Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton


 Amos Holt
 1 years ago
 Views:
Transcription
1 Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton
2
3 II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds
4 131 Newton's Law of Gravitation The gravitational force o o o o o o o Holds us to the Earth Holds Earth in orbit around the Sun Holds the Sun together with the stars in our Galaxy Holds together the Local Group of galaxies Holds together the Local Supercluster of galaxies Attempts to slow the expansion of the Universe Is responsible for black holes Gravity is farreaching and very important!
5 131 Newton's Law of Gravitation Gravitational attraction depends on mass of an object Earth has a large mass and produces a large attraction The force is always attractive, never repulsive Bodies attract each other through gravitational attraction Newton realized this attraction was responsible for maintaining the orbits of celestial bodies Newton's Law of Gravitation defines the strength of this attractive force between particles Between an apple & the Earth: ~0.8 N Between 2 people: < 1 µn
6 131 Newton's Law of Gravitation r F F m 1 m 2 The magnitude of the force is given by: Eq. (131) Where G is the gravitational constant: Eq. (132) The force always points from one particle to the other, so this equation can be written in vector form: Eq. (133)
7 131 Newton's Law of Gravitation M M M The shell theorem describes gravitational attraction for objects Earth is a nesting of shells, so we feel Earth's mass as if it were all located at its centre Gravitational force forms thirdlaw force pairs (i.e. N3L) e.g. Earthapple and appleearth forces are both 0.8 N
8 131 Newton's Law of Gravitation Earthapple and appleearth forces are both ~0.8 N The difference in mass causes the difference in the apple:earth accelerations: ~10 m/s 2 vs. ~ m/s 2
9 Consider the objects of various masses indicated below. The objects are each separated from another object by the distance indicated. In which of these situations is the gravitational force exerted on the two objects the largest? a) #1 b) #2 c) #3 d) #2 and #3 e) #1, #2, and #3
10 132 Gravitation and the Principle of Superposition The principle of superposition applies. i.e. Add the individual forces as vectors: Eq. (135) For a real (extended) object, this becomes an integral: Eq. (136) If the object is a uniform sphere or shell we can treat its mass as being at its centre instead M M M
11 132 Gravitation and the Principle of Superposition Example Summing two forces: Figure 134
12 Consider a system of particles, each of mass m. In which one of the following configurations is the net gravitational force on Particle A the largest? The horizontal or vertical spacing between particles is the same in each case. a) 1 b) 2 c) 4 d) 1 and 2 equally large e) 2 and 4 are equally large
13 133 Gravitation Near the Earth's Surface Combine F = GMm/r 2 and F = ma g : Eq. (1311) Gives magnitude of gravitational acceleration at a given distance from the centre of the Earth Table 131 shows the value for a g for various altitudes above the Earth s surface
14 133 Gravitation Near the Earth's Surface The calculated a g will differ slightly from the measured g at any location on the Earth s surface Three reasons. The Earth. 1. mass is not uniformly distributed 2. is not a perfect sphere 3. rotates
15 133 Gravitation Near Earth's Surface Example Difference in gravitational force and weight due to rotation at the equator: N2L : F N ma g = m V 2, the centripetal acceleration. R Here V = ωr with ω the angular velocity, and F N = mg. Thus g = a g ω 2 R. Exercise for the student. Show this is about m/s 2. Use R=6,400km and ω=2π radians/day. Question: do you weigh more or less at the equator than the Poles? Figure 136
16 135 Gravitational Potential Energy Gravitational potential energy for a twoparticle system is written: Eq. (1321) Note this value is negative and approaches 0 for r The gravitational potential energy of a system is the sum of potential energies for all pairs of particles Proof comes from integrating the force to obtain the work done. i.e. U = W = F dr and using F = GMm. r 2
