Barrons SAT subject test physics second edition

About the Authors Robert Jansen teaches Advanced Placement Physics at Aliso Niguel High School in Aliso Viejo, California He has taught Advanced Placement Physics B since 1998 and the complete Advanced Placement Physics C course, including electricity and magnetism, since 2001 He holds a bachelors degree in psychobiology from the University of California, Los Angeles and a master’s degree in education from Pepperdine University He gravitated toward teaching physics due to the challenging material and a sustained belief that physics does not need to be mysterious and difficult, but rather comprehensible and achievable The result has been a large and competitive physics program where each year over 220 students participate in the AP Physics B and C courses The overarching goal is preparedness and confidence for students who will be studying science during their undergraduate years Greg Young has been teaching high school science for more than twenty years He currently teaches Honors Physics and Chemistry at San Clemente High School in San Clemente, California He holds a bachelor’s degree in biochemistry from the University of California, San Diego and a master’s degree in science education from USC Having always been interested in science and how to make it relevant to others, Greg’s interest in teaching is being able to create interactive lessons that engage students in their learning and form a relevant context for difficult concepts in physics and chemistry Science made interesting is science worth learning © Copyright 2016, 2013 by Barron’s Educational Series, Inc All rights reserved No part of this publication may be reproduced or distributed in any form or by any means without the written permission of the copyright owner All inquiries should be addressed to: Barron’s Educational Series, Inc 250 Wireless Boulevard Hauppauge, New York 11788 www.barronseduc.com eISBN: 978-1-4380-6856-5 Revised e-Book publication: September 2016 CONTENTS Introduction Using This Resource Efficiently The Physics Exam General Examination Strategies Diagnostic Test Diagnostic Test Diagnostic Chart Scoring Your Test Conventions and Graphing Fundamental and Derived Units Graphing Variables Slope and Area Interpreting Graphs Summary Practice Exercises Vectors Coordinate System Scalars Vectors Vector Mathematics Summary Practice Exercises Kinematics in One Dimension Kinematic Quantities Identifying Variables Kinematic Equations Kinematic Graphs Summary Practice Exercises Kinematics in Two Dimensions Independence of Motion True Velocity and Displacement Relative Velocity Projectile Motion Summary Practice Exercises Dynamics Inertia Force Common Forces Force Diagrams Newton’s Laws of Motion Solving Force Problems Summary Practice Exercises Circular Motion Uniform Circular Motion Dynamics in Circular Motion Summary Practice Exercises Energy, Work, and Power Mechanical Energy Work Power Conservation of Energy Summary Practice Exercises Momentum and Impulse Momentum Impulse Conservation of Momentum Energy in Collisions Summary Practice Exercises Gravity Universal Gravity Gravitational Field Circular Orbits Kepler’s Laws Summary Practice Exercises 10 Electric Field Charge Electric Fields Uniform Electric Fields Electric Fields of Point Charges Summary Practice Exercises 11 Electric Potential Potential of Uniform Fields Potential of Point Charges Electric Potential Energy Motion of Charges and Potential Capacitors Summary Practice Exercises 12 Circuit Elements and DC Circuits Principal Components of a DC Circuit DC Circuits Heat and Power Dissipation Summary Practice Exercises 13 Magnetism Permanent or Fixed Magnets Current-Carrying Wires Force on Moving Charges Force on Current-Carrying Wires Electromagnetic Induction Summary Practice Exercises 14 Simple Harmonic Motion Terms Related to SHM Oscillations of Springs Oscillations of Pendulums Graphical Representations of SHM Trends in Oscillations Summary Practice Exercises 15 Waves Traveling Waves Mechanical Waves Electromagnetic Waves Doppler Effect Superposition and Standing Waves Summary Practice Exercises 16 Geometric Optics Ray Model of Light Reflection Refraction Pinhole Camera Thin Lenses Spherical Mirrors Summary Practice Exercises 17 Physical Optics Diffraction Interference of Light Polarization of Light Color Summary Practice Exercises 18 Thermal Properties Thermal Systems Thermal Energy Temperature Thermal Expansion Ideal Gases Heat and Heat Transfer Heating and Cooling Summary Practice Exercises 19 Thermodynamics Internal Energy Energy Transfer in Thermodynamics Energy Model Summarized First Law of Thermodynamics Heat Engines Entropy Second Law of Thermodynamics Summary Practice Exercises 20 Atomic and Quantum Phenomena Development of the Atomic Theory Energy Level