic Motion Frequency f Period T T 1. f Siple haronic otion x ( t) x cos( t ). Aplitude x Phase Angular frequency Since the otion returns to its initial
More informationMore Oscillations! (Today: Harmonic Oscillators)
More Oscillations! (oday: Haronic Oscillators) Movie assignent reinder! Final due HURSDAY April 20 Subit through ecapus Different rubric; reeber to chec it even if you got 00% on your draft: http://sarahspolaor.faculty.wvu.edu/hoe/physics-0
More informationStudent Book pages
Chapter 7 Review Student Boo pages 390 39 Knowledge. Oscillatory otion is otion that repeats itself at regular intervals. For exaple, a ass oscillating on a spring and a pendulu swinging bac and forth..
More informationProblem Set 14: Oscillations AP Physics C Supplementary Problems
Proble Set 14: Oscillations AP Physics C Suppleentary Probles 1 An oscillator consists of a bloc of ass 050 g connected to a spring When set into oscillation with aplitude 35 c, it is observed to repeat
More informationQ5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!
Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In
More informationWileyPLUS Assignment 3. Next Week
WileyPLUS Assignent 3 Chapters 6 & 7 Due Wednesday, Noveber 11 at 11 p Next Wee No labs of tutorials Reebrance Day holiday on Wednesday (no classes) 24 Displaceent, x Mass on a spring ωt = 2π x = A cos
More informationPhysics 41 HW Set 1 Chapter 15 Serway 7 th Edition
Physics HW Set Chapter 5 Serway 7 th Edition Conceptual Questions:, 3, 5,, 6, 9 Q53 You can take φ = π, or equally well, φ = π At t= 0, the particle is at its turning point on the negative side of equilibriu,
More informationwhich proves the motion is simple harmonic. Now A = a 2 + b 2 = =
Worked out Exaples. The potential energy function for the force between two atos in a diatoic olecules can be expressed as follows: a U(x) = b x / x6 where a and b are positive constants and x is the distance
More informationCHAPTER 15: Vibratory Motion
CHAPTER 15: Vibratory Motion courtesy of Richard White courtesy of Richard White 2.) 1.) Two glaring observations can be ade fro the graphic on the previous slide: 1.) The PROJECTION of a point on a circle
More informationL 2. AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) F T2. (b) F NET(Y) = 0
AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) 60 F 1 F g (b) F NE(Y) = 0 F1 F1 = g / cos(60) = g (c) When the string is cut it swings fro top to botto, siilar to the diagra for 1974B1
More informationPH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-1D Spring 013 Oscillations Lectures 35-37 Chapter 15 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 15 Oscillations In this chapter we will cover the following topics: Displaceent,
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More informationA body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of
Chapter 14 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 14 Due: 11:59p on Sunday, Noveber 27, 2016 To understand how points are awarded, read the Grading Policy for this
More informationSimple Harmonic Motion
Siple Haronic Motion Physics Enhanceent Prograe for Gifted Students The Hong Kong Acadey for Gifted Education and Departent of Physics, HKBU Departent of Physics Siple haronic otion In echanical physics,
More informationVIBRATING SYSTEMS. example. Springs obey Hooke s Law. Terminology. L 21 Vibration and Waves [ 2 ]
L 1 Vibration and Waves [ ] Vibrations (oscillations) resonance pendulu springs haronic otion Waves echanical waves sound waves usical instruents VIBRATING SYSTEMS Mass and spring on air trac Mass hanging
More informationPhysics 201 Lecture 29
Phsics 1 ecture 9 Goals ecture 9 v Describe oscillator otion in a siple pendulu v Describe oscillator otion with torques v Introduce daping in SHM v Discuss resonance v Final Ea Details l Sunda, Ma 13th
More informationPage 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position
Physics 3: ecture Today s genda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a spring Vertical spring Energy and siple haronic otion Energy o
More informationHW 6 - Solutions Due November 20, 2017
Conteporary Physics I HW 6 HW 6 - Solutions Due Noveber 20, 2017 1. A 4 kg block is attached to a spring with a spring constant k 200N/, and is stretched an aount 0.2 [5 pts each]. (a) Sketch the potential
More information(b) Frequency is simply the reciprocal of the period: f = 1/T = 2.0 Hz.
