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negative charge. Remember, net charge is always conserved: the positive charge of the wool or glass rod will balance out the negative charge of the rubber rod or silk. The Electroscope The electroscope is a device commonly used—and sometimes included on SAT II Physics—to demonstrate how electric charge works. It consists of a metal bulb connected to a rod, which in turn is connected to two thin leaves of metal contained within an evacuated glass chamber. When a negatively charged object is brought close to the metal bulb, the electrons in the bulb are repelled by the charge in the object and move down the rod to the two thin leaves. As a result, the bulb at the top takes on a positive charge and the two leaves take on a negative charge. The two metal leaves then push apart, as they are both negatively charged, and repel one another. When a positively charged object approaches the metal bulb, the exact opposite happens, but with the same result. Electrons are drawn up toward the bulb, so that the bulb takes on a negative charge and the metal leaves have a positive charge. Because both leaves still have the same charge, they will still push apart. Electric Force There is a certain force associated with electric charge, so when a net charge is produced, a net electric force is also produced. We find electric force at work in anything that runs on batteries or uses a plug, but that isn’t all. Almost all the forces we examine in this book come from electric charges. When two objects “touch” one another—be it in a car crash or a handshake—the atoms of the two objects never actually come into contact. Rather, the atoms in the two objects repel each other by means of an electric force. Coulomb’s Law Electric force is analogous to gravitational force: the attraction or repulsion between two particles is directly proportional to the charge of the two particles and inversely proportional to the square of the distance between them. This relation is expressed mathematically as Coulomb’s Law: In this equation, and are the charges of the two particles, r is the distance between them, and k is a constant of proportionality. In a vacuum, this constant is Coulumb’s constant, , which is approximately N · m 2 / C 2 . Coulomb’s constant is often expressed in terms of a more fundamental constant—the permittivity of free space, , which has a value of C 2 / N · m 2 : 204
If they come up on SAT II Physics, the values for and will be given to you, as will any other values for k when the electric force is acting in some other medium. EXAMPLE Two particles, one with charge +q and the other with charge –q, are a distance r apart. If the distance between the two particles is doubled and the charge of one of the particles is doubled, how does the electric force between them change? According to Coulomb’s Law, the electric force between the two particles is initially If we double one of the charges and double the value of r, we find: Doubling the charge on one of the particles doubles the electric force, but doubling the distance between the particles divides the force by four, so in all, the electric force is half as strong as before. Superposition If you’ve got the hang of vectors, then you shouldn’t have too much trouble with the law of superposition of electric forces. The net force acting on a charged particle is the vector sum of all the forces acting on it. For instance, suppose we have a number of charged particles, , , and . The net force acting on is the force exerted on it by added to the force exerted on it by . More generally, in a system of n particles: where is the force exerted on particle 1 by particle n and is the net force acting on particle 1. The particle in the center of the triangle in the diagram below has no net force acting upon it, because the forces exerted by the three other particles cancel each other out. 205
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SATII PHYSICS (FROM SPARKNOTES.COM)
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The Good • Because SAT II Subject
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Which SAT II Subject Tests to Take
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After grumbling, however, you still
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Waves 15-19% 11-15 Waves 10% 7-8 Op
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negative, so E, and not A, is the c
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including them anyway because it’
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Two positively charged particles, o
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will a visual representation reliev
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Physics Hint 6: Be Flexible Knowing
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There are a number of ways to label
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Adding Parallel Vectors If the vect
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The result of multiplying A by c is
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neither parallel nor perpendicular.