Transitions Ionization Energy/Work Function Photoelectric Effect Summary Practice Exercises 21 Nuclear Reactions Nucleons Subatomic Particles Isotopes The Strong Force Mass-Energy Equivalence Radioactive Decay Fission and Fusion Summary Practice Exercises 22 Relativity Special Theory of Relativity Time, Length, and Mass Summary Practice Exercises 23 Historical Figures and Contemporary Physics Historical Figures Contemporary Physics Practice Exercises Practice Tests Practice Test Diagnostic Chart Scoring Your Test Practice Test Diagnostic Chart Scoring Your Test Practice Test Diagnostic Chart Scoring Your Test Appendix I: Key Equations Mechanics Electricity and Magnetism Simple Harmonic Motion Waves and Optics Thermal Physics/Thermodynamics Atomic and Modern Physics Appendix II: Physical Constants Appendix III: Conversion Factors Metric Conversion Factors Other Conversion Factors Glossary Answers Explained T Introduction he SAT Subject Test in Physics is designed to assess the outcome of completing a college-preparatory physics course in high school Although state and course requirements for physics may vary, all college-preparatory physics courses should address certain core topics and principles The SAT Subject Test in Physics focuses on this common ground The goal of this book is to review the main topics and concepts that are likely to appear on the SAT Subject Test in Physics and help you prepare for the exam USING THIS RESOURCE EFFICIENTLY The chapters are organized to maximize the effectiveness of your study time Each chapter begins with a summary of the topics to be covered, bulleted points of the major topics, and a list of new variables discussed in the chapter The body of the chapter includes a discussion of the topics along with relevant example questions Each chapter also includes a unique “What’s the Trick?” approach to help you solve the questions quickly and effectively The margins contain tips called “If You See ” which point out some of the major insights into critical topics and difficult concepts The end of the chapter contains a bulleted summary along with a table grouping the critical “If You See ” elements as a concentrated review Each chapter is followed by multiple-choice practice questions with answers and explanations QR codes appear throughout the text, next to key examples Each QR code links to an online video explanation of the example problem it is associated with The following QR code is linked to the table of contents for all of the videos available for this text The available video sequences solve selected example problems in a dynamic manner In addition to the chapters that review the exam content, the book includes four complete practice exams The first practice exam should be used as a diagnostic test to assess your current level of understanding of the subject matter and to establish a baseline score to improve upon Ideally, you should take this first diagnostic examination using the same guidelines as an actual SAT Subject Test in Physics: ■ Time limit of hour for 75 multiple-choice questions ■ NO calculators allowed ■ No physics formula sheet is allowed, and none will be provided ■ Correct answers receive point ■ Subtract ¼ point for each incorrect answer ■ Answers left blank receive points Table of Contents for Video Example Problems (Tap or click the below) A complete list of test-taking parameters and how to find your approximate raw score is provided near the end of this introduction You should take the other three examinations after you have completed all or portions of your review Different students will approach this review in a variety of ways Some may choose to work methodically through each chapter, which will require starting well before the actual exam date and setting aside adequate review time Students with limited time may decide to read the important “If You See ” tips in the margins and attempt the end-of-chapter questions to determine if they should study a particular chapter in depth Keep in mind that each chapter builds 33 (D) The work–kinetic energy theorem states that work is equal to a change in kinetic energy Use the work found in the previous answer The object is initially at rest, vi = 34 (E) The work done by gravity is equal to the change in gravitational potential energy, ΔU, as the object moves through the vertical distance of 0.2 m above point Q 698 35 (A) This can be solved using conservation of energy The joules of gravitational potential energy at point P become kinetic energy, K, at point Q 36 (C) Both times, the object is lifted to the same height h at constant velocity To overcome gravity and move the object at constant speed, the upward force must be equal to the force of gravity Therefore, each time the needed force is the same regardless of the time during which the force