Assignment 5 Due: 11:59pm on Wednesday, March 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 6.13 A hand presses down on the book in the figure. Part A Is the normal force of the table on the book larger than, smaller than, or equal to ? ANSWER: Correct mg Equal to Larger than Smaller than mg mg mg Problem 6.2 The three ropes in the figure are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. Part A What is the magnitude of the tension in the third rope? Express your answer using two significant figures. ANSWER: Correct Part B What is the direction of the tension in the third rope? Express your answer using two significant figures. T  3 T3 = 94 N T  3 Typesetting math: 100% ANSWER: Correct The Normal Force When an object rests on a surface, there is always a force perpendicular to the surface; we call this the normal force, denoted by . The two questions to the right will explore the normal force. Part A A man attempts to pick up his suitcase of weight by pulling straight up on the handle. However, he is unable to lift the suitcase from the floor. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man pulls upward on the suitcase? Hint 1. How to approach this problem First, identify the forces that act on the suitcase and draw a free-body diagram. Then use the fact that the suitcase is in equilibrium, , to examine how the forces acting on the suitcase relate to each other. Hint 2. Identify the correct free-body diagram Which of the figures represents the free-body diagram of the suitcase while the man is pulling on the handle with a force of magnitude ? = 58   below horizontal n ws n F = 0 fpull Typesetting math: 100% ANSWER: ANSWER: Correct Part B A B C D The magnitude of the normal force is equal to the magnitude of the weight of the suitcase. The magnitude of the normal force is equal to the magnitude of the weight of the suitcase minus the magnitude of the force of the pull. The magnitude of the normal force is equal to the sum of the magnitude of the force of the pull and the magnitude of the suitcase’s weight. The magnitude of the normal force is greater than the magnitude of the weight of the suitcase. Typesetting math: 100% Now assume that the man of weight is tired and decides to sit on his suitcase. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man is sitting on the suitcase? Hint 1. Identify the correct free-body diagram. Which of the figures represents the free-body diagram while the man is sitting atop the suitcase? Here the vector labeled is a force that has the same magnitude as the man’s weight. ANSWER: wm n wm Typesetting math: 100% ANSWER: Correct Recognize that the normal force acting on an object is not always equal to the weight of that object. This is an important point to understand. Problem 6.5 A construction worker with a weight of 880 stands on a roof that is sloped at 18 . Part A What is the magnitude of the normal force of the roof on the worker? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct A B C D The magnitude of the normal force is equal to the magnitude of the suitcase’s weight. The magnitude of the normal force is equal to the magnitude of the suitcase’s weight minus the magnitude of the man’s weight. The magnitude of the normal force is equal to the sum of the magnitude of the man’s weight and the magnitude of the suitcase’s weight. The magnitude of the normal force is less than the magnitude of the suitcase’s weight. N  n = 840 N Typesetting math: 100% Problem 6.6 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B For diagram the part A, find the value of the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: kg ax x ax = -0.67 m s2 ay, y Typesetting math: 100% Correct Part C For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D For diagram the part C, find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: ay = 0 m s2 ax x ax = 0.67 m s2 ay y Typesetting math: 100% Correct Problem 6.7 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay = 0 m s2 kg ax x ax = 0.99 m s2 Typesetting math: 100% Part B Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay y ay = 0 m s2 ax x ax = -0.18 m s2 ay y ay = 0 m s2 Typesetting math: 100% Problem 6.10 A horizontal rope is tied to a 53.0 box on frictionless ice. What is the tension in the rope if: Part A The box is at rest? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B The box moves at a steady = 4.80 ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C The box = 4.80 and = 4.60 ? Express your answer to three significant figures and include the appropriate units. ANSWER: kg T = 0 N vx m/s T = 0 N vx m/s ax m/s2 Typesetting math: 100% Correct Problem 6.14 It takes the elevator in a skyscraper 4.5 to reach its cruising speed of 11 . A 60 passenger gets aboard on the ground floor. Part A What is the passenger’s weight before the elevator starts moving? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the passenger’s weight while the elevator is speeding up? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the passenger’s weight after the elevator reaches its cruising speed? T = 244 N s m/s kg w = 590 N w = 730 N Typesetting math: 100% Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Block on an Incline A block lies on a plane raised an angle from the horizontal. Three forces act upon the block: , the force of gravity; , the normal force; and , the force of friction. The coefficient of friction is large enough to prevent the block from sliding . Part A Consider coordinate system a, with the x axis along the plane. Which forces lie along the axes? ANSWER: w = 590 N  F  w F n F  f Typesetting math: 100% Correct Part B Which forces lie along the axes of the coordinate system b, in which the y axis is vertical? ANSWER: Correct only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w Typesetting math: 100% Usually the best advice is to choose coordinate system so that the acceleration of the system is directly along one of the coordinate axes. If the system isn’t accelerating, then you are better off choosing the coordinate system with the most vectors along the coordinate axes. But now you are going to ignore that advice. You will find the normal force, , using vertical coordinate system b. In these coordinates you will find the magnitude appearing in both the x and y equations, each multiplied by a trigonometric function. Part C Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the y-axis is also , as shown in the figure. ANSWER: F  n Fn Fn Ff Fw  F n Fny F  n Fn  F  n  Typesetting math: 100% Hint 2. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the x-axis is also , as shown in the figure. ANSWER: ANSWER: Fny = Fncos() F f Ffy F f Ff  F  f  Ffy = Ffsin() Fy = 0 = Fncos() + Ffsin() − Fw Typesetting math: 100% Correct Part D Because the block is not moving, the sum of the x components of the forces acting on the block must be zero. Find an expression for the sum of the x components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the x component of Write an expression for , the x component of the force , using coordinate system b. Express your answer in terms of and . ANSWER: ANSWER: Correct Part E To find the magnitude of the normal force, you must express in terms of since is an unknown. Using the equations you found in the two previous parts, find an expression for involving and but not . Hint 1. How to approach the problem From your answers to the previous two parts you should have two force equations ( and ). Combine these equations to eliminate . The key is to multiply the Fn Ff Fw  F n Fnx F  n Fn  Fnx = −Fnsin() Fx = 0 = −Fnsin() + Ffcos() Fn Fw Ff Fn Fw  Ff Typesetting math: 100% Fy = 0 Fx = 0 Ff equation for the y components by and the equation for the x components by , then add or subtract the two equations to eliminate the term . An alternative motivation for the algebra is to eliminate the trig functions in front of by using the trig identity . At the very least this would result in an equation that is simple to solve for . ANSWER: Correct Congratulations on working this through. Now realize that in coordinate system a, which is aligned with the plane, the y-coordinate equation is , which leads immediately to the result obtained here for . CONCLUSION: A thoughtful examination of which coordinate system to choose can save a lot of algebra. Contact Forces Introduced Learning Goal: To introduce contact forces (normal and friction forces) and to understand that, except for friction forces under certain circumstances, these forces must be determined from: net Force = ma. Two solid objects cannot occupy the same space at the same time. Indeed, when the objects touch, they exert repulsive normal forces on each other, as well as frictional forces that resist their slipping relative to each other. These contact forces arise from a complex interplay between the electrostatic forces between the electrons and ions in the objects and the laws of quantum mechanics. As two surfaces are pushed together these forces increase exponentially over an atomic distance scale, easily becoming strong enough to distort the bulk material in the objects if they approach too close. In everyday experience, contact forces are limited by the deformation or acceleration of the objects, rather than by the fundamental interatomic forces. Hence, we can conclude the following: The magnitude of contact forces is determined by , that is, by the other forces on, and acceleration of, the contacting bodies. The only exception is that the frictional forces cannot exceed (although they can be smaller than this or even zero). Normal and friction forces Two types of contact forces operate in typical mechanics problems, the normal and frictional forces, usually designated by and (or , or something similar) respectively. These are the components of the overall contact force: perpendicular to and parallel to the plane of contact. Kinetic friction when surfaces slide cos  sin  Ff cos() sin() Fn sin2() + cos2 () = 1 Fn Fn = Fwcos() Fy = Fn − FW cos() = 0 Fn F = ma μn n f Ffric n f Typesetting math: 100% When one surface is sliding past the other, experiments show three things about the friction force (denoted ): The frictional force opposes the relative motion at the 1. point of contact, 2. is proportional to the normal force, and 3. the ratio of the magnitude of the frictional force to that of the normal force is fairly constant over a wide range of