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...
In observing human behavior, it is impossible to ________. understand everything about a person all at once choose to limit what you look at in a person find patterns across different kinds of observation make any real progress toward solving the personality puzzle

In observing human behavior, it is impossible to ________. understand everything about a person all at once choose to limit what you look at in a person find patterns across different kinds of observation make any real progress toward solving the personality puzzle

In observing human behavior, it is impossible to ________. understand … Read More...
BI 102 Lab 1 Writing Assignment How did the different concentrations of sucrose impact osmotic rate? This assignment requires you to evaluate a hypothesis and communicate the results of your experiment on the rate of osmosis into sucrose solutions of varying concentrations. The questions below are meant to guide you to reporting the key findings of your experiment and help you think through how to explain the findings and draw conclusions from them in a scientific manner. ASSIGNMENT: Please respond to the following questions to complete your laboratory write up. For this assignment you will only focus on the osmosis of water into sucrose concentrations of varying concentration. Make sure that your write up is accurate, and clearly written so that it is easily readable. A grading rubric is provided on the second page of this assignment. To earn full points on your write up, you must provide answers that align to the “meets” column of your grading rubric as well as meeting all “Quality of Writing and Mechanics” elements described in the rubric. There are also some tips on pages 3-4 of this assignment to help you succeed. FORMAT: • Type your responses, using 1.5 or double spacing. • Include the section headings (Hypothesis, Results, Analysis) and question number (example: 1, 2, 3, etc) in your answers but do not rewrite the question. • Graphs may be made with a computer program (example: Microsoft excel, Mac numbers, etc) or may be neatly produced with a ruler on graphing paper. • Print out the cover sheet on page 2 of this assignment, read and sign the academic honesty statement, and submit it with your write up. Your instructor WILL NOT accept a write up without the signed cover sheet. DUE DATE: Your write up is due at the beginning of class next week. Late assignments will have 1 point deducted per day up to 5 days, at which point the assignment will be assigned 0 points. Hypothesis and Prediction – Part 1 of Rubric 1. What did you think was going to happen in this experiment and why? You may find it helpful to state your answers to these questions as an “if-then” hypothesis-prediction. Be sure you have included a biological rationale that explains WHY you made this hypothesis/prediction. (You worked on this in question 2 on page 10 of this lab activity) Results – Part 2 of Rubric 2. How did the different concentrations of sucrose impact osmotic rate? Answer this question by creating a line graph that shows the results of your experiment. If you need assistance building a graph, there is a Guide to Graphing resource available on your Moodle lab course site. Analysis- Part 3 of Rubric 3. Explain why you think that the results shown in your graph support or refute your hypothesis (remember we never “prove” anything in science). Consider all your data and the overall data pattern as you answer this question. Don’t ignore unusual data that may not seem to fit into a specific patterns (“outliers”). Explain what you think might be behind these unusual data points. 4. What is the biological significance of your results? What biological concepts explain completely why these events happened in the experiment? How do these results help you understand the biology of the cell and how materials move back and forth across the cell membrane? (A hint: refer back to questions 1A-1F on page 10 of this lab activity). Think about giving a specific example. References- Mechanics Checklist 5. Provide at least one full citation (make sure you include an in-text citation that pinpoints where you used this resource) for a resource you made use of in performing the experiment, understanding the concepts and writing this assignment. (Perhaps your lab manual? Your textbook? A website?) If you used more than one resource, you need to cite each one! If you need help with citations, a Guide to Citing References is available on your Moodle lab course site. Please print out and submit this cover sheet with your lab writeup! Lab Writeup Assignment (1) Assessment Rubric-­‐ 10 points total Name: ________________________________________ Element Misses (1 point) Approaches (2 points) Meets (3 points) Hypothesis Clarity/Specificity Testability Rationale ___Hypothesis is unclear and hardto- understand ___Hypothesis is not testable ___No biological rationale for hypothesis or rationale is fully inaccurate ___Hypothesis included is clearly stated, but not specific or lacks specific details __Hypothesis is testable, but not in a feasible way in this lab ___Some foundation for hypothesis, but based in part on biological inaccuracy ___Hypothesis included is clearly stated and very specific ___Hypothesis is testable and could be tested within lab parameters ___Rationale for hypothesis is grounded in accurate biological information Graph Title Axes Variables Key Graph clarity Data accuracy ___Graph lacks a title ___Axes are not labeled ___Variables not addressed in graph ___No key or way to tell data points apart ___Graph is hard to read and comparisons cannot be made: Inappropriate graph type or use of scale ___Data graphed is inaccurate or does not relate to experiment ___Graph has a title that is not very descriptive ___Axes are either unlabeled, or units are unclear or wrong ___Variables addressed in graph, but not on correct axes ___Key included, but is hard to understand ___Graph is somewhat readable, comparisons can be made with difficulty: Appropriate graph type, but not scaled well ___Data graphed is partially accurate; some data is missing ___Graph has a concise, descriptive title ___Axes are labeled, including clarification of units used ___Variables on correct axes ___A clear, easy-to-use key to data points is included ___Graph is clearly readable and comparisons between treatments are easy to make: Graph type and scale are appropriate to data ___Data graphed is accurate and includes all relevant data, including controls (if needed) Analysis Hypothesis Scientific language Data addressed Explanation ___Hypothesis is not addressed ___Hypothesis is described using language like proven, true, or right ___No explanations for data patterns observed in graph or data does not support conclusions. ___No biological explanation for data trends or explanations are completely inaccurate ___Hypothesis is mentioned, but not linked well to data ___Hypothesis is not consistently described as supported or refuted ___Some data considered in conclusions but other data is ignored. Any unusual “outliers” are ignored ___Explanations include minimal or some inaccurate biological concepts ___Hypothesis is evaluated based upon data ___Hypothesis is consistently described as supported or refuted ___All data collected is considered and addressed by conclusions, including presence of outliers, ___Explanations include relevant and accurate biological concepts Quality of Writing and Mechanics: Worth 1 point. Writeup should meet all of the