Chapter 5. (a) During siple haronic otion, the speed is (oentarily) zero when the object is at a turning point (that is, when x = +x or x = x ). Consider that it starts at x = +x and we are told that t
More informationT m. Fapplied. Thur Oct 29. ω = 2πf f = (ω/2π) T = 1/f. k m. ω =
Thur Oct 9 Assignent 10 Mass-Spring Kineatics (x, v, a, t) Dynaics (F,, a) Tie dependence Energy Pendulu Daping and Resonances x Acos( ωt) = v = Aω sin( ωt) a = Aω cos( ωt) ω = spring k f spring = 1 k
More informationPhysics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015
Physics 2210 Fall 2015 sartphysics 20 Conservation of Angular Moentu 21 Siple Haronic Motion 11/23/2015 Exa 4: sartphysics units 14-20 Midter Exa 2: Day: Fri Dec. 04, 2015 Tie: regular class tie Section
More information= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12
Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,
More information2. Which of the following best describes the relationship between force and potential energy?
Work/Energy with Calculus 1. An object oves according to the function x = t 5/ where x is the distance traveled and t is the tie. Its kinetic energy is proportional to (A) t (B) t 5/ (C) t 3 (D) t 3/ (E)
More informationQuestion 1. [14 Marks]
6 Question 1. [14 Marks] R r T! A string is attached to the dru (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is
More informationOscillations: Review (Chapter 12)
Oscillations: Review (Chapter 1) Oscillations: otions that are periodic in tie (i.e. repetitive) o Swinging object (pendulu) o Vibrating object (spring, guitar string, etc.) o Part of ediu (i.e. string,
More informationTUTORIAL 1 SIMPLE HARMONIC MOTION. Instructor: Kazumi Tolich
TUTORIAL 1 SIMPLE HARMONIC MOTION Instructor: Kazui Tolich About tutorials 2 Tutorials are conceptual exercises that should be worked on in groups. Each slide will consist of a series of questions that
More information9 HOOKE S LAW AND SIMPLE HARMONIC MOTION
Experient 9 HOOKE S LAW AND SIMPLE HARMONIC MOTION Objectives 1. Verify Hoo s law,. Measure the force constant of a spring, and 3. Measure the period of oscillation of a spring-ass syste and copare it
More informationPHYS 1443 Section 003 Lecture #22
PHYS 443 Section 003 Lecture # Monda, Nov. 4, 003. Siple Bloc-Spring Sste. Energ of the Siple Haronic Oscillator 3. Pendulu Siple Pendulu Phsical Pendulu orsion Pendulu 4. Siple Haronic Motion and Unifor
More information. The maximum speed m can be doubled by doubling the amplitude, A. 5. The maximum speed of a simple harmonic oscillator is given by v = A
CHAPTER 4: Oscillations Responses to Questions. Exaples are: a child s swing (SHM, for sall oscillations), stereo speaers (coplicated otion, the addition of any SHMs), the blade on a jigsaw (approxiately
More informationOSCILLATIONS AND WAVES
OSCILLATIONS AND WAVES OSCILLATION IS AN EXAMPLE OF PERIODIC MOTION No stories this tie, we are going to get straight to the topic. We say that an event is Periodic in nature when it repeats itself in
More informationSimple Harmonic Motion of Spring
Nae P Physics Date iple Haronic Motion and prings Hooean pring W x U ( x iple Haronic Motion of pring. What are the two criteria for siple haronic otion? - Only restoring forces cause siple haronic otion.