speeds. The constant of proportionality is called the coefficient of kinetic friction, often designated . As long as the sliding continues, the frictional force is then (valid when the surfaces slide by each other). Static friction when surfaces don’t slide When there is no relative motion of the surfaces, the frictional force can assume any value from zero up to a maximum , where is the coefficient of static friction. Invariably, is larger than , in agreement with the observation that when a force is large enough that something breaks loose and starts to slide, it often accelerates. The frictional force for surfaces with no relative motion is therefore (valid when the contacting surfaces have no relative motion). The actual magnitude and direction of the static friction force are such that it (together with other forces on the object) causes the object to remain motionless with respect to the contacting surface as long as the static friction force required does not exceed . The equation is valid only when the surfaces are on the verge of sliding. Part A When two objects slide by one another, which of the following statements about the force of friction between them, is true? ANSWER: Correct Part B fk fk μk fk = μkn μsn μs μs μk fs ! μsn μsn fs = μsn The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μkn μkn μkn Typesetting math: 100% When two objects are in contact with no relative motion, which of the following statements about the frictional force between them, is true? ANSWER: Correct For static friction, the actual magnitude and direction of the friction force are such that it, together with any other forces present, will cause the object to have the observed acceleration. The magnitude of the force cannot exceed . If the magnitude of static friction needed to keep acceleration equal to zero exceeds , then the object will slide subject to the resistance of kinetic friction. Do not automatically assume that unless you are considering a situation in which the magnitude of the static friction force is as large as possible (i.e., when determining at what point an object will just begin to slip). Whether the actual magnitude of the friction force is 0, less than , or equal to depends on the magnitude of the other forces (if any) as well as the acceleration of the object through . Part C When a board with a box on it is slowly tilted to larger and larger angle, common experience shows that the box will at some point “break loose” and start to accelerate down the board. The box begins to slide once the component of gravity acting parallel to the board just begins to exceeds the maximum force of static friction. Which of the following is the most general explanation for why the box accelerates down the board? ANSWER: The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μsn μsn μsn μsn μsn fs = μsn μsn μsn F = ma Fg The force of kinetic friction is smaller than that of maximum static friction, but remains the same. Once the box is moving, is smaller than the force of maximum static friction but larger than the force of kinetic friction. Once the box is moving, is larger than the force of maximum static friction. When the box is stationary, equals the force of static friction, but once the box starts moving, the sliding reduces the normal force, which in turn reduces the friction. Fg Fg Fg Fg Typesetting math: 100% Correct At the point when the box finally does “break loose,” you know that the component of the box’s weight that is parallel to the board just exceeds (i.e., this component of gravitational force on the box has just reached a magnitude such that the force of static friction, which has a maximum value of , can no longer oppose it.) For the box to then accelerate, there must be a net force on the box along the board. Thus, the component of the box’s weight parallel to the board must be greater than the force of kinetic friction. Therefore the force of kinetic friction must be less than the force of static friction which implies , as expected. Part D Consider a problem in which a car of mass is on a road tilted at an angle . The normal force Select the best answer. ANSWER: Correct The key point is that contact forces must be determined from Newton’s equation. In the problem described above, there is not enough information given to determine the normal force (e.g., the acceleration is unknown). Each of the answer options is valid under some conditions ( , the car is sliding down an icy incline, or the car is going around a banked turn), but in fact none is likely to be correct if there are other forces on the car or if the car is accelerating. Do not memorize values for the normal force valid in different problems–you must determine from . Problem 6.17 Bonnie and Clyde are sliding a 323 bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 375 of force while Bonnie pulls forward on a rope with 335 of force. μsn μsn μkn μsn μk < μs M  is found using n = Mg n = Mg cos() n = Mg cos() F  = Ma  = 0 n F = ma kg N N Typesetting math: 100% Part A What is the safe's coefficient of kinetic friction on the bank floor? ANSWER: Correct Problem 6.19 A crate is placed on a horizontal conveyor belt. The materials are such that and . Part A Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: 0.224 10 kg μs = 0.5 μk = 0.3 Typesetting math: 100% Correct Part B Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Part C What is the maximum acceleration the belt can have without the crate slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct amax = 4.9 m s2 Typesetting math: 100% Problem 6.28 A 1100 steel beam is supported by two ropes. Part A What is the tension in rope 1? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. ANSWER: kg T1 = 7000 N Typesetting math: 100% Correct Problem 6.35 The position of a 1.4 mass is given by , where is in seconds. Part A What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.39 T2 = 4800 N kg x = (2t3 − 3t2 )m t t = 0 s F = -8.4 N t = 1 s F = 8.4 N Typesetting math: 100% A rifle with a barrel length of 61 fires a 8 bullet with a horizontal speed of 400 . The bullet strikes a block of wood and penetrates to a depth of 11 . Part A What resistive force (assumed to be constant) does the wood exert on the bullet? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How long does it take the bullet to come to rest after entering the wood? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.45 You and your friend Peter are putting new shingles on a roof pitched at 21 . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0 away, asks you for the box of nails. Rather than carry the 2.0 box of nails down to Peter, you decide to give the box a push and have it slide down to him. Part A If the coefficient of kinetic friction between the box and the roof is 0.55, with what speed should you push the box to have it gently come to rest right at the edge of the roof? Express your answer to two significant figures and include the appropriate units. cm g m/s cm fk = 5800 N = 5.5×10−4 t s  m kg Typesetting math: 100% ANSWER: Correct Problem 6.54 The 2.0 wood box in the figure slides down a vertical wood wall while you push on it at a 45 angle. Part A What magnitude of force should you apply to cause the box to slide down at a constant speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct v = 3.9 ms kg  F = 23 N Typesetting math: 100% Score Summary: Your score on this assignment is 98.8%. You received 114.57 out of a possible total of 116 points. Typesetting math: 100%

Assignment 5 Due: 11:59pm on Wednesday, March 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 6.13 A hand presses down on the book in the figure. Part A Is the normal force of the table on the book larger than, smaller than, or equal to ? ANSWER: Correct mg Equal to Larger than Smaller than mg mg mg Problem 6.2 The three ropes in the figure are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. Part A What is the magnitude of the tension in the third rope? Express your answer using two significant figures. ANSWER: Correct Part B What is the direction of the tension in the third rope? Express your answer using two significant figures. T  3 T3 = 94 N T  3 Typesetting math: 100% ANSWER: Correct The Normal Force When an object rests on a surface, there is always a force perpendicular to the surface; we call this the normal force, denoted by . The two questions to the right will explore the normal force. Part A A man attempts to pick up his suitcase of weight by pulling straight up on the handle. However, he is unable to lift the suitcase from the floor. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man pulls upward on the suitcase? Hint 1. How to approach this problem First, identify the forces that act on the suitcase and draw a free-body diagram. Then use the fact that the suitcase is in equilibrium, , to examine how the forces acting on the suitcase relate to each other. Hint 2. Identify the correct free-body diagram Which of the figures represents the free-body diagram of the suitcase while the man is pulling on the handle with a force of magnitude ? = 58   below horizontal n ws n F = 0 fpull Typesetting math: 100% ANSWER: ANSWER: Correct Part B A B C D The magnitude of the normal force is equal to the magnitude of the weight of the suitcase. The magnitude of the normal force is equal to the magnitude of the weight of the suitcase minus the magnitude of the force of the pull. The magnitude of the normal force is equal to the sum of the magnitude of the force of the pull and the magnitude of the suitcase’s weight. The magnitude of the normal force is greater than the magnitude of the weight of the suitcase. Typesetting math: 100% Now assume that the man of weight is tired and decides to sit on his suitcase. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man is sitting on the suitcase? Hint 1. Identify the correct free-body diagram. Which of the figures represents the free-body diagram while the man is sitting atop the suitcase? Here the vector labeled is a force that has the same magnitude as the man’s weight. ANSWER: wm n wm Typesetting math: 100% ANSWER: Correct Recognize that the normal force acting on an object is not always equal to the weight of that object. This is an important point to understand. Problem 6.5 A construction worker with a weight of 880 stands on a roof that is sloped at 18 . Part A What is the magnitude of the normal force of the roof on the worker? