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magnitude of the force of kinetic friction on an object, are both proportional to the normal force acting on the object in question. We can express this proportionality mathematically as follows: where is the coefficient of kinetic friction, is the coefficient of static friction, and N is the magnitude of the normal force. The coefficients of kinetic and static friction are constants of proportionality that vary from object to object. Note that the equation for static friction is for the maximum value of the static friction. This is because the force of static friction is never greater than the force pushing on an object. If a box has a mass of 10 kg and = 0.5, then: If you push this box with a force less than 49 newtons, the box will not move, and consequently the net force on the box must be zero. If an applied force is less than , then = – . Three Reminders Whenever you need to calculate a frictional force on SAT II Physics, you will be told the value of , which will fall between 0 and 1. Three things are worth noting about frictional forces: 1. The smaller µ is, the more slippery the surface. For instance, ice will have much lower coefficients of friction than Velcro. In cases where , the force of friction is zero, which is the case on ideal frictionless surfaces. 2. The coefficient of kinetic friction is smaller than the coefficient of static friction. That means it takes more force to start a stationary object moving than to keep it in motion. The reverse would be illogical: imagine if you could push on an object with a force greater than the maximum force of static friction but less than the force of kinetic friction. That would mean you could push it hard enough to get it to start moving, but as soon as it starts moving, the force of kinetic friction would push it backward. 3. Frictional forces are directly proportional to the normal force. That’s why it’s harder to slide a heavy object along the floor than a light one. A light coin can slide several meters across a table because the kinetic friction, proportional to the normal force, is quite small. EXAMPLE 64
A student pushes a box that weighs 15 N with a force of 10 N at a 60Âº angle to the perpendicular. The maximum coefficient of static friction between the box and the floor is 0.4. Does the box move? Note that sin 60Âº = 0.866 and cos 60Âº = 0.500. In order to solve this problem, we have to determine whether the horizontal component of is of greater magnitude than the maximum force of static friction. We can break the vector into horizontal and vertical components. The vertical component will push the box harder into the floor, increasing the normal force, while the horizontal component will push against the force of static friction. First, let’s calculate the vertical component of the force so that we can determine the normal force, N, of the box: If we add this force to the weight of the box, we find that the normal force is 15 + 5.0 = 20 N. Thus, the maximum force of static friction is: The force pushing the box forward is the horizontal component of , which is: As we can see, this force is just slightly greater than the maximum force of static friction opposing the push, so the box will slide forward. Tension Consider a box being pulled by a rope. The person pulling one end of the rope is not in contact with the box, yet we know from experience that the box will move in the direction that the rope is pulled. This occurs because the force the person exerts on the rope is transmitted to the box. The force exerted on the box from the rope is called the tension force, and comes into play whenever a force is transmitted across a rope or a cable. The free-body diagram below shows us a box being pulled by a rope, where W is the weight of the box, N is the normal force, T is the tension force, and is the frictional force. 65
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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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Page 19 and 20: Physics Hint 6: Be Flexible Knowing
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Page 23 and 24: Adding Parallel Vectors If the vect
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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
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Page 41 and 42: We can learn two things about the a
Page 43 and 44: Acceleration vs. Time Graphs After
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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: In the diagram above, the weight an
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
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Page 75 and 76: EXAMPLE A water balloon of mass m i
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Page 89 and 90: 8. C When the book reaches the pers
Page 91 and 92: determining what those right number
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Page 95 and 96: calculators, you almost certainly w
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Page 99 and 100: 2. WHAT IS THE ACCELERATION OF THE
Page 101 and 102: Adding these two equations together
Page 103 and 104: force of friction: . Using Newton
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Page 107 and 108: Frequency is given in units of cycl
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Page 111 and 112: The oscillation of a pendulum is mu
Page 113 and 114: 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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