7:30 AM 7:30 AM :30 AM
|
|
- Oswald Spencer
- 6 years ago
- Views:
Transcription
1 Physics 101 Section 3 April 8 th : REVIEW Announcements: n nt Exam #4, today at the same place (Ch ) 18.8) Final Exam: May 11 th (Tuesday), 7:30 AM at Howe- Russell 130 Make up Final: May 15 th (Saturday) 7:30 AM Class Website: 3/
2 m 1 Chapter 13 m Gravitation Newton s law of gravitation, which describes the attractive force between two pointmasses and itsapplicationto to extended objects F G mm = r 1 The acceleration of gravity on the surface of the Earth, above it as well as below it. G = N m / kg 11
3 m Gravitational Potential Energy r The gravitational potential energy is U GmM = r. U = GmM r The negative sign of U expresses the fact that the force is attractive. Assum e: U( r= ) = 0 Note: The gravitational potential energy is not only associated with the mass m but with M as well, i.e., with both objects. If we have three masses m1, m, and m3 positioned as shown in the figure, the potential energy U due to the gravitational forces among the objects is U Gm1 m Gm m Gm m = + + r1 r13 r Wetakeintoaccount each pair once.
4 Gravitational potential energy ΔU = W done by force Conservative force path independent x f ΔU W d g = W done = F g dx x i At Earth s surface, F g ~const. r W = r f r i G mm r dr = GmM r f r i 1 r dr ΔU g = W done = m g y f ( ) dy = mgδy y i If we define U = 0 at infinity, then the work done by taking mass m from R to infinity Note: 1 U U ( r) = W = GmM 0 r GmM U ( r) = r du (r) F (r) = dr d GmM = GmM dr r r 1) As before, U decreases asseparationseparation decreases (more negative) ) Path independent 3) MUST HAVE AT LEAST TWO PARTICLES TO POTENTIAL ENERGY (& force) 4) Knowing potential, you can get force.
5 Escape Velocity v = GM R v = 0 B m The minimum initial speed for which the projectile object m will escape from the gravitational pull of M and will stop at infinity y(point B in the figure). mv GMm EA = K + U = EB = K + U = 0 R E A mv GMm GM = EB = 0 v = R R v A r = m Note: The escape speed does not depend on m.
6 Kepler's First Law. All planets move on elliptical orbits with the Sun at one focus. da Kepler's Second Law. The line that connects a planet to the Sun sweeps out equal areas ΔA in the plane of the orbit in equal da time intervals Δ t : = constant. dt Kepler's second law is equivalent to the law of conservation of angular momentum: da L L= rp = rmv = rmωr = mr ω = = constant dt m
7 Kepler s 3 rd Law The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Gm satm E = m sat r sat Circular Orbit πr sat 3 T = GM r sat r sat 4π T = 4π GM T 3 r sat NOTE: r 3 proportional T Elliptical Orbit When used in the equations, r (radius) and a (semimajor axis) are synonymous y
8 SHW#9 problem 3: Assume the orbital of a lunched satellite around the earth is circular. Show that there is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius and it does not depend on the mass of the satellite. What is the speed and height eg H above the earth s surface at which all synchronous ous satellite (regardless (egadessof mass) must be placed in orbit, assuming the earth is spherical? If a synchronous satellite has a mass m. How much additional kinetic energy is needed for it to escape from the earth? M Em v GM E (a) Since G = m is the centripetal force for a satellite with mass m, v =, r r r which is dependent only on radius r but independent on mass m. (b) For a synchronous satellite, π r r 4h = T = = π r = v GM H GM T E /3 = ( ) π R E E π r GM 3/ E GM ET ; r = RE + H = ( ) π /3 1 E (c) Based upon the condition that mvescape = 0 v v escape escape GM E = r = r π GM E 1/3 = ( ) T GM T GmM r E /3 with ( ) for asynchronous satellite, so that π
9 Chapter 14: Fluids In this chapter we will explore the behavior of fluids. In particular we will study the following: Static fluids: Pressure exerted by a static fluid Methods of measuring pressure Pascal s principle Archimedes principle, buoyancy
10 Fluid: Δm ΔV Δm m ρ = Density of mass Δ V Pressure: p = F A Fluid at rest: p = p +ρgh bottom top Can you calculate the pressure at any depth?
