Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
|
|
- Carmella McCoy
- 8 years ago
- Views:
Transcription
1 Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton
2 II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 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 far-reaching and very important!
3 13-1 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 13-1 Newton's Law of Gravitation r F F m 1 m 2! The magnitude of the force is given by: Eq. (13-1)! Where G is the gravitational constant: Eq. (13-2)! The force always points from one particle to the other, so this equation can be written in vector form: Eq. (13-3)
4 13-1 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 third-law force pairs (i.e. N3L)! e.g. Earth-apple and apple-earth forces are both 0.8 N 13-1 Newton's Law of Gravitation! Earth-apple and apple-earth 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
5 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 # Gravitation and the Principle of Superposition! The principle of superposition applies.! i.e. Add the individual forces as vectors: Eq. (13-5)! For a real (extended) object, this becomes an integral: Eq. (13-6)! If the object is a uniform sphere or shell we can treat its mass as being at its centre instead M M M
6 13-2 Gravitation and the Principle of Superposition Example Summing two forces: Figure 13-4 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
7 13-3 Gravitation Near the Earth's Surface! Combine F = GMm/r 2 and F = ma g : Eq. (13-11)! Gives magnitude of gravitational acceleration at a given distance from the centre of the Earth! Table 13-1 shows the value for a g for various altitudes above the Earth s surface 13-3 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
8 13-3 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 = #R with # the angular velocity, and F N = mg. Thus g = a g "# 2 R.! Exercise for the student. Show this is about m/s 2. Use R=6,400km and!=2" radians/day. Question: do you weigh more or less at the equator than the Poles? Figure Gravitational Potential Energy! Gravitational potential energy for a two-particle system is written: Eq. (13-21)! 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! d r! and using F = GMm. r 2!
9 13-5 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. (13-26) Figure 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
10 13-5 Gravitational Potential Energy 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
11 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) 2_A3: Retrograde Motion of the Planets
12 13-6 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 Planets and Satellites: Kepler's Laws! The orbit is defined by its semi-major axis a and its eccentricity e! An eccentricity of zero corresponds to a circle! Eccentricity of Earth's orbit is
13 Kepler2L: Kepler s 2 nd Law Equal Areas in Equal Times 13-6 Planets and Satellites: Kepler's Laws! Equivalent to Conservation of Angular Momentum! See later in this course.
14 13-6 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 semi-major axis Planets and Satellites: Kepler's Laws
15 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 Satellites: Orbits and Energy! Relating the centripetal acceleration of a satellite to the gravitational force, we can rewrite as energies:! Meaning that: Eq. (13-38)! Therefore the total mechanical energy is: Eq. (13-39) Eq. (13-40)
16 13-7 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 semi-major axis, not its eccentricity! All orbits in Figure have the same energy Figure 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!!
17 13-7 Satellites: Orbits and Energy a) Which orbit (1, 2 or 3?) will the shuttle take when it fires a forward-pointing 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? 13 Summary The Law of Gravitation Superposition Eq. (13-1) Eq. (13-2) 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. (13-5) Eq. (13-11)
18 13 Summary Free-Fall 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. (13-19) Eq. (13-21) Eq. (13-22) 13 Summary Escape Speed Eq. (13-28) Kepler's Laws! The law of orbits: ellipses! The law of areas: equal areas in equal times! The law of periods: Energy in Planetary Motion Eq. (13-42) Kepler's Laws Eq. (13-34)! 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 13-1 Newton's Law
More informationNotes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.
Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the
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 informationA. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.
Q12.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2
More informationNewton s Law of Gravity
Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has
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 informationNewton s Law of Universal Gravitation
Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.
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 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 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 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 information2. Orbits. FER-Zagreb, 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 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 informationGravitation and Newton s Synthesis
Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass
More informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
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 informationUse the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1.
IB PHYSICS: Gravitational Forces Review 1. This question is about gravitation and ocean tides. (b) State Newton s law of universal gravitation. Use the following information to deduce that the gravitational
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 informationPlanetary Orbit Simulator Student Guide
Name: Planetary Orbit Simulator Student Guide Background Material Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages.
