Introduction to SAT II Physics - FreeExamPapers

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Before we start writing down equations and plugging in numbers, we need to choose a coordinate system. This is usually not difficult, but it is vitally important. Let’s make the origin of the system the point where the ball is released from the student’s hand and begins its upward journey, and take the up direction to be positive and the down direction to be negative. We could have chosen other coordinate systems—for instance, we could have made the origin the ground on which the student is standing—but our choice of coordinate system is convenient because in it, = 0, so we won’t have to worry about plugging a value for into our equation. It’s usually possible, and a good idea, to choose a coordinate system that eliminates . Choosing the up direction as positive is simply more intuitive, and thus less likely to lead us astray. It’s generally wise also to choose your coordinate system so that more variables will be positive numbers than negative ones, simply because positive numbers are easier to deal with. WHAT IS THE BALL’S VELOCITY WHEN HE CATCHES IT? We can determine the answer to this question without any math at all. We know the initial velocity, m/s, and the acceleration due to gravity, m/s 2 , and we know that the displacement is x = 0 since the ball’s final position is back in the student’s hand where it started. We need to know the ball’s final velocity, v, so we should look at the kinematic equation that leaves out time, t: Because both x and are zero, the equation comes out to But don’t be hasty and give the answer as 12 m/s: remember that we devised our coordinate system in such a way that the down direction is negative, so the ball’s final velocity is –12 m/s. HOW HIGH DOES THE BALL TRAVEL? We know that at the top of the ball’s trajectory its velocity is zero. That means that we know that = 12 m/s, v = 0, and m/s 2 , and we need to solve for x: HOW LONG DOES IT TAKE THE BALL TO REACH ITS HIGHEST POINT? Having solved for x at the highest point in the trajectory, we now know all four of the other variables related to this point, and can choose any one of the five equations to solve for t. Let’s choose the one that leaves out x: 46
Note that there are certain convenient points in the ball’s trajectory where we can extract a third variable that isn’t mentioned explicitly in the question: we know that x = 0 when the ball is at the level of the student’s hand, and we know that v = 0 at the top of the ball’s trajectory. Two-Dimensional Motion with Uniform Acceleration If you’ve got the hang of 1-D motion, you should have no trouble at all with 2-D motion. The motion of any object moving in two dimensions can be broken into x- and y-components. Then it’s just a matter of solving two separate 1-D kinematic equations. The most common problems of this kind on SAT II Physics involve projectile motion: the motion of an object that is shot, thrown, or in some other way launched into the air. Note that the motion or trajectory of a projectile is a parabola. If we break this motion into x- and y-components, the motion becomes easy to understand. In the y direction, the ball is thrown upward with an initial velocity of and experiences a constant downward acceleration of g = –9.8 m/s 2 . This is exactly the kind of motion we examined in the previous section: if we ignore the x-component, the motion of a projectile is identical to the motion of an object thrown directly up in the air. In the x direction, the ball is thrown forward with an initial velocity of and there is no acceleration acting in the x direction to change this velocity. We have a very simple situation where and is constant. SAT II Physics will probably not expect you to do much calculating in questions dealing with projectile motion. Most likely, it will ask about the relative velocity of the projectile at different points in its trajectory. We can calculate the x- and y-components separately and then combine them to find the velocity of the projectile at any given point: 47
Page 1 and 2: SATII PHYSICS (FROM SPARKNOTES.COM)
Page 3 and 4: The Good • Because SAT II Subject
Page 5 and 6: Which SAT II Subject Tests to Take
Page 7 and 8: After grumbling, however, you still
Page 9 and 10: Waves 15-19% 11-15 Waves 10% 7-8 Op
Page 11 and 12: negative, so E, and not A, is the c
Page 13 and 14: including them anyway because it’
Page 15 and 16: Two positively charged particles, o
Page 17 and 18: will a visual representation reliev
Page 19 and 20: Physics Hint 6: Be Flexible Knowing
Page 21 and 22: There are a number of ways to label
Page 23 and 24: Adding Parallel Vectors If the vect
Page 25 and 26: The result of multiplying A by c is
Page 27 and 28: neither parallel nor perpendicular.
Page 29 and 30: Suppose the hands on a clock are ve
Page 31 and 32: Vector Addition Practice Questions
Page 33 and 34: 2. A The vector 2A has a magnitude
Page 35 and 36: path, Alan has traveled a much grea
Page 37 and 38: school student called Andrea. Andre
Page 39 and 40: centimeters to the left of its star
Page 41 and 42: We can learn two things about the a
Page 43 and 44: Acceleration vs. Time Graphs After
Page 45: The variable represents the object
Page 49 and 50: 1. . An athlete runs four laps of a
Page 51 and 52: 10. . A woman runs 40 m to the nort
Page 53 and 54: We know the total distance the spri
Page 55 and 56: Principles of Natural Philosophy. I
Page 57 and 58: The component form of Newton’s Se
Page 59 and 60: e in the direction. And since the s
Page 61 and 62: which reflects its resistance to be
Page 63 and 64: In the diagram above, the weight an
Page 65 and 66: A student pushes a box that weighs
Page 67 and 68: 1. . Each of the figures below show
Page 69 and 70: 7. . In the figure above, a person
Page 71 and 72: Since the block is motionless, the
Page 73 and 74: When we are told that a person push
Page 75 and 76: EXAMPLE A water balloon of mass m i
Page 77 and 78: The graph above plots the force exe
Page 79 and 80: Though energy is always measured in
Page 81 and 82: there is a negative amount of work
Page 83 and 84: smallest. The answer to question 3
Page 85 and 86: Mechanical Energy Average Power Ins
Page 87 and 88: to a height of 8 m over a time of 4
Page 89 and 90: 8. C When the book reaches the pers
Page 91 and 92: determining what those right number
Page 93 and 94: the ground. The system is initially
Page 95 and 96: 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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The torque that produces the angula
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The masses in the figure above are
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an object sliding down a frictionle
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Velocity Average Angular Accelerati
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3. . What is the direction of the a
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1. D An object that experiences 120
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At the top of the incline, the disk
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from a Latin word meaning “center
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Newton’s Law of Universal Gravita
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when you are beneath the surface of
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EXAMPLE A satellite of mass is laun
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Kepler’s Laws After poring over t
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Practice Questions Questions 1-3 re
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8. . A satellite orbits the Earth a
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Circumference and radius are relate
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learn how heat is transferred from
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heat, like rubber, have a high spec
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Just as specific heat tells us how
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Conduction is the transfer of heat
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Effectively, this equation tells us
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the way that it does. The Laws of T
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There are a number of equivalent fo
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If we know our formulas, this probl
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5. . An ideal gas is enclosed in a
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Asphalt, like most materials, has a
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The things we call atoms today are
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If they come up on SAT II Physics,
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will move in the opposite direction
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Work The work done to move a charge
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Much like gravitational potential e
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3. . A particle of charge +2q exert
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7. . A particle of charge +q is a d
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The vector sum of the three vectors
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Voltage The batteries we use in fla
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This equation tells us that we can
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If the two variables you know are a
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However, each resistor causes a vol
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So = 4 . WHAT IS THE CURRENT RUNNIN
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Consider again the circuit whose to
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This circuit consists of resistors
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The junction rule deals with “jun
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across the loop. We can express the
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capacitance is halved. The proporti
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The Greek letter is called the diel
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4. . Two resistors, and , are ident
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10. . A dielectric is inserted into
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The equivalent capacitance of two c
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The Earth itself acts like a huge b
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Because the velocity vector and the
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A particle with a positive charge o
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The constant is called the permeabi
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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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