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...
ELEC 2000 Semiconductor Devices Homework #1 Choose the answer that best completes the statement or answers the question. (1) Assume the valence electron is removed from a copper atom. The net charge of the atom becomes a. 0 b. +1 c. -1 d. +4 (2) The valence electron of a copper atom experiences what kind of attraction toward the nucleus? a. None b. Weak c. Strong d. Impossible to say (3) How many valence electrons does a silicon atom have? a. 0 b. 1 c. 2 d. 4 (4) Silicon atoms combine into an orderly pattern called a a. Covalent bond b. Crystal c. Semiconductor d. Valence orbit (5) An intrinsic semiconductor has some holes in it at room temperature. What causes these holes? a. Doping b. Free electrons c. Thermal energy d. Valence electrons (6) The merging of a free electron and a hole is called a. Covalent bonding b. Lifetime c. Recombination d. Thermal energy (7) At room temperature an intrinsic silicon crystal acts approximately a. A Battery b. A conductor c. An insulator d. Copper wire (8) The amount of time between the creation of a hole and its disappearance is called a. Doping b. Lifetime c. Recombination d. Valence (9) A conductor has how many type of flow? a. 1 b. 2 c. 3 d. 4 (10) A semiconductor has how many types of flow? a. 1 b. 2 c. 3 d. 4 (11) For semiconductor material, its valence orbit is saturated when it contains a. 1 electron b. Equal (+) and (-) ions c. 4 electrons d. 8 electrons (12) In an intrinsic semiconductor, the number of holes a. Equal the number of free electrons b. Is greater than the number of free electrons c. Is less than the number of free electrons d. None of the above (13) The number of free electrons and holes in an intrinsic semiconductor decreases when the temperature a. Decreases b. Increases c. Stays the same d. None of the above (14) The flow of valence electrons to the right means that holes are flowing to the a. Left b. Right c. Either way d. None of the above (15) Holes act like a. Atoms b. Crystals c. Negative charges d. Positive charges (16) An donor atom has how many valence electrons? a. 1 b. 3 c. 4 d. 5 (17) If you wanted to produce a p-type semiconductor, which of these would you use? a. Acceptor atoms b. Donor atoms c. Pentavalent impurity d. Silicon (18) Electrons are the minority carriers in which type of semiconductor? a. Extrinsic b. Intrinsic c. n-Type d. p-type (19) Silver is the best conductor. How many valence electrons do you think it has? a. 1 b. 4 c. 18 d. 29 (20) Which of the following describes an n-type semiconductor? a. Neutral b. Positively charged c. Negatively charged d. has many holes (21) What is the barrier potential of a silicon diode a room temperature? a. 0.3 V b. 0.7 V c. 1 V d. 2 mV per degree Celsius

ELEC 2000 Semiconductor Devices Homework #1 Choose the answer that best completes the statement or answers the question. (1) Assume the valence electron is removed from a copper atom. The net charge of the atom becomes a. 0 b. +1 c. -1 d. +4 (2) The valence electron of a copper atom experiences what kind of attraction toward the nucleus? a. None b. Weak c. Strong d. Impossible to say (3) How many valence electrons does a silicon atom have? a. 0 b. 1 c. 2 d. 4 (4) Silicon atoms combine into an orderly pattern called a a. Covalent bond b. Crystal c. Semiconductor d. Valence orbit (5) An intrinsic semiconductor has some holes in it at room temperature. What causes these holes? a. Doping b. Free electrons c. Thermal energy d. Valence electrons (6) The merging of a free electron and a hole is called a. Covalent bonding b. Lifetime c. Recombination d. Thermal energy (7) At room temperature an intrinsic silicon crystal acts approximately a. A Battery b. A conductor c. An insulator d. Copper wire (8) The amount of time between the creation of a hole and its disappearance is called a. Doping b. Lifetime c. Recombination d. Valence (9) A conductor has how many type of flow? a. 1 b. 2 c. 3 d. 4 (10) A semiconductor has how many types of flow? a. 1 b. 2 c. 3 d. 4 (11) For semiconductor material, its valence orbit is saturated when it contains a. 1 electron b. Equal (+) and (-) ions c. 4 electrons d. 8 electrons (12) In an intrinsic semiconductor, the number of holes a. Equal the number of free electrons b. Is greater than the number of free electrons c. Is less than the number of free electrons d. None of the above (13) The number of free electrons and holes in an intrinsic semiconductor decreases when the temperature a. Decreases b. Increases c. Stays the same d. None of the above (14) The flow of valence electrons to the right means that holes are flowing to the a. Left b. Right c. Either way d. None of the above (15) Holes act like a. Atoms b. Crystals c. Negative charges d. Positive charges (16) An donor atom has how many valence electrons? a. 1 b. 3 c. 4 d. 5 (17) If you wanted to produce a p-type semiconductor, which of these would you use? a. Acceptor atoms b. Donor atoms c. Pentavalent impurity d. Silicon (18) Electrons are the minority carriers in which type of semiconductor? a. Extrinsic b. Intrinsic c. n-Type d. p-type (19) Silver is the best conductor. How many valence electrons do you think it has? a. 1 b. 4 c. 18 d. 29 (20) Which of the following describes an n-type semiconductor? a. Neutral b. Positively charged c. Negatively charged d. has many holes (21) What is the barrier potential of a silicon diode a room temperature? a. 0.3 V b. 0.7 V c. 1 V d. 2 mV per degree Celsius