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct A B C D The magnitude of the normal force is equal to the magnitude of the suitcase’s weight. The magnitude of the normal force is equal to the magnitude of the suitcase’s weight minus the magnitude of the man’s weight. The magnitude of the normal force is equal to the sum of the magnitude of the man’s weight and the magnitude of the suitcase’s weight. The magnitude of the normal force is less than the magnitude of the suitcase’s weight. N  n = 840 N Typesetting math: 100% Problem 6.6 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B For diagram the part A, find the value of the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: kg ax x ax = -0.67 m s2 ay, y Typesetting math: 100% Correct Part C For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D For diagram the part C, find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: ay = 0 m s2 ax x ax = 0.67 m s2 ay y Typesetting math: 100% Correct Problem 6.7 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay = 0 m s2 kg ax x ax = 0.99 m s2 Typesetting math: 100% Part B Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay y ay = 0 m s2 ax x ax = -0.18 m s2 ay y ay = 0 m s2 Typesetting math: 100% Problem 6.10 A horizontal rope is tied to a 53.0 box on frictionless ice. What is the tension in the rope if: Part A The box is at rest? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B The box moves at a steady = 4.80 ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C The box = 4.80 and = 4.60 ? Express your answer to three significant figures and include the appropriate units. ANSWER: kg T = 0 N vx m/s T = 0 N vx m/s ax m/s2 Typesetting math: 100% Correct Problem 6.14 It takes the elevator in a skyscraper 4.5 to reach its cruising speed of 11 . A 60 passenger gets aboard on the ground floor. Part A What is the passenger’s weight before the elevator starts moving? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the passenger’s weight while the elevator is speeding up? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the passenger’s weight after the elevator reaches its cruising speed? T = 244 N s m/s kg w = 590 N w = 730 N Typesetting math: 100% Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Block on an Incline A block lies on a plane raised an angle from the horizontal. Three forces act upon the block: , the force of gravity; , the normal force; and , the force of friction. The coefficient of friction is large enough to prevent the block from sliding . Part A Consider coordinate system a, with the x axis along the plane. Which forces lie along the axes? ANSWER: w = 590 N  F  w F n F  f Typesetting math: 100% Correct Part B Which forces lie along the axes of the coordinate system b, in which the y axis is vertical? ANSWER: Correct only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w Typesetting math: 100% Usually the best advice is to choose coordinate system so that the acceleration of the system is directly along one of the coordinate axes. If the system isn’t accelerating, then you are better off choosing the coordinate system with the most vectors along the coordinate axes. But now you are going to ignore that advice. You will find the normal force, , using vertical coordinate system b. In these coordinates you will find the magnitude appearing in both the x and y equations, each multiplied by a trigonometric function. Part C Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the y-axis is also , as shown in the figure. ANSWER: F  n Fn Fn Ff Fw  F n Fny F  n Fn  F  n  Typesetting math: 100% Hint 2. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the x-axis is also , as shown in the figure. ANSWER: ANSWER: Fny = Fncos() F f Ffy F f Ff  F  f  Ffy = Ffsin() Fy = 0 = Fncos() + Ffsin() − Fw Typesetting math: 100% Correct Part D Because the block is not moving, the sum of the x components of the forces acting on the block must be zero. Find an expression for the sum of the x components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the x component of Write an expression for , the x component of the force , using coordinate system b. Express your answer in terms of and . ANSWER: ANSWER: Correct Part E To find the magnitude of the normal force, you must express in terms of since is an unknown. Using the equations you found in the two previous parts, find an expression for involving and but not . Hint 1. How to approach the problem From your answers to the previous two parts you should have two force equations ( and ). Combine these equations to eliminate . The key is to multiply the Fn Ff Fw  F n Fnx F  n Fn  Fnx = −Fnsin() Fx = 0 = −Fnsin() + Ffcos() Fn Fw Ff Fn Fw  Ff Typesetting math: 100% Fy = 0 Fx = 0 Ff equation for the y components by and the equation for the x components by , then add or subtract the two equations to eliminate the term . An alternative motivation for the algebra is to eliminate the trig functions in front of by using the trig identity . At the very least this would result in an equation that is simple to solve for . ANSWER: Correct Congratulations on working this through. Now realize that in coordinate system a, which is aligned with the plane, the y-coordinate equation is , which leads immediately to the result obtained here for . CONCLUSION: A thoughtful examination of which coordinate system to choose can save a lot of algebra. Contact Forces Introduced Learning Goal: To introduce contact forces (normal and friction forces) and to understand that, except for friction forces under certain circumstances, these forces must be determined from: net Force = ma. Two solid objects cannot occupy the same space at the same time. Indeed, when the objects touch, they exert repulsive normal forces on each other, as well as frictional forces that resist their slipping relative to each other. These contact forces arise from a complex interplay between the electrostatic forces between the electrons and ions in the objects and the laws of quantum mechanics. As two surfaces are pushed together these forces increase exponentially over an atomic distance scale, easily becoming strong enough to distort the bulk material in the objects if they approach too close. In everyday experience, contact forces are limited by the deformation or acceleration of the objects, rather than by the fundamental interatomic forces. Hence, we can conclude the following: The magnitude of contact forces is determined by , that is, by the other forces on, and acceleration of, the contacting bodies. The only exception is that the frictional forces cannot exceed (although they can be smaller than this or even zero). Normal and friction forces Two types of contact forces operate in typical mechanics problems, the normal and frictional forces, usually designated by and (or , or something similar) respectively. These are the components of the overall contact force: perpendicular to and parallel to the plane of contact. Kinetic friction when surfaces slide cos  sin  Ff cos() sin() Fn sin2() + cos2 () = 1 Fn Fn = Fwcos() Fy = Fn − FW cos() = 0 Fn F = ma μn n f Ffric n f Typesetting math: 100% When one surface is sliding past the other, experiments show three things about the friction force (denoted ): The frictional force opposes the relative motion at the 1. point of contact, 2. is proportional to the normal force, and 3. the ratio of the magnitude of the frictional force to that of the normal force is fairly constant over a wide range of speeds. The constant of proportionality is called the coefficient of kinetic friction, often designated . As long as the sliding continues, the frictional force is then (valid when the surfaces slide by each other). Static friction when surfaces don’t slide When there is no relative motion of the surfaces, the frictional force can assume any value from zero up to a maximum , where is the coefficient of static friction. Invariably, is larger than , in agreement with the observation that when a force is large enough that something breaks loose and starts to slide, it often accelerates. The frictional force for surfaces with no relative motion is therefore (valid when the contacting surfaces have no relative motion). The actual magnitude and direction of the static friction force are such that it (together with other forces on the object) causes the object to remain motionless with respect to the contacting surface as long as the static friction force required does not exceed . The equation is valid only when the surfaces are on the verge of sliding. Part A When two objects slide by one another, which of the following statements about the force of friction between them, is true? ANSWER: Correct Part B fk fk μk fk = μkn μsn μs μs μk fs ! μsn μsn fs = μsn The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μkn μkn μkn Typesetting math: 100% When two objects are in contact with no relative motion, which of the following statements about the frictional force between them, is true? ANSWER: Correct For static friction, the actual magnitude and direction of the friction force are such that it, together with any other forces present, will cause the object to have the observed acceleration. The magnitude of the force cannot exceed . If the magnitude of static friction needed to keep acceleration equal to zero exceeds , then the object will slide subject to the resistance of kinetic friction. Do not automatically assume that unless you are considering a situation in which the magnitude of the static friction force is as large as possible (i.e., when determining at what point an object will just begin to slip). Whether the actual magnitude of the friction force is 0, less than , or equal to depends on the magnitude of the other forces (if any) as well as the acceleration of the object through . Part C When a board with a box on it is slowly tilted to larger and larger angle, common experience shows that the box will at some point “break loose” and start to accelerate down the board. The box begins to slide once the component of gravity acting parallel to the board just begins to exceeds the maximum force of static friction. Which of the following is the most general explanation for why the box accelerates down the board? ANSWER: The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μsn μsn μsn μsn μsn fs = μsn μsn μsn F = ma Fg The force of kinetic friction is smaller than that of