2010 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity


 Dominic Briggs
 1 years ago
 Views:
Transcription
1 Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity
2 4.1 Describing Motion: Examples from Daily Life Some of the topics we will explore: How do we describe motion? (Speed, velocity, acceleration, acceleration of gravity, momentum, angular momentum, force) How is mass different from weight?
3 How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves. It is the distance traveled per unit time speed = distance time Example: 10 m/s units of m s Velocity: The velocity includes speed and direction (In math it is called a vector) Example: 10 m/s, due east Acceleration: A change in velocity. It can be a change in speed or direction. The units are speed/time (m/s 2 ) It can be an increase of velocity (positive acceleration) or a decrease (negative acceleration)
4 All falling objects accelerate at the same rate (not counting friction of air resistance). On Earth, the acceleration of gravity g is g 10 m/s 2 This means that the speed increases 10 m/s with each second of falling. Written in an equation: v = g t The Acceleration of Gravity
5 The Acceleration of Gravity (g) Galileo showed that g, the acceleration of gravity is the same for all falling objects, regardless of their mass. This may seems to contradict our everyday experience. A feather drops slowly to the ground compared with a steel ball. The answer is the air resistance. A force exerted by the air as the object falls. In vacuum ( An example on the Moon surface) both objects will fall at the same rate Apollo 15 demonstration
6 Momentum, force, angular momentum Momentum of an object is the product of its mass and velocity Momentum = mass velocity m v This is called linear momentum A net force changes momentum, which generally means an acceleration (change in velocity). Rotational momentum of a spinning or orbiting object is known as angular momentum. Angular momentum = mass velocity radius = m v r If the mass, the velocity and the radius remain constant, the angular momentum is constant if no force is applied to the body. However, if we change the radius (without applying an external force) the velocity will change to keep the product m v r constant. We will see an example later.
7 Questions For each of the following is there a net force? Y/N 1. A car coming to a stop 2. A bus speeding up 3. An elevator moving up at constant speed 4. A bicycle going around a curve 5. A moon orbiting Jupiter
8 Questions For each of the following is there a net force? Y/N 1. A car coming to a stop: Y 2. A bus speeding up: Y 3. An elevator moving at constant speed: N 4. A bicycle going around a curve: Y 5. A moon orbiting Jupiter: Y
9 How is mass different from weight? Mass the amount of matter in an object Weight the force that acts upon the mass of an object You are weightless in freefall!
10 Question On the Moon: A. My weight is the same, my mass is less. B. My weight is less, my mass is the same. C. My weight is more, my mass is the same. D. My weight is more, my mass is less.
11 Question On the Moon: A. My weight is the same, my mass is less. B. My weight is less, my mass is the same. C. My weight is more, my mass is the same. D. My weight is more, my mass is less.
12 You would weigh less on the Moon (less mass, weaker gravitational force) than on Jupiter or the Sun: Note: Mass weight: The person s mass never changes but the weight does.
13 Why are astronauts weightless in space? There is gravity in space. The gravitational force on the astronaut exerted by the Earth is less than at the surface but not zero. Weightlessness is due to a constant state of freefall. The gravitational force keep pulling the astronaut toward the center of the Earth. Otherwise it will move in a straight line
14 An analogy using a ball attached to a string The inward force keep the ball moving in a circle. The magnitude of the force is F = ma In the case of the astronaut the inward force is the gravitational force.
15 Summary How do we describe motion? Speed = distance / time Speed and direction => velocity Change in velocity => acceleration Momentum = mass x velocity Force causes change in momentum, producing acceleration. Angular Momentum = product of mass x velocity x radius (An example, a sphere)
16 How is mass different from weight? Mass = quantity of matter Weight = force acting on a mass. More specifically is the force of gravity acting on the mass of a body Objects are weightless in freefall.
17 4.2 Newton s Laws of Motion Topics we will explore: How did Newton change our view of the universe? What are Newton s three laws of motion?
18 Aristotle and Newton ideas Aristotle ( B.C.) proposed that the physical laws on Earth did not apply to heavenly motions. His ideas help him support that Earth was the center of the universe. By the time that Newton ( ) began working on his ideas and formulated the laws of motion and gravitation, the Copernican revolution and Galileo discoveries had displaced the Earth from it central position. Newton realized that gravity operated on Earth and heavens.
19 How did Newton change our view of the universe? Sir Isaac Newton ( ) He realized that the same physical laws that operate on Earth also operate in the heavens Heavens and earth were brought together as one universe Discovered laws of motion and gravity But he did much more than that: He experimented with light, designed the first reflecting telescope, invented calculus
20 What are Newton s three laws of motion? Newton s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.
21 Newton s second law of motion: Force = mass F = m a acceleration
22 Newton s third law of motion: For every force, there is always an equal and opposite reaction force.
23 Question How does the force the Earth exerts on you compare with the force you exert on it? A. Earth exerts a larger force on you. B. You exert a larger force on Earth. C. Earth and you exert equal and opposite forces on each other.
24 Thought Question How does the force the Earth exerts on you compare with the force you exert on it? A. Earth exerts a larger force on you. B. You exert a larger force on Earth. C. Earth and you exert equal and opposite forces on each other.
