Introduction to SAT II Physics - FreeExamPapers

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Special Problems in Mechanics THE “SPECIAL PROBLEMS” WE WILL address in this chapter deal with four common mechanical systems: pulleys, inclined planes, springs, and pendulums. These systems pop up on many mechanics problems on SAT II Physics, and it will save you time and points if you familiarize yourself with their quirks. These systems obey the same mechanical rules as the rest of the world, and we will only introduce one principle (Hooke’s Law) that hasn’t been covered in the previous three chapters. However, there are a number of problem-solving techniques that are particular to these sorts of problems, and mastering them will help you get through these problems quickly and easily. The Three-Step Approach to Problem Solving The systems we will look at in this chapter won’t test your knowledge of obscure formulas so much as your problem-solving abilities. The actual physics at work on these systems is generally quite simple—it rarely extends beyond Newton’s three laws and a basic understanding of work and energy—but you’ll need to apply this simple physics in imaginative ways. There are three general steps you can take when approaching any problem in mechanics. Often the problems are simple enough that these steps are unnecessary. However, with the special problems we will tackle in this chapter, following these steps carefully may save you many times over on SAT II Physics. The three steps are: 1. Ask yourself how the system will move: Before you start writing down equations and looking at answer choices, you should develop an intuitive sense of what you’re looking at. In what direction will the objects in the system move? Will they move at all? Once you know what you’re dealing with, you’ll have an easier time figuring out how to approach the problem. 2. Choose a coordinate system: Most systems will only move in one dimension: up and down, left and right, or on an angle in the case of inclined planes. Choose a coordinate system where one direction is negative, the other direction is positive, and, if necessary, choose an origin point that you label 0. Remember: no coordinate system is right or wrong in itself, some are just more convenient than others. The important thing is to be strictly consistent once you’ve chosen a coordinate system, and to be mindful of those subtle but crucial minus signs! 3. Draw free-body diagrams: Most students find mechanics easier than electromagnetism for the simple reason that mechanics problems are easy to visualize. Free-body diagrams allow you to make the most of this advantage. Make sure you’ve accounted for all the forces acting on all the bodies in the system. Make ample use of Newton’s Third Law, and remember that for systems at rest or at a constant velocity, the net force acting on every body in the system must be zero. Students too often think that physics problem solving is just a matter of plugging the right numbers into the right equations. The truth is, physics problem solving is more a matter of 90
determining what those right numbers and right equations are. These three steps should help you do just that. Let’s look at some mechanical systems. Pulleys Pulleys are simple machines that consist of a rope that slides around a disk, called a block. Their main function is to change the direction of the tension force in a rope. The pulley systems that appear on SAT II Physics almost always consist of idealized, massless and frictionless pulleys, and idealized ropes that are massless and that don’t stretch. These somewhat unrealistic parameters mean that: 1. The rope slides without any resistance over the pulley, so that the pulley changes the direction of the tension force without changing its magnitude. 2. You can apply the law of conservation of energy to the system without worrying about the energy of the rope and pulley. 3. You don’t have to factor in the mass of the pulley or rope when calculating the effect of a force exerted on an object attached to a pulley system. The one exception to this rule is the occasional problem you might find regarding the torque applied to a pulley block. In such a problem, you will have to take the pulley’s mass into account. We’ll deal with this special case in Chapter 7, when we look at torque. The Purpose of Pulleys 91
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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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Page 43 and 44: Acceleration vs. Time Graphs After
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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
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Page 55 and 56: Principles of Natural Philosophy. I
Page 57 and 58: The component form of Newton’s Se
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Page 63 and 64: In the diagram above, the weight an
Page 65 and 66: A student pushes a box that weighs
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Page 75 and 76: EXAMPLE A water balloon of mass m i
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Page 101 and 102: Adding these two equations together
Page 103 and 104: force of friction: . Using Newton
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Page 109 and 110: of the spring due to the gravitatio
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Page 113 and 114: Velocity Calculating the velocity o
Page 115 and 116: Practice Questions 1. . Two masses,
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Page 119 and 120: Since the system is in equilibrium,
Page 121 and 122: velocity, v. Linear momentum is den
Page 123 and 124: Conservation of Momentum If we comb
Page 125 and 126: As we might expect, the final veloc
Page 127 and 128: A pool player hits the eight ball,
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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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