maximum static friction, but remains the same. Once the box is moving, is smaller than the force of maximum static friction but larger than the force of kinetic friction. Once the box is moving, is larger than the force of maximum static friction. When the box is stationary, equals the force of static friction, but once the box starts moving, the sliding reduces the normal force, which in turn reduces the friction. Fg Fg Fg Fg Typesetting math: 100% Correct At the point when the box finally does “break loose,” you know that the component of the box’s weight that is parallel to the board just exceeds (i.e., this component of gravitational force on the box has just reached a magnitude such that the force of static friction, which has a maximum value of , can no longer oppose it.) For the box to then accelerate, there must be a net force on the box along the board. Thus, the component of the box’s weight parallel to the board must be greater than the force of kinetic friction. Therefore the force of kinetic friction must be less than the force of static friction which implies , as expected. Part D Consider a problem in which a car of mass is on a road tilted at an angle . The normal force Select the best answer. ANSWER: Correct The key point is that contact forces must be determined from Newton’s equation. In the problem described above, there is not enough information given to determine the normal force (e.g., the acceleration is unknown). Each of the answer options is valid under some conditions ( , the car is sliding down an icy incline, or the car is going around a banked turn), but in fact none is likely to be correct if there are other forces on the car or if the car is accelerating. Do not memorize values for the normal force valid in different problems–you must determine from . Problem 6.17 Bonnie and Clyde are sliding a 323 bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 375 of force while Bonnie pulls forward on a rope with 335 of force. μsn μsn μkn μsn μk < μs M  is found using n = Mg n = Mg cos() n = Mg cos() F  = Ma  = 0 n F = ma kg N N Typesetting math: 100% Part A What is the safe's coefficient of kinetic friction on the bank floor? ANSWER: Correct Problem 6.19 A crate is placed on a horizontal conveyor belt. The materials are such that and . Part A Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: 0.224 10 kg μs = 0.5 μk = 0.3 Typesetting math: 100% Correct Part B Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Part C What is the maximum acceleration the belt can have without the crate slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct amax = 4.9 m s2 Typesetting math: 100% Problem 6.28 A 1100 steel beam is supported by two ropes. Part A What is the tension in rope 1? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. ANSWER: kg T1 = 7000 N Typesetting math: 100% Correct Problem 6.35 The position of a 1.4 mass is given by , where is in seconds. Part A What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.39 T2 = 4800 N kg x = (2t3 − 3t2 )m t t = 0 s F = -8.4 N t = 1 s F = 8.4 N Typesetting math: 100% A rifle with a barrel length of 61 fires a 8 bullet with a horizontal speed of 400 . The bullet strikes a block of wood and penetrates to a depth of 11 . Part A What resistive force (assumed to be constant) does the wood exert on the bullet? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How long does it take the bullet to come to rest after entering the wood? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.45 You and your friend Peter are putting new shingles on a roof pitched at 21 . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0 away, asks you for the box of nails. Rather than carry the 2.0 box of nails down to Peter, you decide to give the box a push and have it slide down to him. Part A If the coefficient of kinetic friction between the box and the roof is 0.55, with what speed should you push the box to have it gently come to rest right at the edge of the roof? Express your answer to two significant figures and include the appropriate units. cm g m/s cm fk = 5800 N = 5.5×10−4 t s  m kg Typesetting math: 100% ANSWER: Correct Problem 6.54 The 2.0 wood box in the figure slides down a vertical wood wall while you push on it at a 45 angle. Part A What magnitude of force should you apply to cause the box to slide down at a constant speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct v = 3.9 ms kg  F = 23 N Typesetting math: 100% Score Summary: Your score on this assignment is 98.8%. You received 114.57 out of a possible total of 116 points. Typesetting math: 100%

Assignment 5 Due: 11:59pm on Wednesday, March 5, 2014 You … Read More...
Problem 3 (25 Points) A bracket is subjected to a 610 N force as shown in the figure. (a) Express the force in Cartesian vector form. (8 points) (b) Determine the moment of the force about point C. (10 points) (c) Determine the moment of the force about line CD. (7 points)

Problem 3 (25 Points) A bracket is subjected to a 610 N force as shown in the figure. (a) Express the force in Cartesian vector form. (8 points) (b) Determine the moment of the force about point C. (10 points) (c) Determine the moment of the force about line CD. (7 points)

  Problem 3 (25 Points) A bracket is subjected to … Read More...
MAE 214 – Fall 2015 Homework 3 Due: October 1, 2015 – Thursday by 1:00 p.m. Total Problems: 4 (including Extra Credit), Total Points: 105 1. Make a solid works part model from the given figure below. All dimensions are in millimeters. All sketches must be fully defined. Also create a drawing sheet and dimension it as shown. You can use a hole call out option under annotation to dimension a counter bore hole. (30 points) Save your part files as follows: My Documents/Homework 3 Folder/Prob1_LastName.SLDPRT My Documents/ Homework 3 Folder/Prob1_LastName.SLDDRW 2. Make a solid works part of the given figure below and also make a drawing sheet – front, top and right side views using 3rd angle projection method. Dimension the views with appropriate dimension technique. All dimensions are in mm. (30 points) Save your part file and drawing sheet as follows: Documents/Homework 3 folder/Problem 2_Last Name.SLDPRT Documents/Homework 3 folder/Problem 2_Last Name.SLDDRW 3. Make a solid works part file for the given figure below. All sketches must be fully defined. Your design tree menu must have advanced features i.e. plane, mirror, and fillet. The spot facing (SF) must be defined in a problem. The inclined cut must be created with an offset sketch and extrude cut or a suitable sketch that uses “up to surface” option. (40 points) Your part model must stick to the isometric view as it is shown here. Save your part file into: My documents/Homework 3 Folder/Problem3_Last Name.SLDPRT Given: A = 76 B = 127 Unit: MMGS ALL ROUNDS (FILLET) EQUAL 6 MM 4. (Extra Credit) Make a solid works part from the given figure below. All sketches must be fully defined. Save your part file to Documents/Homework3 Folder/Prob#4_Last Name.SLDPRT All dimensions are in millimeters. (5 points)

MAE 214 – Fall 2015 Homework 3 Due: October 1, 2015 – Thursday by 1:00 p.m. Total Problems: 4 (including Extra Credit), Total Points: 105 1. Make a solid works part model from the given figure below. All dimensions are in millimeters. All sketches must be fully defined. Also create a drawing sheet and dimension it as shown. You can use a hole call out option under annotation to dimension a counter bore hole. (30 points) Save your part files as follows: My Documents/Homework 3 Folder/Prob1_LastName.SLDPRT My Documents/ Homework 3 Folder/Prob1_LastName.SLDDRW 2. Make a solid works part of the given figure below and also make a drawing sheet – front, top and right side views using 3rd angle projection method. Dimension the views with appropriate dimension technique. All dimensions are in mm. (30 points) Save your part file and drawing sheet as follows: Documents/Homework 3 folder/Problem 2_Last Name.SLDPRT Documents/Homework 3 folder/Problem 2_Last Name.SLDDRW 3. Make a solid works part file for the given figure below. All sketches must be fully defined. Your design tree menu must have advanced features i.e. plane, mirror, and fillet. The spot facing (SF) must be defined in a problem. The inclined cut must be created with an offset sketch and extrude cut or a suitable sketch that uses “up to surface” option. (40 points) Your part model must stick to the isometric view as it is shown here. Save your part file into: My documents/Homework 3 Folder/Problem3_Last Name.SLDPRT Given: A = 76 B = 127 Unit: MMGS ALL ROUNDS (FILLET) EQUAL 6 MM 4. (Extra Credit) Make a solid works part from the given figure below. All sketches must be fully defined. Save your part file to Documents/Homework3 Folder/Prob#4_Last Name.SLDPRT All dimensions are in millimeters. (5 points)

Instructions 1. The next sheet is an example problem from the text. Select the cells at the top of the columns to see the formulas and format. 2. Columns A,B, and C are the input data. Note that the upper boundary is used. Columns D and E are used to calculate the average and sample standard deviation. Column F calculates the z value using the upper boundary (Column B), the average, and the sample standard deviation. Column G is the area (cumulative probability) under the normal curve to the left of the z value in the same manner as Table A. Column H is the area [probability] for each cell. Note that the formula for Row 3 is different than the rest of the rows. Column I is the expected frequency for each cell. It equals the value in Column H times the total number of observed values (110). Column J is the chi-squared value which can be compared to a chi-squared table to determine the observed values (110). This column is really not necessary because the program calculates the observed values (110) and performs the chi-squared test at I21 and K21. Column K is an adjustment to bring the total number of observed values to 110. The chi-squared test for the adjustment gives a probability of 0.971that the distribution is normal. 3. The following sheet, called template, should be copied before using the program. This activity is accomplished by selecting EDIT, selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet, called template (2), in the dialog box. 4. The template is designed for 9 cells. If more or less cells are required, the appropriate changes must be made.