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 Earth-centered
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 informationFrom Aristotle to Newton
From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers
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 informationNiraj Sir GRAVITATION CONCEPTS. Kepler's law of planetry motion
GRAVITATION CONCEPTS Kepler's law of planetry motion (a) Kepler's first law (law of orbit): Every planet revolves around the sun in an elliptical orbit with the sun is situated at one focus of the ellipse.
More informationVersion A Page 1. 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart.
Physics Unit Exam, Kinematics 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. What is the magnitude of the gravitational force exerted by
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 informationHow To Understand The Theory Of Gravity
Newton s Law of Gravity and Kepler s Laws Michael Fowler Phys 142E Lec 9 2/6/09. These notes are partly adapted from my Physics 152 lectures, where more mathematical details can be found. The Universal
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 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 informationPhysics 53. Gravity. Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. Alexander Pope
Physics 53 Gravity Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. Alexander Pope Kepler s laws Explanations of the motion of the celestial bodies sun, moon, planets
More informationAstronomy 1140 Quiz 1 Review
Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality
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 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 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 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 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 informationMath 1302, Week 3 Polar coordinates and orbital motion
Math 130, Week 3 Polar coordinates and orbital motion 1 Motion under a central force We start by considering the motion of the earth E around the (fixed) sun (figure 1). The key point here is that the
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 informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationOrbital Mechanics and Space Geometry
Orbital Mechanics and Space Geometry AERO4701 Space Engineering 3 Week 2 Overview First Hour Co-ordinate Systems and Frames of Reference (Review) Kepler s equations, Orbital Elements Second Hour Orbit
More informationPhysics Midterm Review Packet January 2010
Physics Midterm Review Packet January 2010 This Packet is a Study Guide, not a replacement for studying from your notes, tests, quizzes, and textbook. Midterm Date: Thursday, January 28 th 8:15-10:15 Room:
More informationLecture L17 - Orbit Transfers and Interplanetary Trajectories
S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L17 - Orbit Transfers and Interplanetary Trajectories In this lecture, we will consider how to transfer from one orbit, to another or to
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 informationAstronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:
Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose
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 informationAstromechanics Two-Body Problem (Cont)
5. Orbit Characteristics Astromechanics Two-Body Problem (Cont) We have shown that the in the two-body problem, the orbit of the satellite about the primary (or vice-versa) is a conic section, with the
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 informationThe Gravitational Field
The Gravitational Field The use of multimedia in teaching physics Texts to multimedia presentation Jan Hrnčíř jan.hrncir@gfxs.cz Martin Klejch martin.klejch@gfxs.cz F. X. Šalda Grammar School, Liberec
More informationPhysics 125 Practice Exam #3 Chapters 6-7 Professor Siegel
Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
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 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 informationastronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times.
1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 5. If the distance between the Earth and the Sun were increased,
More informationEDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1
Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time
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 informationRETURN TO THE MOON. Lesson Plan
RETURN TO THE MOON Lesson Plan INSTRUCTIONS FOR TEACHERS Grade Level: 9-12 Curriculum Links: Earth and Space (SNC 1D: D2.1, D2.2, D2.3, D2.4) Group Size: Groups of 2-4 students Preparation time: 1 hour
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 informationBackground Information
Background Information The Second Law of Motion and The Law of Gravitation Student Activities 1. Round and Round They Go! 2. onic Sections - Movement in Newton s Gravitational orce Notes to Teachers Teacher
More informationProblem Set #13 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.0L: Physics I January 3, 06 Prof. Alan Guth Problem Set #3 Solutions Due by :00 am on Friday, January in the bins at the intersection of Buildings
More informationNewton s Law of Universal Gravitation describes the attractive gravitational force that exists between any two bodies with the following equation:
Newton s Laws & Gravitation Newton s Law of Universal Gravitation describes the attractive gravitational force that exists between any two bodies with the following equation: F G = GMm 2 r G is the gravitational
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 informationQ3.2.a The gravitational force exerted by a planet on one of its moons is 3e23 newtons when the moon is at a particular location.