17 135 Gravitational Potential Energy The gravitational force is conservative. The work done by this force does not depend on the path followed by the particles, only the difference in the initial and final positions of the particles. Since the work done is independent of path, so is the gravitational potential energy change Eq. (1326) Figure 1310
18 135 Gravitational Potential Energy For a projectile to escape the gravitational pull of a body, it must come to rest only at infinity (if at all). At rest at infinity: K = 0 and U = 0 (because r ) So K + U must be 0 at surface of the body to escape: This is the escape speed. The minimum value to escape. Rockets launch eastward to take advantage of Earth's rotational speed, to reach v escape more easily
19 135 Gravitational Potential Energy
20 You move a ball of mass m away from a sphere of mass M. 1. Does the gravitational potential energy of the system of the ball and sphere a) Increase, or b) Decrease. 2. Is the Work done by the gravitational force between the ball and the sphere a) Positive work, or b) Negative work r m M
21 In a distant solar system where several planets are orbiting a single star of mass M, a large asteroid collides with a planet of mass m orbiting the star at a distance r. As a result, the planet is ejected from its solar system. What is minimum amount of energy that the planet must receive in the collision to be removed from the solar system? a) b) r c) m M d) e)
22 2_A3: Retrograde Motion of the Planets
23 136 Planets and Satellites: Kepler's Laws The motion of planets in the solar system was a puzzle for astronomers, especially curious motions such as retrograde motion. Johannes Kepler ( ) derived laws of motion using Tycho Brahe's ( ) measurements Figure Figure 1312
24 136 Planets and Satellites: Kepler's Laws The orbit is defined by its semimajor axis a and its eccentricity e An eccentricity of zero corresponds to a circle Eccentricity of Earth's orbit is
25 Kepler2L: Kepler s 2 nd Law Equal Areas in Equal Times
26 136 Planets and Satellites: Kepler's Laws Equivalent to Conservation of Angular Momentum See later in this course.
27 136 Planets and Satellites: Kepler's Laws The law of periods can be written mathematically as: Holds for elliptical orbits if we replace r with a, the semimajor axis.
28 136 Planets and Satellites: Kepler's Laws
29 A spacecraft is in low orbit of the Earth with a period of approximately 90 minutes. By which of the following methods could the spacecraft stay in the same orbit and reduce the period of the orbit? a) Before launch, increase the mass of the spacecraft to increase the centripetal force on it. b) Remove any unnecessary equipment, cargo, and supplies to reduce the mass and decrease its angular momentum. c) Fire rockets to increase the tangential velocity of the ship. d) None of the above methods will achieve the desired effect.
30 137 Satellites: Orbits and Energy Relating the centripetal acceleration of a satellite to the gravitational force, we can rewrite as energies: Eq. (1338) Meaning that: Eq. (1339) Therefore the total mechanical energy is: Eq. (1340)
31 137 Satellites: Orbits and Energy Total energy E is the negative of the kinetic energy For an ellipse, we substitute a for r Therefore the energy of an orbit depends only on its semimajor axis, not its eccentricity All orbits in Figure have the same energy Figure 1315
32 137 Satellites: Circular Orbit Graph of variation in Energy for a circular orbit, radius r Note that: E(r) and U(r) are negative E(r) = K(r) E(r), U(r), K(r) all 0 as r
33 137 Satellites: Orbits and Energy a) Which orbit (1, 2 or 3?) will the shuttle take when it fires a forwardpointing thruster so as to reduce its kinetic energy? b) Is the orbital period T then (i) greater than, (ii) less than or (iii) the same as, that of the circular orbit?