11 Pascal's Principle and the Hydraulic Lever: A change in the pressure applied to an enclosed incompressible liquid is transmitted undiminished toevery portion of the fluid and to the walls of the container. F o = A F o i A i Buoyant Force and Archimedes' Principle When a body is fully or partially submerged in a fluid a buoyant force F b is exerted on the body by the surrounding fluid. This force is directed upward and its magnitude is equal to the weight m f g of the fluid that has been displaced by the body. F b F b = ρ gv f
12 Helium Blimps Length 19 feet Width 50 feet Height 59.5 feet Volume 0,700 cubic feet (5740 m 3 ) Maximum Speed 50 mph Cruise Speed 30 mph Powerplant: Two 10 hp fuel injected, air cooled piston engines What is the maximum load weight of blimp (W L ) in order to fly? ρ He = kg/m 3 & ρ air = 1.1 kg/m 3 W At static equilibrium F = 0 : W He + W L = F B W L F B W He The fluid blimp is in is: air W L = m air g m He g W L = F B W He = ρ air V ship g ρ He V ship g = V ship g( ρ air ρ He ) ( ) = (5740 m 3 )(9.8 m /s ) kg/m/ 3 = 58 kn = 13,000 lbs Maximum Gross Weight 1,840 pounds
13 Chapter 15: Oscillations Displacement, velocity, and acceleration of a simple harmonic oscillator Energy of a simple harmonic oscillator Examples of simple harmonic oscillators: spring mass system, simple pendulum, physical pendulum, torsion pendulum Forced oscillations/resonance
14 Simple harmonic Motion: Kinematics Displacement: ( ω φ ) xt ( ) = x cos t+ m Velocity of SHM dx() t d vt () = = xmcos t+ = xmsin t+ dt dt Acceleration of SHM: ( ω φ) ω ( ω φ) dv() t d at () = = ωxmsin( ωt+ φ) = ω xmcosωt dt dt at () = ω xt (). period (symbol T, units: s) vs. frequency (symbol f, unit: Hz): f = 1. T ππ ω = π f = T
15 SHW #10 The figure gives the position function of a 50g block in simple harmonic oscillation on the end of a spring. The period of the oscillation is s. 1) Find the velocity and acceleration function? ) Find the maximum kinetic energy, potential energy, and total energy. 3) Find the maximum force. 4) If you want to stop the oscillation in a quarter of period, what is minimum kinetic friction coefficient required? (Answer: μ k = 0.0) 0) Solutions: π a) x( t) = xmcos( ωt) with ω = = 3.14(1/ s) and xm = 0.07m T vt ( ) = ωx sin( ωt) m at x t ( ) = ω m cos( ω ) ( ωx ) kx mv m kx ( b) Fmax = kxm; Umax = ; K = = = π m 4π m ( c ) T = = π so that t k = ω k T 1 Since W = F xm = μkmgxm = kxm 1 1 4π m π μ k = kxm = ( ) x 0.0 m = x m = mg mg T T g m m m m m
16 Simple Harmonic Motion : Dynamics ( ω ) Newton's second law we get: F = kx = ma = mω x = m x. Simple Pendulum ω = k and T = π m = π m m C k Gravity plays as the restoring force τ = Iα = Lmgsinθ ( ) SHM : θ(t) = θ max cos( ωt + ϕ) mgl I α θ α ω θ ω = mgl I = mgl ml ( ) = g L Independent of amplitude and mass (in small angle approximation)! Dependent only on L and g
17 Physical Pendulums 1) Torsion pendulum τ = Iα = κθ α = κ I θ SHM : θ(t) = θ max cos( ωt + ϕ) ω = κ I τ = Iα = L( mgsinθ) α mgl θ I mgh ω = What is I? I I = I + mh com. T = π I mgh
18 Problem: The pendulum consists of a uniform disk with radius R and mass M attached to a uniform rod of length L and mass m. (a) what is the rotational inertia of the pendulum? (b) What is the distance between the pivot and the COM? (c) What is the period? (a) The disc has an I=MR / about the COM so. MR MR I(Disc) = + Mh = + M r + L ( ) = ml = nl L I(Rod) 1 + mh 1 + m = ml 3 (b) COM d COM = Ml d + ml r M + m With l d and l r being the the COM of the disc and rod. (c) The period T = π I (M + m)gd
19 wave phenomena. Chapter 16: Waves Types of waves Amplitude, phase, frequency, period, propagation speed of a wave Mechanical waves propagating along a stretched t string ti Principle of superposition of waves Wave interference Standing waves, resonance
20 Description of traveling wave: k = π λ Angular wave number ω = π T Angular frequency Phase and Direction i Wave Velocity phase : kx ± ωt kx ωt Wave traveling in + x direction kx + ωtt Wave traveling in x direction Velocity at which the wave crests move : v wave = λ / T = λf Wave on a τ v wave = = λf μ stretched string
21 Standing Wave: The displacement of a standing wave is given by the equation ( ) = [ ] y x, t = y sin kx cos ωtω t. m The position-dependent amplitude is equal to y sin kx. m n a a n n n a Nodes. These are defined as positions where the standing wave amplitude vanishes. They occur when kx = nπ for n = 0,1,, π x= nπ xn = n λ for n= 0,1,,... λ Antinodes. These are defined d as positions i where the standing wave amplitude is maximum. 1 They occur when kx = n+ π for n= 0,1, 01,... π 1 1 λ x= n+ π x n = n+ for n= 0,1,,... λ Note 1 : The distance between adjacent nodes and antinodes is λ/. Note : The distance between a node and an adjacent antinode is λ/4.