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Click the link to read Chapter 1 of Clausewitz’s On War, and then answer the questions below. http://www.gutenberg.org/files/1946/1946-h/1946-h.htm#2HCH0001 How does Clausewitz define war? A. It is the use of violence to gain wealth. B. It is the way in which states can show their power. C. It is an act of violence intended to compel our opponent to fulfill our will. D. It is no longer a legitimate way to function in a world of international law. E. It is defined by international laws and norms. What are the main motives that cause war, according to Clausewitz? A. Greed and tyranny. B. Instinctive hostility and hostile intention. C. Competition and glory. D. Fear and threat. E. Men and money. What is the polarity principle according to Clausewitz? A. In principle, the world has conflicts that flow from North to South. B. It is like a zero sum game, a win for one yields a loss for the other. C. Two states will tend to find peace before they have to fight. D. The pitch of battle will swing from one end to the other before it ends. E. Humans are both rational and emotional; you must consider both sides. According to Clausewitz the element of War itself is: A. A multifaceted, multiplayer complex system with no central element. B. A duel between two parties on an extensive scale. C. Only made possible through laws that limit violence. D. Completely removed from politics in all aspects. E. Not something that we can understand or study.

Click the link to read Chapter 1 of Clausewitz’s On War, and then answer the questions below. http://www.gutenberg.org/files/1946/1946-h/1946-h.htm#2HCH0001 How does Clausewitz define war? A. It is the use of violence to gain wealth. B. It is the way in which states can show their power. C. It is an act of violence intended to compel our opponent to fulfill our will. D. It is no longer a legitimate way to function in a world of international law. E. It is defined by international laws and norms. What are the main motives that cause war, according to Clausewitz? A. Greed and tyranny. B. Instinctive hostility and hostile intention. C. Competition and glory. D. Fear and threat. E. Men and money. What is the polarity principle according to Clausewitz? A. In principle, the world has conflicts that flow from North to South. B. It is like a zero sum game, a win for one yields a loss for the other. C. Two states will tend to find peace before they have to fight. D. The pitch of battle will swing from one end to the other before it ends. E. Humans are both rational and emotional; you must consider both sides. According to Clausewitz the element of War itself is: A. A multifaceted, multiplayer complex system with no central element. B. A duel between two parties on an extensive scale. C. Only made possible through laws that limit violence. D. Completely removed from politics in all aspects. E. Not something that we can understand or study.

Click the link to read Chapter 1 of Clausewitz’s On … Read More...
Your text describes encryption as: Answers: The transmission of data through telecommunications lines in “scrambled” form The act of ensuring the accuracy, integrity and safety of all E-business processes and resources A “gatekeeper” system that protects a company’s intranets and other computer networks from intrusion by providing a filter and safe transfer point for access to and from the Internet and other networks None of the choices are correct

Your text describes encryption as: Answers: The transmission of data through telecommunications lines in “scrambled” form The act of ensuring the accuracy, integrity and safety of all E-business processes and resources A “gatekeeper” system that protects a company’s intranets and other computer networks from intrusion by providing a filter and safe transfer point for access to and from the Internet and other networks None of the choices are correct

Your text describes encryption as: Answers: The transmission of data … Read More...
. What behaviors indicate psychological distress? Name 5 and explain.

. What behaviors indicate psychological distress? Name 5 and explain.