following criteria! Yes No ☐ ☐ Write up includes your name, the date, and your lab section ☐ ☐ Write up is free from spelling and grammatical errors (make sure you proofread!!) ☐ ☐ Write up is clear and easy-to-understand ☐ ☐ Write up includes full citation for at least one reference with corresponding in-text citation ☐ ☐ All portions of write up are clearly labeled, and question numbers are included Plagiarism refers to the use of original work, ideas, or text that are not your own. This includes cut-and-paste from websites, copying directly from texts, and copying the work of others, including fellow students. Telling someone your answers to the questions (including telling someone how to make their graph, question #2), or asking for the answers to any question, is cheating. (Asking someone how to make the graph for this assignment is NOT the same as asking for help learning excel or some other software). All forms of cheating, including plagiarism and copying of work will result in an immediate zero for the exam, quiz, or assignment. In the case of copying, all parties involved in the unethical behavior will earn zeros. Cheating students will be referred to the Student Conduct Committee for further action. You also have the right to appeal to the Student Conduct Committee. I have read and understand the plagiarism statement. ____________________________________________________ Signature Guidelines for Good Quality Scientific Reports Hypothesis and Prediction: The hypothesis is a tentative explanation for the phenomenon. Remember that: • A good hypothesis and prediction is testable (and should be testable under the conditions of our lab environment; For example, if your hypothesis requires shooting a rocket into space, then its not really testable under our laboratory conditions). • Your explanation can be ruled out through testing, or falsified. • A good hypothesis and prediction is detailed and specific in what it is testing. • A good hypothesis provides a rationale or explanation for why you think your prediction is reasonable and this rationale is based on what we know about biology. • A good prediction is specific and can be tested with a specific experiment. Examples*: I think that diet soda will float and regular soda will sink. {This hypothesis misses the goal. It is not specific as we don’t know where the sodas are floating and sinking, and it does not provide any explanation to explain why the hypothesis makes sense} Because diet soda does not contain sugar and regular soda does, the diet soda will float in a bucket of water, while regular soda will sink. {This hypothesis approaches the goal. It is more specific about the conditions, and it provides a partial explanation about why the hypothesis makes sense, but the connection between sugar and sinking is unclear} If diet soda does not contain sugar, then its density (mass/volume) is lower than that of regular soda which does contain sugar, and so diet soda will float in a bucket of water while regular soda sinks. {This hypothesis meets the goal. It is specific and the rationale- sugar affects density and density is what determines floating or sinking in water- is clearly articulated} *Note that these examples are for different experiments and investigations and NOT about your osmosis lab. They are provided only to help you think about what you need to include in your write up. Graph: The graph is a visual representation of the data you gathered while testing your hypothesis. Remember that: • A graph needs a concise title that clearly describes the data that it is showing. • Data must be put on the correct axes of the graph. In general, the data you collected (representing what you are trying to find out about) goes on the vertical (Y) axis. The supporting data that that describes how, when or under what conditions you collected your data goes on the horizontal (X) axis. (For this reason time nearly always goes on the X-axis). • Axes must be labeled, including the units in which data were recorded • Data points should be clearly marked and identified; a key is helpful if more than one group of data is included in the graph. • The scale of a graph is important. It should be consistent (there should be no change in the units or increments on a single axis) and appropriate to the data you collected Examples: {This graph misses the goal. There is no title, nor is there a key to help distinguish what the data points mean. The scale is too large- from 0 to 100 with an increment of 50, when the maximum number in the graph is 25- and makes it hard to interpret this graph. The x-axis is labeled, but without units (the months) and the y-axis has units, but the label is incomplete- number of what?} {This graph meets the goal. There is a descriptive title, and all of the axes are clearly labeled with units. There is a key so that we can distinguish what each set of data points represent. The dependent variable (number of individuals) is correctly placed on the y-axis with the independent variable of time placed on the x-axis. The scale of 0-30 is appropriate to the data, with each line on the x-axis representing an increment of 5.} 0 50 100 Number Month 0 5 10 15 20 25 30 March April May June July Number of individuals Month (2011) Population size of three different madtom catiCish in the Marais de Cygnes River in Spring/Summer 2011 Brindled madtom Neosho madtom Slender madtom Analysis: You need to evaluate your hypothesis based on the data patterns shown by your graph. Remember that: • You use data to determine support or refute your hypothesis. It is only possible to support a hypothesis, not to “prove” one (that would require testing every possible permutation and combination of factors). Your evaluation of your hypothesis should not be contradicted by the pattern shown by your data. • Refer back to the prediction you made as part of your hypothesis and use your data to justify your decision to support or refute your hypothesis. • In the “if” part of your hypothesis you should have provided a rationale, or explanation for the prediction you made in your hypothesis (“then” part of hypothesis”). Use this to help you explain why you think you observed the specific pattern of data revealed in your graph. • You should consider all of the data you collected in examining the support (or lack of support for your hypothesis). If there are unusual data points or “outliers” that don’t seem to fit the general pattern in your graph, explain what you think those mean. Examples: I was right. Diet Pepsi floated and so did Apricot Nectar. Regular Pepsi sank. Obviously the regular Pepsi was heavier. This helps us understand the concept of density, which is a really important one. {This analysis misses the goal. The hypothesis isn’t actually mentioned and the data is only briefly described. There is no explanation of the importance of the Apricot Nectar results. Finally, there is no connection to how these results help understand density or why it is biologically important} I hypothesized that diet soda would float, and all three cans of diet Pepsi did float while the regular Pepsi sank. This supports my hypothesis. Both types of Pepsi were 8.5 fluid ounces in volume, but the regular Pepsi also contained 16 grams of sugar. This means that the regular Pepsi had 16 more grams of mass provided by the sugar in the same amount of volume. This would lead to an increase in density, which explains why the regular soda cans sank. When we put in a can of Apricot Nectar, which had 19 grams of sugar, it floated. This was unexpected, but I think it is explained by the fact that an Apricot Nectar can had a volume of 7 fluid ounces, but the dimensions of the can are the same as that of a Pepsi can. A same-sized can with less liquid probably has an air space that helped it float. The results of this experiment help us understand how the air bladder of a fish, which creates an air space inside the fish, helps it float in the water and also how seaweeds and other living things with air spaces or other factors that decrease their density keep from sinking to the bottom of the water. {This analysis meets the goal. It clearly ties the hypothesis to the results and outlines what they mean. It describes how the results support the hypothesis, but also explains a possible reason behind the unusual results of the Apricot Nectar. Finally, there is a link to how this experiment helps us understand biology}