22 Standing Waves Summary Notations: Length L Nodes at both ends Tension in String: τ Given mass density: μ Driven at a frequency f This assures nodes at 0 and L λ = L n n th harmonic resonance
23 Problem 16 58: A sting, tied to a sinusodial oscillator at P and running over a support Q, is stretched by a block of mass m. The length is L and the linear density is μ, and the frequency is f. What mass allows the system to set up the fourth harmonic? n = 4 f = n τ = 4 τ = mg L μ L μ L μ
24 Chapter 18 Temperature, Heat, and Thermodynamics Temperature and the zeroth law of thermodynamics Thermometers and temperature scales F vs C vs K Thermal expansion Temperature and heat Specific heat Heat of transformation Heat, work, and the first law of thermodynamics Heat transfer mechanisms First Law of Thermodynamics
25 Temperature and Heat If two objects are NOT in thermal equilibrium, i their temperatures t must be different. To make their temperatures equal (i.e. thermal equilib), HEAT MUST FLOW. HEAT has to do with the transfer of thermal energy. Symbol for HEAT: Q BE VERY CAREFUL ABOUT THE SIGN System particular objecrtor set of objects Environment everythingelse else inthe universe Heat is negative when energy is transferred from the system s thermal energy to its environment (heat is released or lost) Heat is zero when no energy is transferred between the system s thermal energy and its environment (AT THERMAL EQUILIB) Heat is positive when energy is transferred to the system s thermal energy from its environment (heat is absorbed)
26 Thermal expansion Linear Volume ΔL = αl 0 ΔT L = L 0 1+ αδt ( ) ΔV = βv 0 ΔT V = V 0 1+ βδt ( ) Absorption of Heat by solids/liquids (in the same phase) Q = CΔT = C(T f T i ) Change of system energy with change of temperature Heat Transfer Heat Capacity [ J/ºC or cal/ºc ] depends on the material Specific Heat (heat capacity/mass) Q = cmδt = cm(t f T i ) f Water : c water = 1 cal/g. C= 1 Btu /lb. F= 4190 J/kg. C ~ independent of temperature c ~ c(t)
27 Heats of Transformation due to phase transition Heat is transferred in or out of system, but temperature does NOT change: Change of phase Heat of Heat of Fusion Vaporization Q = ±L m ΔT = 0 Amount of heat transferred during phase change depends on L and mass (M) L F F Heat of fusion Solid to liquid (heat is adsorbed : atomic bonds are broken L V Heat of Vaporization Liquid to gas (heat is adsorbed) L S Heat of Sublimation Solid to gas (heat is adsorbed) L F L V H O = 79.5 cal/g = kJ/mol = 333 kj/kg = 539 cal/g = 40.7 kj/mol = 56 kj/kg
1) Law of Orbits - all planets move in elliptical orbits with the Sun at one focus
1) Law of Orbits - all planets move in elliptical orbits with the Sun at one focus 2) Law of equal areas - ANGULAR MOMENTUM IS CONSERVED A line that connects a planet to the Sun sweeps out equal areas
More informationChapter 14 Periodic Motion
Chapter 14 Periodic Motion 1 Describing Oscillation First, we want to describe the kinematical and dynamical quantities associated with Simple Harmonic Motion (SHM), for example, x, v x, a x, and F x.
More informationMock Exam III PH 201, PH 221
Mock Exam III PH 201, PH 221 April 12, 2015 You will have 1 hour to complete this exam, and must answer 7 of the problems correctly to make a perfect score. 1 Chapter Concept Summary Equations: Cutnell
More informationFinal Mock Exam PH 221-1D
Final Mock Exam PH 221-1D April 18, 2015 You will have 2 hours to complete this exam. You must answer 8 questions to make a perfect score of 80. 1 Chapter Concept Summary Equations: Cutnell & Johnson
More informationQ1. A) 46 m/s B) 21 m/s C) 17 m/s D) 52 m/s E) 82 m/s. Ans: v = ( ( 9 8) ( 98)
Coordinator: Dr. Kunwar S. Wednesday, May 24, 207 Page: Q. A hot-air balloon is ascending (going up) at the rate of 4 m/s and when the balloon is 98 m above the ground a package is dropped from it, vertically
More informationAP Physics. Harmonic Motion. Multiple Choice. Test E
AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.
More informationChapter 13: Oscillatory Motions
Chapter 13: Oscillatory Motions Simple harmonic motion Spring and Hooe s law When a mass hanging from a spring and in equilibrium, the Newton s nd law says: Fy ma Fs Fg 0 Fs Fg This means the force due
More informationOscillations. Oscillations and Simple Harmonic Motion
Oscillations AP Physics C Oscillations and Simple Harmonic Motion 1 Equilibrium and Oscillations A marble that is free to roll inside a spherical bowl has an equilibrium position at the bottom of the bowl
More informationLecture 9 Chapter 13 Gravitation. Gravitation
Lecture 9 Chapter 13 Gravitation Gravitation UNIVERSAL GRAVITATION For any two masses in the universe: F = Gm 1m 2 r 2 G = a constant evaluated by Henry Cavendish +F -F m 1 m 2 r Two people pass in a hall.
