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

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

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Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: c t = 0 b a x = 0 xman(t) b c t x(t) = x(0) + vt xman(t) = −b + ct Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: xbus(t) a t x(t) = x(0) + v(0)t + (1/2)at2 vbus(0) = 0 xbus = 1 a 2 t2 tcatch tcatch Typesetting math: 15% Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? xman(tcatch) > xbus(tcatch) xman(tcatch) = xbus(tcatch) xman(tcatch) < xbus(tcatch) c = a  tcatch xman(t) xbus(t) xman(tcatch) = xbus(tcatch) −b+ct = a catch 1 2 t2 catch 1 a −c +b = 0 2 t2 catch tcatch c tcatch cmin c a b 1 a − c + b = 0 2 t2 catch tcatch tcatch Typesetting math: 15% Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? Hint 1. What is the general quadratic equation? The general quadratic equation is , where , \texttip{B}{B}, and \texttip{C}{C} are constants. Depending on the value of the discriminant, \Delta = c^2-2ab, the equation may have Ax2 + Bx + C = 0 x = −B±B2−4AC 2A  = cc − 2ab tcatch c cmin cmin = (2ab) −−−−  c > cmin Ax2 + Bx + C = 0 A Typesetting math: 15% two real valued solutions 1. if \Delta > 0, 2. one real valued solution if \Delta = 0, or 3. two complex valued solutions if \Delta < 0. In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A No; there is no chance he is going to get aboard. Yes; he will get a second chance Typesetting math: 15% Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: C and E E and F A and F C and D B and D Typesetting math: 15% Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F Typesetting math: 15% To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector \texttip{\vec{A}}{A_vec} is decomposed into component vectors \texttip{\vec{A}_{\mit x}}{A_vec_x} and \texttip{\vec{A}_{\mit y}}{A_vec_y} parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector \texttip{\vec{A}}{A_vec}, denoted \texttip{A_{\mit x}}{A_x} and \texttip{A_{\mit y}}{A_y}. TACTICS BOX 3.1 Determining the components of a vector The absolute value |A_x| of the x component \texttip{A_{\mit x}}{A_x} is the magnitude of the component vector \texttip{\vec{A}_{\1. mit x}}{A_vec_x}. The sign of \texttip{A_{\mit x}}{A_x} is positive if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the positive x direction; it is negative if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the negative x direction. 2. 3. The y component \texttip{A_{\mit y}}{A_y} is determined similarly. Part A What is the magnitude of the component vector \texttip{\vec{A}_{\mit x}}{A_vec_x} shown in the figure? Express your answer in meters to one significant figure. ANSWER: Correct |A_x| = 5 \rm m Typesetting math: 15% Part B What is the sign of the y component \texttip{A_{\mit y}}{A_y} of vector \texttip{\vec{A}}{A_vec} shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, \texttip{B_{\mit x}}{B_x} and \texttip{B_{\mit y}}{B_y}, of vector \texttip{\vec{B}}{B_vec} shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. positive negative Typesetting math: 15% ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, \texttip{v_{\mit x}}{1. v_x}, is constant. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by \texttip{g}{g}, is equal to 9.80 \rm{m/s^2} near the surface of the earth. Hence, the y component of its velocity, \texttip{v_{\mit y}}{v_y}, changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time \texttip{t}{t} the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is \texttip{\vec{v}_{\rm 0}}{v_vec_0}. Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time \texttip{t_{\rm 1}}{t_1} with velocity \texttip{\vec{v}_{\rm 1}}{v_1_vec}. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum \texttip{B_{\mit x}}{B_x}, \texttip{B_{\mit y}}{B_y} = -2,-5 \rm m, \rm m Typesetting math: 15% The other point, at time \texttip{t_{\rm 2}}{t_2} with velocity \texttip{\vec{v}_{\rm 2}}{v_2_vec}, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}. Part A How do the speeds \texttip{v_{\rm 0}}{v_0}, \texttip{v_{\rm 1}}{v_1}, and \texttip{v_{\rm 2}}{v_2} (at times \texttip{t_{\rm 0}}{t_0}, \texttip{t_{\rm 1}}{t_1}, and \texttip{t_{\rm 2}}{t_2}) compare? ANSWER: Correct Here \texttip{v_{\rm 0}}{v_0} equals \texttip{v_{\rm 2}}{v_2} by symmetry and both exceed \texttip{v_{\rm 1}}{v_1}. This is because \texttip{v_{\rm 0}}{v_0} and \texttip{v_{\rm 2}}{v_2} include vertical speed as well as the constant horizontal speed. Consider a diagram of the ball at time \texttip{t_{\rm 0}}{t_0}. Recall that \texttip{t_{\rm 0}}{t_0} refers to the instant just after the ball has been launched, so it is still at ground level (x_0 = y_0= 0\;\rm{m}). However, it is already moving with initial velocity \texttip{\vec{v}_{\rm 0}}{v_0_vec}, whose magnitude is v_0 = 30.0\;{\rm m/s} and direction is \theta = 60.0\;{\rm degrees} counterclockwise from the positive x direction. \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 1}}{v_1} = \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 1}}{v_1} > \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 Typesetting math: 15% Part B What are the values of the intial velocity vector components \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{0,x}}{a_0, x} and \texttip{a_{0,y}}{a_0, y} (both in \rm{m/s^2})? Here the subscript 0 means “at time \texttip{t_{\rm 0}}{t_0}.” Hint 1. Determining components of a vector that is aligned with an axis If a vector points along a single axis direction, such as in the positive x direction, its x component will be its full magnitude, whereas its y component will be zero since the vector is perpendicular to the y direction. If the vector points in the negative x direction, its x component will be the negative of its full magnitude. Hint 2. Calculating the components of the initial velocity Notice that the vector \texttip{\vec{v}_{\rm 0}}{v_0_vec} points up and to the right. Since “up” is the positive y axis direction and “to the right” is the positive x axis direction, \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} will both be positive. As shown in the figure, \texttip{v_{0,x}}{v_0, x}, \texttip{v_{0,y}}{v_0, y}, and \texttip{v_{\rm 0}}{v_0} are three sides of a right triangle, one angle of which is \texttip{\theta }{theta}. Thus \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} can be found using the definition of the sine and cosine functions given below. Recall that v_0 = 30.0\;\rm{m/s} and \theta = 60.0\;\rm{degrees} and note that \large{\sin(\theta) = \frac{\rm{length\;of\;opposite\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, y}}{v_0}}, \large{\cos(\theta) = \frac{\rm{length\;of\;adjacent\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, x}}{v_0}.} What are the values of \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y}? Enter your answers numerically in meters per second separated by a comma. ANSWER: ANSWER: 15.0,26.0 \rm{m/s} Typesetting math: 15% Correct Also notice that at time \texttip{t_{\rm 2}}{t_2}, just before the ball lands, its velocity components are v_{2, x} = 15\;\rm{m/s} (the same as always) and v_{2, y} = – 26.0\;\rm{m/s} (the same size but opposite sign from \texttip{v_{0,y}}{v_0, y} by symmetry). The acceleration at time \texttip{t_{\rm 2}}{t_2} will have components (0, -9.80 \rm{m/s^2}), exactly the same as at \texttip{t_{\rm 0}}{t_0}, as required by Rule 2. The peak of the trajectory occurs at time \texttip{t_{\rm 1}}{t_1}. This is the point where the ball reaches its maximum height \texttip{y_{\rm max}}{y_max}. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate. Part C What are the values of the velocity vector components \texttip{v_{1,x}}{v_1, x} and \texttip{v_{1,y}}{v_1, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{1,x}}{a_1, x} and \texttip{a_{1,y}}{a_1, y} (both in \rm{m/s^2})? Here the subscript 1 means that these are all at time \texttip{t_{\rm 1}}{t_1}. ANSWER: 30.0, 0, 0, 0 0, 30.0, 0, 0 15.0, 26.0, 0, 0 30.0, 0, 0, -9.80 0, 30.0, 0, -9.80 15.0, 26.0, 0, -9.80 15.0, 26.0, 0, +9.80 Typesetting math: 15% Correct At the peak of its trajectory the ball continues traveling horizontally at a constant rate. However, at this moment it stops moving up and is about to move back down. This constitutes a downward-directed change in velocity, so the ball is accelerating downward even at the peak. The flight time refers to the total amount of time the ball is in the air, from just after it is launched (\texttip{t_{\rm 0}}{t_0}) until just before it lands (\texttip{t_{\rm 2}}{t_2}). Hence the flight time can be calculated as t_2 – t_0, or just \texttip{t_{\rm 2}}{t_2} in this particular situation since t_0 = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height \texttip{y_{\rm max}}{y_max}, how long would it take to reach the ground? Ignore air resistance. Check all that apply. Hint 1. Kicking a ball of cliff; a related problem Consider two balls, one of which is dropped from rest off the edge of a cliff at the same moment that the other is kicked horizontally off the edge