The term ‘distress’ is commonly used in nursing literature to … Read More...
The diagram 3 forces F1, F2, F3 act on the body. The magnitude and direction of forces F1 and F2 are known and indicated . Also the resultant force R= F1+F2+F3 is know and indicated. Using force decomposition procedure in the Cartesian coordinate system find the magnitude of the force F3 and the angle between line of action of this force and the x direction.

The diagram 3 forces F1, F2, F3 act on the body. The magnitude and direction of forces F1 and F2 are known and indicated . Also the resultant force R= F1+F2+F3 is know and indicated. Using force decomposition procedure in the Cartesian coordinate system find the magnitude of the force F3 and the angle between line of action of this force and the x direction.

Chapter 7 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Book on a Table A book weighing 5 N rests on top of a table. Part A A downward force of magnitude 5 N is exerted on the book by the force of ANSWER: Part B An upward force of magnitude _____ is exerted on the _____ by the table. the table gravity inertia . ANSWER: Part C Do the downward force in Part A and the upward force in Part B constitute a 3rd law pair? You did not open hints for this part. ANSWER: Part D The reaction to the force in Part A is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____ . You did not open hints for this part. ANSWER: 6 N / table 5 N / table 5 N / book 6 N / book yes no Part E The reaction to the force in Part B is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____. ANSWER: Part F Which of Newton’s laws dictates that the forces in Parts A and B are equal and opposite? ANSWER: Part G Which of Newton’s laws dictates that the forces in Parts B and E are equal and opposite? ANSWER: 5 N / earth / book / upward 5 N / book / table / upward 5 N / book / earth / upward 5 N / earth / book / downward 5 N / table / book / upward 5 N / table / earth / upward 5 N / book / table / upward 5 N / table / book / downward 5 N / earth / book / downward Newton’s 1st or 2nd law Newton’s 3rd law Blocks in an Elevator Ranking Task Three blocks are stacked on top of each other inside an elevator as shown in the figure. Answer the following questions with reference to the eight forces defined as follows. the force of the 3 block on the 2 block, , the force of the 2 block on the 3 block, , the force of the 3 block on the 1 block, , the force of the 1 block on the 3 block, , the force of the 2 block on the 1 block, , the force of the 1 block on the 2 block, , the force of the 1 block on the floor, , and the force of the floor on the 1 block, . Part A Assume the elevator is at rest. Rank the magnitude of the forces. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Newton’s 1st or 2nd law Newton’s 3rd law kg kg F3 on 2 kg kg F2 on 3 kg kg F3 on 1 kg kg F1 on 3 kg kg F2 on 1 kg kg F1 on 2 kg F1 on floor kg Ffloor on 1 Part B This question will be shown after you complete previous question(s). Newton’s 3rd Law Discussed Learning Goal: To understand Newton’s 3rd law, which states that a physical interaction always generates a pair of forces on the two interacting bodies. In Principia, Newton wrote: To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. (translation by Cajori) The phrase after the colon (often omitted from textbooks) makes it clear that this is a statement about the nature of force. The central idea is that physical interactions (e.g., due to gravity, bodies touching, or electric forces) cause forces to arise between pairs of bodies. Each pairwise interaction produces a pair of opposite forces, one acting on each body. In summary, each physical interaction between two bodies generates a pair of forces. Whatever the physical cause of the interaction, the force on body A from body B is equal in magnitude and opposite in direction to the force on body B from body A. Incidentally, Newton states that the word “action” denotes both (a) the force due to an interaction and (b) the changes in momentum that it imparts to the two interacting bodies. If you haven’t learned about momentum, don’t worry; for now this is just a statement about the origin of forces. Mark each of the following statements as true or false. If a statement refers to “two bodies” interacting via some force, you are not to assume that these two bodies have the same mass. Part A Every force has one and only one 3rd law pair force. ANSWER: Part B The two forces in each pair act in opposite directions. ANSWER: Part C The two forces in each pair can either both act on the same body or they can act on different bodies. ANSWER: true false true false Part D The two forces in each pair may have different physical origins (for instance, one of the forces could be due to gravity, and its pair force could be due to friction or electric charge). ANSWER: Part E The two forces of a 3rd law pair always act on different bodies. ANSWER: Part F Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.) You did not open hints for this part. ANSWER: true false true false true false Part G According to Newton’s 3rd law, the force on the (smaller) moon due to the (larger) earth is ANSWER: Pulling Three Blocks Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force . The magnitude of the tension in the string between