More informationStatic Equilibrium, Gravitation, Periodic Motion
This test covers static equilibrium, universal gravitation, and simple harmonic motion, with some problems requiring a knowledge of basic calculus. Part I. Multiple Choice 1. 60 A B 10 kg A mass of 10
More informationFigure 1 Answer: = m
Q1. Figure 1 shows a solid cylindrical steel rod of length =.0 m and diameter D =.0 cm. What will be increase in its length when m = 80 kg block is attached to its bottom end? (Young's modulus of steel
More informationE = K + U. p mv. p i = p f. F dt = p. J t 1. a r = v2. F c = m v2. s = rθ. a t = rα. r 2 dm i. m i r 2 i. I ring = MR 2.
v = v i + at x = x i + v i t + 1 2 at2 E = K + U p mv p i = p f L r p = Iω τ r F = rf sin θ v 2 = v 2 i + 2a x F = ma = dp dt = U v dx dt a dv dt = d2 x dt 2 A circle = πr 2 A sphere = 4πr 2 V sphere =
More informationChapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx
Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx When the mass is released, the spring will pull
More informationQuiz 3 July 31, 2007 Chapters 16, 17, 18, 19, 20 Phys 631 Instructor R. A. Lindgren 9:00 am 12:00 am
Quiz 3 July 31, 2007 Chapters 16, 17, 18, 19, 20 Phys 631 Instructor R. A. Lindgren 9:00 am 12:00 am No Books or Notes allowed Calculator without access to formulas allowed. The quiz has two parts. The
More informationRotational motion problems
Rotational motion problems. (Massive pulley) Masses m and m 2 are connected by a string that runs over a pulley of radius R and moment of inertia I. Find the acceleration of the two masses, as well as
More informationChapter 15 Periodic Motion
Chapter 15 Periodic Motion Slide 1-1 Chapter 15 Periodic Motion Concepts Slide 1-2 Section 15.1: Periodic motion and energy Section Goals You will learn to Define the concepts of periodic motion, vibration,
More informationLecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws
Lecture 13 REVIEW Physics 106 Spring 2006 http://web.njit.edu/~sirenko/ What should we know? Vectors addition, subtraction, scalar and vector multiplication Trigonometric functions sinθ, cos θ, tan θ,
More information43. A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,
43. A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms, A) her moment of inertia increases and her rotational kinetic energy remains the same.
More informationSolution to phys101-t112-final Exam
Solution to phys101-t112-final Exam Q1. An 800-N man stands halfway up a 5.0-m long ladder of negligible weight. The base of the ladder is.0m from the wall as shown in Figure 1. Assuming that the wall-ladder
More informationCHAPTER 12 OSCILLATORY MOTION
CHAPTER 1 OSCILLATORY MOTION Before starting the discussion of the chapter s concepts it is worth to define some terms we will use frequently in this chapter: 1. The period of the motion, T, is the time
More informationChapter 15 - Oscillations
The pendulum of the mind oscillates between sense and nonsense, not between right and wrong. -Carl Gustav Jung David J. Starling Penn State Hazleton PHYS 211 Oscillatory motion is motion that is periodic
More informationRotational Kinematics
Rotational Kinematics Rotational Coordinates Ridged objects require six numbers to describe their position and orientation: 3 coordinates 3 axes of rotation Rotational Coordinates Use an angle θ to describe
More informationFundamentals Physics. Chapter 15 Oscillations
Fundamentals Physics Tenth Edition Halliday Chapter 15 Oscillations 15-1 Simple Harmonic Motion (1 of 20) Learning Objectives 15.01 Distinguish simple harmonic motion from other types of periodic motion.
More informationPhysics Exam 1 Formulas
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet. The exam is closed book, and you may have only pens/pencils and a calculator (no stored equations or programs and no graphing). Show
More informationPhysics 2101 Section 6 November 8 th : finish Ch.16
Physics 2101 Section 6 November 8 th : finish Ch.16 Announcement: Exam # 3 (November 13 th ) Lockett 10 (6 7 pm) Nicholson 109, 119 (extra time 5:30 7:30 pm) Covers Chs. 11.7-15 Lecture Notes: http://www.phys.lsu.edu/classes/fall2012/phys2101-6/
More informationOscillatory Motion SHM
Chapter 15 Oscillatory Motion SHM Dr. Armen Kocharian Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A
More informationPhysics 2101 S c e t c i cti n o 3 n 3 March 31st Announcements: Quiz today about Ch. 14 Class Website:
Physics 2101 Section 3 March 31 st Announcements: Quiz today about Ch. 14 Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101 3/ http://www.phys.lsu.edu/~jzhang/teaching.html Simple Harmonic
More informationDepartment of Physics
Department of Physics PHYS101-051 FINAL EXAM Test Code: 100 Tuesday, 4 January 006 in Building 54 Exam Duration: 3 hrs (from 1:30pm to 3:30pm) Name: Student Number: Section Number: Page 1 1. A car starts
More informationFinal Review, Day 1. Announcements: Web page:
Announcements: Final Review, Day 1 Final exam next Wednesday (5/9) at 7:30am in the Coors Event Center. Recitation tomorrow is a review. Please feel free to ask the TA any questions on the course material.
