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Unit 6: Universal Gravitation Part 1 Everything pulls on everything else. Newton’s Law of Universal Gravitation Law of Universal Gravitation: every object attracts every other object with a force that directly proportional to the mass of each object and inversely proportional to the square of the distance between them. Newton’s Law of Universal Gravitation m m Why would you weigh less on a mountain top? Newton’s Law of Universal Gravitation universal gravitational constant, G: describes the strength of gravity in the equation for universal gravitation G = 6.67 × 10−11 N·m2/kg2 the units of G make the force of gravity come out in newtons Newton’s Law of Universal Gravitation Gravity weakens with distance. (weight decreases) • but gravity never drops to zero • The gravitational influence of every object, however small or far, is exerted through all space. Newton’s Law of Universal Gravitation G was first measured 150 years after Newton’s discovery of universal gravitation by a method of measuring the attraction between two masses. G = 6.67 × 10−11 or 0.000 000 000 0667 The extremely low value of G tells us that gravity is a very weak force. It is the weakest of the four fundamental forces. We sense gravitation only when very large masses are involved (like Earth). Universal Gravitation The Earth is round because of gravitation. • Since everything attracts everything else, Earth had attracted itself together before it became solid. • Stars, planets, moons, are all fairly spherical because they have to be. Universal Gravitation Gravity played a role in the formation of the solar system. a. A slightly rotating ball of interstellar gas contracted due to mutual gravitation. b. The rotational speed of the ball of gas increased. c. The increased momentum caused wider paths about the rotational axis, producing an overall disk shape. The greater surface area of the disk promoted cooling and clusters of swirling matter—the birthplace of planets. Universal Gravitation The Expanding Universe According to current scientific understanding, the universe originated and grew from the explosion of a primordial fireball about 15 billion years ago. “Big Bang” theory: the origin of the universe was an explosion of energy as the beginning of matter, space and time. Gravitational Field gravitational field: force field that occupies the space around a massive body so that any mass in the field space experiences a gravitational force We can regard the moon as in contact with the gravitational field of Earth. Gravitational Field A more familiar force field is the magnetic field of a magnet. • Iron filings on near a magnet reveal the shape of the magnet’s magnetic field. • Where the filings are close together, the field is strong. • Earth is a giant magnet, and like all magnets, is surrounded in a magnetic field. Gravitational Field Field lines can also represent the pattern of Earth’s gravitational field. • The field lines are closer together where the gravitational field is stronger. • Any mass near Earth will be accelerated in the direction of the field lines. • Earth’s gravitational field follows the inverse-square law (it’s strongest near Earth surface and weaker at greater distances from Earth). Gravitational Field Inside a Planet The gravitational field of Earth exists inside Earth as well as outside. Imagine a hole drilled completely through Earth. Consider the kind of motion you would undergo if you fell into such a hole. video clip: “Fall Through Earth” Gravitational Field Inside a Planet Where is max velocity? As you fall, your acceleration diminishes. The pull of the mass above partly cancels the pull below. You’d gain speed moving toward the center, and lose speed moving away from the center. The trip would take nearly 45 minutes. Gravitational Field Inside a Planet At the center of Earth, your weight would be zero, because you would be pulled equally by gravity in all directions. Weight and Weightlessness The force of gravity, like any force, causes acceleration. Objects under the influence of gravity are pulled toward each other and accelerate. We are almost always in contact with Earth, so we think of gravity as something that presses us against Earth rather than as something that accelerates us. Weight and Weightlessness The sensation of weight is equal to the force that you exert against a supporting object (the floor). Why? more support force Why? less support Why no weight in free fall? force Four Fundamental Forces • Electromagnetic • Nuclear (strong/weak) m • Gravitational m Four Fundamental Forces Electromagnetic Force – combination of electric & magnetic forces – only force that can attract and repel opposite like Magnets have 2 poles (north / south) Four Fundamental Forces Nuclear Forces (Review from Chem) – Strong and Weak hold the nucleus together overcomes electric repulsion of positive protons involved in radioactivity - 100x stronger than weak - strongest force - shortest distance Four Fundamental Forces Gravitational Force – every object in attracts every other object – depends on mass and distance more mass more force more