25 Question A compact car and a Mack truck have a headon collision. Are the following true or false? 1. The force of the car on the truck is equal and opposite to the force of the truck on the car. 2. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. Momentum : m v 3. The change of velocity of the car is the same as the change of velocity of the truck.
26 Thought Question A compact car and a Mack truck have a headon collision. Are the following true or false? 1. The force of the car on the truck is equal and opposite to the force of the truck on the car. T 2. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. T Momentum : m v 3. The change of velocity of the car is the same as the change of velocity of the truck. F
27 What have we learned? How did Newton change our view of the universe? He discovered laws of motion and gravitation. He realized these same laws of physics were identical in the universe and on Earth. What are Newton s three laws of motion? 1. Object moves at constant velocity if no net force is acting. 2. Force = mass acceleration (F = m a) 3. For every force there is an equal and opposite reaction force.
28 4.3 Conservation Laws in Astronomy Topics we will explore: Why do objects move at constant velocity if no force acts on them? What keeps a planet rotating and orbiting the Sun? Where do objects get their energy?
29 Why do objects move at constant velocity if no force acts on them? Objects continue at constant velocity because of conservation of momentum. The total momentum of interacting objects cannot change unless an external force is acting on them. Interacting objects exchange momentum through equal and opposite forces. The assumption is that there is no release of energy during the impact(elastic collision) If the mass of the two balls is the same, after the collision the second ball will move at the same velocity of the first ball. If the mass of the second ball is larger than the first ball, the velocity of the second ball will be smaller so that the product m x v is constant.
30 What keeps a planet rotating and orbiting the Sun?
31 The mutual gravitational attraction between the Sun and planets is responsible for their motion.
32 In the case of a planet, the force produced by the tension of the string is replaced by the force of the gravitational attraction between the planet and the Sun
33 Conservation of Angular Momentum Angular momentum = mass x velocity x radius = m x v x r The angular momentum of an object cannot change unless an external twisting force or torque (torque = f x r) is acting on it. Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely because of conservation of angular momentum.
34 Conservation of angular momentum also explains why objects rotate faster as they shrink in radius. Left figure Angular momentum 1 = m x v1 x r1 Right figure Angular momentum 2 = m x v2 x r2 In the right figure, r2 is smaller that r1, then v2 must be larger than v1 to keep the product m x v x r constant (conservation of angular momentum)
35 Where do objects get their energy? Conservation of energy Energy cannot appear out of nowhere or cannot disappear into nothingness. But energy can change from one type to another: Transfer from one object to another. An example the collision of two balls where kinetic energy is transferred from one ball to another Energy can change in form, from kinetic to potential to radiative and vice versa Energy can be converted into mass and mass can be converted into energy.
36 Basic Types of Energy Kinetic (motion) E = ½ mv 2 Potential (stored) Gravitational potential energy Ep = m x g x h) Radiative (light) Energy can change type, but cannot be created or destroyed.
37 Thermal Energy: The collective kinetic energy of many particles (for example, in a rock, in air, in water) Thermal energy is related to temperature but it is NOT the same. Temperature is a measure of the average kinetic energy of the particles in a substance.
38 Temperature Scales The Kelvin scale is the scale used mostly in physics, astronomy and science in general The units of the Kelvin scale are Kelvin (K) At zero K, the thermal energy is zero. Molecules and particles have zero velocity at zero K Zero K is absolute Zero. There is no temperature lower than that
39 Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends on both temperature AND density. Example: A fluid (high density) and air (low density) What happens if you put your hand in: Water at 212 F Air at 400 F
40 Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall (h) Ep = m x g x h Ep is potential gravitational energy
41 Gravitational Potential Energy In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. A contracting cloud converts gravitational potential energy to thermal energy. In other words, the temperature of the cloud is low before it start contracting but it can be very high after it finish contracting. The temperature in the central body (star) can be high enough to star the conversion of hydrogen into helium (10 million K).
42 MassEnergy Mass itself is a form of potential energy. Einstein equation of energymass conversion: Mass can be converted into energy and energy can be converted into mass A small amount of mass can release a great deal of energy (for example, an H bomb, a nuclear power reactor). Concentrated energy can spontaneously turn into particles (for example, in particle accelerators). E = mc 2
43 Conservation of Energy Energy can be neither created nor destroyed. It can change form or be exchanged between objects. The total energy content of the universe was determined in the Big Bang and remains the same today.
44 Summary Why do objects move at constant velocity if no force acts on them? Conservation of momentum What keeps a planet rotating and orbiting the Sun? Conservation of angular momentum Where do objects get their energy? Conservation of energy: energy cannot be created or destroyed but can only transformed from one type to another. Energy comes in three basic types: kinetic, potential, radiative.
45 4.4 The Universal Law of Gravitation Let s explore the following topics: What determines the strength of gravity? How does Newton s law of gravity extend Kepler s laws?