More informationPhysics 2101 Section 3 Apr 21st Announcements: Qitz on Friday Midterm #4, April Midterm #4,
Physics 2101 Section 3 Apr 21 st Announcements: Qitz on Friday Midterm #4, April 28 th Final: May 11 th-7:30am Class Website: 6 pm Make up Final: May 15 th -7:30am http://www.phys.lsu.edu/classes/spring2010/phys2101
More informationSolution The light plates are at the same heights. In balance, the pressure at both plates has to be the same. m g A A A F A = F B.
43. A piece of metal rests in a toy wood boat floating in water in a bathtub. If the metal is removed from the boat, and kept out of the water, what happens to the water level in the tub? A) It does not
More informationWrite your name legibly on the top right hand corner of this paper
NAME Phys 631 Summer 2007 Quiz 2 Tuesday July 24, 2007 Instructor R. A. Lindgren 9:00 am 12:00 am Write your name legibly on the top right hand corner of this paper No Books or Notes allowed Calculator
More informationEnergy in Planetary Orbits
Lecture 19: Energy in Orbits, Bohr Atom, Oscillatory Motion 1 Energy in Planetary Orbits Consequences of Kepler s First and Third Laws According to Kepler s First Law of Planetary Motion, all planets move
More informationPh1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004
Ph1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004 Problem 1 (10 points) - The Delivery A crate of mass M, which contains an expensive piece of scientific equipment, is being delivered to Caltech.
More informationMidterm 3 Review (Ch 9-14)
Midterm 3 Review (Ch 9-14) PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Copyright 2008 Pearson Education Inc., publishing as Pearson
More informationThe distance of the object from the equilibrium position is m.
Answers, Even-Numbered Problems, Chapter..4.6.8.0..4.6.8 (a) A = 0.0 m (b).60 s (c) 0.65 Hz Whenever the object is released from rest, its initial displacement equals the amplitude of its SHM. (a) so 0.065
More informationWAVES & SIMPLE HARMONIC MOTION
PROJECT WAVES & SIMPLE HARMONIC MOTION EVERY WAVE, REGARDLESS OF HOW HIGH AND FORCEFUL IT CRESTS, MUST EVENTUALLY COLLAPSE WITHIN ITSELF. - STEFAN ZWEIG What s a Wave? A wave is a wiggle in time and space
More informationAP PHYSICS 1 Learning Objectives Arranged Topically
AP PHYSICS 1 Learning Objectives Arranged Topically with o Big Ideas o Enduring Understandings o Essential Knowledges o Learning Objectives o Science Practices o Correlation to Knight Textbook Chapters
More informationChapter 15 Oscillations
Chapter 15 Oscillations Summary Simple harmonic motion Hook s Law Energy F = kx Pendulums: Simple. Physical, Meter stick Simple Picture of an Oscillation x Frictionless surface F = -kx x SHM in vertical
More informationToday s lecture. WEST VIRGINIA UNIVERSITY Physics
Today s lecture Review of chapters 1-14 Note: I m taking for granted that you ll still know SI/cgs units, order-of-magnitude estimates, etc., so I m focusing on problems. Velocity and acceleration (1d)
More informationMeasurement p. 1 What Is Physics? p. 2 Measuring Things p. 2 The International System of Units p. 2 Changing Units p. 3 Length p. 4 Time p. 5 Mass p.
Measurement p. 1 What Is Physics? p. 2 Measuring Things p. 2 The International System of Units p. 2 Changing Units p. 3 Length p. 4 Time p. 5 Mass p. 7 Review & Summary p. 8 Problems p. 8 Motion Along
More informationWelcome back to Physics 215. Review gravity Oscillations Simple harmonic motion
Welcome back to Physics 215 Review gravity Oscillations Simple harmonic motion Physics 215 Spring 2018 Lecture 14-1 1 Final Exam: Friday May 4 th 5:15-7:15pm Exam will be 2 hours long Have an exam buddy
More informationSummary PHY101 ( 2 ) T / Hanadi Al Harbi
الكمية Physical Quantity القانون Low التعريف Definition الوحدة SI Unit Linear Momentum P = mθ be equal to the mass of an object times its velocity. Kg. m/s vector quantity Stress F \ A the external force
More informationPHYS 1114, Lecture 33, April 10 Contents:
PHYS 1114, Lecture 33, April 10 Contents: 1 This class is o cially cancelled, and has been replaced by the common exam Tuesday, April 11, 5:30 PM. A review and Q&A session is scheduled instead during class
More information4. Find the average velocities and average accelerations of a particle moving in 1-D given its position at various times.