blocks B and C is = 3.00 . Assume that each block has mass = 0.400 . true false greater in magnitude and antiparallel to the force on the earth due to the moon. greater in magnitude and parallel to the force on the earth due to the moon. equal in magnitude but antiparallel to the force on the earth due to the moon. equal in magnitude and parallel to the force on the earth due to the moon. smaller in magnitude and antiparallel to the force on the earth due to the moon. smaller in magnitude and parallel to the force on the earth due to the moon. F T N m kg Part A What is the magnitude of the force? Express your answer numerically in newtons. You did not open hints for this part. ANSWER: Part B What is the tension in the string between block A and block B? Express your answer numerically in newtons You did not open hints for this part. ANSWER: Pulling Two Blocks In the situation shown in the figure, a person is pulling with a constant, nonzero force on string 1, which is attached to block A. Block A is also attached to block B via string 2, as shown. For this problem, assume that neither string stretches and that friction is negligible. Both blocks have finite (nonzero) mass. F F = N TAB TAB = N F Part A Which one of the following statements correctly descibes the relationship between the accelerations of blocks A and B? You did not open hints for this part. ANSWER: Part B How does the magnitude of the tension in string 1, , compare with the tension in string 2, ? You did not open hints for this part. Block A has a larger acceleration than block B. Block B has a larger acceleration than block A. Both blocks have the same acceleration. More information is needed to determine the relationship between the accelerations. T1 T2 ANSWER: Tension in a Massless Rope Learning Goal: To understand the concept of tension and the relationship between tension and force. This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let and (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless, so that its weight is negligible compared with the tension. (This is not a ridiculous approximation–modern rope materials such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.) Consider the three sections of rope labeled a, b, and c in the figure. At point 1, a downward force of magnitude acts on section a. At point 1, an upward force of magnitude acts on section b. At point 1, the tension in the rope is . At point 2, a downward force of magnitude acts on section b. At point 2, an upward force of magnitude acts on section c. At point 2, the tension in the rope is . Assume, too, that the rope is at equilibrium. Part A What is the magnitude of the downward force on section a? Express your answer in terms of the tension . ANSWER: More information is needed to determine the relationship between and . T1 > T2 T1 = T2 T1 < T2 T1 T2 Fu Fd Fad Fbu T1 Fbd Fcu T2 Fad T1 Part B What is the magnitude of the upward force on section b? Express your answer in terms of the tension . ANSWER: Part C The magnitude of the upward force on c, , and the magnitude of the downward force on b, , are equal because of which of Newton's laws? ANSWER: Part D The magnitude of the force is ____ . ANSWER: Fad = Fbu T1 Fbu = Fcu Fbd 1st 2nd 3rd Fbu Fbd Part E Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces? You did not open hints for this part. ANSWER: Part F The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true? Check all that apply. ANSWER: less than greater than equal to Fu > Fd Fu = Fd Fu < Fd The tension in the rope is everywhere the same. The magnitudes of the forces exerted on the two objects by the rope are the same. The forces exerted on the two objects by the rope must be in opposite directions. The forces exerted on the two objects by the rope must be in the direction of the rope. Two Hanging Masses Two blocks with masses and hang one under the other. For this problem, take the positive direction to be upward, and use for the magnitude of the acceleration due to gravity. Case 1: Blocks at rest For Parts A and B assume the blocks are at rest. Part A Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: M1 M2 g T2 M1 M2 g Part B Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: Case 2: Accelerating blocks For Parts C and D the blocks are now accelerating upward (due to the tension in the strings) with acceleration of magnitude . Part C Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , , and . You did not open hints for this part. ANSWER: T2 = T1 M1 M2 g T1 = a T2 M1 M2 a g Part D Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , , and . You did not open hints for this part. ANSWER: Video Tutor: Suspended Balls: Which String Breaks? First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the question at right. You can watch the video again at any point. T2 = T1 M1 M2 a g T1 = Part A A heavy crate is attached to the wall by a light rope, as shown in the figure. Another rope hangs off the opposite edge of the box. If you slowly increase the force on the free rope by pulling on it in a horizontal direction, which rope will break? Ignore friction and the mass of the ropes. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The rope attached to the wall will break. The rope that you are pulling on will break. Both ropes are equally likely to break.