46 What determines the strength of gravity? Newton s universal law of gravitation: 1. Every mass attracts every other mass. 2. The force of attraction is directly proportional to the product of their masses. 3. The force of attraction is inversely proportional to the square of the distance between their centers. G is a constant called gravitational constant
47 Plot of force as function of distance Inverse square law
48 How does Newton s law of gravity extend Kepler s laws? Newton using his gravitational law, the laws of motion, trigonometry and calculus was able to deduce and generalize Kepler s law so they apply not only to planets but to any body orbiting another body. Kepler s first two laws apply to all orbiting objects, not just planets. Newton showed that Kepler s law are a consequence of the law of motion and the universal law of gravitation Ellipses are not the only orbital paths. Orbits can be: bound (ellipses). The objects goes around each other for ever if no external force act on the system Unbound (path that bring an object close to another only once; an example are some comets) Parabola hyperbola The circle, the ellipse, the parabola and the hyperbola are known as conic sections. These curves result from cutting the cone at different angles.
49 A definition of center of mass What s the Center of Mass? The equation for the center of mass: m 1 d 1 = m 2 d 2 (d 1 + d 2 = d)
50 Center of Mass
51 Orbit of bodies of different mass Two stars of about the same mass orbit around each other describing two ellipses of the same size Two stars with different mass, orbit around each other. The lowest mass star describe a larger ellipse. A star and a planet orbit each other. Because of the lower mass of the planet, the orbit of the planet is a large ellipse. Due to the large mass of the star, the center of mass is close (inside) the star. But the star also describe a small ellipse
52 Newton and Kepler s Third Law Newton s laws of gravity and motion showed that the relationship between the orbital period and average orbital distance of a system tells us the total mass of the system. Kepler s third law does not include the mass of the bodies involved. It only relates the period and the average distance Examples of the application of Newton s version of Kepler s law: Earth s orbital period (1 year) and average distance (1 AU) tell us the Sun s mass. Orbital period and distance of a satellite from Earth tell us Earth s mass. Orbital period and distance of a moon of Jupiter tell us Jupiter s mass.
53 Newton s Version of Kepler s Third Law a OR G( M M2) G p p a M M 2 p = orbital period a = average orbital distance (between centers) (M 1 + M 2 ) = sum of object masses
54 The change to Kepler s third law is small in the case of a planet orbiting the Sun, but larger in the case where the two bodies are closer in mass, e.g. Two stars orbiting each other (binary star system). Newton s version of Kepler s revised 3rd law: P 2 a 3 M total : Proportional For PlanetSun systems: M total = M Sun + M planet M sun (M planet small compared with M Sun )
55 An application of the modified Kepler 3 rd Law to Jupiter and its satellites We want to obtain the mass of the Jupiter using the mean distance (a) of one of its moon (For example Io) and its orbital period (P) M total = M Jupiter + M Io But the mass of Io is much smaller than the mass of Jupiter The mass of Io can be neglected If a is in AU and P is in years, we can substitute the proportional sign for an equal sign M Jupiter =a 3 / P 2 The mass of Jupiter will be in solar mass
56 Summary What determines the strength of gravity? Force is directly proportional to the product of the masses (M 1 M 2 ) Force is inversely proportional to the square of the separation d How does Newton s law of gravity allow us to extend Kepler s laws? Applies to other objects, not just planets Includes unbound orbit shapes: parabola, hyperbola Can be used to measure mass of orbiting systems
57 4.5 Orbits, Tides, and the Acceleration of Gravity Our goals for learning: How do gravity and energy together allow us to understand orbits? How does gravity cause tides? Why do all objects fall at the same rate?
58 How do gravity and energy together allow us to understand orbits? Total orbital energy (gravitational potential energy+ kinetic energy) stays constant if there is no external force. Gravitational potential energy proportional to r Kinetic energy proportional to v 2 Total orbital energy stays constant. When a planet is closer to the Sun, it has more kinetic energy (larger v) and less gravitational potential energy (smaller r) When the planet moves to a point farther from the Sun, the kinetic energy is converted into gravitational potential energy. Orbits cannot change spontaneously. To change an orbit it is necessary to apply an external force
59 Changing an Orbit If an object can gain or lose orbital energy, it can change its orbit. So what can make an object gain or lose orbital energy? Friction or atmospheric drag Examples: The ISS (International Space Station) A gravitational encounter Example: Comets
60 Escape Velocity If an object gains enough orbital energy, it may change its orbit and escape (change from a bound to unbound orbit). Escape velocity from Earth 11 km/s from sea level (about 40,000 km/hr) G is gravitational constant M is mass of the object R is the distance above the object center To calculate the escape velocity from the surface, R is the radius of the object
61 How does gravity cause tides? Gravitational attraction weaker here Gravitational attraction stronger here Moon s gravity pulls harder on near side of Earth than on far side. Difference in Moon s gravitational pull stretches Earth. What causes the tidal effect is the differential gravitational attraction
62 Inverse square law How can we understand the differential gravitational attraction
63 The differential gravitational force and the tidal effect
64 Does the Sun has a tidal effect on the Earth? The Sun has much more mass than the Moon. The Sun gravitational attraction on the Earth is larger than the Moon gravitational attraction. But the Sun is much farther away than the Moon. The differential gravitational attraction of the Sun on the near and far side of the Earth is smaller than the effect of the Moon Both the Sun and the Moon cause tidal effect on Earth The moon has a larger differential gravitational attraction and causes larger tides.