of the cliff. Which ball reaches the level ground at the base of the cliff first? Ignore air resistance. Hint 1. Comparing position, velocity, and acceleration of the two balls Both balls start at the same height and have the same initial y velocity (v_{0,y} = 0) as well as the same acceleration (\vec a = g downward). They differ only in their x velocity (one is 0, 0, 0, 0 0, 0, 0, -9.80 15.0, 0, 0, 0 15.0, 0, 0, -9.80 0, 26.0, 0, 0 0, 26.0, 0, -9.80 15.0, 26.0, 0, 0 15.0, 26.0, 0, -9.80 Typesetting math: 15% zero, the other nonzero). This difference will affect their x motion but not their y motion. ANSWER: ANSWER: Correct In projectile motion over level ground, it takes an object just as long to rise from the ground to the peak as it takes for it to fall from the peak back to the ground. The range \texttip{R}{R} of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as x_2 – x_0, or just \texttip{x_{\rm 2}}{x_2} in this particular situation since x_0 = 0. Range can be calculated as the product of the flight time \texttip{t_{\rm 2}}{t_2} and the x component of the velocity \texttip{v_{\mit x}}{v_x} (which is the same at all times, so v_x = v_{0,x}). The value of \texttip{v_{\mit x}}{v_x} can be found from the launch speed \texttip{v_{\rm 0}}{v_0} and the launch angle \texttip{\theta }{theta} using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from \texttip{v_{\rm 0}}{v_0} and \texttip{\theta }{theta} using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (x_0 = y_0 = 0) at time t_0 = 0 with initial speed \texttip{v_{\rm 0}}{v_0} and launch angle \texttip{\theta }{theta} measured from the horizontal. As was the case above, \texttip{t_{\rm 2}}{t_2} refers to the flight time and \texttip{R}{R} refers to the range of the projectile. flight time: \large{t_2 = \frac{2 v_{0, y}}{g} = \frac{2 v_0 \sin(\theta)}{g}} range: \large{R = v_x t_2 = \frac{v_0^2 \sin(2\theta)}{g}} The ball that falls straight down strikes the ground first. The ball that was kicked so it moves horizontally as it falls strikes the ground first. Both balls strike the ground at the same time. \texttip{t_{\rm 0}}{t_0} t_1 – t_0 \texttip{t_{\rm 2}}{t_2} t_2 – t_1 \large{\frac{t_2 – t_0}{2}} Typesetting math: 15% In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. ANSWER: Correct A solid understanding of the concepts of projectile motion will take you far, including giving you additional insight into the solution of projectile motion problems numerically. Even when the object does not land at the same height from which is was launched, the rules given in the introduction will still be useful. Recall that air resistance is assumed to be negligible here, so this projectile motion analysis may not be the best choice for describing things like frisbees or feathers, whose motion is strongly influenced by air. The value of the gravitational free-fall acceleration \texttip{g}{g} is also assumed to be constant, which may not be appropriate for objects that move vertically through distances of hundreds of kilometers, like rockets or missiles. However, for problems that involve relatively dense projectiles moving close to the surface of the earth, these assumptions are reasonable. A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 \;{\rm m}/{\rm s}^{2}. Part A How much horizontal force \texttip{F}{F} must a sprinter of mass 64{\rm kg} exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Increase \texttip{v_{\rm 0}}{v_0} above 30 \rm{m/s}. Reduce \texttip{v_{\rm 0}}{v_0} below 30 \rm{m/s}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to 45 \rm{degrees}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to less than 30 \rm{degrees}. Increase \texttip{\theta }{theta} from 60 \rm{degrees} up toward 90 \rm{degrees}. Typesetting math: 15% Hint 1. Newton’s 2nd law of motion According to Newton’s 2nd law of motion, if a net external force \texttip{F_{\rm net}}{F_net} acts on a body, the body accelerates, and the net force is equal to the mass \texttip{m}{m} of the body times the acceleration \texttip{a}{a} of the body: F_{\rm net} = ma. ANSWER: Co

Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: c t = 0 b a x = 0 xman(t) b c t x(t) = x(0) + vt xman(t) = −b + ct Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: xbus(t) a t x(t) = x(0) + v(0)t + (1/2)at2 vbus(0) = 0 xbus = 1 a 2 t2 tcatch tcatch Typesetting math: 15% Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? xman(tcatch) > xbus(tcatch) xman(tcatch) = xbus(tcatch) xman(tcatch) < xbus(tcatch) c = a  tcatch xman(t) xbus(t) xman(tcatch) = xbus(tcatch) −b+ct = a catch 1 2 t2 catch 1 a −c +b = 0 2 t2 catch tcatch c tcatch cmin c a b 1 a − c + b = 0 2 t2 catch tcatch tcatch Typesetting math: 15% Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? Hint 1. What is the general quadratic equation? The general quadratic equation is , where , \texttip{B}{B}, and \texttip{C}{C} are constants. Depending on the value of the discriminant, \Delta = c^2-2ab, the equation may have Ax2 + Bx + C = 0 x = −B±B2−4AC 2A  = cc − 2ab tcatch c cmin cmin = (2ab) −−−−  c > cmin Ax2 + Bx + C = 0 A Typesetting math: 15% two real valued solutions 1. if \Delta > 0, 2. one real valued solution if \Delta = 0, or 3. two complex valued solutions if \Delta < 0. In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A No; there is no chance he is going to get aboard. Yes; he will get a second chance Typesetting math: 15% Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: C and E E and F A and F C and D B and D Typesetting math: 15% Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F Typesetting math: 15% To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector \texttip{\vec{A}}{A_vec} is decomposed into component vectors \texttip{\vec{A}_{\mit x}}{A_vec_x} and \texttip{\vec{A}_{\mit y}}{A_vec_y} parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector \texttip{\vec{A}}{A_vec}, denoted \texttip{A_{\mit x}}{A_x} and \texttip{A_{\mit y}}{A_y}. TACTICS BOX 3.1 Determining the components of a vector The absolute value |A_x| of the x component \texttip{A_{\mit x}}{A_x} is the magnitude of the component vector \texttip{\vec{A}_{\1. mit x}}{A_vec_x}. The sign of \texttip{A_{\mit x}}{A_x} is positive if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the positive x direction; it is negative if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the negative x direction. 2. 3. The y component \texttip{A_{\mit y}}{A_y} is determined similarly. Part A What is the magnitude of the component vector \texttip{\vec{A}_{\mit x}}{A_vec_x} shown in the figure? Express your answer in meters to one significant figure. ANSWER: Correct |A_x| = 5 \rm m Typesetting math: 15% Part B What is the sign of the y component \texttip{A_{\mit y}}{A_y} of vector \texttip{\vec{A}}{A_vec} shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, \texttip{B_{\mit x}}{B_x} and \texttip{B_{\mit y}}{B_y}, of vector \texttip{\vec{B}}{B_vec} shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. positive negative Typesetting math: 15% ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, \texttip{v_{\mit x}}{1. v_x}, is constant. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by \texttip{g}{g}, is equal to 9.80 \rm{m/s^2} near the surface of the earth. Hence, the y component of its velocity, \texttip{v_{\mit y}}{v_y}, changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time \texttip{t}{t} the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is \texttip{\vec{v}_{\rm 0}}{v_vec_0}. Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time \texttip{t_{\rm 1}}{t_1} with velocity \texttip{\vec{v}_{\rm 1}}{v_1_vec}. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum \texttip{B_{\mit x}}{B_x}, \texttip{B_{\mit y}}{B_y} = -2,-5 \rm m, \rm m Typesetting math: 15% The other point, at time \texttip{t_{\rm 2}}{t_2} with velocity \texttip{\vec{v}_{\rm 2}}{v_2_vec}, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}. Part A How do the speeds \texttip{v_{\rm 0}}{v_0}, \texttip{v_{\rm 1}}{v_1}, and \texttip{v_{\rm 2}}{v_2} (at times \texttip{t_{\rm 0}}{t_0}, \texttip{t_{\rm 1}}{t_1}, and \texttip{t_{\rm 2}}{t_2}) compare? ANSWER: Correct Here \texttip{v_{\rm 0}}{v_0} equals \texttip{v_{\rm 2}}{v_2} by symmetry and both exceed \texttip{v_{\rm 1}}{v_1}. This is because \texttip{v_{\rm 0}}{v_0} and \texttip{v_{\rm 2}}{v_2} include vertical speed as well as the constant horizontal speed. Consider a diagram of the ball at time \texttip{t_{\rm 0}}{t_0}. Recall that \texttip{t_{\rm 0}}{t_0} refers to the instant just after the ball has been launched, so it is still at ground level (x_0 = y_0= 0\;\rm{m}). However, it is already moving with initial velocity \texttip{\vec{v}_{\rm 0}}{v_0_vec}, whose magnitude is v_0 = 30.0\;{\rm m/s} and direction is \theta = 60.0\;{\rm degrees} counterclockwise from the positive x direction. \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 1}}{v_1} = \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 1}}{v_1} > \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 Typesetting math: 15% Part