Chapter 7 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Book on a Table A book weighing 5 N rests on top of a table. Part A A downward force of magnitude 5 N is exerted on the book by the force of ANSWER: Part B An upward force of magnitude _____ is exerted on the _____ by the table. the table gravity inertia . ANSWER: Part C Do the downward force in Part A and the upward force in Part B constitute a 3rd law pair? You did not open hints for this part. ANSWER: Part D The reaction to the force in Part A is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____ . You did not open hints for this part. ANSWER: 6 N / table 5 N / table 5 N / book 6 N / book yes no Part E The reaction to the force in Part B is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____. ANSWER: Part F Which of Newton’s laws dictates that the forces in Parts A and B are equal and opposite? ANSWER: Part G Which of Newton’s laws dictates that the forces in Parts B and E are equal and opposite? ANSWER: 5 N / earth / book / upward 5 N / book / table / upward 5 N / book / earth / upward 5 N / earth / book / downward 5 N / table / book / upward 5 N / table / earth / upward 5 N / book / table / upward 5 N / table / book / downward 5 N / earth / book / downward Newton’s 1st or 2nd law Newton’s 3rd law Blocks in an Elevator Ranking Task Three blocks are stacked on top of each other inside an elevator as shown in the figure. Answer the following questions with reference to the eight forces defined as follows. the force of the 3 block on the 2 block, , the force of the 2 block on the 3 block, , the force of the 3 block on the 1 block, , the force of the 1 block on the 3 block, , the force of the 2 block on the 1 block, , the force of the 1 block on the 2 block, , the force of the 1 block on the floor, , and the force of the floor on the 1 block, . Part A Assume the elevator is at rest. Rank the magnitude of the forces. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Newton’s 1st or 2nd law Newton’s 3rd law kg kg F3 on 2 kg kg F2 on 3 kg kg F3 on 1 kg kg F1 on 3 kg kg F2 on 1 kg kg F1 on 2 kg F1 on floor kg Ffloor on 1 Part B This question will be shown after you complete previous question(s). Newton’s 3rd Law Discussed Learning Goal: To understand Newton’s 3rd law, which states that a physical interaction always generates a pair of forces on the two interacting bodies. In Principia, Newton wrote: To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. (translation by Cajori) The phrase after the colon (often omitted from textbooks) makes it clear that this is a statement about the nature of force. The central idea is that physical interactions (e.g., due to gravity, bodies touching, or electric forces) cause forces to arise between pairs of bodies. Each pairwise interaction produces a pair of opposite forces, one acting on each body. In summary, each physical interaction between two bodies generates a pair of forces. Whatever the physical cause of the interaction, the force on body A from body B is equal in magnitude and opposite in direction to the force on body B from body A. Incidentally, Newton states that the word “action” denotes both (a) the force due to an interaction and (b) the changes in momentum that it imparts to the two interacting bodies. If you haven’t learned about momentum, don’t worry; for now this is just a statement about the origin of forces. Mark each of the following statements as true or false. If a statement refers to “two bodies” interacting via some force, you are not to assume that these two bodies have the same mass. Part A Every force has one and only one 3rd law pair force. ANSWER: Part B The two forces in each pair act in opposite directions. ANSWER: Part C The two forces in each pair can either both act on the same body or they can act on different bodies. ANSWER: true false true false Part D The two forces in each pair may have different physical origins (for instance, one of the forces could be due to gravity, and its pair force could be due to friction or electric charge). ANSWER: Part E The two forces of a 3rd law pair always act on different bodies. ANSWER: Part F Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.) You did not open hints for this part. ANSWER: true false true false true false Part G According to Newton’s 3rd law, the force on the (smaller) moon due to the (larger) earth is ANSWER: Pulling Three Blocks Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force . The magnitude of the tension in the string between blocks B and C is = 3.00 . Assume that each block has mass = 0.400 . true false greater in magnitude and antiparallel to the force on the earth due to the moon. greater in magnitude and parallel to the force on the earth due to the moon. equal in magnitude but antiparallel to the force on the earth due to the moon. equal in magnitude and parallel to the force on the earth due to the moon. smaller