65 Tides and Phases Size of tides depends on the phase of the Moon. Spring tides occur at new and full moon. The tidal forces of the Sun and the Moon add together Spring tides Neap tides occur at first quarter and third quarter moon when the Sun and the Moon tidal forces act at 90degrees from each other Neap tides The Earth develop two bulges. A consequence of this is that every 24 hours there are two high tides and two low tides.
66 Tidal Friction If the Earth didn t rotate, the tidal bulges would be oriented along the EarthMoon line. Since the Earth rotate faster (24 hours) than the Moon orbital period (27 days), the tidal bulge is displaced a few degrees ahead from the line connecting the EarthMoon. The slight misalignment of the bulges has two important effects: It slow down the Earth rotation and pulls the Moon ahead increasing the orbital distance Tidal friction dissipate rotational energy. This gradually slows Earth s rotation (and makes the Moon get farther from Earth). Tidal friction caused the Moon to lock in synchronous rotation. The result is that the Moon rotational period coincides with the orbital period.
67 Why do all objects fall at the same rate? a rock F g F g G M M Earth rock 2 M rock R Earth a rock G M EarthM rock 2 R Earth M rock G M Earth 2 R Earth The gravitational acceleration of an object like a rock does not depend on its mass because M rock in the equation for acceleration cancels M rock in the equation for gravitational force. This coincidence was not understood by Newton, even if his equations show it and it was not understood for 240 years. Until 1915 when Einstein discovered that it not a coincidence, it is a consequence of his General theory of relativity. This is something deeper about the nature of gravity.
68 What have we learned? How do gravity and energy together allow us to understand orbits? Change in total energy is needed to change orbit Adding enough energy (escape velocity) and the object leaves. How does gravity cause tides? The Moon s gravity stretches Earth and its oceans (Differential gravitational force). Why do all objects fall at the same rate? The mass of object in Newton s second law exactly cancels the mass in law of gravitation.
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Copyright 2012 Pearson Education, Inc.
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 1 4.1 Describing Motion: Examples from Everyday Life Our goals for learning: How do we describe motion? How is mass different
More informationAgenda Announce: 4.1 Describing Motion. Tests. How do we describe motion?
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity Agenda Announce: Stony Brook talk this Friday on Precision Cosmology Project Part I due in one week before class: one paragraph
More information4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion Our goals for learning: How do we describe motion? How is mass different from weight? How do we describe
More informationHow do we describe motion?
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves $ speed = distance!#"units
More information9/13/ Describing Motion: Examples from Everyday Life. Chapter 4: Making Sense of the Universe Understanding Motion, Energy, and Gravity
9/13/17 Lecture Outline 4.1 Describing Motion: Examples from Everyday Life Chapter 4: Making Sense of the Universe Understanding Motion, Energy, and Gravity Our goals for learning: How do we describe motion?
More informationHow do we describe motion?
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves example: speed of
More informationHow do we describe motion?
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity If I have seen farther than others, it is because I have stood on the shoulders of giants. Sir Isaac Newton (1642 1727)
More information4.3 Conservation Laws in Astronomy
4.3 Conservation Laws in Astronomy Our goals for learning: Why do objects move at constant velocity if no force acts on them? What keeps a planet rotating and orbiting the Sun? Where do objects get their
More informationToday. Laws of Motion. Conservation Laws. Gravity. tides
Today Laws of Motion Conservation Laws Gravity tides Newton s Laws of Motion Our goals for learning: Newton s three laws of motion Universal Gravity How did Newton change our view of the universe? He realized
More informationMaking Sense of the Universe: Understanding Motion, Energy, and Gravity Pearson Education, Inc.
Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Our goals for learning: How do we describe motion? How is mass different from weight?
More informationAdios Cassini! Crashed into Saturn 9/15/17 after 20 years in space. https://saturn.jpl.nasa.gov/mission/grandfinale/overview/
Adios Cassini! Crashed into Saturn 9/15/17 after 20 years in space https://saturn.jpl.nasa.gov/mission/grandfinale/overview/ Laws of Motion Conservation Laws Gravity tides Today Why are astronauts weightless
More informationLecture: October 1, 2010
Lecture: October 1, 2010 How long would it take to walk to Alpha Centauri? Announcements: Next Observatory Opportunity: Wednesday October 6 Phases of Matter the phases solid liquid gas plasma depend on
More informationUnderstanding Motion, Energy & Gravity
Speed, Velocity & Acceleration Understanding Motion, Energy & Gravity Chapter 4 speed: distance traveled per unit time (e.g., m/s, mph, km/ hr) velocity: speed & direction acceleration: change in velocity
More informationWhere do objects get their energy?
Where do objects get their energy? Energy makes matter move. Energy is always 'conserved' Conservation of Energy Energy can neither be created nor destroyed The total energy content of the universe was
More informationIn this chapter, you will consider the force of gravity:
Gravity Chapter 5 Guidepost In this chapter, you will consider the force of gravity: What were Galileo s insights about motion and gravity? What were Newton s insights about motion and gravity? How does
More informationClassical mechanics: conservation laws and gravity
Classical mechanics: conservation laws and gravity The homework that would ordinarily have been due today is now due Thursday at midnight. There will be a normal assignment due next Tuesday You should
More informationAnnouncements. HW #2 is online now at MasteringAstronomy.com. Due next Mon at 11pm. For today: finish reading chapter 4.