distance less force – WEAKEST universal force, but … acts over LONGEST DISTANCE Unit 6: Electrostatics and Fields Part 2 Electricity at rest: forces between charges and their behavior in materials. Electrical Forces and Charges What if two forces acted on you that were each billions of times stronger than gravity? The enormous attractive and repulsive electrical forces between the charges in Earth and the charges in your body balance out. Electrical Forces and Charges Electrical forces are from subatomic particles. (protons attract electrons, but electrons repel other electrons) Electrical Forces and Charges like…repel opposite…attract like…repel charge: fundamental electrical property causing mutual attractions or repulsions between electrons or protons. Conservation of Charge Electrons and protons have electric charge. In a neutral atom, there are as many electrons as protons, so there is no net charge. ions Conservation of Charge A charged object has an imbalance by adding or removing electrons. Demo Electrons are neither created nor destroyed, but are simply transferred from one material to another. This principle is known as: conservation of ____________ of charge charge Conservation of Charge think! If you scuff electrons onto your shoes while walking across a rug, are you negatively or positively charged? Answer: You have more electrons and are negatively charged. Coulomb’s Law What is this? Newton’s Law of Universal Gravitation (2 masses attract according to an inverse square law) Coulomb’s Law Coulomb’s Law d -distance between charges. q1 -quantity of one charge. q2 -quantity of another charge. k -constant. charge is in coulombs (C) 1 C = 6.24 × 1018 electrons (1 C passes through a 100-W light bulb in 1 s) Coulomb’s Law Coulomb’s Law k = 9,000,000,000 N·m2/C2 (9.0 x 109 N·m2/C2) If a pair of charges of 1 C each were 1 m apart, the force of repulsion between the two charges 9 billion N would be _______________. (more than 10 times the weight of a battleship! ) Coulomb’s Law Newton’s Law of Universal Gravitation Coulomb’s Law Coulomb’s Law think! What is the main significance of the fact that G in Newton’s law of gravitation is a very small number and k in Coulomb’s law is a very large number? Answer: gravity is a weak force, but… the electrical force is enormously strong. Coulomb’s Law think! How will the electrostatic force compare when charges are twice the distance apart? Answer: (inverse-square law) at twice the distance, the force will be one fourth as much. Quick Quiz! 1. If a neutral atom has 22 protons in its nucleus, the number of surrounding electrons is… A. less than 22. B. exactly 22. C. more than 22. D. unknown. Quick Quiz. 2. When we say charge is conserved, we mean that charge can… A. be saved, like money in a bank. B. only be transferred from one place to another. C. take equivalent forms. D. be created or destroyed, as in nuclear reactions. Quick Quiz. 3. A difference between Newton’s law of gravity and Coulomb’s law is that only one of these… A. is a fundamental physical law. B. uses a proportionality constant. C. applies the inverse-square law. D. involves repulsive and attractive forces. Conductors and Insulators conductors: materials through which electric charge flows Metals are good conductors for the motion of electric charges because their electrons are “loose” in a “sea of electrons” Conductors and Insulators insulators: poor conductors with tightly bound electrons (rubber, glass, plastic, wood, cloth) Charge flows more easily through hundreds of kilometers of metal wire than through the few centimeters of insulating material. Conductors and Insulators semiconductors: materials that can be made to act as insulators or as conductors. Atoms in a semiconductor hold their electrons until given small energy boosts. Charging by Friction and Contact charged by friction charged by contact ? + ++ + + + + Charging by Induction charged by induction (no direct contact) Charging by Induction grounding: allowing charges to move off (or onto) a conductor by touching. Charging by Induction The negatively charged bottoms of clouds induce a positive charge on Earth’s surface. Most lightning is an electrical discharge between oppositely charged parts of clouds. Charging by Induction think! Why does the negative rod in the Figure 1 have the same charge before and after, but not when charging takes place in the Figure 2? Figure 1 Figure 2 Answer: No contact was made. The transfer of charge by contact reduced the negative charge on the rod. Charging In summary, objects are electrically charged in 3 ways: • By friction, when electrons are transferred by rubbing from one object to another. • By contact, when electrons are transferred by direct contact without rubbing. • By induction, when electrons are gathered or dispersed by a nearby charge without contact. Quick Quiz! 1. Which is the predominant carrier of charge in copper wire? A. protons B. electrons C. ions D. neutrons Quick Quiz. 2. When you scuff electrons off a rug with your shoes, your shoes are then… A. negatively charged. B. positively charged. C. ionic. D. electrically neutral. Quick Quiz. 3. When a cloud that