BI 102 Lab 1 Writing Assignment How did the different concentrations of sucrose impact osmotic rate? This assignment requires you to evaluate a hypothesis and communicate the results of your experiment on the rate of osmosis into sucrose solutions of varying concentrations. The questions below are meant to guide you to reporting the key findings of your experiment and help you think through how to explain the findings and draw conclusions from them in a scientific manner. ASSIGNMENT: Please respond to the following questions to complete your laboratory write up. For this assignment you will only focus on the osmosis of water into sucrose concentrations of varying concentration. Make sure that your write up is accurate, and clearly written so that it is easily readable. A grading rubric is provided on the second page of this assignment. To earn full points on your write up, you must provide answers that align to the “meets” column of your grading rubric as well as meeting all “Quality of Writing and Mechanics” elements described in the rubric. There are also some tips on pages 3-4 of this assignment to help you succeed. FORMAT: • Type your responses, using 1.5 or double spacing. • Include the section headings (Hypothesis, Results, Analysis) and question number (example: 1, 2, 3, etc) in your answers but do not rewrite the question. • Graphs may be made with a computer program (example: Microsoft excel, Mac numbers, etc) or may be neatly produced with a ruler on graphing paper. • Print out the cover sheet on page 2 of this assignment, read and sign the academic honesty statement, and submit it with your write up. Your instructor WILL NOT accept a write up without the signed cover sheet. DUE DATE: Your write up is due at the beginning of class next week. Late assignments will have 1 point deducted per day up to 5 days, at which point the assignment will be assigned 0 points. Hypothesis and Prediction – Part 1 of Rubric 1. What did you think was going to happen in this experiment and why? You may find it helpful to state your answers to these questions as an “if-then” hypothesis-prediction. Be sure you have included a biological rationale that explains WHY you made this hypothesis/prediction. (You worked on this in question 2 on page 10 of this lab activity) Results – Part 2 of Rubric 2. How did the different concentrations of sucrose impact osmotic rate? Answer this question by creating a line graph that shows the results of your experiment. If you need assistance building a graph, there is a Guide to Graphing resource available on your Moodle lab course site. Analysis- Part 3 of Rubric 3. Explain why you think that the results shown in your graph support or refute your hypothesis (remember we never “prove” anything in science). Consider all your data and the overall data pattern as you answer this question. Don’t ignore unusual data that may not seem to fit into a specific patterns (“outliers”). Explain what you think might be behind these unusual data points. 4. What is the biological significance of your results? What biological concepts explain completely why these events happened in the experiment? How do these results help you understand the biology of the cell and how materials move back and forth across the cell membrane? (A hint: refer back to questions 1A-1F on page 10 of this lab activity). Think about giving a specific example. References- Mechanics Checklist 5. Provide at least one full citation (make sure you include an in-text citation that pinpoints where you used this resource) for a resource you made use of in performing the experiment, understanding the concepts and writing this assignment. (Perhaps your lab manual? Your textbook? A website?) If you used more than one resource, you need to cite each one! If you need help with citations, a Guide to Citing References is available on your Moodle lab course site. Please print out and submit this cover sheet with your lab writeup! Lab Writeup Assignment (1) Assessment Rubric-­‐ 10 points total Name: ________________________________________ Element Misses (1 point) Approaches (2 points) Meets (3 points) Hypothesis Clarity/Specificity Testability Rationale ___Hypothesis is unclear and hardto- understand ___Hypothesis is not testable ___No biological rationale for hypothesis or rationale is fully inaccurate ___Hypothesis included is clearly stated, but not specific or lacks specific details __Hypothesis is testable, but not in a feasible way in this lab ___Some foundation for hypothesis, but based in part on biological inaccuracy ___Hypothesis included is clearly stated and very specific ___Hypothesis is testable and could be tested within lab parameters ___Rationale for hypothesis is grounded in accurate biological information Graph Title Axes Variables Key Graph clarity Data accuracy ___Graph lacks a title ___Axes are not labeled ___Variables not addressed in graph ___No key or way to tell data points apart ___Graph is hard to read and comparisons cannot be made: Inappropriate graph type or use of scale ___Data graphed is inaccurate or does not relate to experiment ___Graph has a title that is not very descriptive ___Axes are either unlabeled, or units are unclear or wrong ___Variables addressed in graph, but not on correct axes ___Key included, but is hard to understand ___Graph is somewhat readable, comparisons can be made with difficulty: Appropriate graph type, but not scaled well ___Data graphed is partially accurate; some data is missing ___Graph has a concise, descriptive title ___Axes are labeled, including clarification of units used ___Variables on correct axes ___A clear, easy-to-use key to data points is included ___Graph is clearly readable and comparisons between treatments are easy to make: Graph type and scale are appropriate to data ___Data graphed is accurate and includes all relevant data, including controls (if needed) Analysis Hypothesis Scientific language Data addressed Explanation ___Hypothesis is not addressed ___Hypothesis is described using language like proven, true, or right ___No explanations for data patterns observed in graph or data does not support conclusions. ___No biological explanation for data trends or explanations are completely inaccurate ___Hypothesis is mentioned, but not linked well to data ___Hypothesis is not consistently described as supported or refuted ___Some data considered in conclusions but other data is ignored. Any unusual “outliers” are ignored ___Explanations include minimal or some inaccurate biological concepts ___Hypothesis is evaluated based upon data ___Hypothesis is consistently described as supported or refuted ___All data collected