B What are the values of the intial velocity vector components \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{0,x}}{a_0, x} and \texttip{a_{0,y}}{a_0, y} (both in \rm{m/s^2})? Here the subscript 0 means “at time \texttip{t_{\rm 0}}{t_0}.” Hint 1. Determining components of a vector that is aligned with an axis If a vector points along a single axis direction, such as in the positive x direction, its x component will be its full magnitude, whereas its y component will be zero since the vector is perpendicular to the y direction. If the vector points in the negative x direction, its x component will be the negative of its full magnitude. Hint 2. Calculating the components of the initial velocity Notice that the vector \texttip{\vec{v}_{\rm 0}}{v_0_vec} points up and to the right. Since “up” is the positive y axis direction and “to the right” is the positive x axis direction, \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} will both be positive. As shown in the figure, \texttip{v_{0,x}}{v_0, x}, \texttip{v_{0,y}}{v_0, y}, and \texttip{v_{\rm 0}}{v_0} are three sides of a right triangle, one angle of which is \texttip{\theta }{theta}. Thus \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} can be found using the definition of the sine and cosine functions given below. Recall that v_0 = 30.0\;\rm{m/s} and \theta = 60.0\;\rm{degrees} and note that \large{\sin(\theta) = \frac{\rm{length\;of\;opposite\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, y}}{v_0}}, \large{\cos(\theta) = \frac{\rm{length\;of\;adjacent\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, x}}{v_0}.} What are the values of \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y}? Enter your answers numerically in meters per second separated by a comma. ANSWER: ANSWER: 15.0,26.0 \rm{m/s} Typesetting math: 15% Correct Also notice that at time \texttip{t_{\rm 2}}{t_2}, just before the ball lands, its velocity components are v_{2, x} = 15\;\rm{m/s} (the same as always) and v_{2, y} = – 26.0\;\rm{m/s} (the same size but opposite sign from \texttip{v_{0,y}}{v_0, y} by symmetry). The acceleration at time \texttip{t_{\rm 2}}{t_2} will have components (0, -9.80 \rm{m/s^2}), exactly the same as at \texttip{t_{\rm 0}}{t_0}, as required by Rule 2. The peak of the trajectory occurs at time \texttip{t_{\rm 1}}{t_1}. This is the point where the ball reaches its maximum height \texttip{y_{\rm max}}{y_max}. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate. Part C What are the values of the velocity vector components \texttip{v_{1,x}}{v_1, x} and \texttip{v_{1,y}}{v_1, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{1,x}}{a_1, x} and \texttip{a_{1,y}}{a_1, y} (both in \rm{m/s^2})? Here the subscript 1 means that these are all at time \texttip{t_{\rm 1}}{t_1}. ANSWER: 30.0, 0, 0, 0 0, 30.0, 0, 0 15.0, 26.0, 0, 0 30.0, 0, 0, -9.80 0, 30.0, 0, -9.80 15.0, 26.0, 0, -9.80 15.0, 26.0, 0, +9.80 Typesetting math: 15% Correct At the peak of its trajectory the ball continues traveling horizontally at a constant rate. However, at this moment it stops moving up and is about to move back down. This constitutes a downward-directed change in velocity, so the ball is accelerating downward even at the peak. The flight time refers to the total amount of time the ball is in the air, from just after it is launched (\texttip{t_{\rm 0}}{t_0}) until just before it lands (\texttip{t_{\rm 2}}{t_2}). Hence the flight time can be calculated as t_2 – t_0, or just \texttip{t_{\rm 2}}{t_2} in this particular situation since t_0 = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height \texttip{y_{\rm max}}{y_max}, how long would it take to reach the ground? Ignore air resistance. Check all that apply. Hint 1. Kicking a ball of cliff; a related problem Consider two balls, one of which is dropped from rest off the edge of a cliff at the same moment that the other is kicked horizontally off the edge of the cliff. Which ball reaches the level ground at the base of the cliff first? Ignore air resistance. Hint 1. Comparing position, velocity, and acceleration of the two balls Both balls start at the same height and have the same initial y velocity (v_{0,y} = 0) as well as the same acceleration (\vec a = g downward). They differ only in their x velocity (one is 0, 0, 0, 0 0, 0, 0, -9.80 15.0, 0, 0, 0 15.0, 0, 0, -9.80 0, 26.0, 0, 0 0, 26.0, 0, -9.80 15.0, 26.0, 0, 0 15.0, 26.0, 0, -9.80 Typesetting math: 15% zero, the other nonzero). This difference will affect their x motion but not their y motion. ANSWER: ANSWER: Correct In projectile motion over level ground, it takes an object just as long to rise from the ground to the peak as it takes for it to fall from the peak back to the ground. The range \texttip{R}{R} of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as x_2 – x_0, or just \texttip{x_{\rm 2}}{x_2} in this particular situation since x_0 = 0. Range can be calculated as the product of the flight time \texttip{t_{\rm 2}}{t_2} and the x component of the velocity \texttip{v_{\mit x}}{v_x} (which is the same at all times, so v_x = v_{0,x}). The value of \texttip{v_{\mit x}}{v_x} can be found from the launch speed \texttip{v_{\rm 0}}{v_0} and the launch angle \texttip{\theta }{theta} using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from \texttip{v_{\rm 0}}{v_0} and \texttip{\theta }{theta} using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (x_0 = y_0 = 0) at time t_0 = 0 with initial speed \texttip{v_{\rm 0}}{v_0} and launch angle \texttip{\theta }{theta} measured from the horizontal. As was the case above, \texttip{t_{\rm 2}}{t_2} refers to the flight time and \texttip{R}{R} refers to the range of the projectile. flight time: \large{t_2 = \frac{2 v_{0, y}}{g} = \frac{2 v_0 \sin(\theta)}{g}} range: \large{R = v_x t_2 = \frac{v_0^2 \sin(2\theta)}{g}} The ball that falls straight down strikes the ground first. The ball that was kicked so it moves horizontally as it falls strikes the ground first. Both balls strike the ground at the same time. \texttip{t_{\rm 0}}{t_0} t_1 – t_0 \texttip{t_{\rm 2}}{t_2} t_2 – t_1 \large{\frac{t_2 – t_0}{2}} Typesetting math: 15% In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. ANSWER: Correct A solid understanding of the concepts of projectile motion will take you far, including giving you additional insight into the solution of projectile motion problems numerically. Even when the object does not land at the same height from which is was launched, the rules given in the introduction will still be useful. Recall that air resistance is assumed to be negligible here, so this projectile motion analysis may not be the best choice for describing things like frisbees or feathers, whose motion is strongly influenced by air. The value of the gravitational free-fall acceleration \texttip{g}{g} is also assumed to be constant, which may not be appropriate for objects that move vertically through distances of hundreds of kilometers, like rockets or missiles. However, for problems that involve relatively dense projectiles moving close to the surface of the earth, these assumptions are reasonable. A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 \;{\rm m}/{\rm s}^{2}. Part A How much horizontal force \texttip{F}{F} must a sprinter of mass 64{\rm kg} exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Increase \texttip{v_{\rm 0}}{v_0} above 30 \rm{m/s}. Reduce \texttip{v_{\rm 0}}{v_0} below 30 \rm{m/s}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to 45 \rm{degrees}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to less than 30 \rm{degrees}. Increase \texttip{\theta }{theta} from 60 \rm{degrees} up toward 90 \rm{degrees}. Typesetting math: 15% Hint 1. Newton’s 2nd law of motion According to Newton’s 2nd law of motion, if a net external force \texttip{F_{\rm net}}{F_net} acts on a body, the body accelerates, and the net force is equal to the mass \texttip{m}{m} of the body times the acceleration \texttip{a}{a} of the body: F_{\rm net} = ma. ANSWER: Co