is negatively charged on its bottom and positively charged on its top moves over the ground below, the ground acquires… A. a negative charge. B. a positive charge. C. no charge since the cloud is electrically neutral. D. an electrically grounded state. Unit 6: Electrostatics and Fields Part 3 An electric field is a storehouse of energy. Electric Fields electric field: force field that surrounds an electric charge An electric field has both magnitude and direction. vector gravitational force field electrostatic force field Electric Fields Imagine a small positive “test charge” placed in an electric field. • the field (E) is strongest where force (F) on a test charge is greatest (longest vector) repulsive force • test charge gives direction attractive force with same magnitude, opposite direction Electric Field Lines Magnitude is shown by: a. vector length b. distance between field lines VIDEO 5:57 Electric Field Lines a. Field lines from a positive charge go to infinity. b. For equal but opposite charges, the field lines go from positive and to negative charge. c. Between two oppositely charged capacitor plates, field lines are evenly spaced. (opposite charges) (like charges) inside ring? (oppositely charged plates) like or opposite? Electric Shielding When a car is struck by lightning, the occupant inside the car is completely safe. The electrons shower down upon the car, repel and spread over the outer metal surface. The electric fields inside the car cancel to almost zero. Video Clip – Lightning Car 5:16 Electric Shielding Shielding : • free charges arrange on the surface to cancel fields inside. Quick Quiz ! 1. An electric field has… A. no direction. B. only magnitude. C. both magnitude and direction. D. the same strength throughout. Quick Quiz. 2. In the electric field surrounding a group of charged particles, field strength is greater where field lines are… A. thickest. B. longest. C. farthest apart. D. closest. Quick Quiz. 3. Electrons on the surface of a conductor will arrange themselves so that the electric field… A. inside cancels to zero. B. follows the inverse-square law. C. tends toward a state of minimum energy. D. is shielded from external charges. Electric Fields The strength of an electric field (E) on a test charge (q) experiencing a force (F) at a point is: F E= q VIDEO 12:12 The force (F) on a charge (q) at a point in an electric field (E) is: F = qE • A charge of –2 C is placed in an electric field of strength 5000 N/C. What force is experienced by the charge? F = qE F = (–2)(5000) F = –10000 N • What is the strength of an electric field that exerts a force of 50 N on a particle with a charge of 0.05 C? F E= q 50 E= 0.05 E = 1000 N/C Electric Field Lines VIDEO 3:13 Electric Field Lines #1 X Y + + -Z Electric Field Lines #2 Electrical Potential Energy Objects have potential energy from location. a. Gravitational PE of weight is transferred into KE. b. Electrical PE of charge is transferred into KE. Electrical Potential Energy electrical potential energy: PE of a charge due to its location in an electric field. Work is done in pushing the charge against the electric field. (work = energy gained by the charge) VIDEO1 8:08 VIDEO2 3:45 If the charge is released, it will accelerate away from the sphere as electrical PE transforms into KE. Electric Potential push 1 charge against an electric field requires an amount of work. push 2 charges against the same field requires twice as much work. 2 charges have twice the electrical PE as 1 10 charges have ten times the electrical PE But they would both have the SAME electrical potential energy per charge. Electric Potential electric potential: electrical PE per charge At each location the PE per charge will be the same. PE = 10 J q=1C more charge, more electrical PE, PE = 20 J but… q=2C Electric Potential 5000 The charge is typically less than a millionth of a coulomb. Therefore, the energy is very small—about a thousandth of a joule. 0.001 J 5000 V = 0.0000002 C A high voltage requires great energy only if a great amount of charge is involved. Electric Potential think! With twice as much charge on one object, is the electrical potential energy the same or twice as great? Is the electric potential be the same or is it be twice as great? Answer: Twice as much charge has twice as much electrical potential energy, because it takes twice as much work to bring the object to that location. The electric potential would be the same, because the electric potential = 2 PE 2q Quick Quiz! 1. The potential energy of a compressed spring and the potential energy of a charged object both depend… A. only on the work done on them. B. only on their locations in their respective fields. C. on their locations in their respective fields and on the work done on them. D. on their kinetic energies exceeding their potential energies. Quick Quiz. 2. How is electric potential is related to electrical potential energy? A. The two terms are different names for the same concept. B. Electric potential is the ratio of electrical potential energy per charge. C. Both are measured using the units of coulomb. D. Both are measured using only the units of joules.