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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

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 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!

5 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

6 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)

7 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

8 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

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 13-2 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

11 13-2 Gravitation and the Principle of Superposition Example Summing two forces: Figure 13-4

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 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

14 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

15 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 = 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 13-6

16 13-5 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 dr and using F = GMm. r 2

17 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 13-10

18 13-5 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 13-5 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 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 13-12

24 13-6 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

25 Kepler2L: Kepler s 2 nd Law Equal Areas in Equal Times

26 13-6 Planets and Satellites: Kepler's Laws Equivalent to Conservation of Angular Momentum See later in this course.

27 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.

28 13-6 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 13-7 Satellites: Orbits and Energy Relating the centripetal acceleration of a satellite to the gravitational force, we can rewrite as energies: Eq. (13-38) Meaning that: Eq. (13-39) Therefore the total mechanical energy is: Eq. (13-40)

31 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 13-15

32 13-7 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 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?

34 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)

35 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)

36 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: Eq. (13-34) Energy in Planetary Motion Eq. (13-42) 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 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 information

Orbital Mechanics. Angular Momentum

Orbital 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 information

Penn State University Physics 211 ORBITAL MECHANICS 1

Penn 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 information

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12

2. 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 information

Name: 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 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 information

PHY121 #8 Midterm I 3.06.2013

PHY121 #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 information

Lecture 13. Gravity in the Solar System

Lecture 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 information

Chapter 5: Circular Motion, the Planets, and Gravity

Chapter 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 information

Satellites and Space Stations

Satellites 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 information

Section 4: The Basics of Satellite Orbits

Section 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 information

Unit 8 Lesson 2 Gravity and the Solar System

Unit 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 information

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION

USING 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 information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 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 information

Solar 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? 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 information

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

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 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 information

Name Class Date. true

Name 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 information

Chapter 3.8 & 6 Solutions

Chapter 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 information

C 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

C 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 information

AE554 Applied Orbital Mechanics. Hafta 1 Egemen Đmre

AE554 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 information

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION

DIRECT 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 information

Physics 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 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 information

3600 s 1 h. 24 h 1 day. 1 day

3600 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 information

Orbital Mechanics and Space Geometry

Orbital 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 information

VELOCITY, ACCELERATION, FORCE

VELOCITY, 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 information

Exam # 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 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 information

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 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 information

Solar 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 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 information

8.012 Physics I: Classical Mechanics Fall 2008

8.012 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 information

Chapter 25.1: Models of our Solar System

Chapter 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 information

Presentation of problem T1 (9 points): The Maribo Meteorite

Presentation 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 information

11. Rotation Translational Motion: Rotational Motion:

11. 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 information

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm 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 information

The orbit of Halley s Comet

The 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 information

Vocabulary - Understanding Revolution in. our Solar System

Vocabulary - 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 information

Fundamental Mechanics: Supplementary Exercises

Fundamental 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 information

CHAPTER 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. 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 information

Physics 211 Lecture 4

Physics 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 information

Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same.

Kinetic 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 information

RETURN TO THE MOON. Lesson Plan

RETURN 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 information

The Solar Wobble or Gravity, Rosettes and Inertia

The 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 information

Lectures on Gravity Michael Fowler, University of Virginia, Physics 152 Notes, May, 2007

Lectures 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 information

Earth in the Solar System

Earth 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 information

4 Gravity: A Force of Attraction

4 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 information

The Solar System. Unit 4 covers the following framework standards: ES 10 and PS 11. Content was adapted the following:

The 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 information

Lecture PowerPoints. Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli

Lecture 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 information

Exam 1 Review Questions PHY 2425 - Exam 1

Exam 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 information

State Newton's second law of motion for a particle, defining carefully each term used.

State 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 information

The Solar System. Source http://starchild.gsfc.nasa.gov/docs/starchild/solar_system_level1/solar_system.html

The 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 information

Notes on Elastic and Inelastic Collisions

Notes 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 information

Carol and Charles see their pencils fall exactly straight down.

Carol 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 information

Science Standard 4 Earth in Space Grade Level Expectations

Science 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 information

Solution Derivations for Capa #11

Solution 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 information

Fluid 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 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 information

Free 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) 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 information

Periods of Western Astronomy. Chapter 1. Prehistoric Astronomy. Prehistoric Astronomy. The Celestial Sphere. Stonehenge. History of Astronomy

Periods 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 information

Review Assessment: Lec 02 Quiz

Review 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 information

KINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES

KINEMATICS 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 information

At the skate park on the ramp

At 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

Astrodynamics (AERO0024)

Astrodynamics (AERO0024) Astrodynamics (AERO0024) 6. Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Course Outline THEMATIC UNIT 1: ORBITAL DYNAMICS Lecture 02: The Two-Body Problem Lecture 03:

More information

Angular acceleration α

Angular acceleration α Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

More information

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS 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 information

Physics: 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 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 buckle-up? A) the first law

More information

Section 1 Gravity: A Force of Attraction

Section 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 information

KERN 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 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 information

B) 286 m C) 325 m D) 367 m Answer: B

B) 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 information

Physics Competitions Vol 13 No 2 2011 & Vol.14 No 1 2012. A few good orbits. 400 088. # Corresponding author: anikets@hbcse.tifr.res.