More informationDiscussion Examples Chapter 13: Oscillations About Equilibrium
Discussion Exaples Chapter 13: Oscillations About Equilibriu 17. he position of a ass on a spring is given by x 6.5 c cos t 0.88 s. (a) What is the period,, of this otion? (b) Where is the ass at t 0.5
More informationPearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
Pearson Education Liited Edinburgh Gate Harlow Esse CM0 JE England and Associated Copanies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk Pearson Education Liited 04 All rights
More informationExperiment 2: Hooke s Law
COMSATS Institute of Inforation Technology, Islaabad Capus PHYS-108 Experient 2: Hooke s Law Hooke s Law is a physical principle that states that a spring stretched (extended) or copressed by soe distance
More informationChapter 11 Simple Harmonic Motion
Chapter 11 Siple Haronic Motion "We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances." Isaac Newton 11.1 Introduction to Periodic Motion
More informationUSEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS. By: Ian Blokland, Augustana Campus, University of Alberta
1 USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS By: Ian Bloland, Augustana Capus, University of Alberta For: Physics Olypiad Weeend, April 6, 008, UofA Introduction: Physicists often attept to solve
More informationUnit 14 Harmonic Motion. Your Comments
Today s Concepts: Periodic Motion Siple - Mass on spring Daped Forced Resonance Siple - Pendulu Unit 1, Slide 1 Your Coents Please go through the three equations for siple haronic otion and phase angle
More information5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page
5/09/06 PHYSICS 13 Exa #1 NAME FEYNMAN Please write down your nae also on the back side of the last page 1 he figure shows a horizontal planks of length =50 c, and ass M= 1 Kg, pivoted at one end. he planks
More informationPhysics 4A Solutions to Chapter 15 Homework
Physics 4A Solutions to Chapter 15 Hoework Chapter 15 Questions:, 8, 1 Exercises & Probles 6, 5, 31, 41, 59, 7, 73, 88, 90 Answers to Questions: Q 15- (a) toward -x (b) toward +x (c) between -x and 0 (d)
More information4.7. Springs and Conservation of Energy. Conservation of Mechanical Energy
Springs and Conservation of Energy Most drivers try to avoid collisions, but not at a deolition derby like the one shown in Figure 1. The point of a deolition derby is to crash your car into as any other
More informationPearson Physics Level 20 Unit IV Oscillatory Motion and Mechanical Waves: Chapter 7 Solutions
Pearson Physics Level 0 Unit IV Oscillatory Motion and Mechanical Waves: Chapter 7 Solutions Student Boo page 345 Exaple 7. Practice Probles. 60 s T 5.00 in in 300 s f T 300 s 3 3.33 0 Hz The frequency
More informationCourse Information. Physics 1C Waves, optics and modern physics. Grades. Class Schedule. Clickers. Homework
Course Inforation Physics 1C Waves, optics and odern physics Instructor: Melvin Oaura eail: oaura@physics.ucsd.edu Course Syllabus on the web page http://physics.ucsd.edu/ students/courses/fall2009/physics1c
More informationPhysics 120 Final Examination
Physics 120 Final Exaination 12 August, 1998 Nae Tie: 3 hours Signature Calculator and one forula sheet allowed Student nuber Show coplete solutions to questions 3 to 8. This exaination has 8 questions.
More informationm potential kinetic forms of energy.
Spring, Chapter : A. near the surface of the earth. The forces of gravity and an ideal spring are conservative forces. With only the forces of an ideal spring and gravity acting on a ass, energy F F will
More information27 Oscillations: Introduction, Mass on a Spring
Chapter 7 Oscillations: Introduction, Mass on a Spring 7 Oscillations: Introduction, Mass on a Spring If a siple haronic oscillation proble does not involve the tie, you should probably be using conservation
More informationPhysics 2107 Oscillations using Springs Experiment 2
PY07 Oscillations using Springs Experient Physics 07 Oscillations using Springs Experient Prelab Read the following bacground/setup and ensure you are failiar with the concepts and theory required for
More informationForce and dynamics with a spring, analytic approach
Force and dynaics with a spring, analytic approach It ay strie you as strange that the first force we will discuss will be that of a spring. It is not one of the four Universal forces and we don t use
More information3. Period Law: Simplified proof for circular orbits Equate gravitational and centripetal forces
Physics 106 Lecture 10 Kepler s Laws and Planetary Motion-continued SJ 7 th ed.: Chap 1., 1.6 Kepler s laws of planetary otion Orbit Law Area Law Period Law Satellite and planetary orbits Orbits, potential,
More informationm A 9. The length of a simple pendulum with a period on Earth of one second is most nearly (A) 0.12 m (B) 0.25 m (C) 0.50 m (D) 1.0 m (E) 10.