in magnitude and antiparallel to the force on the earth due to the moon. smaller in magnitude and parallel to the force on the earth due to the moon. F T N m kg Part A What is the magnitude of the force? Express your answer numerically in newtons. You did not open hints for this part. ANSWER: Part B What is the tension in the string between block A and block B? Express your answer numerically in newtons You did not open hints for this part. ANSWER: Pulling Two Blocks In the situation shown in the figure, a person is pulling with a constant, nonzero force on string 1, which is attached to block A. Block A is also attached to block B via string 2, as shown. For this problem, assume that neither string stretches and that friction is negligible. Both blocks have finite (nonzero) mass. F F = N TAB TAB = N F Part A Which one of the following statements correctly descibes the relationship between the accelerations of blocks A and B? You did not open hints for this part. ANSWER: Part B How does the magnitude of the tension in string 1, , compare with the tension in string 2, ? You did not open hints for this part. Block A has a larger acceleration than block B. Block B has a larger acceleration than block A. Both blocks have the same acceleration. More information is needed to determine the relationship between the accelerations. T1 T2 ANSWER: Tension in a Massless Rope Learning Goal: To understand the concept of tension and the relationship between tension and force. This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let and (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless, so that its weight is negligible compared with the tension. (This is not a ridiculous approximation–modern rope materials such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.) Consider the three sections of rope labeled a, b, and c in the figure. At point 1, a downward force of magnitude acts on section a. At point 1, an upward force of magnitude acts on section b. At point 1, the tension in the rope is . At point 2, a downward force of magnitude acts on section b. At point 2, an upward force of magnitude acts on section c. At point 2, the tension in the rope is . Assume, too, that the rope is at equilibrium. Part A What is the magnitude of the downward force on section a? Express your answer in terms of the tension . ANSWER: More information is needed to determine the relationship between and . T1 > T2 T1 = T2 T1 < T2 T1 T2 Fu Fd Fad Fbu T1 Fbd Fcu T2 Fad T1 Part B What is the magnitude of the upward force on section b? Express your answer in terms of the tension . ANSWER: Part C The magnitude of the upward force on c, , and the magnitude of the downward force on b, , are equal because of which of Newton's laws? ANSWER: Part D The magnitude of the force is ____ . ANSWER: Fad = Fbu T1 Fbu = Fcu Fbd 1st 2nd 3rd Fbu Fbd Part E Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces? You did not open hints for this part. ANSWER: Part F The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true? Check all that apply. ANSWER: less than greater than equal to Fu > Fd Fu = Fd Fu < Fd The tension in the rope is everywhere the same. The magnitudes of the forces exerted on the two objects by the rope are the same. The forces exerted on the two objects by the rope must be in opposite directions. The forces exerted on the two objects by the rope must be in the direction of the rope. Two Hanging Masses Two blocks with masses and hang one under the other. For this problem, take the positive direction to be upward, and use for the magnitude of the acceleration due to gravity. Case 1: Blocks at rest For Parts A and B assume the blocks are at rest. Part A Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: M1 M2 g T2 M1 M2 g Part B Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: Case 2: Accelerating blocks For Parts C and D the blocks are now accelerating upward (due to the tension in the strings) with acceleration of magnitude . Part C Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , , and . You did not open hints for this part. ANSWER: T2 = T1 M1 M2 g T1 = a T2 M1 M2 a g Part D Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , , and . You did not open hints for this part. ANSWER: Video Tutor: Suspended Balls: Which String Breaks? First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the question at right. You can watch the video again at any point. T2 = T1 M1 M2 a g T1 = Part A A heavy crate is attached to the wall by a light rope, as shown in the figure. Another rope hangs off the opposite edge of the box. If you slowly increase the force on the free rope by pulling on it in a horizontal direction, which rope will break? Ignore friction and the mass of the ropes. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The rope attached to the wall will break. The rope that you are pulling on will break. Both ropes are equally likely to break.