Announcements HW #2 is online now at MasteringAstronomy.com. Due next Mon at 11pm. For today: finish reading chapter 4. Exam buyback extra credit due here NOW! Not late extracredit accepted. Public Service
More information7.4 Universal Gravitation
Circular Motion Velocity is a vector quantity, which means that it involves both speed (magnitude) and direction. Therefore an object traveling at a constant speed can still accelerate if the direction
More information12Feb18. Newton's Laws. Newton's Laws. Prelude to Newton's Laws
Newton's Laws Newton's Laws Before Isaac Newton There were facts and laws about the way the physical world worked, but no explanations After Newton There was a unified system that explained those facts
More informationNewton's Laws. Before Isaac Newton
Newton's Laws Before Isaac Newton Newton's Laws There were facts and laws about the way the physical world worked, but no explanations After Newton There was a unified system that explained those facts
More informationJames T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Chapter 3 Force and Motion
James T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Chapter 3 Force and Motion Force and Motion Cause and Effect In chapter 2 we studied motion but not its cause. In this chapter we will look at both
More informationForces, Momentum, & Gravity. Force and Motion Cause and Effect. Student Learning Objectives 2/16/2016
Forces, Momentum, & Gravity (Chapter 3) Force and Motion Cause and Effect In chapter 2 we studied motion but not its cause. In this chapter we will look at both force and motion the cause and effect. We
More informationChapter 4: Energy, Motion, Gravity. Enter Isaac Newton, who pretty much gave birth to classical physics
Chapter 4: Energy, Motion, Gravity Enter Isaac Newton, who pretty much gave birth to classical physics Know all of Kepler s Laws well Chapter 4 Key Points Acceleration proportional to force, inverse to
More informationChapter 3  Gravity and Motion. Copyright (c) The McGrawHill Companies, Inc. Permission required for reproduction or display.
Chapter 3  Gravity and Motion Copyright (c) The McGrawHill Companies, Inc. Permission required for reproduction or display. In 1687 Isaac Newton published the Principia in which he set out his concept
More informationGravity & The Distances to Stars. Lecture 8. Homework 2 open Exam on Tuesday in class bring ID and #2 pencil
1 Gravity & The Distances to Stars Lecture 8 Homework 2 open Exam on Tuesday in class bring ID and #2 pencil 2 Preparing for the Exam 1 Exams in this class are multiple choice, but the questions can be
More informationBasics of Kepler and Newton. Orbits of the planets, moons,
Basics of Kepler and Newton Orbits of the planets, moons, Kepler s Laws, as derived by Newton. Kepler s Laws Universal Law of Gravity Three Laws of Motion Deriving Kepler s Laws Recall: The Copernican
More informationColumn Statistics for: test1 Count: 108 Average: 33.3 Median: 33.0 Maximum: 49.0 Minimum: 12.0 Standard Deviation: 8.37
Test 1 Result: Section 1 Column Statistics for: test1 Count: 108 Average: 33.3 Median: 33.0 Maximum: 49.0 Minimum: 12.0 Standard Deviation: 8.37 1 Test 1 Result: Section 2 Column Statistics for: Test1
More informationPhysics. Chapter 9 Gravity
Physics Chapter 9 Gravity The Newtonian Synthesis Gravity is a Universal Force The Newtonian Synthesis According to legend, Newton discovered gravity while sitting under an apple tree. The Falling Moon
More informationChapter 9 Lecture. Pearson Physics. Gravity and Circular Motion. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 9 Lecture Pearson Physics Gravity and Circular Motion Prepared by Chris Chiaverina Chapter Contents Newton's Law of Universal Gravity Applications of Gravity Circular Motion Planetary Motion and
More informationToday. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws of Planetary Motion. Laws of Motion. in physics
Planetary Motion Today Tycho Brahe s Observations Kepler s Laws of Planetary Motion Laws of Motion in physics Page from 1640 text in the KSL rare book collection That the Earth may be a Planet the seeming
More informationIsaac Newton & Gravity
Isaac Newton & Gravity Isaac Newton was born in England in 1642 the year that Galileo died. Newton would extend Galileo s study on the motion of bodies, correctly deduce the form of the gravitational force,
More informationFORCE AND MOTION CHAPTER 3
FORCE AND MOTION CHAPTER 3 Review: Important Equations Chapter 2 Definitions Average speed: Acceleration: v = d t v = Δd a = Δv Δt = v v 0 t t 0 Δt = d d 0 t t 0 Derived Final velocity: Distance fallen:
More informationGravitation and the Motion of the Planets
Gravitation and the Motion of the Planets 1 Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets go around
More informationAP PhysicsB Universal Gravitation Introduction: Kepler s Laws of Planetary Motion: Newton s Law of Universal Gravitation: Performance Objectives:
AP PhysicsB Universal Gravitation Introduction: Astronomy is the oldest science. Practical needs and imagination acted together to give astronomy an early importance. For thousands of years, the motions
More informationBasic Physics Content
Basic Physics Content The purpose of these 38 questions is to let me know what your initial grasp is of the material that lies ahead. This is not graded, so don t stress out. Enjoy thinking about and answering
More information1. Which of the following correctly lists our cosmic address from small to large?