34 13 Summary The Law of Gravitation Superposition Eq. (131) Eq. (132) Gravitational Behavior of Uniform Spherical Shells The net force on an external object: calculate as if all the mass were concentrated at the centre of the shell Gravitational Acceleration Eq. (135) Eq. (1311)
35 13 Summary FreeFall Acceleration and Weight Earth's mass is not uniformly distributed, the planet is not spherical, and it rotates: the calculated and measured values of acceleration differ Gravitational Potential Energy Gravitation within a Spherical Shell A uniform shell exerts no net force on a particle inside Inside a solid sphere: Potential Energy of a System Eq. (1319) Eq. (1321) Eq. (1322)
36 13 Summary Escape Speed Eq. (1328) Kepler's Laws The law of orbits: ellipses The law of areas: equal areas in equal times The law of periods: Eq. (1334) Energy in Planetary Motion Eq. (1342) Kepler's Laws Gravitation and acceleration are equivalent
Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 131 Newton's Law
More informationOrbital Mechanics. Angular Momentum
Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely
More informationPenn State University Physics 211 ORBITAL MECHANICS 1
ORBITAL MECHANICS 1 PURPOSE The purpose of this laboratory project is to calculate, verify and then simulate various satellite orbit scenarios for an artificial satellite orbiting the earth. First, there
More information2. Orbits. FERZagreb, Satellite communication systems 2011/12
2. Orbits Topics Orbit types Kepler and Newton laws Coverage area Influence of Earth 1 Orbit types According to inclination angle Equatorial Polar Inclinational orbit According to shape Circular orbit
More informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Why are celestial motions and forces important? They explain the world around
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationLecture 13. Gravity in the Solar System
Lecture 13 Gravity in the Solar System Guiding Questions 1. How was the heliocentric model established? What are monumental steps in the history of the heliocentric model? 2. How do Kepler s three laws
More informationChapter 5: Circular Motion, the Planets, and Gravity
Chapter 5: Circular Motion, the Planets, and Gravity 1. Earth s gravity attracts a person with a force of 120 lbs. The force with which the Earth is attracted towards the person is A. Zero. B. Small but
More informationSatellites and Space Stations
Satellites and Space Stations A satellite is an object or a body that revolves around another object, which is usually much larger in mass. Natural satellites include the planets, which revolve around
More informationSection 4: The Basics of Satellite Orbits
Section 4: The Basics of Satellite Orbits MOTION IN SPACE VS. MOTION IN THE ATMOSPHERE The motion of objects in the atmosphere differs in three important ways from the motion of objects in space. First,
More informationUnit 8 Lesson 2 Gravity and the Solar System
Unit 8 Lesson 2 Gravity and the Solar System Gravity What is gravity? Gravity is a force of attraction between objects that is due to their masses and the distances between them. Every object in the universe
More informationUSING MS EXCEL FOR DATA ANALYSIS AND SIMULATION
USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION Ian Cooper School of Physics The University of Sydney i.cooper@physics.usyd.edu.au Introduction The numerical calculations performed by scientists and engineers
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationSolar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?
Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earthcentered
More informationG U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M
G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD
More informationName Class Date. true
Exercises 131 The Falling Apple (page 233) 1 Describe the legend of Newton s discovery that gravity extends throughout the universe According to legend, Newton saw an apple fall from a tree and realized
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationAE554 Applied Orbital Mechanics. Hafta 1 Egemen Đmre
AE554 Applied Orbital Mechanics Hafta 1 Egemen Đmre A bit of history the beginning Astronomy: Science of heavens. (Ancient Greeks). Astronomy existed several thousand years BC Perfect universe (like circles
More informationDIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION
1 DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION Daniel S. Orton email: dsorton1@gmail.com Abstract: There are many longstanding
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More information3600 s 1 h. 24 h 1 day. 1 day
Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationOrbital Mechanics and Space Geometry
Orbital Mechanics and Space Geometry AERO4701 Space Engineering 3 Week 2 Overview First Hour Coordinate Systems and Frames of Reference (Review) Kepler s equations, Orbital Elements Second Hour Orbit
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationExam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti
Exam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti INSTRUCTIONS: Please, use the `bubble sheet and a pencil # 2 to answer the exam questions, by marking
More informationLecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014
Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,
More informationSolar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System
Solar System Fundamentals What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Properties of Planets What is a planet? Defined finally in August 2006!