Instructions 1. The next sheet is an example problem from the text. Select the cells at the top of the columns to see the formulas and format. 2. Columns A,B, and C are the input data. Note that the upper boundary is used. Columns D and E are used to calculate the average and sample standard deviation. Column F calculates the z value using the upper boundary (Column B), the average, and the sample standard deviation. Column G is the area (cumulative probability) under the normal curve to the left of the z value in the same manner as Table A. Column H is the area [probability] for each cell. Note that the formula for Row 3 is different than the rest of the rows. Column I is the expected frequency for each cell. It equals the value in Column H times the total number of observed values (110). Column J is the chi-squared value which can be compared to a chi-squared table to determine the observed values (110). This column is really not necessary because the program calculates the observed values (110) and performs the chi-squared test at I21 and K21. Column K is an adjustment to bring the total number of observed values to 110. The chi-squared test for the adjustment gives a probability of 0.971that the distribution is normal. 3. The following sheet, called template, should be copied before using the program. This activity is accomplished by selecting EDIT, selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet, called template (2), in the dialog box. 4. The template is designed for 9 cells. If more or less cells are required, the appropriate changes must be made.

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Assignment One Suggested Due Date: July 17th In this assignment you will read three articles You will answer questions about Hayek, Lucas, and Mankiw et. al. which consider just those particular articles. Then at the end of the assignment there is a cluster of questions that deal with both Lucas and Mankiw et al where you will have an opportunity to compare and contrast those two articles. When you have completed the assignment, place it in the appropriate drop box in WTClass. Hayek: The Use of Knowledge in Society http://www.econlib.org/library/Essays/hykKnw1.html Adapted from Michael K. Salemi “The Use of Knowledge in Society” F. A. Hayek Discussion Questions 1.1. “The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form, but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess (H.3)” a. What does Hayek mean by a “rational economic order”? b. What does Hayek mean by “dispersed bits of incomplete and frequently contradictory knowledge”? c. Why is Hayek critical of the common assumptions in economic analysis that buyers, sellers, producers and the economist all know every relevant thing about the economy? d. What, in summary, does Hayek mean by the quoted statement? 1.2. What, according to Hayek, is the information needed to operate effectively in a complex market economy? a. What does Hayek mean by “planning”? b. What is the minimum information needed by economic planners and individuals? c. Does the minimum differ for planners and for individuals? How? Why? d. What happens when some individuals possess more information than other individuals? e. What does Hayek mean when he says (H.16) “…the sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form”? f. Why, according to Hayek, can the “information problem” be solved by “the price system”? 1.3. Why, according to Hayek, is the true function of the price system the communication of information? a. Why does Hayek use the term ‘marvel’ in his discussion of the economy of knowledge? b. What does Hayek mean when he says (H.26) “…man has been able to develop that division of labor on which our civilization is based because he happened to stumble upon a method which made it possible”? Read Robert Lucas’ “Some Macroeconomics for the 21st Century” in the Journal of Economic Perspectives. (Skip the appendix.) All four of these links go to the same article. Some of the links might not be accessible to you, but I think that at least one of them should work for all of you. https://www.aeaweb.org/articles.php?doi=10.1257/jep.14.1.159 http://www.jstor.org/stable/2647059 http://www.econ.psu.edu/~aur10/Econ%20570%20Fall%202009/Lucas%20JEP%202000.pdf http://faculty.georgetown.edu/mh5/class/econ102/readings/Macro_21st_Century.pdf 1. According to Lucas, why has the world’s economy grown so much since 1960? 2. According to Lucas, why do some nations grow faster than others? 3. According to Lucas, why will growth and inequality decrease in the next 100 years? 4. Is Lucas’ model in this paper “economics?” Read Greg Mankiw, Romer and Wiel’s article in The Quarterly Journal of Economics. http://www.econ.nyu.edu/user/debraj/Courses/Readings/MankiwRomerWeil.pdf 1. Many economists think the Solow Growth Model is of limited use. (One of my professors at OU stated that it took economists 50 years to figure out that their growth model has nothing to do with growth.) But does the Solow model give “…the right answer to the questions it is designed to address?” 2. Why is human capital important when testing the Solow model against the data? 3. Explain how the authors conclude that the incomes of the world’s nations are converging? Now that you’ve answered questions about Lucas and Mankiw et al separately, consider this question: Both of these papers develop the notion that the economies of the world’s nations will tend to “converge” over time. Compare and contrast the way(s) in which the papers advance the idea of convergence. Assignment Two Due Date July 24th This assignment is very straight forward. You’ll read two papers and answer questions about each of them. Read Krugman’s paper on unemployment http://www.kc.frb.org/PUBLICAT/ECONREV/EconRevArchive/1994/4Q94KRUG.pdf 1. What is the difference between structural and cyclical unemployment? In this context, what is the difference between Europe and the US? What is the evidence that Krugman uses to back his opinion? 2. What is the natural rate of unemployment? Why is it higher/rising in Europe? Again, what is the evidence? 3. What is the relationship between the rising unemployment in Europe and the rise in inequality in the US. (What does Krugman mean by inequality?) 4. What is NOT to blame for either the rise in unemployment or inequality? 5. What policies, if any, can be put into place to combat rising inequality/unemployment? 6. Are you convinced by Krugman’s argument which rules out globalization as the likely cause for high European unemployment and high US wage inequality? 7. Consider Table 2 in Krugman. Why does Krugman include Table 2 in his paper? In other words, what point is strengthened by the data in Table 2 and why is it crucial to Krugman’s larger thesis? NOW, recreate the data for Table 2 for either the UK or US for the latest year possible. Has anything changed as a result of the Great Recession? Read Thomas Sargent’s paper about the credibility of “Reaganonomics.” http://minneapolisfed.contentdm.oclc.org/cdm/ref/collection/p15334coll1/id/366 http://minneapolisfed.contentdm.oclc.org/cdm/singleitem/collection/p15334coll1/id/366/rec/1 You might like this: http://www.ispot.tv/ad/7Lj9/ally-bank-predictions-featuring-thomas-sargent 1. What is a dynamic game? 2. Why should we think of monetary and fiscal policy as dynamic game? Who are the players and what are the strategies? 3. When are government budgets inflationary? (Again, think in terms of a game.) 4. What are the consequences if the monetary authority does not coordinate with fiscal policy agents? 5. Has Sargent done of good job characterizing the interplay between policymakers in the government, the central bank, and the public? 6. What is the connection between policy coordination and credibility? 7. Why, according to Sargent, were Reagan’s fiscal and monetary policy regimes “incredible?” Explain carefully. Assignment Three Due Date July 31 Read Taylor, Miskin, Obstfeld and Rogoff. Answer the questions for each article, then answer the final cluster that requires you to consider Miskin, Obstfeld and Rogoff. Suggested due date: January 2nd. Read John Taylor’s article about monetary transmission mechanisms. http://web.econ.unito.it/bagliano/ecmon_readings/taylor_jep95.pdf Also, to understand traditional monetary policy, listen to this: http://www.econtalk.org/archives/2008/08/john_taylor_on.html These questions refer to the article, not the podcast. 1. How does monetary policy (or changes in monetary policy) affect output and inflation? In other words, what is the monetary policy transmission mechanism? 2. What is the importance of financial market prices in Taylor’s view? 3. What is the importance of rational expectations and rigidities in the prices of labor and goods? 4. What is a reaction function? Why is a reaction function important? 5. What is an “optimal monetary policy rule?” 6. Has the monetary transmission mechanism changed? How? 7. What are the criticisms of Taylor’s views? How does he respond? What do you think? Read Mishkin’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.3 1. What is a financial crisis? 2. How did adverse selection and moral hazard contribute to the financial crisis in Mexico and East Asia in the 1990s? What are adverse selection and moral hazard? 3. Did irresponsible monetary and fiscal policy contribute to the crisis in the 90s? Why or why not? 4. How is it possible for the IMF to help in a crisis when a domestic central bank might not be able to help. 5. What should the US learn (or have learned??) from the crisis in the 90s? Read Rogoff’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 Answer the questions and place the answers in the appropriate drop box in WTClass. 1. According to Rogoff, is the status quo in international lending viable or not? Explain. 2. Can the IMF handle international financial crises? Why or why not? 3. Rogoff gives six solutions to save the global financial system (deep pockets lender of last resort, an international financial crisis manager, an international bankruptcy court, an international regulator, international deposit insurance corporation, and a world monetary authority.) What is wrong with all of these? 4. Can developing economies cope with speculative capital flows without help? Explain. 5. What will be (should be) the role that equity financing play in developing country projects? Read Obstfeld on Global Capital Markets: http://www.nber.org/papers/w6559.pdf 1. Look at table 1 and figure 1. How does Obstfeld use the data in that table to suggest that 1) markets became less open then more open in the 20th century. 