acts Moving the object the same vertical distance h requires the same amount of work against the force of gravity However, in order to this in half the amount of time, twice the power is needed 699 37 (C) Momentum is conserved before and after the collision 38 (D) Impulse, J, is equal to the force multiplied by the change in time It is also equal to the mass multiplied by the change in velocity, which is known as the change in momentum It is not equal to the momentum itself but, rather, the change in momentum 700 39 (C) Mass is not affected by changes in the acceleration of gravity Even though the problem asks for the mass on the Moon, the weight on Earth can be used to determine the mass on Earth This value is equal to the mass on the Moon 701 40 (B) Try each possibility in Newton’s law of gravitation Choice B results in the largest possible gravity 41 (E) According to Newton’s third law, the two charges pull on each other with the same force 702 42 (E) Coulomb’s law is very similar to Newton’s law of universal gravitation When the –1 C charge is at point P, the radial distance will be of what it was originally The result is consistent with the inverse square law 703 43 (B) Identify the charges as charge 1, q1, and charge 2, q2 The electric field points toward the negative charge, so the electric field of charge 1, E1, points toward charge The electric field points away from the positive charge, so the electric field of charge 2, E2, points away from charge These two vectors can be added using vector addition to find the total electric field due to both charges The resulting electric field points in the −x direction 44 (D) Since the spheres are positively charged, they will repel one another As they begin to move farther away from one another, the force acting on them will decrease according to Coulomb’s law A reduction in force leads to a reduction in acceleration Velocity, however, will continue to increase because even though acceleration is decreasing, it continues to act in the direction of motion and continues to increase the speed of the charged spheres 45 (D) Protons and electrons have the same magnitude of charge, e, but opposite signs As a result, the charged electric plates apply an equal electric force on the similarly charged proton and electron, but in opposite directions The acceleration of each particle is dependent upon its mass Electrons have a much smaller mass than protons As a result, the same force applied to an electron will cause the electron to have a greater acceleration than the more massive proton 704 46 (C) This problem can be solved using conservation of energy The electric potential energy is converted into kinetic energy 47 (C) Capacitance is proportional to the area of the plates divided by the distance between them Doubling both area and distance will result in the capacitance remaining the same 705 48 (B) The resistors can be added in parallel to determine their total resistance Apply Ohm’s law, V = IR, to find the current 49 (A) Resistor is wired in parallel, and the voltage drop across it will be equal to the voltage of the battery Use Ohm’s law, V = IR, to solve for the current flowing through R1 706 50 (E) Power can be determined two ways The current flowing through R3 can be found in the same manner as in the previous problem Then the power can be determined as follows: Instead, it could have been determined directly using: 51 (B) A bulb with less resistance will allow more current to flow In households, the voltage is constant So increasing the current will increase the power according to P = IV Power is the rate of energy dissipation Increasing the power increases a bulb’s brightness 52 (E) The right-hand rule states that the thumb of the right hand points in the direction of motion of a charged particle (the −x-direction in this case), the extended fingers point in the direction of the magnetic field (down the page in this case), and the palm of the hand points in the direction of the force (out of the page in this case) However, the particle is an electron Electrons experience the complete opposite force So the direction of force is into the page, –z-direction As an alternative, you can use the left hand to determine the direction of magnetic force on negative charges 53 (A) In this case, the charged proton is moving parallel to the magnetic field No magnetic force acts on the proton if it is moving completely parallel to the field 54 (C) The right-hand rule states that the thumb of the right hand points in the direction of either the motion of a charged particle or the current in a wire (the −z-direction in this case), the extended fingers point in the direction of the magnetic field (down the page in this case), and the palm of the hand points in the direction of the force (to the left of the page in