is considered and addressed by conclusions, including presence of outliers, ___Explanations include relevant and accurate biological concepts Quality of Writing and Mechanics: Worth 1 point. Writeup should meet all of the following criteria! Yes No ☐ ☐ Write up includes your name, the date, and your lab section ☐ ☐ Write up is free from spelling and grammatical errors (make sure you proofread!!) ☐ ☐ Write up is clear and easy-to-understand ☐ ☐ Write up includes full citation for at least one reference with corresponding in-text citation ☐ ☐ All portions of write up are clearly labeled, and question numbers are included Plagiarism refers to the use of original work, ideas, or text that are not your own. This includes cut-and-paste from websites, copying directly from texts, and copying the work of others, including fellow students. Telling someone your answers to the questions (including telling someone how to make their graph, question #2), or asking for the answers to any question, is cheating. (Asking someone how to make the graph for this assignment is NOT the same as asking for help learning excel or some other software). All forms of cheating, including plagiarism and copying of work will result in an immediate zero for the exam, quiz, or assignment. In the case of copying, all parties involved in the unethical behavior will earn zeros. Cheating students will be referred to the Student Conduct Committee for further action. You also have the right to appeal to the Student Conduct Committee. I have read and understand the plagiarism statement. ____________________________________________________ Signature Guidelines for Good Quality Scientific Reports Hypothesis and Prediction: The hypothesis is a tentative explanation for the phenomenon. Remember that: • A good hypothesis and prediction is testable (and should be testable under the conditions of our lab environment; For example, if your hypothesis requires shooting a rocket into space, then its not really testable under our laboratory conditions). • Your explanation can be ruled out through testing, or falsified. • A good hypothesis and prediction is detailed and specific in what it is testing. • A good hypothesis provides a rationale or explanation for why you think your prediction is reasonable and this rationale is based on what we know about biology. • A good prediction is specific and can be tested with a specific experiment. Examples*: I think that diet soda will float and regular soda will sink. {This hypothesis misses the goal. It is not specific as we don’t know where the sodas are floating and sinking, and it does not provide any explanation to explain why the hypothesis makes sense} Because diet soda does not contain sugar and regular soda does, the diet soda will float in a bucket of water, while regular soda will sink. {This hypothesis approaches the goal. It is more specific about the conditions, and it provides a partial explanation about why the hypothesis makes sense, but the connection between sugar and sinking is unclear} If diet soda does not contain sugar, then its density (mass/volume) is lower than that of regular soda which does contain sugar, and so diet soda will float in a bucket of water while regular soda sinks. {This hypothesis meets the goal. It is specific and the rationale- sugar affects density and density is what determines floating or sinking in water- is clearly articulated} *Note that these examples are for different experiments and investigations and NOT about your osmosis lab. They are provided only to help you think about what you need to include in your write up. Graph: The graph is a visual representation of the data you gathered while testing your hypothesis. Remember that: • A graph needs a concise title that clearly describes the data that it is showing. • Data must be put on the correct axes of the graph. In general, the data you collected (representing what you are trying to find out about) goes on the vertical (Y) axis. The supporting data that that describes how, when or under what conditions you collected your data goes on the horizontal (X) axis. (For this reason time nearly always goes on the X-axis). • Axes must be labeled, including the units in which data were recorded • Data points should be clearly marked and identified; a key is helpful if more than one group of data is included in the graph. • The scale of a graph is important. It should be consistent (there should be no change in the units or increments on a single axis) and appropriate to the data you collected Examples: {This graph misses the goal. There is no title, nor is there a key to help distinguish what the data points mean. The scale is too large- from 0 to 100 with an increment of 50, when the maximum number in the graph is 25- and makes it hard to interpret this graph. The x-axis is labeled, but without units (the months) and the y-axis has units, but the label is incomplete- number of what?} {This graph meets the goal. There is a descriptive title, and all of the axes are clearly labeled with units. There is a key so that we can distinguish what each set of data points represent. The dependent variable (number of individuals) is correctly placed on the y-axis with the independent variable of time placed on the x-axis. The scale of 0-30 is appropriate to the data, with each line on the x-axis representing an increment of 5.} 0 50 100 Number Month 0 5 10 15 20 25 30 March April May June July Number of individuals Month (2011) Population size of three different madtom catiCish in the Marais de Cygnes River in Spring/Summer 2011 Brindled madtom Neosho madtom Slender madtom Analysis: You need to evaluate your hypothesis based on the data patterns shown by your graph. Remember that: • You use data to determine support or refute your hypothesis. It is only possible to support a hypothesis, not to “prove” one (that would require testing every possible permutation and combination of factors). Your evaluation of your hypothesis should not be contradicted by the pattern shown by your data. • Refer back to the prediction you made as part of your hypothesis and use your data to justify your decision to support or refute your hypothesis. • In the “if” part of your hypothesis you should have provided a rationale, or explanation for the prediction you made in your hypothesis (“then” part of hypothesis”). Use this to help you explain why you think you observed the specific pattern of data revealed in your graph. • You should consider all of the data you collected in examining the support (or lack of support for your hypothesis). If there are unusual data points or “outliers” that don’t seem to fit the general pattern in your graph, explain what you think those mean. Examples: I was right. Diet Pepsi floated and so did Apricot Nectar. Regular Pepsi sank. Obviously the regular Pepsi was heavier. This helps us understand the concept of density, which is a really important one. {This analysis misses the goal. The hypothesis isn’t actually mentioned and the data is only briefly described. There is no explanation of the importance of the Apricot Nectar results. Finally, there is no connection to how these results help understand density or why it is biologically important} I hypothesized that diet soda would float, and all three cans of diet Pepsi did float while the regular Pepsi sank. This supports my hypothesis. Both types of Pepsi were 8.5 fluid ounces in volume, but the regular Pepsi also contained 16 grams of sugar. This means that the regular Pepsi had 16 more grams of mass provided by the sugar in the same amount of volume. This would lead to an increase in density, which explains why the regular soda cans sank. When we put in a can of Apricot Nectar, which had 19 grams of sugar, it floated. This was unexpected, but I think it is explained by the fact that an Apricot Nectar can had a volume of 7 fluid ounces, but the dimensions of the can are the same as that of a Pepsi can. A same-sized can with less liquid probably has an air space that helped it float. The results of this experiment help us understand how the air bladder of a fish, which creates an air space inside the fish, helps it float in the water and also how seaweeds and other living things with air spaces or other factors that decrease their density keep from sinking to the bottom of the water. {This analysis meets the goal. It clearly ties the hypothesis to the results and outlines what they mean. It describes how the results support the hypothesis, but also explains a possible reason behind the unusual results of the Apricot Nectar. Finally, there is a link to how this experiment helps us understand biology}