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Sex, Gender, and Popular Culture Spring 2015 Look through popular magazines, and see if you can find advertisements that objectify women in order to sell a product. Alternately, you may use an advertisement on television (but make sure to provide a link to the ad so I can see it!). Study these images then write a paper about objectification that deals with all or some of the following: • What effect(s), if any, do you think the objectification of women’s bodies has on our culture? • Jean Kilbourne states “turning a human being into a thing is almost always the first step toward justifying violence against that person.” What do you think she means by this? Do you agree with her reasoning? Why or why not? • Some people would argue that depicting a woman’s body as an object is a form of art. What is your opinion of this point of view? Explain your reasoning. • Why do you think that women are objectified more often than men are? • How does sexualization and objectification play out differently across racial lines? • Kilbourne explains that the consequences of being objectified are different – and more serious – for women than for men. Do you agree? How is the world different for women than it is for men? How do objectified images of women interact with those in our culture differently from the way images of men do? Why is it important to look at images in the context of the culture? • What is the difference between sexual objectification and sexual subjectification? (Ros Gill ) • How do ads construct violent white masculinity and how does that vision of masculinity hurt both men and women? Throughout your written analysis, be sure to make clear and specific reference to the images you selected, and please submit these images with your paper. Make sure you engage with and reference to at least 4 of the following authors: Kilbourne, Bordo, Hunter & Soto, Rose, Durham, Gill, Katz, Schuchardt, Ono and Buescher. Guidelines:  Keep your content focused on structural, systemic, institutional factors rather than the individual: BE ANALYTICAL NOT ANECDOTAL.  Avoid using the first person or including personal stories/reactions. You must make sure to actively engage with your readings: these essays need to be informed and framed by the theoretical material you have been reading this semester.  Keep within the 4-6 page limit; use 12-point font, double spacing and 1-inch margins.  Use formal writing conventions (introduction/thesis statement, body, conclusion) and correct grammar. Resources may be cited within the text of your paper, i.e. (Walters, 2013).

Sex, Gender, and Popular Culture Spring 2015 Look through popular magazines, and see if you can find advertisements that objectify women in order to sell a product. Alternately, you may use an advertisement on television (but make sure to provide a link to the ad so I can see it!). Study these images then write a paper about objectification that deals with all or some of the following: • What effect(s), if any, do you think the objectification of women’s bodies has on our culture? • Jean Kilbourne states “turning a human being into a thing is almost always the first step toward justifying violence against that person.” What do you think she means by this? Do you agree with her reasoning? Why or why not? • Some people would argue that depicting a woman’s body as an object is a form of art. What is your opinion of this point of view? Explain your reasoning. • Why do you think that women are objectified more often than men are? • How does sexualization and objectification play out differently across racial lines? • Kilbourne explains that the consequences of being objectified are different – and more serious – for women than for men. Do you agree? How is the world different for women than it is for men? How do objectified images of women interact with those in our culture differently from the way images of men do? Why is it important to look at images in the context of the culture? • What is the difference between sexual objectification and sexual subjectification? (Ros Gill ) • How do ads construct violent white masculinity and how does that vision of masculinity hurt both men and women? Throughout your written analysis, be sure to make clear and specific reference to the images you selected, and please submit these images with your paper. Make sure you engage with and reference to at least 4 of the following authors: Kilbourne, Bordo, Hunter & Soto, Rose, Durham, Gill, Katz, Schuchardt, Ono and Buescher. Guidelines:  Keep your content focused on structural, systemic, institutional factors rather than the individual: BE ANALYTICAL NOT ANECDOTAL.  Avoid using the first person or including personal stories/reactions. You must make sure to actively engage with your readings: these essays need to be informed and framed by the theoretical material you have been reading this semester.  Keep within the 4-6 page limit; use 12-point font, double spacing and 1-inch margins.  Use formal writing conventions (introduction/thesis statement, body, conclusion) and correct grammar. Resources may be cited within the text of your paper, i.e. (Walters, 2013).

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Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 1 of 57 5/9/2014 8:02 PM Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 2 of 57 5/9/2014 8:02 PM Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? = = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 3 of 57 5/9/2014 8:02 PM Hint 1. What is the general quadratic equation? The general quadratic equation is , where , , and are constants. Depending on the value of the discriminant, , the equation may have two real valued 1. solutions if , 2. one real valued solution if , or 3. two complex valued solutions if . In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. No; there is no chance he is going to get aboard. Yes; he will get a second chance Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 4 of 57 5/9/2014 8:02 PM ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: C and E E and F A and F C and D B and D C and D A and F E and F A and B E and D Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 5 of 57 5/9/2014 8:02 PM Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 2. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. ANSWER: A and F A and E D and B C and D E and F Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 6 of 57 5/9/2014 8:02 PM Correct Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. = 5 positive negative Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 7 of 57 5/9/2014 8:02 PM ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth’s gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, , is constant. 1. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by , is equal to 9.80 near the surface of the earth. Hence, the y component of its velocity, , changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time corresponds to the moment just after the ball is launched from position and . Its launch velocity, also called the initial velocity, is . Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time with velocity . Its position at this moment is denoted by or since it is at its maximum height. The other point, at time with velocity , corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is , also known as ( since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence . Part A , = -2,-5 , Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 8 of 57 5/9/2014 8:02 PM How do the speeds , , and (at times ,

Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 1 of 57 5/9/2014 8:02 PM Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 2 of 57 5/9/2014 8:02 PM Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? = = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 3 of 57 5/9/2014 8:02 PM Hint 1. What is the general quadratic equation? The general quadratic equation is , where , , and are constants. Depending on the value of the discriminant, , the equation may have two real valued 1. solutions if , 2. one real valued solution if , or 3. two complex valued solutions if . In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. No; there is no chance he is going to get aboard. Yes; he will get a second chance Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 4 of 57 5/9/2014 8:02 PM ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: C and E E and F A and F C and D B and D C and D A and F E and F A and B E and D Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 5 of 57 5/9/2014 8:02 PM Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 2. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. ANSWER: A and F A and E D and B C and D E and F Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 6 of 57 5/9/2014 8:02 PM Correct Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. = 5 positive negative Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 7 of 57 5/9/2014 8:02 PM ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth’s gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, , is constant. 1. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by , is equal to 9.80 near the surface of the earth. Hence, the y component of its velocity, , changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time corresponds to the moment just after the ball is launched from position and . Its launch velocity, also called the initial velocity, is . Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time with velocity . Its position at this moment is denoted by or since it is at its maximum height. The other point, at time with velocity , corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is , also known as ( since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence . Part A , = -2,-5 , Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 8 of 57 5/9/2014 8:02 PM How do the speeds , , and (at times ,

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Essay list

Essay list

      Some students have a background or story … Read More...