this case, the –x-direction) 55 (D) Reversing the magnet would reverse the direction of the current 56 (B) At position II, the total energy is in the form of kinetic energy, K, and potential energy is zero 57 (E) At position I, the constant force of gravity is greater than the variable force of the spring At position III, the variable force of the spring is greater than the constant force of gravity At position II, the constant force of gravity is equal to but in the opposite direction of the variable force of the spring Therefore, there is no net force at position II 707 58 (D) The period of a spring depends on the mass and the spring constant The period of an oscillating spring-mass system is proportional to the square root of the suspended mass Doubling mass m would result in increasing the period to T 59 (B) At the nodes, waves add destructively and there is zero amplitude 60 (C) Light intensity is directly proportional to the amplitude of a wave Frequency and wavelength have no effect on the intensity of light 61 (C) Beat frequency is the difference between two interfering waveform frequencies fbeat = f1 − f2 = 12 Hz − 8.0 Hz = 4.0 Hz 62 (B) As the index of refraction increases, the angle measured between the light ray and a normal line drawn perpendicular to the surface of the medium decreases Medium has the smallest angle and therefore the greatest index of refraction Medium has a slightly larger angle and a slightly smaller index of refraction Medium has the largest angle and the smallest index of refraction 63 (A) Interference is constructive when the path length difference is a whole number of wavelengths The second bright maximum occurs at a path length difference of 2λ 64 (E) Each of these statements is true 708 65 (E) During this process, the ice must first melt at a constant temperature according to the formula: Then the melted ice must rise in temperature by 50 K Keep in mind that even though the temperature is given in degrees Celsius, the difference in temperatures is required and the difference is the same for both the Celsius and Kelvin scales The sum of melting the ice and then heating the liquid water is 100,000 J 709 66 (C) For this process, the 10 grams of water (0.01 kg) must be boiled at its boilin g temperature of 100°C The heat required is given by the following formula at that constant temperature: 67 (E) Entropy always increases for an isolated system that is reaching equilibrium This is the second law of thermodynamics 710 68 (B) The amount of heat, Q, transferred through an object is inversely proportional to the length, L, that that heat must transverse while moving through the object as shown in the equation below Doubling the distance that heat must travel cuts the amount of heat transferred in half 711 69 (A) Adding heat to a system of gas is positive and removing heat is negative Doing work o n a system is positive while work done by the system is negative Use the first law of thermodynamics 70 (A) The current is directly proportional to the intensity of the light 71 (E) When the frequency of the light is increased, the energy of each photon is increased, E = hf Photons with higher energies will emit electrons with higher kinetic energies, K = hf − ϕ The ejected electrons arrive at the opposite plate of the photocell, creating a potential energy and a proportional potential difference between the plates of the photocell qV = K Therefore, increasing the frequency increases both the kinetic energy of the ejected electrons and the resulting voltage of the photocell 72 (E) Fusion results when there is an increase in the atomic number Hydrogen has an atomic number of 1, and helium has an atomic number of The fusing together of hydrogen atoms produces helium 73 (C) Isotopes have the same elemental symbol but a different number of neutrons Both of these forms of uranium have the same atomic number, 92, but their masses vary depending upon the number of neutrons Uranium-238 has 146 neutrons, while uranium-235 has 143 neutrons 74 (D) Adding neutrons adds to only the strong force Adding neutrons cannot add to the electrostatic force because neutrons have a neutral charge 75 (E) This is the definition of a transistor 712 ... events in the world of physics Format of the SAT Subject Examination in Physics The following bulleted list describes the overall format of the SAT Subject Test in Physics ■ The test is hour and consists... Contemporary Physics Historical Figures Contemporary Physics Practice Exercises Practice Tests Practice Test Diagnostic Chart Scoring Your Test Practice Test Diagnostic Chart Scoring Your Test Practice Test. .. key physics formulas and having a working knowledge of how to manipulate variables are crucial for success THE PHYSICS EXAM A complete outline of the contents of the SAT Subject Test in Physics