2. What is the “openness trilemma?” What are the economic and/or policy trade-offs with having a global, open and integrated financial system? 3. How does economic integration impact a nation’s ability to tax capital? Can you think of some high profile cases in the news lately that illustrate this fact? (Hint: you should be able to.) 4. What is the international diversification puzzle? What market failures have arisen (if any) have arisen due to more integration and openness? Comparing Obstfeld, Miskin, and Rogoff 1. Would the authors’ advice about policies to reduce the costs of financial integration be the same? Why or why not? 2. Would the authors’ agree that we need an international regulatory body to stave off international financial crises? Why or why not? 3. What is your opinion? Is it good to have a global financial market? Why or why not? Assignment Four Due Date August 7 Straight forward assignment: Read and answer the questions. Read Arnold Kling’s history of the policies that created the great recession http://mercatus.org/publication/not-what-they-had-mind-history-policies-produced-financial-crisis-2008 1. Using only the executive summary, what does Kling think caused the Financial Crisis of 2008? (Use only one sentence.) 2. One page 5, what is “the fact?” and what does this “fact” mean to you? 3. Briefly summarize the four components of the Financial Crisis? 4. On page 10, Kling states, “These property bubbles (in the U.K. and Spain) cannot be blamed on U.S. policy.” How confident are you on that point? Is Kling wrong? 5. Kling’s matrix of causes, gives almost all weight to what two factors? What three factors are almost completely not responsible? 6. Many have blamed designer financial (my term) like CDS and CDO and the shadow banking system for the collapse. How do these fit into Kling’s narrative? 7. Outline the progression of policy that caused/responded to economic conditions in the 30s, 70s and 80s and 00s. 8. What role did the mortgage interest deduction have on housing market? 9. What institution invented and allowed the expansion of mortgage-backed securities? 10. What is regulatory arbitrage? 11. Why did the Basel agreement create an advantage for mortgage securitization? 12. Did the Federal Reserve (and presumably other regulatory agencies know and even encourage regulatory capital arbitrage? What author does Kling cite to establish this? 13. What did the 2002 modification of the Basel Rules do to capital requirements? (See figure 4) 14. Summarize the Shadow Regulatory Committee’s statement 160. 15. Did non market institutions, such as the IMF and Bernanke, think, in 2006, that financial innovation had make the banking sector more or less fragile? 16. What is time inconsistency? (You can look this up elsewhere.) 17. How might “barriers to entry” by related to “safety and soundness?” 18. A Curmudgeon is an old man who is easily annoyed and angered. He also complains a lot. (I had to look it up.) I think I’ll change my xbox gamertag to this word, but I’ll bet it is taken. 19. How did credit scoring and credit default swaps enlarge the mortgage securities market? 20. Why, up until 2007, did we think that monetary expansion was all that was needed to mitigate the impact of financial crises? 21. Suppose that financial markets are inherently unstable. What does this mean are two goals of regulation and regulators? 22. Why are type two errors so problematic? (Two reasons.) 23. How could we make the banking sector easy to fix? Assignment Five Due August 13 Read the linked lectures and answer the questions. Lecture 1 http://econlog.econlib.org/archives/2008/11/lectures_in_mac.html 1.1 Why do you think macroeconomic realities must be reconciled with microeconomic analysis? (This is not a rhetorical question, but it will be hard for you to answer. There is no “wrong” answer you could give. Just think about it for a few minutes.) Lecture 2 http://econlog.econlib.org/archives/2008/11/lectures_in_mac_1.html 2.1 Consider this article after you have read Hayek. How do prices and wages perform the function of “central planning?” 2.2 Kling makes that claim that, because most workers do not do manual labor anymore, the economy is different that it was in 1930. Assuming he is correct, do you think central planning would be harder today or easier? Why? Lecture 3 http://econlog.econlib.org/archives/2008/11/lectures_on_mac.html 3.1 Give a one sentence definition of structural unemployment, of frictional unemployment and of cyclical unemployment. Lecture 4 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_1.html 4.1 So, why does the economy adjust employment rather than wages? Lecture 5 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_2.html 5.1 Kling gives 5 reasons the DotCom recession was worse than the previous two recessions (at least in duration). Which reason do you think is the most compelling? Lecture 6 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_3.html 6.1 Why are Keynesian remedies (blunt fiscal and monetary policy measures) less appropriate in a post industrial economy, according to Kling? Lecture 7 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_4.html 7.1 Why is it so hard to separate finance and government, according to Kling? Lecture 8 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_5.html 8.1 Why is American Express Travelers Checks so interesting? Do credit cards work in a similar way? (I really don’t know the answer to this one. I just know that credit cards have made travelers checks obsolete.) Lecture 9. http://econlog.econlib.org/archives/2008/12/lectures_on_mac_6.html 9.1 According to this article, why do we have banks (financial sector or financial intermediation?) Lecture 10 http://econlog.econlib.org/archives/2008/12/lectures_on_mac_7.html 10.1 Why are banks better than barter, according to this leture? 10.2 Politics tends to favor bailouts of failed firms. Why is this exactly wrong?

Assignment One Suggested Due Date: July 17th In this assignment you will read three articles You will answer questions about Hayek, Lucas, and Mankiw et. al. which consider just those particular articles. Then at the end of the assignment there is a cluster of questions that deal with both Lucas and Mankiw et al where you will have an opportunity to compare and contrast those two articles. When you have completed the assignment, place it in the appropriate drop box in WTClass. Hayek: The Use of Knowledge in Society http://www.econlib.org/library/Essays/hykKnw1.html Adapted from Michael K. Salemi “The Use of Knowledge in Society” F. A. Hayek Discussion Questions 1.1. “The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form, but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess (H.3)” a. What does Hayek mean by a “rational economic order”? b. What does Hayek mean by “dispersed bits of incomplete and frequently contradictory knowledge”? c. Why is Hayek critical of the common assumptions in economic analysis that buyers, sellers, producers and the economist all know every relevant thing about the economy? d. What, in summary, does Hayek mean by the quoted statement? 1.2. What, according to Hayek, is the information needed to operate effectively in a complex market economy? a. What does Hayek mean by “planning”? b. What is the minimum information needed by economic planners and individuals? c. Does the minimum differ for planners and for individuals? How? Why? d. What happens when some individuals possess more information than other individuals? e. What does Hayek mean when he says (H.16) “…the sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form”? f. Why, according to Hayek, can the “information problem” be solved by “the price system”? 1.3. Why, according to Hayek, is the true function of the price system the communication of information? a. Why does Hayek use the term ‘marvel’ in his discussion of the economy of knowledge? b. What does Hayek mean when he says (H.26) “…man has been able to develop that division of labor on which our civilization is based because he happened to stumble upon a method which made it possible”? Read Robert Lucas’ “Some Macroeconomics for the 21st Century” in the Journal of Economic Perspectives. (Skip the appendix.) All four of these links go to the same article. Some of the links might not be accessible to you, but I think that at least one of them should work for all of you. https://www.aeaweb.org/articles.php?doi=10.1257/jep.14.1.159 http://www.jstor.org/stable/2647059 http://www.econ.psu.edu/~aur10/Econ%20570%20Fall%202009/Lucas%20JEP%202000.pdf http://faculty.georgetown.edu/mh5/class/econ102/readings/Macro_21st_Century.pdf 1. According to Lucas, why has the world’s economy grown so much since 1960? 2. According to Lucas, why do some nations grow faster than others? 3. According to Lucas, why will growth and inequality decrease in the next 100 years? 4. Is Lucas’ model in this paper “economics?” Read Greg Mankiw, Romer and Wiel’s article in The Quarterly Journal of Economics. http://www.econ.nyu.edu/user/debraj/Courses/Readings/MankiwRomerWeil.pdf 1. Many economists think the Solow Growth Model is of limited use. (One of my professors at OU stated that it took economists 50 years to figure out that their growth model has nothing to do with growth.) But does the Solow model give “…the right answer to the questions it is designed to address?” 2. Why is human capital important when testing the Solow model against the data? 3. Explain how the authors conclude that the incomes of the world’s nations are converging? Now that you’ve answered questions about Lucas and Mankiw et al separately, consider this question: Both of these papers develop the notion that the economies of the world’s nations will tend to “converge” over time. Compare and contrast the way(s) in which the papers advance the idea of convergence. Assignment Two Due Date July 24th This assignment is very straight forward. You’ll read two papers and answer questions about each of them. Read Krugman’s paper on unemployment http://www.kc.frb.org/PUBLICAT/ECONREV/EconRevArchive/1994/4Q94KRUG.pdf 1. What is the difference between structural and cyclical unemployment? In this context, what is the difference between Europe and the US? What is the evidence that Krugman uses to back his opinion? 2. What is the natural rate of unemployment? Why is it higher/rising in Europe? Again, what is the evidence? 