PHYSICS 201: TEST 1 STUDY SHEET 1. Convert a quantity from one set of units to another set of units. 2. Convert a 2-D vector from rectangular form (components) to polar form (magnitude and angle), or from
More informationMODEL PAPER CLASS XI PHYSICS (GROUP 1) BLUEPRINT Name of chapter (1)
sr. no. MODEL PAPER CLASS XI PHYSICS (GROUP ) BLUEPRINT Name of chapter VSAQ () SA-I (2) SA-II (3) Value based (4) LA(5) Total 70 Physical world and measurement 3 2 Kinematics 2 3,3 5 3 Laws of motion
More informationA B = AB cos θ = 100. = 6t. a(t) = d2 r(t) a(t = 2) = 12 ĵ
1. A ball is thrown vertically upward from the Earth s surface and falls back to Earth. Which of the graphs below best symbolizes its speed v(t) as a function of time, neglecting air resistance: The answer
More informationPhysics 8, Fall 2013, equation sheet work in progress
(Chapter 1: foundations) 1 year 3.16 10 7 s Physics 8, Fall 2013, equation sheet work in progress circumference of earth 40 10 6 m speed of light c = 2.9979 10 8 m/s mass of proton or neutron 1 amu ( atomic
More informationGrade XI. Physics Exam Preparation Booklet. Chapter-wise Important Questions. #GrowWithGreen
Grade XI Physics Exam Preparation Booklet Chapter-wise Important Questions #GrowWithGreen Units and Measurements Q1. After reading the physics book, Anamika recalled and noted down the expression for the
More informationChapter 13. Gravitation
Chapter 13 Gravitation e = c/a A note about eccentricity For a circle c = 0 à e = 0 a Orbit Examples Mercury has the highest eccentricity of any planet (a) e Mercury = 0.21 Halley s comet has an orbit
More informationNewton s Gravitational Law
1 Newton s Gravitational Law Gravity exists because bodies have masses. Newton s Gravitational Law states that the force of attraction between two point masses is directly proportional to the product of
More informationPhysics 8, Fall 2011, equation sheet work in progress
1 year 3.16 10 7 s Physics 8, Fall 2011, equation sheet work in progress circumference of earth 40 10 6 m speed of light c = 2.9979 10 8 m/s mass of proton or neutron 1 amu ( atomic mass unit ) = 1 1.66
More informationMass on a Horizontal Spring
Course- B.Sc. Applied Physical Science (Computer Science) Year- IInd, Sem- IVth Subject Physics Paper- XIVth, Electromagnetic Theory Lecture No. 22, Simple Harmonic Motion Introduction Hello friends in
More informationChapter 14. Oscillations. Oscillations Introductory Terminology Simple Harmonic Motion:
Chapter 14 Oscillations Oscillations Introductory Terminology Simple Harmonic Motion: Kinematics Energy Examples of Simple Harmonic Oscillators Damped and Forced Oscillations. Resonance. Periodic Motion
More informationOscillations. PHYS 101 Previous Exam Problems CHAPTER. Simple harmonic motion Mass-spring system Energy in SHM Pendulums
PHYS 101 Previous Exam Problems CHAPTER 15 Oscillations Simple harmonic motion Mass-spring system Energy in SHM Pendulums 1. The displacement of a particle oscillating along the x axis is given as a function
More informationChapter 13. Gravitation
Chapter 13 Gravitation 13.2 Newton s Law of Gravitation Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G =6.67 x10 11 Nm 2 /kg 2
More informationLecture XXVI. Morris Swartz Dept. of Physics and Astronomy Johns Hopkins University November 5, 2003
Lecture XXVI Morris Swartz Dept. of Physics and Astronomy Johns Hopins University morris@jhu.edu November 5, 2003 Lecture XXVI: Oscillations Oscillations are periodic motions. There are many examples of
More information(b) The period T and the angular frequency ω of uniform rotation are related to the cyclic frequency f as. , ω = 2πf =
PHY 302 K. Solutions for problem set #9. Non-textbook problem #1: (a) Rotation frequency of 1 Hz means one revolution per second, or 60 revolutions per minute (RPM). The pre-lp vinyl disks rotated at 78
More informationb) (6) What is the volume of the iron cube, in m 3?
General Physics I Exam 4 - Chs. 10,11,12 - Fluids, Waves, Sound Nov. 14, 2012 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show formulas used, essential steps, and results
More informationChapter 15. Oscillations
Chapter 15 Oscillations 15.1 Simple Harmonic Motion Oscillatory Motion: Motion which is periodic in time; motion that repeats itself in time. Examples: SHM: Power line oscillates when the wind blows past.
More informationMass on a Spring C2: Simple Harmonic Motion. Simple Harmonic Motion. Announcements Week 12D1
Simple Harmonic Motion 8.01 Week 1D1 Today s Reading Assignment MIT 8.01 Course Notes Chapter 3 Simple Harmonic Motion Sections 3.1-3.4 1 Announcements Sunday Tutoring in 6-15 from 1-5 pm Problem Set 9
More informationPhysics 41 HW Set 1 Chapter 15 Serway 8 th ( 7 th )
Conceptual Q: 4 (7), 7 (), 8 (6) Physics 4 HW Set Chapter 5 Serway 8 th ( 7 th ) Q4(7) Answer (c). The equilibrium position is 5 cm below the starting point. The motion is symmetric about the equilibrium
More informationGrade XI. Physics Exam Preparation Booklet. Chapter-wise Important Questions. #GrowWithGreen
Grade XI Physics Exam Preparation Booklet Chapter-wise Important Questions #GrowWithGreen Units and Measurements Q1. After reading the physics book, Anamika recalled and noted down the expression for the
More informationAP Physics 1 Second Semester Final Exam Review
AP Physics 1 Second Semester Final Exam Review Chapter 7: Circular Motion 1. What does centripetal mean? What direction does it indicate?. Does the centripetal force do work on the object it is rotating?