____ types of asphalt paving are in common use. Two Four Three Five ___ is the act of remodeling the existing land form to provide a level area for a structure, create circulation paths, and create drainage and landscape features. Grading Excavating Sheeting Caissoning ____ foundations use long wood, concrete, or steel piles that are driven into the earth. Pile Mat Spread Caisson ____ hammers use a heavy weight lifted up vertical rails called leads. Diesel Vibratory Single-acting steam Drop ____ of soil refers to increasing its density by mechanically forcing the soil particles closer together. Blending Compaction Shaking Consolidation ____ are temporary watertight enclosures used either in water-bearing soil or directly in water. Cofferdams Caissons Slurries Sheet pilings The ____ was developed by the U.S. Army Corps of Engineers to classify soils for use in roads, embankments, and foundations. Unified Soil Classification System American Association of State Highway and Transportation Officials System Chicago Center for Green Technologies American Society of Testing and Materials ____ piles utilize heavy-gauge steel pipes that are driven with an open end. H Precast concrete Pipe Timber A ____ test ascertains the consistency of a soil sample near the plastic limit. dry strength toughness soil coarseness shaking ____ techniques involve lowering the level of subsurface water on a site to allow excavation to occur in a dry and stable environment. Underpinning Excavating Dewatering Sheeting Clays and silty clay soils can be stabilized through the addition of ____, which produces a chemical reaction. calcium carbon ore lime ____ foundations are reinforced concrete slabs several feet in thickness that cover the entire footprint of a building. Pile Mat Spread Caisson ____, in the form of sheet piling, lagging, and slurry walls, is used to hold up the face of an excavation. Excavating Grading Anchoring Sheeting Predominantly granular soils that have minute amounts of clay particles can be stabilized by blending them with ____. Portland cement asphalt rock salt lime A ____ foundation is a pier that is drilled into the earth, filled with the required reinforcing steel, and poured with concrete. caisson spread mat pile

____ types of asphalt paving are in common use. Two Four Three Five ___ is the act of remodeling the existing land form to provide a level area for a structure, create circulation paths, and create drainage and landscape features. Grading Excavating Sheeting Caissoning ____ foundations use long wood, concrete, or steel piles that are driven into the earth. Pile Mat Spread Caisson ____ hammers use a heavy weight lifted up vertical rails called leads. Diesel Vibratory Single-acting steam Drop ____ of soil refers to increasing its density by mechanically forcing the soil particles closer together. Blending Compaction Shaking Consolidation ____ are temporary watertight enclosures used either in water-bearing soil or directly in water. Cofferdams Caissons Slurries Sheet pilings The ____ was developed by the U.S. Army Corps of Engineers to classify soils for use in roads, embankments, and foundations. Unified Soil Classification System American Association of State Highway and Transportation Officials System Chicago Center for Green Technologies American Society of Testing and Materials ____ piles utilize heavy-gauge steel pipes that are driven with an open end. H Precast concrete Pipe Timber A ____ test ascertains the consistency of a soil sample near the plastic limit. dry strength toughness soil coarseness shaking ____ techniques involve lowering the level of subsurface water on a site to allow excavation to occur in a dry and stable environment. Underpinning Excavating Dewatering Sheeting Clays and silty clay soils can be stabilized through the addition of ____, which produces a chemical reaction. calcium carbon ore lime ____ foundations are reinforced concrete slabs several feet in thickness that cover the entire footprint of a building. Pile Mat Spread Caisson ____, in the form of sheet piling, lagging, and slurry walls, is used to hold up the face of an excavation. Excavating Grading Anchoring Sheeting Predominantly granular soils that have minute amounts of clay particles can be stabilized by blending them with ____. Portland cement asphalt rock salt lime A ____ foundation is a pier that is drilled into the earth, filled with the required reinforcing steel, and poured with concrete. caisson spread mat pile

____ types of asphalt paving are in common use. Two … Read More...
http://www.econlib.org/library/Smith/smWN1.html#B.I,%20Ch.1,%20Of%20the%20Division%20of%20Labor What does Smith mean by division of labor, and how does it affect production? A. He means that each person does their own work to benefit themselves by creating goods. This creates well-crafted goods. B. He argues that in order to become more efficient, we need to put everyone in the same workhouses and eliminate division. C. He says that the division of labor provides farmers with the opportunity to become involved in manufacturing. D. He means that each person makes one small part of a good very quickly, but this is bad for the quality of production overall. E. He means that by having each individual specialize in one thing, they can work together to create products more efficiently and effectively. Which of the following is NOT an example of the circumstances by which the division of labor improves efficiency? A. A doll-making company stops allowing each employee to make one whole doll each and instead appoints each employee to create one part of the doll. B. A family of rug makers buys a loom to speed up their production. C. A mechanic opens a new shop to be nearer to the market. D. A factory changes the responsibilities of its employees so that one group handles heavy boxes and the other group does precision sewing. E. A baker who used to make a dozen cookies at a time buys a giant mixer and oven that enable him to make 20 dozen cookies at a time. Considering the global system of states, what do you think the allegory of the pins has to offer? A. It suggests that there could be a natural harmony of interests among states because they can divide labor among themselves to the benefit of everyone. B. It suggests that states can never be secure enough to cooperate because every state is equally capable of producing the same things. C. It suggests that a central authority is necessary to help states cooperate, in the same way that a manager oversees operations at a factory. D. The allegory of the pins is a great way to think about how wars come about, because states won’t cooperate with each other like pin-makers do. E. The allegory of the pins shows us that there is no natural harmony of interests between states. Smith sees the development of industry, technology, and the division of labor as A. generally positive but not progressive. The lives of many people may improve, but the world will generally stay the same. B. generally positive and progressive. The world is improving because of these changes, and it will continue to improve. C. generally negative. The creation of new technologies and the division of labor are harmful to all humans, both the wealthy and the poor. D. generally negative. The creation of the division of labor only benefits the wealthy at the expense of the poor. E. both positive and negative. Smith thinks that technology hurts us, while the division of labor helps society progress and develop. http://www.youtube.com/watch?v=RUwS1uAdUcI What point is Hans Rosling trying to make when he describes the global health pre-test? A. He is trying to show how the average person has no idea of the true state of global health. B. He is trying to illustrate how we tend to carry around outdated notions about the state of global health. C. He is trying to make us see that the less-developed countries are far worse off than we ever thought. D. He is trying to drive home the idea that global health has not improved over time despite foreign aid and improvements in medicine. E. He is trying to warn us about the rapid growth in world population. Rosling shows us that we tend to think about global health in terms of “we and them.” Who are the “we” and who are the “them”? A. “We” refers to academics, students, and scholars; “them” refers to the uneducated. B. “We” refers to the average person; “them” refers to politicians and global leaders. C. “We” refers to the wealthy; “them” refers to the poor. D. “We” refers to the Western world; “them” refers to the Third World. E. “We” refers to students; “them” refers to professors. In the life expectancy and fertility rate demonstration, what do the statistics reveal? A. Over time, developed countries produced small families and long lives, whereas developing countries produced large families and short lives. B. The world today looks much like it did in 1962 despite our attempts to help poorer countries develop. C. All countries in the world, even the poorer ones, are trending toward longer lives and smaller families. D. Developed countries are trending toward smaller families but shorter lives. E. All countries tend to make gains and losses in fertility and lifespan, but in the long run there is no significant change. What point does Rosling make about life expectancy in Vietnam as compared to the United States? To what does he attribute the change? A. He indicates that economic change preceded social change. B. He suggests that markets and free trade resulted in the increase in life expectancy. C. He says that the data indicates that the Vietnam War contributed to the decrease in life expectancy during that time, but that it recovered shortly