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Lab Description: Follow the instructions in the lab tasks below to behaviorially create and simulate a flip-flop. Afterwards, you will create a register and Arithmetic Logic Unit (ALU). Refer to Module 7 from the Digilent Real Digital website for more information about ALUs. These two components are the main components required to create an accumulator datapath. This accumulator datapath will act like a simple processor; the ALU will execute simple arithmetic/logic operations and each result will be stored in the register. In an accumulator, the value of the register will be upedated with each operation; the register is used as an input to the ALU and the newly computed result of the operation will be stored back into the register. You will create and implement this accumulator datapath in the last task of this lab. However, you will need to add an additional component to enable it to clearly operate on the FPGA board. You will create and use a clock divider to create a slower version of the FPGA board’s clock when you implement the accumulator datapath on the FPGA board. Refer to Module 10 from the Digilent Real Digital website for more information about clock dividers. Lab Tasks: 1. Create a behavioral VHDL module for a Rising-Edge Triggered (RET) D-Flip-Flop (DFF): a. In your design, use inputs “D” (data), “CLK” (the clock), “RST” (an asynchronous reset), “SET” (a synchronous set or preset signal), “CE” (clock enable), and output “Q” b. Create a VHDL test bench and simulate the flip-flop. Be sure to show the following behaviors with your simulation: i. The output “Q” sampling a ‘0’ from the input “D” ii. The output “Q” sampling a ‘1’ from the input “D” iii. The correct operation of the asynchronous reset iv. The correct operation of the synchronous preset v. The correct operation of the clock enable c. Include a screenshot of your simulation on the lab’s cover sheet. Label each of these behaviors on the waveform (it is ok to print out your cover sheet and write each behavior on the waveform). 2. Create a behavioral VHDL module for a 4-bit Arithmetic Logic Unit (ALU): a. I suggest you refer to Module 7 from the Digilent Real Digital website (in particular, the sections about ALU circuits and behavioral VHDL ALU descriptions). This 4-bit ALU will calculate arithmetic and logical expressions on two 4-bit numbers. Use behavioral expressions for the arithmetic and logic expressions (do not use port map statements to create a structural design using your ripple-carry adder from lab 3). Assume that the select input (or opcode) is 2-bits and is defined as shown in the table below: Opcode Function 00 A 01 A plus 1 10 A plus B 11 A and B b. Create a VHDL test bench to test your ALU. Use two input signal (the 4-bit values for A and B) combinations to test each operation of the ALU. Simulate your design and verify your output. Include a screenshot of your simulation on the lab’s cover sheet. 3. Create an accumulator datapath: a. First, create a 4-bit register. This is very similar to your flip-flop design from lab task 1. Ensure that your 4-bit register has inputs “D” (data), “CLK” (the clock), and “RST” (an asynchronous reset), and an output “Q”. Create a test bench and ensure that your 4-bit register operates correctly. b. Next, create a design module for the accumulator datapath and import your 4-bit register, 4-bit ALU, and seven-sgement display decoder (from lab 2) as components to this system. Connect your register, ALU, and seven-segment display decoder as follows: i. Connect the output of your ALU to the “D” input of your register ii. Connect the “Q” output of your register to both the “A” input of your ALU and the input of your seven-segement display iii. You should be left with four overall inputs: the “B” input of your ALU, the opcode input of your ALU, the CLK, and RST iv. You should be left with one overall output: the seven-segment display output c. Create a test bench to simulate the behavior of your accumulator datapath. In your test bench, simulate a few clock cycles to verify the correct operation of your system. d. Before implementing this system on the FPGA board, create and add one additional component to your system. Create and add a clock divider to this system; the input will be the board’s clock and the output will be a slower version of the clock to use for the register. Design your clock divider to slow the clock frequency to 1 Hz (1 clock cycle per second). Note that the clock on the lab FPGA board (Spartan 3) has a frequency of 50 MHz. If you purchased your board, the FPGA Basys 3 or Nexys 4 DDR FPGA board has a frequency of 100 MHz. I highly recommend taking a look at “Binary counters in VHDL” from Module 10 from the Digilent Real Digital website for information about clock dividers. e. Now, implement this system on the FPGA board. Connect the data input to four switches, connect the ALU opcode inputs to two buttons, the RST signal to one button, the CLK signal to the board’s clock, and the seven-segment display output to the seven-segment display. f. Ask the instructor to check your design, simulation waveforms, and FPGA board implementation of your circuit