1. Which of the following correctly lists our cosmic address from small to large? (a) Earth, solar system, Milky Way Galaxy, Local Group, Local Super Cluster, universe (b) Earth, solar system, Milky Way
More informationMotion. Argument: (i) Forces are needed to keep things moving, because they stop when the forces are taken away (evidence horse pulling a carriage).
1 Motion Aristotle s Study Aristotle s Law of Motion This law of motion was based on false assumptions. He believed that an object moved only if something was pushing it. His arguments were based on everyday
More informationGravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields
Gravity Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields Simulation Synchronous Rotation https://www.youtube.com/watch?v=ozib_l eg75q SunEarthMoon System https://vimeo.com/16015937
More informationN t ew on L s aws Monday, February 2
Newton s Laws Monday, February Isaac Newton (1643177): English Discovered: three laws of motion, one law of universal gravitation. Newton s great book: Newton s laws are universal in scope, and mathematical
More informationAnnouncements. True or False: When a rocket blasts off, it pushes off the ground in order to launch itself into the air.
Astronomy 101, Oct. 23, 2008 Announcements Homework #4 available today at 11:00 AM (after lecture!) Due Sunday, 11/2, before midnight. Final exam date, time, and place: Monday, Dec. 15, 10:30 AM, Hasbrouck
More informationClassical mechanics: Newton s laws of motion
Classical mechanics: Newton s laws of motion Homework next week will be due on Thursday next week You will soon be receiving student evaluations Occam s razor Given two competing and equally successful
More informationIsaac Newton and the Laws of Motion and Gravitation 2
Isaac Newton and the Laws of Motion and Gravitation 2 ASTR 101 3/21/2018 Center of Mass motion Oblate shape of planets due to rotation Tidal forces and tidal locking Discovery of Neptune 1 Center of Mass
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 informationForces. A force is a push or a pull on an object
Forces Forces A force is a push or a pull on an object Arrows are used to represent forces. The direction of the arrow represent the direction the force that exist or being applied. Forces A net force
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimetersized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton
More informationThe Solar System CHAPTER 6. Vocabulary. star an object in space that makes its own light and heat. moon an object that circles around a planet
CHAPTER 6 The Solar System Vocabulary star an object in space that makes its own light and heat moon an object that circles around a planet Sun astronomical unit the distance between Earth and the Sun
More informationAnswer Key for Exam C
Answer Key for Exam C 2 points each Choose the answer that best completes the question. Read each problem carefully and read through all the answers. Take your time. If a question is unclear, ask for clarification
More informationDescribing Motion. Newton Newton s Laws of Motion. Position Velocity. Acceleration. Key Concepts: Lecture 9
Key Concepts: Lecture 9 Newton Newton s Laws of Motion More on Kepler s Laws Describing Motion Position Velocity Rate of change of position (speed & direction) 80 km/hr Acceleration 40 km/hr Rate of change
More informationAstronomy Picture of the Day
Astronomy Picture of the Day Something Cool Einstein Ring Something Cool Einstein Ring Something Cool Einstein Ring Astronomy News Article Read an interesting astronomical news article from spaceref.com
More informationThe Acceleration of Gravity (g)
The Acceleration of Gravity (g) Galileo demonstrated that g is the same for all objects, regardless of their mass! Confirmed by Apollo astronauts on the Moon, where there is no air resistance. https://www.youtube.com/watch?v=5c5_doeyafk
More informationg = Gm / r 2 The Big Idea
The Big Idea Over 2500 years ago Aristotle proposed two laws of physics governing motion. One for Earthly bodies (objects on Earth) that states objects naturally go in straight lines and one for Heavenly
More informationAP Physics Multiple Choice Practice Gravitation
AP Physics Multiple Choice Practice Gravitation 1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each
More informationChapter 5 Lecture Notes
Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414  Strauss Constants: G = 6.67 1011 Nm 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular
More informationKepler Galileo and Newton
Kepler Galileo and Newton Kepler: determined the motion of the planets. Understanding this motion was determined by physicists like Galileo and Newton and many others. Needed to develop Physics as a science:
More informationBy; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors
By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors What is gravity? Gravity is defined as the force of attraction by which terrestrial bodies tend to fall
More informationSAMPLE First Midterm Exam
Astronomy 1000 Dr C. Barnbaum SAMPLE First Midterm Exam Note: This is a sample exam. It is NOT the exam you will take. I give out sample exams so that you will have an understanding of the depth of knowledge
More informationStudy Guide Solutions
Study Guide Solutions Table of Contents Chapter 1 A Physics Toolkit... 3 Vocabulary Review... 3 Section 1.1: Mathematics and Physics... 3 Section 1.2: Measurement... 3 Section 1.3: Graphing Data... 4 Chapter
More informationChapter 12 Forces and Motion
Chapter 12 Forces and Motion GOAL: Students will be able to interpret and apply Newton s three laws of motion and analyze the motion of an object in terms of its position, velocity, and acceleration. Standard:
More informationFinding Extrasolar Planets. I
ExtraSolar Planets Finding Extrasolar Planets. I Direct Searches Direct searches are difficult because stars are so bright. How Bright are Planets? Planets shine by reflected light. The amount reflected
More informationMeasuring Force You may have measured forces using a spring scale. The of the spring in the scale depends on the amount of (a type of ) acting on it.