P Physics Multiple Choice Practice Oscillations. ass, attache to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu isplaceent fro its equilibriu position is. What
More informationPH 221-2A Fall Waves - I. Lectures Chapter 16 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-A Fall 014 Waves - I Lectures 4-5 Chapter 16 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will
More informationma x = -bv x + F rod.
Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous
More informationMany objects vibrate or oscillate an object on the end of a spring, a tuning
An object attached to a coil spring can exhibit oscillatory otion. Many kinds of oscillatory otion are sinusoidal in tie, or nearly so, and are referred to as siple haronic otion. Real systes generally
More information( ) ( ) 1. (a) The amplitude is half the range of the displacement, or x m = 1.0 mm.
1. (a) The aplitude is half the range of the displaceent, or x = 1.0. (b) The axiu speed v is related to the aplitude x by v = ωx, where ω is the angular frequency. Since ω = πf, where f is the frequency,
More information1 (40) Gravitational Systems Two heavy spherical (radius 0.05R) objects are located at fixed positions along
(40) Gravitational Systes Two heavy spherical (radius 0.05) objects are located at fixed positions along 2M 2M 0 an axis in space. The first ass is centered at r = 0 and has a ass of 2M. The second ass
More informationIn the session you will be divided into groups and perform four separate experiments:
Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track
More informationChapter 1: Basics of Vibrations for Simple Mechanical Systems
Chapter 1: Basics of Vibrations for Siple Mechanical Systes Introduction: The fundaentals of Sound and Vibrations are part of the broader field of echanics, with strong connections to classical echanics,
More informationCE573 Structural Dynamics [Fall 2008]
CE573 Structural Dynaics [Fall 2008] 1) A rigid vehicle weighing 2000 lb, oving horizontally at a velocity of 12 ft/sec, is stopped by a barrier consisting of wire ropes stretched between two rigid anchors
More information8.1 Force Laws Hooke s Law
8.1 Force Laws There are forces that don't change appreciably fro one instant to another, which we refer to as constant in tie, and forces that don't change appreciably fro one point to another, which
More informationPearson Physics Level 20 Unit IV Oscillatory Motion and Mechanical Waves: Unit IV Review Solutions
Pearson Physics Level 0 Unit IV Oscillatory Motion and Mechanical Waves: Unit IV Review Solutions Student Book pages 440 443 Vocabulary. aplitude: axiu displaceent of an oscillation antinodes: points of
More information9. h = R. 10. h = 3 R
Version PREVIEW Torque Chap. 8 sizeore (13756) 1 This print-out should have 3 questions. ultiple-choice questions ay continue on the next colun or page find all choices before answering. Note in the dropped
More informationNB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016
NB1140: Physics 1A - Classical echanics and Therodynaics Proble set 2 - Forces and energy Week 2: 21-25 Noveber 2016 Proble 1. Why force is transitted uniforly through a assless string, a assless spring,
More informationPHYS 102 Previous Exam Problems
PHYS 102 Previous Exa Probles CHAPTER 16 Waves Transverse waves on a string Power Interference of waves Standing waves Resonance on a string 1. The displaceent of a string carrying a traveling sinusoidal
More informationPage 1. Physics 131: Lecture 22. SHM and Circles. Today s Agenda. Position. Velocity. Position and Velocity. Acceleration. v Asin.