Physics 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 information

Problem 6.40 and 6.41 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITS-Pilani

Problem 6.40 and 6.41 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITS-Pilani Problem 6.40 and 6.4 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITS-Pilani 6.40 A wheel with fine teeth is attached to the end of a spring with constant k and unstretched length

More information

Orbital Dynamics: Formulary

Orbital 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 information

8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight

8. 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 information

Educator Guide to S LAR SYSTEM. 1875 El Prado, San Diego CA 92101 (619) 238-1233 www.rhfleet.org

Educator Guide to S LAR SYSTEM. 1875 El Prado, San Diego CA 92101 (619) 238-1233 www.rhfleet.org Educator Guide to S LAR SYSTEM 1875 El Prado, San Diego CA 92101 (619) 238-1233 www.rhfleet.org Pre-Visit Activity: Orbital Paths Materials: Plastic Plate Marble Scissors To Do: 1. Put the plate on a flat

More information

Interaction 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 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 information

Chapter 7: Momentum and Impulse

Chapter 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 information

Lecture 7 Formation of the Solar System. Nebular Theory. Origin of the Solar System. Origin of the Solar System. The Solar Nebula

Lecture 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 information

State Newton's second law of motion for a particle, defining carefully each term used.

State 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 information

Study Guide: Solar System

Study 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 information

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE

Physics 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 information

AS COMPETITION PAPER 2008

AS 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 information

If 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

If 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 information

Salem 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 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 information

Physics B AP Review Packet: Mechanics Name:

Physics 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 information

Artificial Satellites Earth & Sky

Artificial 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 information

Lecture Presentation Chapter 7 Rotational Motion

Lecture 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 information

Dynamics of Iain M. Banks Orbitals. Richard Kennaway. 12 October 2005

Dynamics 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 information

Problem Set #8 Solutions

Problem 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 information

EDUH 1017 - SPORTS MECHANICS

EDUH 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 information

SYLLABUS 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. 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 information

1-2. What is the name given to the path of the Sun as seen from Earth? a.) Equinox b.) Celestial equator c.) Solstice d.

1-2. 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 1-1. 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 1-2. What is the name given to the path of the Sun as seen from Earth? a.)

More information

Development of an automated satellite network management system

Development 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 information

1 of 7 9/5/2009 6:12 PM

1 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 information

Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis

Exam 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 information

Newton s proof of the connection between

Newton s proof of the connection between Elliptical Orbit 1/r 2 Force Jeffrey Prentis, Bryan Fulton, and Carol Hesse, University of Michigan-Dearborn, Dearborn, MI Laura Mazzino, University of Louisiana, Lafayette, LA Newton s proof of the connection

More information

Lab 7: Gravity and Jupiter's Moons

Lab 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 information

General Certificate of Education (A-level) January 2013 Physics A PHYA4 (Specification 2450) Unit 4: Fields and further mechanics Final Mark Scheme

General Certificate of Education (A-level) January 2013 Physics A PHYA4 (Specification 2450) Unit 4: Fields and further mechanics Final Mark Scheme Version 1.1 General Certificate of Education (A-level) January 013 Physics A PHYA4 (Specification 450) Unit 4: Fields and further mechanics Final Mark Scheme Mark schemes are prepared by the Principal

More information

Section 2. Satellite Orbits

Section 2. Satellite Orbits Section 2. Satellite Orbits References Kidder and Vonder Haar: chapter 2 Stephens: chapter 1, pp. 25-30 Rees: chapter 9, pp. 174-192 In order to understand satellites and the remote sounding data obtained

More information

Data 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. 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 (2014-2015) DARK MATTER AND THE UNIVERSE 2 HOURS Answer question

More information

Tidal forces in the Solar System

Tidal 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 information

Tidal Forces and their Effects in the Solar System

Tidal 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 information

Orbital Dynamics with Maple (sll --- v1.0, February 2012)

Orbital 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 information

Physics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal

Physics 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 3-D We have defined the velocit and acceleration of a particle as the first and second

More information

Chapter 15.3 Galaxy Evolution

Chapter 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