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Chapter 6 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 PSS 6.1 Equilibrium Problems Learning Goal: To practice Problem-Solving Strategy 6.1 for equilibrium problems. A pair of students are lifting a heavy trunk on move-in day. Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity . Each rope makes an angle with respect to the vertical. The gravitational force acting on the trunk has magnitude . Find the tension in each rope. PROBLEM-SOLVING STRATEGY 6.1 Equilibrium problems MODEL: Make simplifying assumptions. VISUALIZE: Establish a coordinate system, define symbols, and identify what the problem is asking you to find. This is the process of translating words into symbols. Identify all forces acting on the object, and show them on a free-body diagram. These elements form the pictorial representation of the problem. SOLVE: The mathematical representation is based on Newton’s first law: . The vector sum of the forces is found directly from the free-body diagram. v  FG T F  = = net i F  i 0 ASSESS: Check if your result has the correct units, is reasonable, and answers the question. Model The trunk is moving at a constant velocity. This means that you can model it as a particle in dynamic equilibrium and apply the strategy above. Furthermore, you can ignore the masses of the ropes and the ring because it is reasonable to assume that their combined weight is much less than the weight of the trunk. Visualize Part A The most convenient coordinate system for this problem is one in which the y axis is vertical and the ropes both lie in the xy plane, as shown below. Identify the forces acting on the trunk, and then draw a free-body diagram of the trunk in the diagram below. The black dot represents the trunk as it is lifted by the students. Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded. ANSWER: Part B This question will be shown after you complete previous question(s). Solve Part C This question will be shown after you complete previous question(s). Assess Part D This question will be shown after you complete previous question(s). A Gymnast on a Rope A gymnast of mass 70.0 hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value for the acceleration of gravity. Part A Calculate the tension in the rope if the gymnast hangs motionless on the rope. Express your answer in newtons. You did not open hints for this part. ANSWER: Part B Calculate the tension in the rope if the gymnast climbs the rope at a constant rate. Express your answer in newtons. You did not open hints for this part. kg 9.81m/s2 T T = N T ANSWER: Part C Calculate the tension in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: Part D Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: T = N T m/s2 T = N T m/s2 T = N Applying Newton’s 2nd Law Learning Goal: To learn a systematic approach to solving Newton’s 2nd law problems using a simple example. Once you have decided to solve a problem using Newton’s 2nd law, there are steps that will lead you to a solution. One such prescription is the following: Visualize the problem and identify special cases. Isolate each body and draw the forces acting on it. Choose a coordinate system for each body. Apply Newton’s 2nd law to each body. Write equations for the constraints and other given information. Solve the resulting equations symbolically. Check that your answer has the correct dimensions and satisfies special cases. If numbers are given in the problem, plug them in and check that the answer makes sense. Think about generalizations or simplfications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass that is pulled up a frictionless plane inclined at angle with respect to the horizontal by a perfect string that passes over a perfect pulley to a block of mass that is hanging vertically. Visualize the problem and identify special cases First examine the problem by drawing a picture and visualizing the motion. Apply Newton’s 2nd law, , to each body in your mind. Don’t worry about which quantities are given. Think about the forces on each body: How are these consistent with the direction of the acceleration for that body? Can you think of any special cases that you can solve quickly now and use to test your understanding later? m2  m1 F = ma One special case in this problem is if , in which case block 1 would simply fall freely under the acceleration of gravity: . Part A Consider another special case in which the inclined plane is vertical ( ). In this case, for what value of would the acceleration of the two blocks be equal to zero? Express your answer in terms of some or all of the variables and . ANSWER: Isolate each body and draw the forces acting on it A force diagram should include only real forces that act on the body and satisfy Newton’s 3rd law. One way to check if the forces are real is to detrmine whether they are part of a Newton’s 3rd law pair, that is, whether they result from a physical interaction that also causes an opposite force on some other body, which may not be part of the problem. Do not decompose the forces into components, and do not include resultant forces that are combinations of other real forces like centripetal force or fictitious forces like the “centrifugal” force. Assign each force a symbol, but don’t start to solve the problem at this point. Part B Which of the four drawings is a correct force diagram for this problem? = 0 m2 = −g a 1 j ^  = /2 m1 m2 g m1 = ANSWER: Choose a coordinate system for each body Newton’s 2nd law, , is a vector equation. To add or subtract vectors it is often easiest to decompose each vector into components. Whereas a particular set of vector components is only valid in a particular coordinate system, the vector equality holds in any coordinate system, giving you freedom to pick a coordinate system that most simplifies the equations that result from the component equations. It’s generally best to pick a coordinate system where the acceleration of the system lies directly on one of the coordinate axes. If there is no acceleration, then pick a coordinate system with as many unknowns as possible along the coordinate axes. Vectors that lie along the axes appear in only one of the equations for each component, rather than in two equations with trigonometric prefactors. Note that it is sometimes advantageous to use different coordinate systems for each body in the problem. In this problem, you should use Cartesian coordinates and your axes should be stationary with respect to the inclined plane. Part C Given the criteria just described, what orientation of the coordinate axes would be best to use in this problem? In the answer options, “tilted” means with the x axis oriented parallel to the plane (i.e., at angle to the horizontal), and “level” means with the x axis horizontal. ANSWER: Apply Newton’s 2nd law to each body a b c d F  = ma  tilted for both block 1 and block 2 tilted for block 1 and level for block 2 level for block 1 and tilted for block 2 level for both block 1 and block 2 Part D What is , the sum of the x components of the forces acting on block 2? Take forces acting up the incline to be positive. Express your answer in terms of some or all of the variables tension , , the magnitude of the acceleration of gravity , and . You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Lifting a Bucket A 6- bucket of water is being pulled straight up by a string at a constant speed. F2x T m2 g  m2a2x =F2x = kg Part A What is the tension in the rope? ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Friction Force on a Dancer on a Drawbridge A dancer is standing on one leg on a drawbridge that is about to open. The coefficients of static and kinetic friction between the drawbridge and the dancer’s foot are and , respectively. represents the normal force exerted on the dancer by the bridge, and represents the gravitational force exerted on the dancer, as shown in the drawing . For all the questions, we can assume that the bridge is a perfectly flat surface and lacks the curvature characteristic of most bridges. about 42 about 60 about 78 0 because the bucket has no acceleration. N N N N μs μk n F  g Part A Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the x component of the friction force, ? Express your answer in terms of some or all of the variables , , and/or . You did not open hints for this part. ANSWER: Part B The drawbridge then starts to rise and the dancer continues to stand on one leg. The drawbridge stops just at the point where the dancer is on the verge of slipping. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. F  f n μs μk Ff = Ff n μs μk  You did not open hints for this part. ANSWER: Part C Then, because the bridge is old and poorly designed, it falls a little bit and then jerks. This causes the person to start to slide down the bridge at a constant speed. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. ANSWER: Part D The bridge starts to come back down again. The dancer stops sliding. However, again because of the age and design of the bridge it never makes it all the way down; rather it stops half a meter short. This half a meter corresponds to an angle degree (see the diagram, which has the angle exaggerated). What is the force of friction now? Express your answer in terms of some or all of the variables , , and . Ff = Ff n μs μk  Ff =   1 Ff  n Fg You did not open hints for this part. ANSWER: Kinetic Friction Ranking Task Below are eight crates of different mass. The crates are attached to massless ropes, as indicated in the picture, where the ropes are marked by letters. Each crate is being pulled to the right at the same constant speed. The coefficient of kinetic friction between each crate and the surface on which it slides is the same for all eight crates. Ff = Part A Rank the ropes on the basis of the force each exerts on the crate immediately to its left. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Pushing a Block Learning Goal: To understand kinetic and static friction. A block of mass lies on a horizontal table. The coefficient of static friction between the block and the table is . The coefficient of kinetic friction is , with . Part A m μs μk μk < μs If the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from the table), what is the magnitude of the force due to friction? You did not open hints for this part. ANSWER: Part B Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With what force must you be pushing the block just before the block begins to move? Express the magnitude of in terms of some or all the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. ANSWER: Part C Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of the friction force? Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. Ffriction = F F μs μk m g F = μs μk m g ANSWER: Part D Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration of the block after it begins to move. Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . 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. Ffriction = a μs μk m g a =

Chapter 6 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 PSS 6.1 Equilibrium Problems Learning Goal: To practice Problem-Solving Strategy 6.1 for equilibrium problems. A pair of students are lifting a heavy trunk on move-in day. Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity . Each rope makes an angle with respect to the vertical. The gravitational force acting on the trunk has magnitude . Find the tension in each rope. PROBLEM-SOLVING STRATEGY 6.1 Equilibrium problems MODEL: Make simplifying assumptions. VISUALIZE: Establish a coordinate system, define symbols, and identify what the problem is asking you to find. This is the process of translating words into symbols. Identify all forces acting on the object, and show them on a free-body diagram. These elements form the pictorial representation of the problem. SOLVE: The mathematical representation is based on Newton’s first law: . The vector sum of the forces is found directly from the free-body diagram. v  FG T F  = = net i F  i 0 ASSESS: Check if your result has the correct units, is reasonable, and answers the question. Model The trunk is moving at a constant velocity. This means that you can model it as a particle in dynamic equilibrium and apply the strategy above. Furthermore, you can ignore the masses of the ropes and the ring because it is reasonable to assume that their combined weight is much less than the weight of the trunk. Visualize Part A The most convenient coordinate system for this problem is one in which the y axis is vertical and the ropes both lie in the xy plane, as shown below. Identify the forces acting on the trunk, and then draw a free-body diagram of the trunk in the diagram below. The black dot represents the trunk as it is lifted by the students. Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded. ANSWER: Part B This question will be shown after you complete previous question(s). Solve Part C This question will be shown after you complete previous question(s). Assess Part D This question will be shown after you complete previous question(s). A Gymnast on a Rope A gymnast of mass 70.0 hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value for the acceleration of gravity. Part A Calculate the tension in the rope if the gymnast hangs motionless on the rope. Express your answer in newtons. You did not open hints for this part. ANSWER: Part B Calculate the tension in the rope if the gymnast climbs the rope at a constant rate. Express your answer in newtons. You did not open hints for this part. kg 9.81m/s2 T T = N T ANSWER: Part C Calculate the tension in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: Part D Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: T = N T m/s2 T = N T m/s2 T = N Applying Newton’s 2nd Law Learning Goal: To learn a systematic approach to solving Newton’s 2nd law problems using a simple example. Once you have decided to solve a problem using Newton’s 