More informationChapter 16 Waves in One Dimension
Lecture Outline Chapter 16 Waves in One Dimension Slide 16-1 Chapter 16: Waves in One Dimension Chapter Goal: To study the kinematic and dynamics of wave motion, i.e., the transport of energy through a
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 informationSimple Harmonic Motion
Simple Harmonic Motion (FIZ 101E - Summer 2018) July 29, 2018 Contents 1 Introduction 2 2 The Spring-Mass System 2 3 The Energy in SHM 5 4 The Simple Pendulum 6 5 The Physical Pendulum 8 6 The Damped Oscillations
More informationPHY2020 Test 2 November 5, Name:
1 PHY2020 Test 2 November 5, 2014 Name: sin(30) = 1/2 cos(30) = 3/2 tan(30) = 3/3 sin(60) = 3/2 cos(60) = 1/2 tan(60) = 3 sin(45) = cos(45) = 2/2 tan(45) = 1 sin(37) = cos(53) = 0.6 cos(37) = sin(53) =
More informationConsider a particle in 1D at position x(t), subject to a force F (x), so that mẍ = F (x). Define the kinetic energy to be.
Chapter 4 Energy and Stability 4.1 Energy in 1D Consider a particle in 1D at position x(t), subject to a force F (x), so that mẍ = F (x). Define the kinetic energy to be T = 1 2 mẋ2 and the potential energy
More informationkg C 10 C = J J = J kg C 20 C = J J = J J
Seat: PHYS 1500 (Spring 2007) Exam #3, V1 Name: 5 pts 1. A pendulum is made with a length of string of negligible mass with a 0.25 kg mass at the end. A 2nd pendulum is identical except the mass is 0.50
More informationd 2 x dt 2 = ω2 x x(t) = A cos(ωt + φ) k m ω spring = E SHO = 1 2 ka2 L g T = 2π F g = G m 1m 2 r 2 g = F g m = G m r 2
F s = k s I ring = MR 2 I disk = 1 2 MR2 I sphere = 2 5 MR2 d 2 x dt 2 = ω2 x x(t) = A cos(ωt + φ) ω = 2πf = 2π T U g = G m 1m 2 r ( 4π T 2 2 = GM ) r I rod,cm = 1 12 ML2 I rod,end = 1 ML2 I = I CM + MR
More informationPC 1141 : AY 2012 /13
NUS Physics Society Past Year Paper Solutions PC 1141 : AY 2012 /13 Compiled by: NUS Physics Society Past Year Solution Team Yeo Zhen Yuan Ryan Goh Published on: November 17, 2015 1. An egg of mass 0.050
More informationChapter 16 Mechanical Waves
Chapter 6 Mechanical Waves A wave is a disturbance that travels, or propagates, without the transport of matter. Examples: sound/ultrasonic wave, EM waves, and earthquake wave. Mechanical waves, such as
More information2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity
2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity Energy 7 4 Kinematics Free fall Collisions 3 5 Dynamics
More informationSolutions Practice Test - PHYS 211 Final Exam (New Material)
Solutions Practice Test - PHYS 11 Final Exam (New Material) 1C The question talks about gravitational forces, and so we need to use our new equation for gravitational force: F = Gm1m / r What we need to
More informationω = 0 a = 0 = α P = constant L = constant dt = 0 = d Equilibrium when: τ i = 0 τ net τ i Static Equilibrium when: F z = 0 F net = F i = ma = d P
Equilibrium when: F net = F i τ net = τ i a = 0 = α dp = 0 = d L = ma = d P = 0 = I α = d L = 0 P = constant L = constant F x = 0 τ i = 0 F y = 0 F z = 0 Static Equilibrium when: P = 0 L = 0 v com = 0
More informationChapter 5 Oscillatory Motion
Chapter 5 Oscillatory Motion Simple Harmonic Motion An object moves with simple harmonic motion whenever its acceleration is proportional to its displacement from some equilibrium position and is oppositely
More informationKinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
More informationPHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011
PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this
More informationChapter 13 Solutions
Chapter 3 Solutions 3. x = (4.00 m) cos (3.00πt + π) Compare this with x = A cos (ωt + φ) to find (a) ω = πf = 3.00π or f =.50 Hz T = f = 0.667 s A = 4.00 m (c) φ = π rad (d) x(t = 0.50 s) = (4.00 m) cos
More informationQ = CΔT = C(T f T i )
Linear scale : need 2 points to define Fahrenheit [ F] Celsius [ C] Kelvin [K] Conversion factors K C C F Expansion in 1-D T F = 9 T 5 C + 32 T C = T K 273.15 ΔL = αl 0 ΔT ( ) L = L 0 1+ αδt 0 th Law of
More informationSimple Harmonic Motion Test Tuesday 11/7
Simple Harmonic Motion Test Tuesday 11/7 Chapter 11 Vibrations and Waves 1 If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is
More informationSlide 1 / 70. Simple Harmonic Motion
Slide 1 / 70 Simple Harmonic Motion Slide 2 / 70 SHM and Circular Motion There is a deep connection between Simple Harmonic Motion (SHM) and Uniform Circular Motion (UCM). Simple Harmonic Motion can be
More informationExam 3 Practice Solutions
Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at
More informationPart I Multiple Choice (4 points. ea.)