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
More informationChapter 25.1: Models of our Solar System
Chapter 25.1: Models of our Solar System Objectives: Compare & Contrast geocentric and heliocentric models of the solar sytem. Describe the orbits of planets explain how gravity and inertia keep the planets
More informationPresentation of problem T1 (9 points): The Maribo Meteorite
Presentation of problem T1 (9 points): The Maribo Meteorite Definitions Meteoroid. A small particle (typically smaller than 1 m) from a comet or an asteroid. Meteorite: A meteoroid that impacts the ground
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationThe orbit of Halley s Comet
The orbit of Halley s Comet Given this information Orbital period = 76 yrs Aphelion distance = 35.3 AU Observed comet in 1682 and predicted return 1758 Questions: How close does HC approach the Sun? What
More informationVocabulary  Understanding Revolution in. our Solar System
Vocabulary  Understanding Revolution in Universe Galaxy Solar system Planet Moon Comet Asteroid Meteor(ite) Heliocentric Geocentric Satellite Terrestrial planets Jovian (gas) planets Gravity our Solar
More informationFundamental Mechanics: Supplementary Exercises
Phys 131 Fall 2015 Fundamental Mechanics: Supplementary Exercises 1 Motion diagrams: horizontal motion A car moves to the right. For an initial period it slows down and after that it speeds up. Which of
More informationCHAPTER 11. 4 Halley s comet has a period of about 76 y. What is its mean distance from the sun? R mean = (1 AU)(76) 2/3 (see Problem 3)
CHAPTER 11 1* True or false: (a) Kepler s law of equal areas implies that gravity varies inversely with the square of the distance. (b) The planet closest to the sun, on the average, has the shortest period
More informationPhysics 211 Lecture 4
Physics 211 Lecture 4 Today's Concepts: Newton s Laws a) Acceleration is caused by forces b) Force changes momentum c) Forces always come in pairs d) Good reference frames Mechanics Lecture 4, Slide 1
More informationKinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same.
1. A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall
More informationRETURN TO THE MOON. Lesson Plan
RETURN TO THE MOON Lesson Plan INSTRUCTIONS FOR TEACHERS Grade Level: 912 Curriculum Links: Earth and Space (SNC 1D: D2.1, D2.2, D2.3, D2.4) Group Size: Groups of 24 students Preparation time: 1 hour
More informationThe Solar Wobble or Gravity, Rosettes and Inertia
The Solar Wobble or Gravity, Rosettes and Inertia john.erich.ebner@gmail.com http:blackholeformulas.com February 10, 2015 Abstract Our objective is to show that the sun moves. At least it wobbles. Any
More informationLectures on Gravity Michael Fowler, University of Virginia, Physics 152 Notes, May, 2007
Lectures on Gravity Michael Fowler, University of Virginia, Physics 15 Notes, May, 007 DISCOVERING GRAVITY...3 Terrestrial Gravity: Galileo Analyzes a Cannonball Trajectory...3 Moving Up: Newton Puts the
More informationEarth in the Solar System
Copyright 2011 Study Island  All rights reserved. Directions: Challenge yourself! Print out the quiz or get a pen/pencil and paper and record your answers to the questions below. Check your answers with
More information4 Gravity: A Force of Attraction
CHAPTER 1 SECTION Matter in Motion 4 Gravity: A Force of Attraction BEFORE YOU READ After you read this section, you should be able to answer these questions: What is gravity? How are weight and mass different?
More informationThe Solar System. Unit 4 covers the following framework standards: ES 10 and PS 11. Content was adapted the following:
Unit 4 The Solar System Chapter 7 ~ The History of the Solar System o Section 1 ~ The Formation of the Solar System o Section 2 ~ Observing the Solar System Chapter 8 ~ The Parts the Solar System o Section
More informationLecture PowerPoints. Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli
Lecture PowerPoints Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the
More informationExam 1 Review Questions PHY 2425  Exam 1
Exam 1 Review Questions PHY 2425  Exam 1 Exam 1H Rev Ques.doc  1  Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationThe Solar System. Source http://starchild.gsfc.nasa.gov/docs/starchild/solar_system_level1/solar_system.html
The Solar System What is the solar system? It is our Sun and everything that travels around it. Our solar system is elliptical in shape. That means it is shaped like an egg. Earth s orbit is nearly circular.