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Suppose the hands on a clock are ve
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Vector Addition Practice Questions
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2. A The vector 2A has a magnitude
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path, Alan has traveled a much grea
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school student called Andrea. Andre
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centimeters to the left of its star
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We can learn two things about the a
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Acceleration vs. Time Graphs After
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The variable represents the object
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Note that there are certain conveni
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1. . An athlete runs four laps of a
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10. . A woman runs 40 m to the nort
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We know the total distance the spri
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Principles of Natural Philosophy. I
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The component form of Newton’s Se
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e in the direction. And since the s
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which reflects its resistance to be
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In the diagram above, the weight an
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A student pushes a box that weighs
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1. . Each of the figures below show
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7. . In the figure above, a person
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Since the block is motionless, the
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When we are told that a person push
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EXAMPLE A water balloon of mass m i
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The graph above plots the force exe
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Though energy is always measured in
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there is a negative amount of work
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smallest. The answer to question 3
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Mechanical Energy Average Power Ins
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to a height of 8 m over a time of 4
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8. C When the book reaches the pers
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determining what those right number
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the ground. The system is initially
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calculators, you almost certainly w
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and minimize M.” With such a ques
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2. WHAT IS THE ACCELERATION OF THE
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Adding these two equations together
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force of friction: . Using Newton
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m, placed on a frictionless surface
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Frequency is given in units of cycl
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of the spring due to the gravitatio
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The oscillation of a pendulum is mu
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Velocity Calculating the velocity o
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Practice Questions 1. . Two masses,
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7. . An object of mass 3 kg is atta
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Since the system is in equilibrium,
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velocity, v. Linear momentum is den
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Conservation of Momentum If we comb
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As we might expect, the final veloc
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A pool player hits the eight ball,
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two-dimensional collision is effect
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For a System of Two Particles For a
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At the front end of the boat, the f
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4. . A scattering experiment is don
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1. B The athlete imparts a certain
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7. E Momentum is conserved in this
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The diver’s translational motion
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30 π/6 45 π/4 60 π/3 90 π/2 180
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elative position to one another. As
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acceleration given its angular velo
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To find the direction of a rigid bo
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A student exerts a force of 50 N on
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Page 163 and 164: 1. D An object that experiences 120
Page 165 and 166: At the top of the incline, the disk
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Page 169 and 170: Newton’s Law of Universal Gravita
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Page 173 and 174: EXAMPLE A satellite of mass is laun
Page 175 and 176: Kepler’s Laws After poring over t
Page 177 and 178: Practice Questions Questions 1-3 re
Page 179 and 180: 8. . A satellite orbits the Earth a
Page 181 and 182: Circumference and radius are relate
Page 183 and 184: learn how heat is transferred from
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Page 187 and 188: Just as specific heat tells us how
Page 189 and 190: Conduction is the transfer of heat
Page 191 and 192: Effectively, this equation tells us
Page 193 and 194: the way that it does. The Laws of T
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Page 197 and 198: If we know our formulas, this probl
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Page 201 and 202: Asphalt, like most materials, has a
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Page 207 and 208: will move in the opposite direction
Page 209 and 210: Work The work done to move a charge
Page 211 and 212: Much like gravitational potential e
Page 213 and 214: 3. . A particle of charge +2q exert
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Page 219 and 220: Voltage The batteries we use in fla
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Page 225 and 226: However, each resistor causes a vol
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Page 229 and 230: Consider again the circuit whose to
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Page 233 and 234: The junction rule deals with “jun
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Page 241 and 242: 4. . Two resistors, and , are ident
Page 243 and 244: 10. . A dielectric is inserted into
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1. . The pointer on a compass is th
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7. . A positively charged particle
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1. B To solve this problem, it is h
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If the particle is to move at a con
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flowing in the counterclockwise dir
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Next, let’s calculate the flux th
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Remember that field lines come out
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Magnetic Flux Faraday’s Law / Len
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5. . A wire carrying 5.0 V is appli
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In this equation, A is the amplitud
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Ernst attaches a stretched string t
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A string is tied to a pole at one e
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other. The principle of superpositi
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Nodes The crests and troughs of a s
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The Doppler Effect So far we have o
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Practice Questions 1. . Which of th
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6. . Two pulses travel along a stri
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1. B Simple harmonic motion is defi
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where and are the frequency heard b
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A higher frequency—and thus a sho
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The phenomenon of refraction result
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Since we know that the ratio of / i
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The four basic kinds of optical ins
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You can test all this yourself with
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Because is a positive number, we kn
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As the diagram shows us, and as the
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At any point P on the back screen,
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Note that the pattern is brightest
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One of the more common ways of test
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3. . When the orange light passes f
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9. . Sound waves do not exhibit pol
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7. E Only concave mirrors and conve
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For people who believed that light
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What does this all mean? Time is re
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A spaceship flying toward the Earth
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Rutherford’s Gold Foil Experiment
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The Wave Theory of Electromagnetic
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The Problem with Rutherford’s Mod
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Don’t worry: you don’t need to
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A hydrogen atom is energized so tha
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where is the uncertainty in a parti
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electrons have mass, it is so negli
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chapters on mechanics are the resul
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You won’t need to calculate the n
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Photoelectro n Radius of Electron O
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5. . An electron is accelerated thr
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according to the formula , where l
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In radioactive substances, the numb
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A scale for measuring temperature,
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The points of maximum displacement
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Electromagnetic spectrum The spectr
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The amount of time it takes for one
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Given the period, T, and semimajor
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The substance that is displaced as
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A back-and-forth movement about an
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Refracted ray Refraction Restoring
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T Tail Tangent A body or set of bod
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Weber Weight The force involved in
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pinpointing what you need to study
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If you got a question wrong because
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