Forces 12.1 Name 1 A is a push or a pull that on an. How do forces affect the motion of an object? Measuring Force You may have measured forces using a spring scale. The of the spring in the scale depends
More informationAP Physics 1 Chapter 7 Circular Motion and Gravitation
AP Physics 1 Chapter 7 Circular Motion and Gravitation Chapter 7: Circular Motion and Angular Measure Gravitation Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular
More informationPlease turn on your clickers
Please turn on your clickers HW #1, due 1 week from today Quiz in class Wednesday Sections meet in Planetarium Honors meeting tonight in my office Sterling 5520 at 5:306pm Newton s First Law An object
More informationPhysics Mechanics Lecture 30 Gravitational Energy
Physics 170  Mechanics Lecture 30 Gravitational Energy Gravitational Potential Energy Gravitational potential energy of an object of mass m a distance r from the Earth s center: Gravitational Potential
More informationConceptual Physics Fundamentals
Conceptual Physics Fundamentals Chapter 6: GRAVITY, PROJECTILES, AND SATELLITES This lecture will help you understand: The Universal Law of Gravity The Universal Gravitational Constant, G Gravity and Distance:
More informationFirst exam next Wednesday. Today in class Review: Motion, Gravity. Gravity and Orbits. Review: Motion. Newton s Laws of Motion. Gravity and Orbits
Review: s of First exam next Wednesday Today in class Review:, Gravity Gravity and Gravity and Review: s of Review: Gravity and Newton s laws of motion Review: s of 1. Momentum (qualitative) 2. Force and
More informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016 Why are celestial motions and forces important? They explain the world around us.
More informationNewton, Einstein, and Gravity
Newton, Einstein, and Gravity I have not been able to discover the cause of those properties of gravity from phenomena, and I feign no hypotheses...and to us it is enough that gravity does really exist,
More informationTest 1 Review Chapter 1 Our place in the universe
Test 1 Review Bring Gator 1 ID card Bring pencil #2 with eraser No use of calculator or any electronic device during the exam We provide the scantrons Formulas will be projected on the screen You can use
More informationHow big is the Universe and where are we in it?
Announcements Results of clicker questions from Monday are on ICON. First homework is graded on ICON. Next homework due one minute before midnight on Tuesday, September 6. Labs start this week. All lab
More informationChapter: The Laws of Motion
Table of Contents Chapter: The Laws of Motion Section 1: Newton s Second Law Section 2: Gravity Section 3: The Third Law of Motion 1 Newton s Second Law Force, Mass, and Acceleration Newton s first law
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationCopyright 2010 Pearson Education, Inc. GRAVITY. Chapter 12
GRAVITY Chapter 12 Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationUnit 3 Lesson 2 Gravity and the Solar System. Copyright Houghton Mifflin Harcourt Publishing Company
Florida Benchmarks SC.8.N.1.4 Explain how hypotheses are valuable if they lead to further investigations, even if they turn out not to be supported by the data. SC.8.N.1.5 Analyze the methods used to develop
More information1301W.600 Lecture 18. November 15, 2017
1301W.600 Lecture 18 November 15, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:308:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program
More informationASTR 150. Planetarium Shows begin Sept 9th. Register your iclicker! Last time: The Night Sky Today: Motion and Gravity. Info on course website
Planetarium Shows begin Sept 9th Info on course website Register your iclicker! Last time: The Night Sky Today: Motion and Gravity ASTR 150 Hang on tight! Most math all semester get it over with right
More informationGravitation. Objectives. The apple and the Moon. Equations 6/2/14. Describe the historical development of the concepts of gravitational force.
Gravitation Objectives Describe the historical development of the concepts of gravitational force. Describe and calculate how the magnitude of the gravitational force between two objects depends on their
More informationCircular Motion and Gravitation Notes 1 Centripetal Acceleration and Force
Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force This unit we will investigate the special case of kinematics and dynamics of objects in uniform circular motion. First let s consider
More informationMotion, Energy, and Gravity. Reminder to take out your clicker and turn it on!
Motion, Energy, and Gravity Reminder to take out your clicker and turn it on! Attendance Quiz Are you here today? Here! (a) yes (b) no (c) Opening Day is here! x Clickers I have not been able to download
More informationPhysics Mechanics. Lecture 29 Gravitation
1 Physics 170  Mechanics Lecture 29 Gravitation Newton, following an idea suggested by Robert Hooke, hypothesized that the force of gravity acting on the planets is inversely proportional to their distances
More informationAY2 Winter 2017 Midterm Exam Prof. C. Rockosi February 14, Name and Student ID Section Day/Time
AY2 Winter 2017 Midterm Exam Prof. C. Rockosi February 14, 2017 Name and Student ID Section Day/Time Write your name and student ID number on this printed exam, and fill them in on your Scantron form.