3. What is the relationship between the rising unemployment in Europe and the rise in inequality in the US. (What does Krugman mean by inequality?) 4. What is NOT to blame for either the rise in unemployment or inequality? 5. What policies, if any, can be put into place to combat rising inequality/unemployment? 6. Are you convinced by Krugman’s argument which rules out globalization as the likely cause for high European unemployment and high US wage inequality? 7. Consider Table 2 in Krugman. Why does Krugman include Table 2 in his paper? In other words, what point is strengthened by the data in Table 2 and why is it crucial to Krugman’s larger thesis? NOW, recreate the data for Table 2 for either the UK or US for the latest year possible. Has anything changed as a result of the Great Recession? Read Thomas Sargent’s paper about the credibility of “Reaganonomics.” http://minneapolisfed.contentdm.oclc.org/cdm/ref/collection/p15334coll1/id/366 http://minneapolisfed.contentdm.oclc.org/cdm/singleitem/collection/p15334coll1/id/366/rec/1 You might like this: http://www.ispot.tv/ad/7Lj9/ally-bank-predictions-featuring-thomas-sargent 1. What is a dynamic game? 2. Why should we think of monetary and fiscal policy as dynamic game? Who are the players and what are the strategies? 3. When are government budgets inflationary? (Again, think in terms of a game.) 4. What are the consequences if the monetary authority does not coordinate with fiscal policy agents? 5. Has Sargent done of good job characterizing the interplay between policymakers in the government, the central bank, and the public? 6. What is the connection between policy coordination and credibility? 7. Why, according to Sargent, were Reagan’s fiscal and monetary policy regimes “incredible?” Explain carefully. Assignment Three Due Date July 31 Read Taylor, Miskin, Obstfeld and Rogoff. Answer the questions for each article, then answer the final cluster that requires you to consider Miskin, Obstfeld and Rogoff. Suggested due date: January 2nd. Read John Taylor’s article about monetary transmission mechanisms. http://web.econ.unito.it/bagliano/ecmon_readings/taylor_jep95.pdf Also, to understand traditional monetary policy, listen to this: http://www.econtalk.org/archives/2008/08/john_taylor_on.html These questions refer to the article, not the podcast. 1. How does monetary policy (or changes in monetary policy) affect output and inflation? In other words, what is the monetary policy transmission mechanism? 2. What is the importance of financial market prices in Taylor’s view? 3. What is the importance of rational expectations and rigidities in the prices of labor and goods? 4. What is a reaction function? Why is a reaction function important? 5. What is an “optimal monetary policy rule?” 6. Has the monetary transmission mechanism changed? How? 7. What are the criticisms of Taylor’s views? How does he respond? What do you think? Read Mishkin’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.3 1. What is a financial crisis? 2. How did adverse selection and moral hazard contribute to the financial crisis in Mexico and East Asia in the 1990s? What are adverse selection and moral hazard? 3. Did irresponsible monetary and fiscal policy contribute to the crisis in the 90s? Why or why not? 4. How is it possible for the IMF to help in a crisis when a domestic central bank might not be able to help. 5. What should the US learn (or have learned??) from the crisis in the 90s? Read Rogoff’s article about global financial instability. http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.21 Answer the questions and place the answers in the appropriate drop box in WTClass. 1. According to Rogoff, is the status quo in international lending viable or not? Explain. 2. Can the IMF handle international financial crises? Why or why not? 3. Rogoff gives six solutions to save the global financial system (deep pockets lender of last resort, an international financial crisis manager, an international bankruptcy court, an international regulator, international deposit insurance corporation, and a world monetary authority.) What is wrong with all of these? 4. Can developing economies cope with speculative capital flows without help? Explain. 5. What will be (should be) the role that equity financing play in developing country projects? Read Obstfeld on Global Capital Markets: http://www.nber.org/papers/w6559.pdf 1. Look at table 1 and figure 1. How does Obstfeld use the data in that table to suggest that 1) markets became less open then more open in the 20th century. 2. What is the “openness trilemma?” What are the economic and/or policy trade-offs with having a global, open and integrated financial system? 3. How does economic integration impact a nation’s ability to tax capital? Can you think of some high profile cases in the news lately that illustrate this fact? (Hint: you should be able to.) 4. What is the international diversification puzzle? What market failures have arisen (if any) have arisen due to more integration and openness? Comparing Obstfeld, Miskin, and Rogoff 1. Would the authors’ advice about policies to reduce the costs of financial integration be the same? Why or why not? 2. Would the authors’ agree that we need an international regulatory body to stave off international financial crises? Why or why not? 3. What is your opinion? Is it good to have a global financial market? Why or why not? Assignment Four Due Date August 7 Straight forward assignment: Read and answer the questions. Read Arnold Kling’s history of the policies that created the great recession http://mercatus.org/publication/not-what-they-had-mind-history-policies-produced-financial-crisis-2008 1. Using only the executive summary, what does Kling think caused the Financial Crisis of 2008? (Use only one sentence.) 2. One page 5, what is “the fact?” and what does this “fact” mean to you? 3. Briefly summarize the four components of the Financial Crisis? 4. On page 10, Kling states, “These property bubbles (in the U.K. and Spain) cannot be blamed on U.S. policy.” How confident are you on that point? Is Kling wrong? 5. Kling’s matrix of causes, gives almost all weight to what two factors? What three factors are almost completely not responsible? 6. Many have blamed designer financial (my term) like CDS and CDO and the shadow banking system for the collapse. How do these fit into Kling’s narrative? 7. Outline the progression of policy that caused/responded to economic conditions in the 30s, 70s and 80s and 00s. 8. What role did the mortgage interest deduction have on housing market? 9. What institution invented and allowed the expansion of mortgage-backed securities? 10. What is regulatory arbitrage? 11. Why did the Basel agreement create an advantage for mortgage securitization? 12. Did the Federal Reserve (and presumably other regulatory agencies know and even encourage regulatory capital arbitrage? What author does Kling cite to establish this? 13. What did the 2002 modification of the Basel Rules do to capital requirements? (See figure 4) 14. Summarize the Shadow Regulatory Committee’s statement 160. 15. Did non market institutions, such as the IMF and Bernanke, think, in 2006, that financial innovation had make the banking sector more or less fragile? 16. What is time inconsistency? (You can look this up elsewhere.) 17. How might “barriers to entry” by related to “safety and soundness?” 18. A Curmudgeon is an old man who is easily annoyed and angered. He also complains a lot. (I had to look it up.) I think I’ll change my xbox gamertag to this word, but I’ll bet it is taken. 19. How did credit scoring and credit default swaps enlarge the mortgage securities market? 20. Why, up until 2007, did we think that monetary expansion was all that was needed to mitigate the impact of financial crises? 21. Suppose that financial markets are inherently unstable. What does this mean are two goals of regulation and regulators? 22. Why are type two errors so problematic? (Two reasons.) 23. How could we make the banking sector easy to fix? Assignment Five Due August 13 Read the linked lectures and answer the questions. Lecture 1 http://econlog.econlib.org/archives/2008/11/lectures_in_mac.html 1.1 Why do you think macroeconomic realities must be reconciled with microeconomic analysis? (This is not a rhetorical question, but it will be hard for you to answer. There is no “wrong” answer you could give. Just think about it for a few minutes.) Lecture 2 http://econlog.econlib.org/archives/2008/11/lectures_in_mac_1.html 2.1 Consider this article after you have read Hayek. How do prices and wages perform the function of “central planning?” 2.2 Kling makes that claim that, because most workers do not do manual labor anymore, the economy is different that it was in 1930. Assuming he is correct, do you think central planning would be harder today or easier? Why? Lecture 3 http://econlog.econlib.org/archives/2008/11/lectures_on_mac.html 3.1 Give a one sentence definition of structural unemployment, of frictional unemployment and of cyclical unemployment. Lecture 4 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_1.html 4.1 So, why does the economy adjust employment rather than wages? Lecture 5 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_2.html 5.1 Kling gives 5 reasons the DotCom recession was worse than the previous two recessions (at least in duration). Which reason do you think is the most compelling? Lecture 6 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_3.html 6.1 Why are Keynesian remedies (blunt fiscal and monetary policy measures) less appropriate in a post industrial economy, according to Kling? Lecture 7 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_4.html 7.1 Why is it so hard to separate finance and government, according to Kling? Lecture 8 http://econlog.econlib.org/archives/2008/11/lectures_on_mac_5.html 8.1 Why is American Express Travelers Checks so interesting? Do credit cards work in a similar way? (I really don’t know the answer to this one. I just know that credit cards have made travelers checks obsolete.) Lecture 9. http://econlog.econlib.org/archives/2008/12/lectures_on_mac_6.html 9.1 According to this article, why do we have banks (financial sector or financial intermediation?) Lecture 10 http://econlog.econlib.org/archives/2008/12/lectures_on_mac_7.html 10.1 Why are banks better than barter, according to this leture? 10.2 Politics tends to favor bailouts of failed firms. Why is this exactly wrong?