thereafter. D. He says that social change in Asia preceded economic change, and life expectancy in Vietnam increased despite the war. E. He indicates that Vietnam was equal to the United States in life expectancy before the war. According to Rosling, how are regional statistics about child survival rates and GDP potentially misleading? A. Countries have an incentive to lie about the actual survival rates because they want foreign assistance. B. Statistics for the individual countries in a region are often vastly different. C. Regional statistics give us a strong sense of how we can understand development within one region, but it does not allow us to compare across regions. D. The data available over time and from countries within regions is often poorly collected and incomplete. E. Child survival rates cannot be compared regionally, since each culture has a different sense of how important children are. What is Rosling’s main point about statistical databases? A. The data is available but not readily accessible, so we need to create networks to solve that problem. B. The data that comes from these databases is often flawed and unreliable. C. It doesn’t matter whether we have access to these databases because the data can’t be used in an interesting way. D. Statistics can’t tell us very much, but we should do our best to make use of the information we do have. E. The information that could be true is too hard to sort out from what isn’t true because we don’t know how strong the data really is. http://www.marxists.org/archive/lenin/works/1916/imp-hsc/ch10.htm#v22zz99h-298-GUESS Click the link at left to read Chapter 10 of Imperialism, The Highest Stage of Capitalism, then answer the questions below. According to Lenin, what is the fundamental source of a monopoly? A. It is a natural effect of human behavior. B. It is the result of governments and police systems. C. Its source is rooted in democracy. D. It comes from the concentration of production at a high stage. E. It is what follows a socialist system. What are the principal types or manifestations of monopoly capitalism? A. Monopolistic capitalist associations like cartels, syndicates and trusts; and monopolies as a result of colonial policy. B. Monopolization of raw materials and monopolization of finance capital. C. Monopolization of governing structures and monopolies of oligarchies. D. Monopolist capitalist associations like cartels, syndicates and trusts; and monopolies as a result of colonial policy AND monopolization of raw materials and monopolization of finance capital. E. Monopolization of raw materials and monopolization of finance capital AND monopolization of governing structures and monopolies of oligarchies. What is the definition of a rentier state according to Lenin? A. A state that colonizes other states. B. A state whose bourgeoisie live off the export of capital. C. A poor state. D. A wealthy state. E. A colonized state. Overall Lenin’s analysis of the state of capitalism is concerned with: A. The interactions between states. B. The interactions within states. C. The ownership of industry and organizations. D. The interactions within states AND the ownership of industry and organizations. E. All of these options. http://view.vzaar.com/1194665/flashplayer Watch the video at left, and then answer the questions below. The Marshall Plan was developed by the United States after World War II. What was its purpose? A. to feed the hungry of Europe B. to stem the spread of communism C. to maintain an American military presence in Europe D. to feed the hungry of Europe AND to stem the spread of communism E. to stem the spread of communism AND to maintain an American military presence in Europe What kind of aid was sent at first? A. foods, fertilizers, and machines for agriculture B. books, paper, and radios for education C. clothing, medical supplies, and construction equipment D. mostly cash in the form of loans and grants E. people with business expertise to help develop the economy What kind of aid did the United States send to Greece to help its farmers? A. tractors B. mules C. seeds D. fertilizer E. all of these options What was one way that the United States influenced public opinion in Italy during the elections described in the video? A. The United States provided significant food aid to Italy so that the Italians would be inclined to vote against the Communists. B. The Italians had been impressed by the strength and loyalty of the American soldiers, and were inclined to listen to them during the elections. C. There was a large number of young Italians who followed American fashion and culture. D. Italian immigrants in the United States wrote letters to their families in Italy urging them not to vote for Communists. E. The Greeks showed the Italians how much the Americans had helped them, warning that supporting a Communist candidate would mean sacrificing American aid. How did Pope Pius XII undermine the strength of the Communist Party in Italy? A. He encouraged Italians to go out and vote. B. He warned that the Communist Party would legalize abortion. C. He excommunicated many members of the Communist Party. D. He made a speech in support of capitalism. E. He declared that Communists should not be baptized. http://www.youtube.com/watch?v=KVhWqwnZ1eM Use the video at left to answer the questions below. Hans Rosling shares how his students discuss “we” versus “them.” To whom are his students referring? A. the United States and Mexico B. Christians and Muslims C. Democrats and Republicans D. Europe and Asia E. none of these options According to Rosling, what factors contribute to a better quality of life for people in developing countries? A. family planning B. soap and water C. investment D. vaccinations E. all of these options Using his data, Rosling demonstrates a great shift in Mexico. What change does his data demonstrate? A. a decrease in drug usage B. a decrease in the number of jobs available C. an increase in average life expenctancy D. an increase in the rate of violent crime E. all of these options Instead of “developing” and “developed,” Rosling divides countries into four categories. Which of the following is NOT one of them? A. high-income countries B. middle-income countries C. low-income countries D. no-income countries E. collapsing countries Rosling discusses the increased life expectancy in both China and the United States. How are the situations different? A. The U.S. and China are on different continents. B. The life expectancy in China rose much higher than it did in the U.S. C. China first expanded its life expectancy and then grew economically, whereas the U.S. did the reverse. D. Average income and life expectancy steadily increased in the U.S., but they steadily decreased in China. E. all of these options Rosling shows a chart that demonstrates the regional income distribution of the world from 1970 to 2015. During that time, what has happened in South and East Asia? A. Money has flowed out of Asia to developing countries in Africa. B. The average income of citizens of South and East Asia has increased over the last 30 years. C. The average income of citizens of South and East Asia has decreased over the last 30 years. D. The average income of citizens of South and East Asia has surpassed that of Europe and North America. E. There has been no change. Click here to access GapMinder, the data visualizer that Hans Rosling uses. In 2010, which of the following countries had both a higher per-capita GDP and a higher life expectancy than the United States? A. France B. Japan C. Denmark D. Singapore E. Kuwait http://www.garretthardinsociety.org/articles/art_tragedy_of_the_commons.html http://www.youtube.com/watch?v=8a4S23uXIcM The Tragedy of the Commons What is the rough definition of the “commons” given in the article? A. any private property on which others trespass B. behavior that everyone considers to be normal C. a cow that lives in a herd D. government-administered benefits, like unemployment or Social Security E. a shared resource What does Hardin mean by describing pollution as a reverse tragedy of the commons? A. Rather than causing a problem, it resolves a problem. B. Pollution costs us money rather than making us money. C. We are putting something into the commons rather than removing something from it. D. It starts at the other end of the biological pyramid. E. Humans see less of it as time goes on. Hardin says “the air and waters surrounding us cannot readily be fenced, and so the tragedy of the commons as a cesspool must be prevented by different means.” What are those means? A. establishing more international treaties to protect the environment B. using laws or taxes to make the polluter pay for pollution C. punishing consumers for generating waste D. raising awareness about environmental issues E. developing greener products Pacific Garbage Dump According to the news report, what percent of the Gyre is made of plastic? A. 50 percent B. 60 percent C. 70 percent D. 80 percent E. 90 percent Where does the majority of the plastic in the Gyre come from? A. barges that dump trash in the ocean B. storm drains from land C. people throwing litter off boats into the ocean D. remnants from movie sets filmed at sea E. fishing boats processing their catch What does Charles Moore mean by the “throwaway concept”? A. the habitual use of disposable plastic packaging B. the mistaken view that marine ecosystems are infinitely renewable C. a general lack of interest in recycling D. the willingness to discard effective but small-scale environmental policies in deference to broader E. people throwing away their lives in pursuit of money In what way does the Great Pacific Gyre