More informationAP Physics C Textbook Problems
AP Physics C Textbook Problems Chapter 13 Pages 412 416 HW16: 03. A 200kg object and a 500kg object are separated by 0.400 m. Find the net gravitational force exerted by these objects on a 50.0kg object
More informationExam 1 Astronomy 114. Part 1
Exam 1 Astronomy 114 Part 1 [140] Select the most appropriate answer among the choices given. 1. If the Moon is setting at 6AM, the phase of the Moon must be (A) first quarter. (B) third quarter. (C)
More informationChapter 4 Newton s Laws
Chapter 4 Newton s Laws Isaac Newton 16421727 Some inventions and discoveries: 3 laws of motion Universal law of gravity Calculus Ideas on: Sound Light Thermodynamics Reflecting telescope In this chapter,
More informationAst ch 45 practice Test Multiple Choice
Ast ch 45 practice Test Multiple Choice 1. The distance from Alexandria to Syene is about 500 miles. On the summer solstice the sun is directly overhead at noon in Syene. At Alexandria on the summer solstice,
More informationThe graph shows how an external force applied to an object of mass 2.0 kg varies with time. The object is initially at rest.
T22 [195 marks] 1. The graph shows how an external force applied to an object of mass 2.0 kg varies with time. The object is initially at rest. What is the speed of the object after 0.60 s? A. 7.0 ms
More informationIn the absence of an external force, the momentum of an object remains unchanged conservation of momentum. In this. rotating objects tend to
Rotating objects tend to keep rotating while non rotating objects tend to remain nonrotating. In the absence of an external force, the momentum of an object remains unchanged conservation of momentum.
More information1 Forces. 2 Energy & Work. GS 104, Exam II Review
1 Forces 1. What is a force? 2. Is weight a force? 3. Define weight and mass. 4. In European countries, they measure their weight in kg and in the United States we measure our weight in pounds (lbs). Who
More informationThe force of gravity holds us on Earth and helps objects in space stay
96 R E A D I N G The force of gravity holds us on Earth and helps objects in space stay in orbit. The planets in the Solar System could not continue to orbit the Sun without the force of gravity. Astronauts
More informationA mass is suspended by a string from a fixed point. The mass moves with constant speed along a circular path in a [1 mark] horizontal plane.
T6 [200 marks] 1. A mass is suspended by a string from a fixed point. The mass moves with constant speed along a circular path in a horizontal plane. The resultant force acting on the mass is A. zero.
More informationWHAT WE KNOW. Scientists observe that every object in the universe is moving away from each other. Objects furthest away are moving the fastest. So..
ASTRONOMY THE BIG BANG THEORY WHAT WE KNOW Scientists observe that every object in the universe is moving away from each other. Objects furthest away are moving the fastest. So.. WHAT DOES THIS MEAN? If
More informationQuestion 8.1: the following: (a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting
More informationPhysics 1100: Uniform Circular Motion & Gravity
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Physics 1100: Uniform Circular Motion & Gravity 1. In the diagram below, an object travels over a hill, down a valley, and around a loop the loop at constant
More informationChapter 5 Part 2. Newton s Law of Universal Gravitation, Satellites, and Weightlessness
Chapter 5 Part 2 Newton s Law of Universal Gravitation, Satellites, and Weightlessness Newton s ideas about gravity Newton knew that a force exerted on an object causes an acceleration. Most forces occurred
More informationLecture 19: The Moon & Mercury. The Moon & Mercury. The Moon & Mercury
Lecture 19: The Moon & Mercury The Moon & Mercury The Moon and Mercury are similar in some ways They both have: Heavily cratered Dark colored surfaces No atmosphere No water They also have some interesting
More informationGravitation. Luis Anchordoqui
Gravitation Kepler's law and Newton's Synthesis The nighttime sky with its myriad stars and shinning planets has always fascinated people on Earth. Towards the end of the XVI century the astronomer Tycho
More informationAstronomy Lesson 8.1 Astronomy s Movers and Shakers
8 Astronomers.notebook Astronomy Lesson 8.1 Astronomy s Movers and Shakers Aristotle 384 322 BCE Heavenly objects must move on circular paths at constant speeds. Earth is motionless at the center of the
More informationPractice Test for Midterm Exam
A.P. Physics Practice Test for Midterm Exam Kinematics 1. Which of the following statements are about uniformly accelerated motion? Select two answers. a) If an object s acceleration is constant then it
More informationChapter 4. The Laws of Motion
Chapter 4 The Laws of Motion Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical Mechanics does not
More informationMOTION IN THE SOLAR SYSTEM ENGAGE, EXPLORE, EXPLAIN
MOTION IN THE SOLAR SYSTEM ENGAGE, EXPLORE, EXPLAIN ENGAGE THE ATTRACTION TANGO THE ATTRACTION TANGO In your science journal, on the next clean page, title the page with The Attraction Tango. In your group,
More informationPSC 1121 Spring 2017 Final Exam Review
Physical Science Final Exam Review Disclaimer: this review was taken from notes, homework and other resources. This review will help you study for the exam. Only reviewing it won t guarantee that you have
More information