2nd law, there are steps that will lead you to a solution. One such prescription is the following: Visualize the problem and identify special cases. Isolate each body and draw the forces acting on it. Choose a coordinate system for each body. Apply Newton’s 2nd law to each body. Write equations for the constraints and other given information. Solve the resulting equations symbolically. Check that your answer has the correct dimensions and satisfies special cases. If numbers are given in the problem, plug them in and check that the answer makes sense. Think about generalizations or simplfications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass that is pulled up a frictionless plane inclined at angle with respect to the horizontal by a perfect string that passes over a perfect pulley to a block of mass that is hanging vertically. Visualize the problem and identify special cases First examine the problem by drawing a picture and visualizing the motion. Apply Newton’s 2nd law, , to each body in your mind. Don’t worry about which quantities are given. Think about the forces on each body: How are these consistent with the direction of the acceleration for that body? Can you think of any special cases that you can solve quickly now and use to test your understanding later? m2  m1 F = ma One special case in this problem is if , in which case block 1 would simply fall freely under the acceleration of gravity: . Part A Consider another special case in which the inclined plane is vertical ( ). In this case, for what value of would the acceleration of the two blocks be equal to zero? Express your answer in terms of some or all of the variables and . ANSWER: Isolate each body and draw the forces acting on it A force diagram should include only real forces that act on the body and satisfy Newton’s 3rd law. One way to check if the forces are real is to detrmine whether they are part of a Newton’s 3rd law pair, that is, whether they result from a physical interaction that also causes an opposite force on some other body, which may not be part of the problem. Do not decompose the forces into components, and do not include resultant forces that are combinations of other real forces like centripetal force or fictitious forces like the “centrifugal” force. Assign each force a symbol, but don’t start to solve the problem at this point. Part B Which of the four drawings is a correct force diagram for this problem? = 0 m2 = −g a 1 j ^  = /2 m1 m2 g m1 = ANSWER: Choose a coordinate system for each body Newton’s 2nd law, , is a vector equation. To add or subtract vectors it is often easiest to decompose each vector into components. Whereas a particular set of vector components is only valid in a particular coordinate system, the vector equality holds in any coordinate system, giving you freedom to pick a coordinate system that most simplifies the equations that result from the component equations. It’s generally best to pick a coordinate system where the acceleration of the system lies directly on one of the coordinate axes. If there is no acceleration, then pick a coordinate system with as many unknowns as possible along the coordinate axes. Vectors that lie along the axes appear in only one of the equations for each component, rather than in two equations with trigonometric prefactors. Note that it is sometimes advantageous to use different coordinate systems for each body in the problem. In this problem, you should use Cartesian coordinates and your axes should be stationary with respect to the inclined plane. Part C Given the criteria just described, what orientation of the coordinate axes would be best to use in this problem? In the answer options, “tilted” means with the x axis oriented parallel to the plane (i.e., at angle to the horizontal), and “level” means with the x axis horizontal. ANSWER: Apply Newton’s 2nd law to each body a b c d F  = ma  tilted for both block 1 and block 2 tilted for block 1 and level for block 2 level for block 1 and tilted for block 2 level for both block 1 and block 2 Part D What is , the sum of the x components of the forces acting on block 2? Take forces acting up the incline to be positive. Express your answer in terms of some or all of the variables tension , , the magnitude of the acceleration of gravity , and . You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Lifting a Bucket A 6- bucket of water is being pulled straight up by a string at a constant speed. F2x T m2 g  m2a2x =F2x = kg Part A What is the tension in the rope? ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Friction Force on a Dancer on a Drawbridge A dancer is standing on one leg on a drawbridge that is about to open. The coefficients of static and kinetic friction between the drawbridge and the dancer’s foot are and , respectively. represents the normal force exerted on the dancer by the bridge, and represents the gravitational force exerted on the dancer, as shown in the drawing . For all the questions, we can assume that the bridge is a perfectly flat surface and lacks the curvature characteristic of most bridges. about 42 about 60 about 78 0 because the bucket has no acceleration. N N N N μs μk n F  g Part A Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the x component of the friction force, ? Express your answer in terms of some or all of the variables , , and/or . You did not open hints for this part. ANSWER: Part B The drawbridge then starts to rise and the dancer continues to stand on one leg. The drawbridge stops just at the point where the dancer is on the verge of slipping. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. F  f n μs μk Ff = Ff n μs μk  You did not open hints for this part. ANSWER: Part C Then, because the bridge is old and poorly designed, it falls a little bit and then jerks. This causes the person to start to slide down the bridge at a constant speed. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. ANSWER: Part D The bridge starts to come back down again. The dancer stops sliding. However, again because of the age and design of the bridge it never makes it all the way down; rather it stops half a meter short. This half a meter corresponds to an angle degree (see the diagram, which has the angle exaggerated). What is the force of friction now? Express your answer in terms of some or all of the variables , , and . Ff = Ff n μs μk  Ff =   1 Ff  n Fg You did not open hints for this part. ANSWER: Kinetic Friction Ranking Task Below are eight crates of different mass. The crates are attached to massless ropes, as indicated in the picture, where the ropes are marked by letters. Each crate is being pulled to the right at the same constant speed. The coefficient of kinetic friction between each crate and the surface on which it slides is the same for all eight crates. Ff = Part A Rank the ropes on the basis of the force each exerts on the crate immediately to its left. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Pushing a Block Learning Goal: To understand kinetic and static friction. A block of mass lies on a horizontal table. The coefficient of static friction between the block and the table is . The coefficient of kinetic friction is , with . Part A m μs μk μk < μs If the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from the table), what is the magnitude of the force due to friction? You did not open hints for this part. ANSWER: Part B Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With what force must you be pushing the block just before the block begins to move? Express the magnitude of in terms of some or all the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. ANSWER: Part C Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of the friction force? Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. Ffriction = F F μs μk m g F = μs μk m g ANSWER: Part D Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration of the block after it begins to move. Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . 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. Ffriction = a μs μk m g a =