Lab Description: Follow the instructions in the lab tasks below to behaviorially create and simulate a flip-flop. Afterwards, you will create a register and Arithmetic Logic Unit (ALU). Refer to Module 7 from the Digilent Real Digital website for more information about ALUs. These two components are the main components required to create an accumulator datapath. This accumulator datapath will act like a simple processor; the ALU will execute simple arithmetic/logic operations and each result will be stored in the register. In an accumulator, the value of the register will be upedated with each operation; the register is used as an input to the ALU and the newly computed result of the operation will be stored back into the register. You will create and implement this accumulator datapath in the last task of this lab. However, you will need to add an additional component to enable it to clearly operate on the FPGA board. You will create and use a clock divider to create a slower version of the FPGA board’s clock when you implement the accumulator datapath on the FPGA board. Refer to Module 10 from the Digilent Real Digital website for more information about clock dividers. Lab Tasks: 1. Create a behavioral VHDL module for a Rising-Edge Triggered (RET) D-Flip-Flop (DFF): a. In your design, use inputs “D” (data), “CLK” (the clock), “RST” (an asynchronous reset), “SET” (a synchronous set or preset signal), “CE” (clock enable), and output “Q” b. Create a VHDL test bench and simulate the flip-flop. Be sure to show the following behaviors with your simulation: i. The output “Q” sampling a ‘0’ from the input “D” ii. The output “Q” sampling a ‘1’ from the input “D” iii. The correct operation of the asynchronous reset iv. The correct operation of the synchronous preset v. The correct operation of the clock enable c. Include a screenshot of your simulation on the lab’s cover sheet. Label each of these behaviors on the waveform (it is ok to print out your cover sheet and write each behavior on the waveform). 2. Create a behavioral VHDL module for a 4-bit Arithmetic Logic Unit (ALU): a. I suggest you refer to Module 7 from the Digilent Real Digital website (in particular, the sections about ALU circuits and behavioral VHDL ALU descriptions). This 4-bit ALU will calculate arithmetic and logical expressions on two 4-bit numbers. Use behavioral expressions for the arithmetic and logic expressions (do not use port map statements to create a structural design using your ripple-carry adder from lab 3). Assume that the select input (or opcode) is 2-bits and is defined as shown in the table below: Opcode Function 00 A 01 A plus 1 10 A plus B 11 A and B b. Create a VHDL test bench to test your ALU. Use two input signal (the 4-bit values for A and B) combinations to test each operation of the ALU. Simulate your design and verify your output. Include a screenshot of your simulation on the lab’s cover sheet. 3. Create an accumulator datapath: a. First, create a 4-bit register. This is very similar to your flip-flop design from lab task 1. Ensure that your 4-bit register has inputs “D” (data), “CLK” (the clock), and “RST” (an asynchronous reset), and an output “Q”. Create a test bench and ensure that your 4-bit register operates correctly. b. Next, create a design module for the accumulator datapath and import your 4-bit register, 4-bit ALU, and seven-sgement display decoder (from lab 2) as components to this system. Connect your register, ALU, and seven-segment display decoder as follows: i. Connect the output of your ALU to the “D” input of your register ii. Connect the “Q” output of your register to both the “A” input of your ALU and the input of your seven-segement display iii. You should be left with four overall inputs: the “B” input of your ALU, the opcode input of your ALU, the CLK, and RST iv. You should be left with one overall output: the seven-segment display output c. Create a test bench to simulate the behavior of your accumulator datapath. In your test bench, simulate a few clock cycles to verify the correct operation of your system. d. Before implementing this system on the FPGA board, create and add one additional component to your system. Create and add a clock divider to this system; the input will be the board’s clock and the output will be a slower version of the clock to use for the register. Design your clock divider to slow the clock frequency to 1 Hz (1 clock cycle per second). Note that the clock on the lab FPGA board (Spartan 3) has a frequency of 50 MHz. If you purchased your board, the FPGA Basys 3 or Nexys 4 DDR FPGA board has a frequency of 100 MHz. I highly recommend taking a look at “Binary counters in VHDL” from Module 10 from the Digilent Real Digital website for information about clock dividers. e. Now, implement this system on the FPGA board. Connect the data input to four switches, connect the ALU opcode inputs to two buttons, the RST signal to one button, the CLK signal to the board’s clock, and the seven-segment display output to the seven-segment display. f. Ask the instructor to check your design, simulation waveforms, and FPGA board implementation of your circuit

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Computer/information Security Q1. Identify legislative and regulative requirements relative to information security for a bank

Computer/information Security Q1. Identify legislative and regulative requirements relative to information security for a bank

Computer/information Security     Q1. Identify legislative and regulative requirements relative to … Read More...
Three forces and a couple act on the triangle body, (a) Express the three forces and the couple in Cartesian vector form , (b) Resolve each of the three forces into a force and a couple at point A , (c) Determine by vector addition the resultant force R= {F1 and the resultant couple C={C1 of the system acting on the body point A.

Three forces and a couple act on the triangle body, (a) Express the three forces and the couple in Cartesian vector form , (b) Resolve each of the three forces into a force and a couple at point A , (c) Determine by vector addition the resultant force R= {F1 and the resultant couple C={C1 of the system acting on the body point A.