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Physics of Technology PHYS 1800 Lecture 12 Introduction Circular Motion and Gravitational Force Section 0 Lecture 1 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 1 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet Date Day Lecture Jan 5 M Class Admin: Intro.Physics Phenomena 6 T Problem solving and math 7 W Units, Scalars, Vectors, 9 F* Speed and Velocity Jan 12 M Acceleration 14 W Free Falling Objects 16 F* Projectile Motion Jan 19 M Martin Luther King 21 W Newton’s Laws 23 F* Mass and Weight Jan 26 M Motion with Friction 28 W Review 29 Th Test 1 30 F Circular Motion Feb 2 M Planetary Motion and Gravity 4 W Energy 6 F* Harmonic Motion Feb 9 M Momentum 11 W Impulse and Collisions 13Introduction F* Rotational Section 0 Motion Lecture 1 Slide 2 Feb 16 M Presidents Day 17 Tu Angular Momentum (Virtual Monday) 18 W Review 19 H Test 2 INTRODUCTION TO Modern Physics PHYX 2710 20 F* Static Fluids, Pressure Fall 2004 Feb 23 M Flotation 25 W Fluids in Motion 27 F* Temperature and Heat Mar 2 M First Law of Thermodynamics Physics of Technology—PHYS 1800 4 W Spring 2009Heat flow and Greenhouse CircularEffect Motion and *Homework Handout 6 F* Climate Change Chapter Homework Due 1 App. B, C 1 2 2 3 3 1 No Class 4 4 2 4 1-4 1-4 5 3 5 6 6 4 7 7 8 5 No Class 8 5-8 5-8 9 9 9 10 6 10 10 Gravitational Force 7 Lecture 12 Slide 2 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 3 Introduction and Review INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 3 Does the circular motion of the moon around the Earth ... ... have anything inIntroduction common with Section 0 Lecture 1 circular motion on Earth? Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 4 Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT-1 or m/s) Acceleration—how fast velocity is changing with time (LT-2 or m/s2) Force— what is required to change to motion of a body (MLT-2 or kgm/s2) We will focus on a special kind of force, termed a central forces that results from change in direction of velocity. Introduction Section 0 Lecture 1 Slide 5 Now look at a specific central force, the force due to gravity. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 5 Newton’s Laws in Review • 1st Law —a special case of the 2nd Law for statics, with a=0 or Fnet=0 • An objects velocity remains unchanged, unless a force acts on the object. • 2nd Law (and 1st Law)—How motion of a object is effected by a force. – The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force. F ma units : 1 newton = 1 N = 1 kg m s2 • Introduction Section 0 Lecture 1 Slide 6 3rd Law —Forces come from interactions with other objects. • For every action (force), there is an equal but opposite reaction (force). INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 6 The Math Approach • We are going to explore a different kind of central force that is no longer constant, but is proportional to 1/r2. ag k/r2 v f v0 at or a v f vo t 1 2 vo vo v f vo d t t v0t at 2 2 2 2 We will take a pragmatic approach (hindsight is 20-20!) Introduction Section 0 Lecture 1 Slide 7 We simply replace the force of the “string” with the force of gravity INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Tstring Fgravity k r2 Circular Motion and Gravitational Force Lecture 12 Slide 7 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 8 Historical Perspectives INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 8 Historical Perspective on Gravity Hart’s list of most influential people in the history of the world: Newton (2)* Einstein (10) Galileo Galilei (12)* Aristotle (13)*** Copernicus (19) * Kepler (75) * Explore a trail of science from the early Greeks through work today at USU to improve our understanding and scientific models for the interaction of two masses through gravity. Introduction Section 0 *(even though they got the wrong answer on the test) Lecture INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Simmon’s list of most influential scientists in the history of the world Newton (1) * (and 2 and 6 and 40) Einstein (2) 1 Galileo Slide 9 Galilei (7) * Copernicus (9) * Kepler (10) * Tyco Brahe (22) * Aristotle (an honorable mentioned) *** Circular Motion and Gravitational Force Lecture 12 Slide 9 Historical Perspective on Gravity Aristotle Circular orbits Geocentric This works pretty well for the orbits of the Sun, Moon Introduction Section 0 and stars, but not so well for planets. Lecture 1 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 10 Historical Perspective on Gravity Ptolemy Epicycle orbits Geocentric This works pretty well for the orbits of the Sun, Moon and stars, Introduction Section and a little better for0 Lecture planets. 1 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 11 Planetary Motion • Retrograde motion occurs in a planet’s orbit when the planet appears to move against the background of stars Introduction Section 0 Lecture 1 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 12 Historical Perspective on Gravity Copernicus and Galelio Circular or Epicycle orbits Heliocentric This works pretty well for the orbits of the Sun, Moon and stars, Introduction and a better forSection 0 Lecture planets. Cleans up the retrograde motion (mostly) 1 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 13 Historical Perspective on Gravity So who is right? Team Geo: Aristotle/Ptolemy Team Helio: Copernicus/Galileo Tyco Barhe Enter the “last great naked-eye astronomer. A phenomenal set of data showed slight Introduction Section 0 Lecture inconsistencies in our descriptions of astronomical orbits. 