Physics 3: ecture Today s enda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a sprin Vertical sprin Enery and siple haronic otion Enery o a sprin
More informationIn this chapter we will start the discussion on wave phenomena. We will study the following topics:
Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will study the following topics: Types of waves Aplitude, phase, frequency, period, propagation speed of a wave Mechanical
More informationOscillations Equations 0. Out of the followin functions representin otion of a particle which represents SHM I) y = sinωt cosωt 3 II) y = sin ωt III) IV) 3 y = 5cos 3ωt 4 y = + ωt+ ω t a) Only IV does
More information1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy
AP Physics Multiple Choice Practice Wor-Energy 1. A ass attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is
More informationTOPIC E: OSCILLATIONS SPRING 2018
TOPIC E: OSCILLATIONS SPRING 018 1. Introduction 1.1 Overview 1. Degrees of freedo 1.3 Siple haronic otion. Undaped free oscillation.1 Generalised ass-spring syste: siple haronic otion. Natural frequency
More informationFlipping Physics Lecture Notes: Free Response Question #1 - AP Physics Exam Solutions
2015 FRQ #1 Free Response Question #1 - AP Physics 1-2015 Exa Solutions (a) First off, we know both blocks have a force of gravity acting downward on the. et s label the F & F. We also know there is a
More informationSimple and Compound Harmonic Motion
Siple Copound Haronic Motion Prelab: visit this site: http://en.wiipedia.org/wii/noral_odes Purpose To deterine the noral ode frequencies of two systes:. a single ass - two springs syste (Figure );. two
More informationEN40: Dynamics and Vibrations. Final Examination Tuesday May 15, 2011
EN40: ynaics and Vibrations Final Exaination Tuesday May 15, 011 School of Engineering rown University NME: General Instructions No collaboration of any ind is peritted on this exaination. You ay use double
More informationBALLISTIC PENDULUM. EXPERIMENT: Measuring the Projectile Speed Consider a steel ball of mass
BALLISTIC PENDULUM INTRODUCTION: In this experient you will use the principles of conservation of oentu and energy to deterine the speed of a horizontally projected ball and use this speed to predict the
More informationDefinition of Work, The basics
Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define
More informationDETECTION OF NONLINEARITY IN VIBRATIONAL SYSTEMS USING THE SECOND TIME DERIVATIVE OF ABSOLUTE ACCELERATION
DETECTION OF NONLINEARITY IN VIBRATIONAL SYSTEMS USING THE SECOND TIME DERIVATIVE OF ABSOLUTE ACCELERATION Masaki WAKUI 1 and Jun IYAMA and Tsuyoshi KOYAMA 3 ABSTRACT This paper shows a criteria to detect
More informationFor a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ).
Reading: Energy 1, 2. Key concepts: Scalar products, work, kinetic energy, work-energy theore; potential energy, total energy, conservation of echanical energy, equilibriu and turning points. 1.! In 1-D
More informationSHM stuff the story continues
SHM stuff the story continues Siple haronic Motion && + ω solution A cos t ( ω + α ) Siple haronic Motion + viscous daping b & + ω & + Viscous daping force A e b t Viscous daped aplitude Viscous daped
More information2009 Academic Challenge
009 Acadeic Challenge PHYSICS TEST - REGIONAL This Test Consists of 5 Questions Physics Test Production Tea Len Stor, Eastern Illinois University Author/Tea Leader Doug Brandt, Eastern Illinois University
More information15 Newton s Laws #2: Kinds of Forces, Creating Free Body Diagrams
Chapter 15 ewton s Laws #2: inds of s, Creating ree Body Diagras 15 ewton s Laws #2: inds of s, Creating ree Body Diagras re is no force of otion acting on an object. Once you have the force or forces
More informationPhysics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10
There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference
More information1B If the stick is pivoted about point P a distance h = 10 cm from the center of mass, the period of oscillation is equal to (in seconds)
05/07/03 HYSICS 3 Exa #1 Use g 10 /s in your calculations. NAME Feynan lease write your nae also on the back side of this exa 1. 1A A unifor thin stick of ass M 0. Kg and length 60 c is pivoted at one
More informationPHY 101 General Physics I (Oscillations, Waves I and II) 2017/18 academic session
PHY 101 General Physics I (Oscillations, Waves I and II) 017/18 acadeic session Segun Fawole PhD (AMInstP) Dept. of Physics & Engr. Physics Obafei Awolowo University, Ile-Ife, Nigeria. eail: gofawole@oauife.edu.ng