represent issues like global warming a tragedy of the commons? A. because all the plastic trash in it comes from the United States B. because it kills the albatross and makes it impossible for them to reproduce C. surbecause the countries rounding the Pacific Ocean are polluting the water in a way that affects the quality of the resource for all, but no one is specifically accountable for it D. because it causes marine life to compete for increasingly scarce nutrients in the ocean E. because nations in the region all collectively agreed to dump their trash in the Pacific http://www.npr.org/news/specials/climate/video/ http://ngm.nationalgeographic.com/climateconnections/climate-map http://www.npr.org/news/specials/climate/video/wildchronicles.html Use the links provided at left to answer the questions below. Global Warming: It’s All About Carbon How does carbon give us fuel? A. When you burn things that contain carbon the bonds break, giving off energy. B. Burning things creates carbon out of other elements as a result of combustion. C. Carbon is created after oxygen and hydrogen get released. D. Carbon bonds are created thereby giving off energy. E. Carbon is made into fuel by refining oil. National Geographic Climate Map What geographic areas have seen the most significant changes in temperature? A. The African continent. B. The Pacific Ocean. C. The Atlantic Ocean. D. The Arctic Ocean. E. The Indian Ocean. Why does it matter that rain fall steadily rather than in downpours? A. For those countries accustomed to steady rain fall, downpours are actually more efficient ways to catch water. B. Downpours in regions accustomed to steady fall makes them more prone to flooding and damage. C. In general, as long as regions get either steady fall or downpours most things will stay the same. D. Downpours are always more beneficial to crop growth than steady rain. E. Steady rain is always more beneficial to crop growth than downpours. Climate Change Threatens Kona Coffee What is unique about the climate in Hawaii, making it a good place to grow coffee? A. The elevation is high, the nights are cool and the days are humid. B. The elevation is low, the nights are warm and the days are dry. C. The elevation is high, the nights are warm and the days are dry. D. The elevation is low, the nights are cool and the days are dry. E. The elevation is high, the nights are warm and the days are humid. What specific temperature pattern have experts noted about the region where Kona coffee is grown in Hawaii? A. There has been no significant change but the bean production has dropped. B. The nights have warmed up, even though the days have cooled. C. There has been an increase in bean production with the change in climate. D. The nights have cooled even more so than before. E. There has been universally hot days all the way around.

http://www.econlib.org/library/Smith/smWN1.html#B.I,%20Ch.1,%20Of%20the%20Division%20of%20Labor What does Smith mean by division of labor, and how does it affect production? A. He means that each person does their own work to benefit themselves by creating goods. This creates well-crafted goods. B. He argues that in order to become more efficient, we need to put everyone in the same workhouses and eliminate division. C. He says that the division of labor provides farmers with the opportunity to become involved in manufacturing. D. He means that each person makes one small part of a good very quickly, but this is bad for the quality of production overall. E. He means that by having each individual specialize in one thing, they can work together to create products more efficiently and effectively. Which of the following is NOT an example of the circumstances by which the division of labor improves efficiency? A. A doll-making company stops allowing each employee to make one whole doll each and instead appoints each employee to create one part of the doll. B. A family of rug makers buys a loom to speed up their production. C. A mechanic opens a new shop to be nearer to the market. D. A factory changes the responsibilities of its employees so that one group handles heavy boxes and the other group does precision sewing. E. A baker who used to make a dozen cookies at a time buys a giant mixer and oven that enable him to make 20 dozen cookies at a time. Considering the global system of states, what do you think the allegory of the pins has to offer? A. It suggests that there could be a natural harmony of interests among states because they can divide labor among themselves to the benefit of everyone. B. It suggests that states can never be secure enough to cooperate because every state is equally capable of producing the same things. C. It suggests that a central authority is necessary to help states cooperate, in the same way that a manager oversees operations at a factory. D. The allegory of the pins is a great way to think about how wars come about, because states won’t cooperate with each other like pin-makers do. E. The allegory of the pins shows us that there is no natural harmony of interests between states. Smith sees the development of industry, technology, and the division of labor as A. generally positive but not progressive. The lives of many people may improve, but the world will generally stay the same. B. generally positive and progressive. The world is improving because of these changes, and it will continue to improve. C. generally negative. The creation of new technologies and the division of labor are harmful to all humans, both the wealthy and the poor. D. generally negative. The creation of the division of labor only benefits the wealthy at the expense of the poor. E. both positive and negative. Smith thinks that technology hurts us, while the division of labor helps society progress and develop. http://www.youtube.com/watch?v=RUwS1uAdUcI What point is Hans Rosling trying to make when he describes the global health pre-test? A. He is trying to show how the average person has no idea of the true state of global health. B. He is trying to illustrate how we tend to carry around outdated notions about the state of global health. C. He is trying to make us see that the less-developed countries are far worse off than we ever thought. D. He is trying to drive home the idea that global health has not improved over time despite foreign aid and improvements in medicine. E. He is trying to warn us about the rapid growth in world population. Rosling shows us that we tend to think about global health in terms of “we and them.” Who are the “we” and who are the “them”? A. “We” refers to academics, students, and scholars; “them” refers to the uneducated. B. “We” refers to the average person; “them” refers to politicians and global leaders. C. “We” refers to the wealthy; “them” refers to the poor. D. “We” refers to the Western world; “them” refers to the Third World. E. “We” refers to students; “them” refers to professors. In the life expectancy and fertility rate demonstration, what do the statistics reveal? A. Over time, developed countries produced small families and long lives, whereas developing countries produced large families and short lives. B. The world today looks much like it did in 1962 despite our attempts to help poorer countries develop. C. All countries in the world, even the poorer ones, are trending toward longer lives and smaller families. D. Developed countries are trending toward smaller families but shorter lives. E. All countries tend to make gains and losses in fertility and lifespan, but in the long run there is no significant change. What point does Rosling make about life expectancy in Vietnam as compared to the United States? To what does he attribute the change? A. He indicates that economic change preceded social change. B. He suggests that markets and free trade resulted in the increase in life expectancy. C. He says that the data indicates that the Vietnam War contributed to the decrease in life expectancy during that time, but that it recovered shortly thereafter. D. He says that social change in Asia preceded economic change, and life expectancy in Vietnam increased despite the war. E. He indicates that Vietnam was equal to the United States in life expectancy before the war. According to Rosling, how are regional statistics about child survival rates and GDP potentially misleading? A. Countries have an incentive to lie about the actual survival rates because they want foreign assistance. B. Statistics for the individual countries in a region are often vastly different. C. Regional statistics give us a strong sense of how we can understand development within one region, but it does not allow us to compare across regions. D. The data available over time and from countries within regions is often poorly collected and incomplete. E. Child survival rates cannot be compared regionally, since each culture has a different sense of how important children are. What is Rosling’s main point about statistical databases? A. The data is available but not readily accessible, so we need to create networks to solve that problem. B. The data that comes from these databases is often flawed and unreliable. C. It doesn’t matter whether we have access to these databases because the data can’t be used in an interesting way. D. Statistics can’t tell us very much, but we should do our best to make use of the information we do have. E. The information that could be true is too hard to sort out from what isn’t true because we don’t know how strong the data really is. http://www.marxists.org/archive/lenin/works/1916/imp-hsc/ch10.htm#v22zz99h-298-GUESS Click the link at left to read Chapter 10 of Imperialism, The Highest Stage of Capitalism, then answer