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Assignment 1: Coulomb’s Law Due: 8:00am on Wednesday, January 11, 2012 Note: To understand how points are awarded, read your instructor’s Grading Policy. [Switch to Standard Assignment View] Coulomb’s Law Tutorial Learning Goal: To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them. Coulomb’s law describes the force that two charged particles exert on each other (by Newton’s third law, those two forces must be equal and opposite). The force exerted by particle 2 (with charge ) on particle 1 (with charge ) is proportional to the charge of each particle and inversely proportional to the square of the distance between them: , where and is the unit vector pointing from particle 2 to particle 1. The force vector will be parallel or antiparallel to the direction of , parallel if the product and antiparallel if ; the force is attractive if the charges are of opposite sign and repulsive if the charges are of the same sign. Part A Consider two positively charged particles, one of charge (particle 0) fixed at the origin, and another of charge (particle 1) fixed on the y-axis at . What is the net force on particle 0 due to particle 1? Express your answer (a vector) using any or all of , , , , , , and . ANSWER: = Correct Part B Now add a third, negatively charged, particle, whose charge is (particle 2). Particle 2 fixed on the y-axis at position . What is the new net force on particle 0, from particle 1 and particle 2? Express your answer (a vector) using any or all of , , , , , , , , and . ANSWER: = Correct Part C Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of and , the repulsion and attraction should balance each other, resulting in no net force. For what ratio is there no net force on particle 0? Express your answer in terms of any or all of the following variables: , , , . ANSWER: = Correct Part D Now add a fourth charged particle, particle 3, with positive charge , fixed in the yz-plane at . What is the net force on particle 0 due solely to this charge? Hint D.1 Find the magnitude of force from particle 3 Hint not displayed Hint D.2 Vector components Hint not displayed Express your answer (a vector) using , , , , , , and . Include only the force caused by particle 3. ANSWER: = Correct Exercise 21.4 You have a pure (24-karat) gold ring with mass . Gold has an atomic mass of and an atomic number of . Part A How many protons are in the ring? ANSWER: = 4.27×1024 Correct Part B What is their total positive charge? ANSWER: = 6.83×105 Correct Part C If the ring carries no net charge, how many electrons are in it? ANSWER: = 4.27×1024 Correct Exercise 21.22 Two point charges are placed on the x-axis as follows: charge = 4.05 is located at 0.197 , and charge = 5.00 is at -0.296 . Part A What is the magnitude of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: = 2.55×10−6 Correct Part B What is the direction of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: to the + direction to the – direction perpendicular to the -axis the force is zero Correct Problem 21.66 A charge 4.97 is placed at the origin of an xy-coordinate system, and a charge -1.99 is placed on the positive x-axis at = 3.98 . A third particle, of charge 6.05 is now placed at the point = 3.98 , = 3.01 . Part A Find the x-component of the total force exerted on the third charge by the other two. ANSWER: = 8.66×10−5 Correct Part B Find the y-component of the total force exerted on the third charge by the other two. ANSWER: = −5.40×10−5 Correct Part C Find the magnitude of the total force acting on the third charge. ANSWER: = 1.02×10−4 Correct Part D Find the direction of the total force acting on the third charge. ANSWER: = -0.557 Correct between and +x-axis Problem 21.68 Two identical spheres with mass are hung from silk threads of length , as shown in the figure . Each sphere has the same charge, so . The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Part A Suppose that the angle is small, and find the equilibrium separation between the spheres (Hint: If is small, then .) Express your answer in terms of the variables , , and appropriate constants. ANSWER: = Correct

Assignment 1: Coulomb’s Law Due: 8:00am on Wednesday, January 11, 2012 Note: To understand how points are awarded, read your instructor’s Grading Policy. [Switch to Standard Assignment View] Coulomb’s Law Tutorial Learning Goal: To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them. Coulomb’s law describes the force that two charged particles exert on each other (by Newton’s third law, those two forces must be equal and opposite). The force exerted by particle 2 (with charge ) on particle 1 (with charge ) is proportional to the charge of each particle and inversely proportional to the square of the distance between them: , where and is the unit vector pointing from particle 2 to particle 1. The force vector will be parallel or antiparallel to the direction of , parallel if the product and antiparallel if ; the force is attractive if the charges are of opposite sign and repulsive if the charges are of the same sign. Part A Consider two positively charged particles, one of charge (particle 0) fixed at the origin, and another of charge (particle 1) fixed on the y-axis at . What is the net force on particle 0 due to particle 1? Express your answer (a vector) using any or all of , , , , , , and . ANSWER: = Correct Part B Now add a third, negatively charged, particle, whose charge is (particle 2). Particle 2 fixed on the y-axis at position . What is the new net force on particle 0, from particle 1 and particle 2? Express your answer (a vector) using any or all of , , , , , , , , and . ANSWER: = Correct Part C Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of and , the repulsion and attraction should balance each other, resulting in no net force. For what ratio is there no net force on particle 0? Express your answer in terms of any or all of the following variables: , , , . ANSWER: = Correct Part D Now add a fourth charged particle, particle 3, with positive charge , fixed in the yz-plane at . What is the net force on particle 0 due solely to this charge? Hint D.1 Find the magnitude of force from particle 3 Hint not displayed Hint D.2 Vector components Hint not displayed Express your answer (a vector) using , , , , , , and . Include only the force caused by particle 3. ANSWER: = Correct Exercise 21.4 You have a pure (24-karat) gold ring with mass . Gold has an atomic mass of and an atomic number of . Part A How many protons are in the ring? ANSWER: = 4.27×1024 Correct Part B What is their total positive charge? ANSWER: = 6.83×105 Correct Part C If the ring carries no net charge, how many electrons are in it? ANSWER: = 4.27×1024 Correct Exercise 21.22 Two point charges are placed on the x-axis as follows: charge = 4.05 is located at 0.197 , and charge = 5.00 is at -0.296 . Part A What is the magnitude of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: = 2.55×10−6 Correct Part B What is the direction of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: to the + direction to the – direction perpendicular to the -axis the force is zero Correct Problem 21.66 A charge 4.97 is placed at the origin of an xy-coordinate system, and a charge -1.99 is placed on the positive x-axis at = 3.98 . A third particle, of charge 6.05 is now placed at the point = 3.98 , = 3.01 . Part A Find the x-component of the total force exerted on the third charge by the other two. ANSWER: = 8.66×10−5 Correct Part B Find the y-component of the total force exerted on the third charge by the other two. ANSWER: = −5.40×10−5 Correct Part C Find the magnitude of the total force acting on the third charge. ANSWER: = 1.02×10−4 Correct Part D Find the direction of the total force acting on the third charge. ANSWER: = -0.557 Correct between and +x-axis Problem 21.68 Two identical spheres with mass are hung from silk threads of length , as shown in the figure . Each sphere has the same charge, so . The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Part A Suppose that the angle is small, and find the equilibrium separation between the spheres (Hint: If is small, then .) Express your answer in terms of the variables , , and appropriate constants. ANSWER: = Correct

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