Introduction to SAT II Physics - FreeExamPapers

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Curved Position vs. Time Graphs This is all well and good, but how do you calculate the velocity of a curved position vs. time graph? Well, the bad news is that you’d need calculus. The good news is that SAT II Physics doesn’t expect you to use calculus, so if you are given a curved position vs. time graph, you will only be asked qualitative questions and won’t be expected to make any calculations. A few points on the graph will probably be labeled, and you will have to identify which point has the greatest or least velocity. Remember, the point with the greatest slope has the greatest velocity, and the point with the least slope has the least velocity. The turning points of the graph, the tops of the “hills” and the bottoms of the “valleys” where the slope is zero, have zero velocity. In this graph, for example, the velocity is zero at points A and C, greatest at point D, and smallest at point B. The velocity at point B is smallest because the slope at that point is negative. Because velocity is a vector quantity, the velocity at B would be a large negative number. However, the speed at B is greater even than the speed at D: speed is a scalar quantity, and so it is always positive. The slope at B is even steeper than at D, so the speed is greatest at B. Velocity vs. Time Graphs Velocity vs. time graphs are the most eloquent kind of graph we’ll be looking at here. They tell us very directly what the velocity of an object is at any given time, and they provide subtle means for determining both the position and acceleration of the same object over time. The “object” whose velocity is graphed below is our ever-industrious ant, a little later in the day. 40
We can learn two things about the ant’s velocity by a quick glance at the graph. First, we can tell exactly how fast it is going at any given time. For instance, we can see that, two seconds after it started to move, the ant is moving at 2 cm/s. Second, we can tell in which direction the ant is moving. From t = 0 to t = 4, the velocity is positive, meaning that the ant is moving to the right. From t = 4 to t = 7, the velocity is negative, meaning that the ant is moving to the left. Calculating Acceleration We can calculate acceleration on a velocity vs. time graph in the same way that we calculate velocity on a position vs. time graph. Acceleration is the rate of change of the velocity vector, , which expresses itself as the slope of the velocity vs. time graph. For a velocity vs. time graph, the acceleration at time t is equal to the slope of the line at t. What is the acceleration of our ant at t = 2.5 and t = 4? Looking quickly at the graph, we see that the slope of the line at t = 2.5 is zero and hence the acceleration is likewise zero. The slope of the graph between t = 3 and t = 5 is constant, so we can calculate the acceleration at t = 4 by calculating the average acceleration between t = 3 and t = 5: The minus sign tells us that acceleration is in the leftward direction, since we’ve defined the y- coordinates in such a way that right is positive and left is negative. At t = 3, the ant is moving to the right at 2 cm/s, so a leftward acceleration means that the ant begins to slow down. Looking at the graph, we can see that the ant comes to a stop at t = 4, and then begins accelerating to the right. Calculating Displacement Velocity vs. time graphs can also tell us about an object’s displacement. Because velocity is a measure of displacement over time, we can infer that: Graphically, this means that the displacement in a given time interval is equal to the area under the graph during that same time interval. If the graph is above the t-axis, then the positive 41
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: centimeters to the left of its star
Page 43 and 44: Acceleration vs. Time Graphs After
Page 45 and 46: The variable represents the object
Page 47 and 48: Note that there are certain conveni
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
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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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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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