More informationNotes on Elastic and Inelastic Collisions
Notes on Elastic and Inelastic Collisions In any collision of 2 bodies, their net momentus conserved. That is, the net momentum vector of the bodies just after the collision is the same as it was just
More informationCarol and Charles see their pencils fall exactly straight down.
Section 241 1. Carol is in a railroad car on a train moving west along a straight stretch of track at a constant speed of 120 km/h, and Charles is in a railroad car on a train at rest on a siding along
More informationScience Standard 4 Earth in Space Grade Level Expectations
Science Standard 4 Earth in Space Grade Level Expectations Science Standard 4 Earth in Space Our Solar System is a collection of gravitationally interacting bodies that include Earth and the Moon. Universal
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform
More informationFluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture  20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all
More informationFree Fall: Observing and Analyzing the Free Fall Motion of a Bouncing PingPong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)
Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing PingPong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure
More informationPeriods of Western Astronomy. Chapter 1. Prehistoric Astronomy. Prehistoric Astronomy. The Celestial Sphere. Stonehenge. History of Astronomy
Periods of Western Astronomy Chapter 1 History of Astronomy Western astronomy divides into 4 periods Prehistoric (before 500 B.C.) Cyclical motions of Sun, Moon and stars observed Keeping time and determining
More informationReview Assessment: Lec 02 Quiz
COURSES > PHYSICS GUEST SITE > CONTROL PANEL > 1ST SEM. QUIZZES > REVIEW ASSESSMENT: LEC 02 QUIZ Review Assessment: Lec 02 Quiz Name: Status : Score: Instructions: Lec 02 Quiz Completed 20 out of 100 points
More informationKINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES
KINEMTICS OF PRTICLES RELTIVE MOTION WITH RESPECT TO TRNSLTING XES In the previous articles, we have described particle motion using coordinates with respect to fixed reference axes. The displacements,
More informationAt the skate park on the ramp
At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 6. Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Course Outline THEMATIC UNIT 1: ORBITAL DYNAMICS Lecture 02: The TwoBody Problem Lecture 03:
More informationAngular acceleration α
Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 70 Linear and Circular Motion Compared Slide 7 Linear and Circular Kinematics Compared Slide 7
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationSection 1 Gravity: A Force of Attraction
Section 1 Gravity: A Force of Attraction Key Concept Gravity is a force of attraction between objects that is due to their masses. What You Will Learn Gravity affects all matter, including the parts of
More informationKERN COMMUNITY COLLEGE DISTRICT CERRO COSO COLLEGE PHYS C111 COURSE OUTLINE OF RECORD
KERN COMMUNITY COLLEGE DISTRICT CERRO COSO COLLEGE PHYS C111 COURSE OUTLINE OF RECORD 1. DISCIPLINE AND COURSE NUMBER: PHYS C111 2. COURSE TITLE: Mechanics 3. SHORT BANWEB TITLE: Mechanics 4. COURSE AUTHOR:
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationPhysics Competitions Vol 13 No 2 2011 & Vol.14 No 1 2012. A few good orbits. 400 088. # Corresponding author: anikets@hbcse.tifr.res.
A few good orbits Chiraag Juvekar 1, Mehul Jain 1 and Aniket Sule 2,# 1 Indian Institute of Technology (Bombay), Mumbai, Maharashtra, India  400 076. 2 Homi Bhabha Centre for Science Education (HBCSE).