1 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 14 Historical Perspective on Gravity Kepler Tycho’s assistant painstakingly analyzed all that careful data. This works pretty well for the orbits of the Sun, Moon and stars, Introduction Section 0 Lecture and a little better for planets. 1 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 15 Kepler’s First Law of Planetary Motion Kepler was able to show that the orbits of the planets around the sun are ellipses, with the sun at one focus. Introduction Section 0 Lecture 1 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 16 Kepler’s Second Law of Planetary Motion • Because planets move faster when nearer to the sun, the radius line for each planet sweeps out equal areas in equal times. Introduction Section 0 Lecture 1 Slide 17 • The two blue sections each cover the same span of time and have equal area. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 17 Kepler’s Third Law of Planetary Motion • The period (T) of an orbit is the time it takes for one complete cycle around the sun. • The cube of the average radius (r) about the sun is proportional to the square of the period of the orbit. Introduction Section 0 Lecture 1 T r 2 3 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 18 Historical Perspective on Gravity Newton Enter Newton to tie it all up in a neat bundle Found the form of the force that fit into Newton’s Laws that fully explained all the planetary observations (except very detailed orbital Introduction Section 0 motion and precessions). Lecture 1 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 19 Historical Perspective on Gravity Newton To get Kepler’s Laws of Planetary Motion to match with Newton’s Laws of (general) Motion Fcentripetal v Newton set the centripetal force to a central force proportional to 1/r2. Introduction Section 0 Lecture 1 2 r k r2 Fgravity Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 20 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 21 Newton’s Universal Law of Gravitation INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 21 Newton’s Law of Universal Gravitation • Newton recognized the similarity between the motion of a projectile on Earth and the orbit of the moon. • If a projectile is fired with enough velocity, it could fall towards Earth but never reach the surface. • The projectile would be in orbit. • Newton’s law of universal gravitation says the gravitational force between two objects is proportional to the mass of each object, and inversely proportional to the square of the distance between the two objects. Introduction • Section 0 Lecture 1 Slide 22 G is the Universal gravitational constant G. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Fgravity Circular Motion and Gravitational Force Gm1m2 r2 Lecture 12 Slide 22 Historical Perspective on Gravity Cavendish Developed a clever way to measure the weak gravitational force between small masses. Confirmed Newton’s Law of Universal Gravitation (and in essence measured the mass of the Earth in comparison GmM earth Fgravity to the kg mass standard). r2 The effect the 320 kg balls of the 1.5 kg balls was about that of a grain of sand! Introduction Section 0 Lecture 1 Slide 23 That’s 20 parts per billion precision!!! INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Wikeapedia has a nice description of the experiment. Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 23 Historical Perspective on Gravity Cavendish Fgravity Measured the mass of the Earth in comparison to the kg mass standard. Introduction Section 0 Lecture 1 so g Set weight equal to gravitational attraction, then solved for (little) g. GmM earth mg W 2 rearth GM earth 2 rearth Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 24 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 25 Extensions to Newton’s Law of Gravitation INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 25 Three equal masses are located as shown. What is the direction of the total force acting on m2? a) b) c) d) To the left. To the right. The forces cancel such that the total force is zero. Section 0toLecture 1 Slide 26 It Introduction is impossible determine from the figure. There will be a net force acting on m2 toward m1. The third mass exerts a force of attraction to the right, but since it is farther away that force is less than the force exerted by m1 to the left. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 26 Extensions to Newton’s Theory of Gravity Complex Motion Problems Consider the Sun, Earth, Moon system (the three body problem). Fgravity GmM earth r2 Approximating the complex forces using Newton’s Laws leads to very accurate solutions to the problem. Introduction Section 0 Lecture 1 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 27 The Moon and Other Satellites Phases of the moon result from the changes in the positions of the moon, Earth, and sun. Introduction Section 0 Lecture 1 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 28 An artist depicts a portion of the night sky as shown. Is this view possible? a) Yes b) No No. There are no stars between the Earth and the moon. (Maybe Section 0 blinking Introduction lights of a passing jet?) Lecture 1 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 