More informationCommon Exam 2 Physics 111 Fall 2006 Name A
Coon Ea Physics Fall 006 Nae A Total Nuber of Points is 5 (Multiple Choice and Worout Probles). Multiple Choice Probles are Point per Question..) A toy car oving at constant speed copletes one lap around
More informationWater a) 48 o b) 53 o c) 41.5 o d) 44 o. Glass. PHYSICS 223 Exam-2 NAME II III IV
PHYSICS 3 Exa- NAME. In the figure shown, light travels fro aterial I, through three layers of other aterials with surfaces parallel to one another, and then back into another layer of aterial I. The refractions
More informationProblem T1. Main sequence stars (11 points)
Proble T1. Main sequence stars 11 points Part. Lifetie of Sun points i..7 pts Since the Sun behaves as a perfectly black body it s total radiation power can be expressed fro the Stefan- Boltzann law as
More informationHORIZONTAL MOTION WITH RESISTANCE
DOING PHYSICS WITH MATLAB MECHANICS HORIZONTAL MOTION WITH RESISTANCE Ian Cooper School of Physics, Uniersity of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS ec_fr_b. This script
More informationName Period. What force did your partner s exert on yours? Write your answer in the blank below:
Nae Period Lesson 7: Newton s Third Law and Passive Forces 7.1 Experient: Newton s 3 rd Law Forces of Interaction (a) Tea up with a partner to hook two spring scales together to perfor the next experient:
More informationEN40: Dynamics and Vibrations. Final Examination Monday May : 2pm-5pm
EN40: Dynaics and Vibrations Final Exaination Monday May 13 013: p-5p School of Engineering Brown University NAME: General Instructions No collaboration of any kind is peritted on this exaination. You
More informationPhysics 221B: Solution to HW # 6. 1) Born-Oppenheimer for Coupled Harmonic Oscillators
Physics B: Solution to HW # 6 ) Born-Oppenheier for Coupled Haronic Oscillators This proble is eant to convince you of the validity of the Born-Oppenheier BO) Approxiation through a toy odel of coupled
More informationQ1. The displacement of a string carrying a traveling sinusoidal wave is given by:
Coordinator: A. Mekki Saturday, Noveber, 008 Page: 1 Q1. The displaceent of a string carrying a traveling sinusoidal wave is given by: y( x, t) = y sin( kx ω t + ϕ). At tie t = 0 the point at x = 0 has
More informationNAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40%
NAME NUMER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002 PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2.5 Q1 ( ) 2 Q2 Q3 Total 40% Use the followings: Magnitude of acceleration due to gravity
More informationOSCILLATIONS CHAPTER FOURTEEN 14.1 INTRODUCTION
CHAPTER FOURTEEN OSCILLATIONS 14.1 INTRODUCTION 14.1 Introduction 14. Periodic and oscilatory otions 14.3 Siple haronic otion 14.4 Siple haronic otion and unifor circular otion 14.5 Velocity and acceleration
More informationSRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES
SRI LANKAN PHYSICS OLYMPIAD - 5 MULTIPLE CHOICE TEST QUESTIONS ONE HOUR AND 5 MINUTES INSTRUCTIONS This test contains ultiple choice questions. Your answer to each question ust be arked on the answer sheet
More informationDepartment of Physics Preliminary Exam January 3 6, 2006
Departent of Physics Preliinary Exa January 3 6, 2006 Day 1: Classical Mechanics Tuesday, January 3, 2006 9:00 a.. 12:00 p.. Instructions: 1. Write the answer to each question on a separate sheet of paper.
More informationPHYS 1443 Section 003 Lecture #21 Wednesday, Nov. 19, 2003 Dr. Mystery Lecturer
PHYS 443 Section 003 Lecture # Wednesday, Nov. 9, 003 Dr. Mystery Lecturer. Fluid Dyanics : Flow rate and Continuity Equation. Bernoulli s Equation 3. Siple Haronic Motion 4. Siple Bloc-Spring Syste 5.
More informationQuiz 5 PRACTICE--Ch12.1, 13.1, 14.1
Nae: Class: Date: ID: A Quiz 5 PRACTICE--Ch2., 3., 4. Multiple Choice Identify the choice that best copletes the stateent or answers the question.. A bea of light in air is incident at an angle of 35 to
More informationXI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com
XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.co https://prootephysics.wordpress.co [MOTION] CHAPTER NO. 3 In this chapter we are going to discuss otion in one diension in which we
More informationdt dt THE AIR TRACK (II)
THE AIR TRACK (II) References: [] The Air Track (I) - First Year Physics Laoratory Manual (PHY38Y and PHYY) [] Berkeley Physics Laoratory, nd edition, McGraw-Hill Book Copany [3] E. Hecht: Physics: Calculus,
More information