More informationProblem 6.40 and 6.41 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITSPilani
Problem 6.40 and 6.4 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITSPilani 6.40 A wheel with fine teeth is attached to the end of a spring with constant k and unstretched length
More informationOrbital Dynamics: Formulary
Orbital Dynamics: Formulary 1 Introduction Prof. Dr. D. Stoffer Department of Mathematics, ETH Zurich Newton s law of motion: The net force on an object is equal to the mass of the object multiplied by
More information8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight
1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled
More informationEducator Guide to S LAR SYSTEM. 1875 El Prado, San Diego CA 92101 (619) 2381233 www.rhfleet.org
Educator Guide to S LAR SYSTEM 1875 El Prado, San Diego CA 92101 (619) 2381233 www.rhfleet.org PreVisit Activity: Orbital Paths Materials: Plastic Plate Marble Scissors To Do: 1. Put the plate on a flat
More informationInteraction of Energy and Matter Gravity Measurement: Using Doppler Shifts to Measure Mass Concentration TEACHER GUIDE
Interaction of Energy and Matter Gravity Measurement: Using Doppler Shifts to Measure Mass Concentration TEACHER GUIDE EMR and the Dawn Mission Electromagnetic radiation (EMR) will play a major role in
More informationChapter 7: Momentum and Impulse
Chapter 7: Momentum and Impulse 1. When a baseball bat hits the ball, the impulse delivered to the ball is increased by A. follow through on the swing. B. rapidly stopping the bat after impact. C. letting
More informationLecture 7 Formation of the Solar System. Nebular Theory. Origin of the Solar System. Origin of the Solar System. The Solar Nebula
Origin of the Solar System Lecture 7 Formation of the Solar System Reading: Chapter 9 Quiz#2 Today: Lecture 60 minutes, then quiz 20 minutes. Homework#1 will be returned on Thursday. Our theory must explain
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationStudy Guide: Solar System
Study Guide: Solar System 1. How many planets are there in the solar system? 2. What is the correct order of all the planets in the solar system? 3. Where can a comet be located in the solar system? 4.
More informationPhysics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE
1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object
More informationAS COMPETITION PAPER 2008
AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question
More informationIf the particle is moving, its position will change. If its speed and direction are steady, then we can write its position after time t as
1 Linear Mechanics 1.1 Motion in a Line 1.1.1 The Fundamentals 1.1.1.1 Kinematics Mechanics is all about motion. We start with the simplest kind of motion the motion of small dots or particles. Such a
More informationSalem Community College Course Syllabus. Course Title: Physics I. Course Code: PHY 101. Lecture Hours: 2 Laboratory Hours: 4 Credits: 4
Salem Community College Course Syllabus Course Title: Physics I Course Code: PHY 101 Lecture Hours: 2 Laboratory Hours: 4 Credits: 4 Course Description: The basic principles of classical physics are explored
More informationPhysics B AP Review Packet: Mechanics Name:
Name: Position Location of a particle in space. (x) or (x,y) or (x,y,z) Distance The total length of the path traveled by an object. Does not depend upon direction. Displacement The change in position
More informationArtificial Satellites Earth & Sky
Artificial Satellites Earth & Sky Name: Introduction In this lab, you will have the opportunity to find out when satellites may be visible from the RPI campus, and if any are visible during the activity,
More informationLecture Presentation Chapter 7 Rotational Motion
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
More informationDynamics of Iain M. Banks Orbitals. Richard Kennaway. 12 October 2005
Dynamics of Iain M. Banks Orbitals Richard Kennaway 12 October 2005 Note This is a draft in progress, and as such may contain errors. Please do not cite this without permission. 1 The problem An Orbital
More informationProblem Set #8 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01L: Physics I November 7, 2015 Prof. Alan Guth Problem Set #8 Solutions Due by 11:00 am on Friday, November 6 in the bins at the intersection
More informationEDUH 1017  SPORTS MECHANICS
4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH 1017  SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use
More informationSYLLABUS FORM WESTCHESTER COMMUNITY COLLEGE Valhalla, NY lo595. l. Course #: PHYSC 111 2. NAME OF ORIGINATOR /REVISOR: Dr.