29 Extensions to Newton’s Theory of Gravity Complex Motion Problems NASA predicts elaborate orbits for spacecraft like the Solar Probe Mission to the Sun or the CassiniHuygens Mission to Saturn and its moons. Introduction Section 0 Lecture 1 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 30 Extensions to Newton’s Theory of Gravity But… Using retroreflectors left by the Apollo astronauts, we measure the moon's distance with staggering precision: better than a few cm out of 385,000 km (about 20 parts per trillion!!!) Results of this long-term experiment are: • The moon is spiralling away from Earth at a rate of 38 mm/yr. • The moon probably has a liquid core of about 20% of the Moon's radius. • The universal force of gravity is very stable. The experiments have put an upper limit on the change in G of less than 1 part in 1011 since 1969. • Results strongly supporting the validity of the Strong Equivalence Principle. Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Slide 31 • Einstein’s General Theory of Relativity predicts the moon's orbit to within the accuracy of the laser ranging measurements. Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 31 Extensions to Newton’s Theory of Gravity Einstein’s Special Theory of Relativity Based on how E&M works, Einstein postulated: • The laws of physics are the same for all observers in uniform motion relative to one another (Galileo’s principle of relativity), • The speed of light in a vacuum, c, is the same for all observers, regardless of their relative motion or of the motion of the source of the light. Some surprising results these are: Relativity of simultaneity: Two events, simultaneous for some observer, may not be simultaneous for another observer if the observers are in relative motion. Introduction Section 0clocks Lecture are 1 Slide 32 Time dilation: Moving measured to tick more slowly than an observer's "stationary" clock. Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer. Mass-energy equivalence: E = mc2. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 32 Extensions to Newton’s Theory of Gravity General Theory of Relativity Einstein’s theory special relativity and Newton's law of universal gravitation. Equivalence Principle: Inertial mass in Newton's second law, F = ma, mysteriously equals the gravitational mass in Newton's law of universal gravitation Classical tests predicted by Einstein Introduction Sectionverified) 0 Lecture 1 Slide 33 (and subsequently • Perihelion precession of Mercury • Deflection of light by the Sun • Gravitational redshift of light Fgravity GmM earth r2 R 12 g R g INTRODUCTION TO Modern Physics PHYX 2710 8 G T 4 c Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 33 Extensions to Newton’s Theory of Gravity Current Problems in Gravity Is Einstein’s General Theory of Relativity the final word? (Maybe not) Do gravitational waves exist? (Yes, maybe) Are G and Λ truly constants? (Controversial evidence say NO!) What happens when black holes (or galaxies) collide? Can General Relativity be merged with Quantum Mechanics? (QM has been tested to 17 decimal places- ~10 parts per quintillion, Introduction Lecture 1 Slide 34 even though we Section don’t0 really understand how to interpret the theory.) Is there a 5th force in nature? INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 34 USU Perspective on Gravity Hart’s list of most influential people in the history of the world: Newton (2)* Einstein (10) Galileo Galilei (12)* Aristole (13)*** Copernicus (19) * Kepler (75) * Work today at USU Larsen, Torre and Wheeler *(even though they got the wrong answer on the test) Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Simmon’s list of most influential scientists in the history of the world Newton (1) * (and 2 and 6 and 40) Einstein (2) Slide 35 Galilei (7) * Galileo Copernicus (9) * Kepler (10) * Tyco Brahe (22) * Aristole (an honorable mentioned) *** Circular Motion and Gravitational Force Lecture 12 Slide 35 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 36 Comments on the Nature of Scientific Theories INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 36 Lessons from the Theory of Gravity Scientific Theories Are NOT Static Aristotle was extended by Ptolemy, who was corrected by Copernicus, who was generalized by Galileo, who was supplemented by Brahe, who provided Kepler with data, who was merged with laws of motion by Newton, who was quantified by Cavendish, who was supplanted by Einstein, who was expanded by Einstein himself, who was tested by 20th century scientists Introduction 0 Lecture 1 by Slide 37 and cosmology… andSection challenged QM But they can describe a lot of what goes on in the world around us. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 37 Lessons from the Theory of Gravity Scientific Theories are descriptions of nature, based ultimately on our observations… But they do not attempt to state what their origins are or why they exist. Scientific theories address where, when and how, but not whyIntroduction Section 0 Lecture 1 Slide 38 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 38 Physics of Technology Next Lab/Demo: Circular Motion & Gravity Energy & Oscillations Thursday 1:30-2:45 ESLC 53 Ch 5 Next Class: Wednesday 10:30-11:20 Slide 39 BUS 318 room Read Ch 5 Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Circular Motion and Gravitational Force Lecture 12 Slide 39