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Collaborative report Situation D: Proposal for Kindle-like devices/electronic textbooks to be used for textbook/academic purposes (institutions of higher ed would be audience). Situation: As any college student knows, textbooks for classes are expensive and students are not likely to keep some textbooks related to classes outside of one’s major. Some students will return these books to the bookstore in an effort to recoup some of their money, while others will offer them directly to other students at a discounted price. Bookstores tend to make most of their textbook-related income from selling used textbooks, while publishers make money from new editions. Additionally, many textbook editions come with a Website companion to enhance instruction with those textbooks. Kindle is a portable device with which someone can access texts electronically by purchasing them, usually at a discounted price off the print-version. Kindle is the original product, but Apple has a similar device too. These devices tend to cost over $200. However, there is discussion about their use as an option for textbook purchases. Also, bookstores have implemented a rental system; however, not all textbooks are available for rental, much as not all textbooks have an electronic version yet. You work for Learned Books, a textbook publisher that is trying to think of ways to balance its desire for profitability with students’ desire to reign in book-related expenses. You understand that a company that can appeal to the market’s concerns, considering increased competition from online retail sources, will be able to stay in business. Your group is tasked with ascertaining how LB can do this. One idea is to develop a rental system, another involves joining forces with manufacturers of Kindle-like devices and offering discounted versions of texts to students electronically through e-readers or PCs that can easily access the Internet. Students could purchase the electronic version outright or purchase the electronic version but have access to it for a limited, 12 month period (rental basis). ***Research how are such devices and electronic versions being used for textbook purposes, considering various expenses for producing electronic versions of textbooks and readability concerns? Document Feasibility study/Proposal: Develop a document in which you articulate your assessment of these ideas, integrating at least one graphic and an executive summary. The document should be 2-3 pages long and include formal elements as needed.

Collaborative report Situation D: Proposal for Kindle-like devices/electronic textbooks to be used for textbook/academic purposes (institutions of higher ed would be audience). Situation: As any college student knows, textbooks for classes are expensive and students are not likely to keep some textbooks related to classes outside of one’s major. Some students will return these books to the bookstore in an effort to recoup some of their money, while others will offer them directly to other students at a discounted price. Bookstores tend to make most of their textbook-related income from selling used textbooks, while publishers make money from new editions. Additionally, many textbook editions come with a Website companion to enhance instruction with those textbooks. Kindle is a portable device with which someone can access texts electronically by purchasing them, usually at a discounted price off the print-version. Kindle is the original product, but Apple has a similar device too. These devices tend to cost over $200. However, there is discussion about their use as an option for textbook purchases. Also, bookstores have implemented a rental system; however, not all textbooks are available for rental, much as not all textbooks have an electronic version yet. You work for Learned Books, a textbook publisher that is trying to think of ways to balance its desire for profitability with students’ desire to reign in book-related expenses. You understand that a company that can appeal to the market’s concerns, considering increased competition from online retail sources, will be able to stay in business. Your group is tasked with ascertaining how LB can do this. One idea is to develop a rental system, another involves joining forces with manufacturers of Kindle-like devices and offering discounted versions of texts to students electronically through e-readers or PCs that can easily access the Internet. Students could purchase the electronic version outright or purchase the electronic version but have access to it for a limited, 12 month period (rental basis). ***Research how are such devices and electronic versions being used for textbook purposes, considering various expenses for producing electronic versions of textbooks and readability concerns? Document Feasibility study/Proposal: Develop a document in which you articulate your assessment of these ideas, integrating at least one graphic and an executive summary. The document should be 2-3 pages long and include formal elements as needed.

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. 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...
Which statement regarding science technology is false? Select one: Science technology has brought about life-improving discoveries, such as antibiotics. Science technology helps us to understand the causes of cancer. Science technology is a basis for all ethical or moral decisions. Science technology may ease the feeding of the world population by producing new plant strains. Scientific experimentation may make use of a model instead of an actual subject.

Which statement regarding science technology is false? Select one: Science technology has brought about life-improving discoveries, such as antibiotics. Science technology helps us to understand the causes of cancer. Science technology is a basis for all ethical or moral decisions. Science technology may ease the feeding of the world population by producing new plant strains. Scientific experimentation may make use of a model instead of an actual subject.

Which statement regarding science technology is false? Select one: Science … Read More...
Understanding how students use technology outside of school can help teachers to understand effective ways to use technology in the classroom. In 2009 the Kaiser Family Foundation produced a report on the media use of children 8–18 years old that quickly gained widespread notice. These results have implications for teachers, parents, and students. What are the implications?

Understanding how students use technology outside of school can help teachers to understand effective ways to use technology in the classroom. In 2009 the Kaiser Family Foundation produced a report on the media use of children 8–18 years old that quickly gained widespread notice. These results have implications for teachers, parents, and students. What are the implications?

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