SYLLABUS FORM WESTCHESTER COMMUNITY COLLEGE Valhalla, NY lo595 l. Course #: PHYSC 111 2. NAME OF ORIGINATOR /REVISOR: Dr. Neil Basescu NAME OF COURSE: College Physics 1 with Lab 3. CURRENT DATE: 4/24/13
More information12. What is the name given to the path of the Sun as seen from Earth? a.) Equinox b.) Celestial equator c.) Solstice d.
Chapter 1 11. How long does it take the Earth to orbit the Sun? a.) one sidereal day b.) one month c.) one year X d.) one hour 12. What is the name given to the path of the Sun as seen from Earth? a.)
More informationDevelopment of an automated satellite network management system
Development of an automated satellite network management system Iasonas Kytros Christos Porios Nikitas Terzoudis Varvara Chatzipavlou Coach: Sitsanlis Ilias February 2013 Abstract In this paper we present
More information1 of 7 9/5/2009 6:12 PM
1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More informationExam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis
* By request, but I m not vouching for these since I didn t write them Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis There are extra office hours today & tomorrow Lots of practice exams
More informationNewton s proof of the connection between
Elliptical Orbit 1/r 2 Force Jeffrey Prentis, Bryan Fulton, and Carol Hesse, University of MichiganDearborn, Dearborn, MI Laura Mazzino, University of Louisiana, Lafayette, LA Newton s proof of the connection
More informationLab 7: Gravity and Jupiter's Moons
Lab 7: Gravity and Jupiter's Moons Image of Galileo Spacecraft Gravity is the force that binds all astronomical structures. Clusters of galaxies are gravitationally bound into the largest structures in
More informationGeneral Certificate of Education (Alevel) January 2013 Physics A PHYA4 (Specification 2450) Unit 4: Fields and further mechanics Final Mark Scheme
Version 1.1 General Certificate of Education (Alevel) January 013 Physics A PHYA4 (Specification 450) Unit 4: Fields and further mechanics Final Mark Scheme Mark schemes are prepared by the Principal
More informationSection 2. Satellite Orbits
Section 2. Satellite Orbits References Kidder and Vonder Haar: chapter 2 Stephens: chapter 1, pp. 2530 Rees: chapter 9, pp. 174192 In order to understand satellites and the remote sounding data obtained
More informationData Provided: A formula sheet and table of physical constants is attached to this paper. DARK MATTER AND THE UNIVERSE
Data Provided: A formula sheet and table of physical constants is attached to this paper. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn Semester (20142015) DARK MATTER AND THE UNIVERSE 2 HOURS Answer question
More informationTidal forces in the Solar System
Tidal forces in the Solar System Introduction As anywhere else in the Universe, gravity is the basic and fundamental principle that rules the shape and permanent motion of all the celestial bodies inside
More informationTidal Forces and their Effects in the Solar System
Tidal Forces and their Effects in the Solar System Richard McDonald September 10, 2005 Introduction For most residents of Earth, tides are synonymous with the daily rise and fall of sea levels, and there
More informationOrbital Dynamics with Maple (sll  v1.0, February 2012)
Orbital Dynamics with Maple (sll  v1.0, February 2012) Kepler s Laws of Orbital Motion Orbital theory is one of the great triumphs mathematical astronomy. The first understanding of orbits was published
More informationPhysics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal
Phsics 53 Kinematics 2 Our nature consists in movement; absolute rest is death. Pascal Velocit and Acceleration in 3D We have defined the velocit and acceleration of a particle as the first and second
More informationChapter 15.3 Galaxy Evolution
Chapter 15.3 Galaxy Evolution Elliptical Galaxies Spiral Galaxies Irregular Galaxies Are there any connections between the three types of galaxies? How do galaxies form? How do galaxies evolve? P.S. You
More information