Q3.2.a The gravitational force exerted by a planet on one of its moons is 3e23 newtons when the moon is at a particular location. If the mass of the moon were three times as large, what would the force
More informationBHS Freshman Physics Review. Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science.
BHS Freshman Physics Review Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science. Galileo (1564-1642): 1 st true scientist and 1 st person to use
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
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 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 informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationConceptual: 1, 3, 5, 6, 8, 16, 18, 19. Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65. Conceptual Questions
Conceptual: 1, 3, 5, 6, 8, 16, 18, 19 Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65 Conceptual Questions 1. The magnetic field cannot be described as the magnetic force per unit charge
More informationNewton s Laws of Motion
Newton s Laws of Motion The Earth revolves around the sun in an elliptical orbit. The moon orbits the Earth in the same way. But what keeps the Earth and the moon in orbit? Why don t they just fly off
More informationLab 7: Rotational Motion
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125
More informationPractice TEST 2. Explain your reasoning
Practice TEST 2 1. Imagine taking an elevator ride from the1 st floor to the 10 th floor of a building. While moving between the 1 st and 2 nd floors the elevator speeds up, but then moves at a constant
More informationGRADE 8 SCIENCE INSTRUCTIONAL TASKS. Gravity
GRADE 8 SCIENCE INSTRUCTIONAL TASKS Gravity Grade-Level Expectations The exercises in these instructional tasks address content related to the following science grade-level expectation(s): ESS-M-C3 Relate
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 informationChapter 9 Circular Motion Dynamics
Chapter 9 Circular Motion Dynamics 9. Introduction Newton s Second Law and Circular Motion... 9. Universal Law of Gravitation and the Circular Orbit of the Moon... 9.. Universal Law of Gravitation... 3
More informationThe Two-Body Problem
The Two-Body Problem Abstract In my short essay on Kepler s laws of planetary motion and Newton s law of universal gravitation, the trajectory of one massive object near another was shown to be a conic
More information8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential
8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential energy, e.g. a ball in your hand has more potential energy
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 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 informationHow To Understand General Relativity
Chapter S3 Spacetime and Gravity What are the major ideas of special relativity? Spacetime Special relativity showed that space and time are not absolute Instead they are inextricably linked in a four-dimensional
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 informationChapter 6 Circular Motion
Chapter 6 Circular Motion 6.1 Introduction... 1 6.2 Cylindrical Coordinate System... 2 6.2.1 Unit Vectors... 3 6.2.2 Infinitesimal Line, Area, and Volume Elements in Cylindrical Coordinates... 4 Example
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
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 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 informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationCarol and Charles see their pencils fall exactly straight down.
Section 24-1 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 informationChapter 6. Work and Energy
Chapter 6 Work and Energy The concept of forces acting on a mass (one object) is intimately related to the concept of ENERGY production or storage. A mass accelerated to a non-zero speed carries energy
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 informationFree Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)
Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure
More informationLab 6: Kepler's Laws. Introduction. Section 1: First Law
Lab 6: Kepler's Laws Purpose: to learn that orbit shapes are ellipses, gravity and orbital velocity are related, and force of gravity and orbital period are related. Materials: 2 thumbtacks, 1 pencil,
More informationSPEED, VELOCITY, AND ACCELERATION
reflect Look at the picture of people running across a field. What words come to mind? Maybe you think about the word speed to describe how fast the people are running. You might think of the word acceleration
More informationNewton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009
Newton s Laws Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Imaginary Cannon Newton was familiar with Galileo s analysis of projectile motion, and decided to take it one step further. He imagined
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 informationExercise: Estimating the Mass of Jupiter Difficulty: Medium
Exercise: Estimating the Mass of Jupiter Difficulty: Medium OBJECTIVE The July / August observing notes for 010 state that Jupiter rises at dusk. The great planet is now starting its grand showing for
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 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 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 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 information