ach xam usually consists of 10 ultiple choice questions which are conceptual in nature. They are often based upon the assigned thought questions from the homework. There are also 4 problems in each exam,
More informationPhys 2101 Gabriela González
Phys 2101 Gabriela González Newton s law : F = Gm 1 m 2 /r 2 Explains why apples fall, why the planets move around the Sun, sciencebulletins.amnh.org And in YouTube! Explains just as well as Newtons why
More informationLectures Chapter 10 (Cutnell & Johnson, Physics 7 th edition)
PH 201-4A spring 2007 Simple Harmonic Motion Lectures 24-25 Chapter 10 (Cutnell & Johnson, Physics 7 th edition) 1 The Ideal Spring Springs are objects that exhibit elastic behavior. It will return back
More informationCHAPTER 11 TEST REVIEW
AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM CHAPTER TEST
More informationPractice Problems for Exam 2 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 008 Practice Problems for Exam Solutions Part I Concept Questions: Circle your answer. 1) A spring-loaded toy dart gun
More informationPhysics 2101, Final Exam, Form A
Physics 2101, Final Exam, Form A December 11, 2007 Name: SOLUTIONS Section: (Circle one) 1 (Rupnik, MWF 7:40am) 2 (Rupnik, MWF 9:40am) 3 (González, MWF 2:40pm) 4 (Pearson, TTh 9:10am) 5 (Pearson, TTh 12:10pm)
More informationMechanics Oscillations Simple Harmonic Motion
Mechanics Oscillations Simple Harmonic Motion Lana Sheridan De Anza College Dec 3, 2018 Last time gravity Newton s universal law of gravitation gravitational field gravitational potential energy Overview
More informationUniform Circular Motion
Circular Motion Uniform Circular Motion Uniform Circular Motion Traveling with a constant speed in a circular path Even though the speed is constant, the acceleration is non-zero The acceleration responsible
More informationLecture 16. Gravitation
Lecture 16 Gravitation Today s Topics: The Gravitational Force Satellites in Circular Orbits Apparent Weightlessness lliptical Orbits and angular momentum Kepler s Laws of Orbital Motion Gravitational
More informationOscillations Simple Harmonic Motion
Oscillations Simple Harmonic Motion Lana Sheridan De Anza College Dec 1, 2017 Overview oscillations simple harmonic motion (SHM) spring systems energy in SHM pendula damped oscillations Oscillations and
More informationEssential Physics I. Lecture 9:
Essential Physics I E I Lecture 9: 15-06-15 Last lecture: review Conservation of momentum: p = m v p before = p after m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f m 1 m 1 m 2 m 2 Elastic collision: +
More informationSimple and Physical Pendulums Challenge Problem Solutions
Simple and Physical Pendulums Challenge Problem Solutions Problem 1 Solutions: For this problem, the answers to parts a) through d) will rely on an analysis of the pendulum motion. There are two conventional
More informationMomentum Circular Motion and Gravitation Rotational Motion Fluid Mechanics
Momentum Circular Motion and Gravitation Rotational Motion Fluid Mechanics Momentum Momentum Collisions between objects can be evaluated using the laws of conservation of energy and of momentum. Momentum
More informationPHY 2130 EXAM 3 A April 3, 2013
PHY 130 EXAM 3 A April 3, 013 Name (print): (Last) (First) WSU ID Number (9 digit): Please circle your quiz section: Monday Tuesday Wednesday Thursday 11:45 AM (K. Dhindsa) 10:40 AM (J. Huang) 11:45 AM
More informationPHYSICS. Course Structure. Unit Topics Marks. Physical World and Measurement. 1 Physical World. 2 Units and Measurements.
PHYSICS Course Structure Unit Topics Marks I Physical World and Measurement 1 Physical World 2 Units and Measurements II Kinematics 3 Motion in a Straight Line 23 4 Motion in a Plane III Laws of Motion
More informationFIFTH MIDTERM -- REVIEW PROBLEMS
Physics 2210 Fall 2005 Paolo Gondolor FIFTH MIDTERM -- REVIEW PROBLEMS A solution set is available on the course web page in pdf format (no solutions for 27-29). 7 1. Assume that the planet Uranus has
More information