the questions below. According to Lenin, what is the fundamental source of a monopoly? A. It is a natural effect of human behavior. B. It is the result of governments and police systems. C. Its source is rooted in democracy. D. It comes from the concentration of production at a high stage. E. It is what follows a socialist system. What are the principal types or manifestations of monopoly capitalism? A. Monopolistic capitalist associations like cartels, syndicates and trusts; and monopolies as a result of colonial policy. B. Monopolization of raw materials and monopolization of finance capital. C. Monopolization of governing structures and monopolies of oligarchies. D. Monopolist capitalist associations like cartels, syndicates and trusts; and monopolies as a result of colonial policy AND monopolization of raw materials and monopolization of finance capital. E. Monopolization of raw materials and monopolization of finance capital AND monopolization of governing structures and monopolies of oligarchies. What is the definition of a rentier state according to Lenin? A. A state that colonizes other states. B. A state whose bourgeoisie live off the export of capital. C. A poor state. D. A wealthy state. E. A colonized state. Overall Lenin’s analysis of the state of capitalism is concerned with: A. The interactions between states. B. The interactions within states. C. The ownership of industry and organizations. D. The interactions within states AND the ownership of industry and organizations. E. All of these options. http://view.vzaar.com/1194665/flashplayer Watch the video at left, and then answer the questions below. The Marshall Plan was developed by the United States after World War II. What was its purpose? A. to feed the hungry of Europe B. to stem the spread of communism C. to maintain an American military presence in Europe D. to feed the hungry of Europe AND to stem the spread of communism E. to stem the spread of communism AND to maintain an American military presence in Europe What kind of aid was sent at first? A. foods, fertilizers, and machines for agriculture B. books, paper, and radios for education C. clothing, medical supplies, and construction equipment D. mostly cash in the form of loans and grants E. people with business expertise to help develop the economy What kind of aid did the United States send to Greece to help its farmers? A. tractors B. mules C. seeds D. fertilizer E. all of these options What was one way that the United States influenced public opinion in Italy during the elections described in the video? A. The United States provided significant food aid to Italy so that the Italians would be inclined to vote against the Communists. B. The Italians had been impressed by the strength and loyalty of the American soldiers, and were inclined to listen to them during the elections. C. There was a large number of young Italians who followed American fashion and culture. D. Italian immigrants in the United States wrote letters to their families in Italy urging them not to vote for Communists. E. The Greeks showed the Italians how much the Americans had helped them, warning that supporting a Communist candidate would mean sacrificing American aid. How did Pope Pius XII undermine the strength of the Communist Party in Italy? A. He encouraged Italians to go out and vote. B. He warned that the Communist Party would legalize abortion. C. He excommunicated many members of the Communist Party. D. He made a speech in support of capitalism. E. He declared that Communists should not be baptized. http://www.youtube.com/watch?v=KVhWqwnZ1eM Use the video at left to answer the questions below. Hans Rosling shares how his students discuss “we” versus “them.” To whom are his students referring? A. the United States and Mexico B. Christians and Muslims C. Democrats and Republicans D. Europe and Asia E. none of these options According to Rosling, what factors contribute to a better quality of life for people in developing countries? A. family planning B. soap and water C. investment D. vaccinations E. all of these options Using his data, Rosling demonstrates a great shift in Mexico. What change does his data demonstrate? A. a decrease in drug usage B. a decrease in the number of jobs available C. an increase in average life expenctancy D. an increase in the rate of violent crime E. all of these options Instead of “developing” and “developed,” Rosling divides countries into four categories. Which of the following is NOT one of them? A. high-income countries B. middle-income countries C. low-income countries D. no-income countries E. collapsing countries Rosling discusses the increased life expectancy in both China and the United States. How are the situations different? A. The U.S. and China are on different continents. B. The life expectancy in China rose much higher than it did in the U.S. C. China first expanded its life expectancy and then grew economically, whereas the U.S. did the reverse. D. Average income and life expectancy steadily increased in the U.S., but they steadily decreased in China. E. all of these options Rosling shows a chart that demonstrates the regional income distribution of the world from 1970 to 2015. During that time, what has happened in South and East Asia? A. Money has flowed out of Asia to developing countries in Africa. B. The average income of citizens of South and East Asia has increased over the last 30 years. C. The average income of citizens of South and East Asia has decreased over the last 30 years. D. The average income of citizens of South and East Asia has surpassed that of Europe and North America. E. There has been no change. Click here to access GapMinder, the data visualizer that Hans Rosling uses. In 2010, which of the following countries had both a higher per-capita GDP and a higher life expectancy than the United States? A. France B. Japan C. Denmark D. Singapore E. Kuwait http://www.garretthardinsociety.org/articles/art_tragedy_of_the_commons.html http://www.youtube.com/watch?v=8a4S23uXIcM The Tragedy of the Commons What is the rough definition of the “commons” given in the article? A. any private property on which others trespass B. behavior that everyone considers to be normal C. a cow that lives in a herd D. government-administered benefits, like unemployment or Social Security E. a shared resource What does Hardin mean by describing pollution as a reverse tragedy of the commons? A. Rather than causing a problem, it resolves a problem. B. Pollution costs us money rather than making us money. C. We are putting something into the commons rather than removing something from it. D. It starts at the other end of the biological pyramid. E. Humans see less of it as time goes on. Hardin says “the air and waters surrounding us cannot readily be fenced, and so the tragedy of the commons as a cesspool must be prevented by different means.” What are those means? A. establishing more international treaties to protect the environment B. using laws or taxes to make the polluter pay for pollution C. punishing consumers for generating waste D. raising awareness about environmental issues E. developing greener products Pacific Garbage Dump According to the news report, what percent of the Gyre is made of plastic? A. 50 percent B. 60 percent C. 70 percent D. 80 percent E. 90 percent Where does the majority of the plastic in the Gyre come from? A. barges that dump trash in the ocean B. storm drains from land C. people throwing litter off boats into the ocean D. remnants from movie sets filmed at sea E. fishing boats processing their catch What does Charles Moore mean by the “throwaway concept”? A. the habitual use of disposable plastic packaging B. the mistaken view that marine ecosystems are infinitely renewable C. a general lack of interest in recycling D. the willingness to discard effective but small-scale environmental policies in deference to broader E. people throwing away their lives in pursuit of money In what way does the Great Pacific Gyre represent issues like global warming a tragedy of the commons? A. because all the plastic trash in it comes from the United States B. because it kills the albatross and makes it impossible for them to reproduce C. surbecause the countries rounding the Pacific Ocean are polluting the water in a way that affects the quality of the resource for all, but no one is specifically accountable for it D. because it causes marine life to compete for increasingly scarce nutrients in the ocean E. because nations in the region all collectively agreed to dump their trash in the Pacific http://www.npr.org/news/specials/climate/video/ http://ngm.nationalgeographic.com/climateconnections/climate-map http://www.npr.org/news/specials/climate/video/wildchronicles.html Use the links provided at left to answer the questions below. Global Warming: It’s All About Carbon How does carbon give us fuel? A. When you burn things that contain carbon the bonds break, giving off energy. B. Burning things creates carbon out of other elements as a result of combustion. C. Carbon is created after oxygen and hydrogen get released. D. Carbon bonds are created thereby giving off energy. E. Carbon is made into fuel by refining oil. National Geographic Climate Map What geographic areas have seen the most significant changes in temperature? A. The African continent. B. The Pacific Ocean. C. The Atlantic Ocean. D. The Arctic Ocean. E. The Indian Ocean. Why does it matter that rain fall steadily rather than in downpours? A. For those countries accustomed to steady rain fall, downpours are actually more efficient ways to catch water. B. Downpours in regions accustomed to steady fall makes them more prone to flooding and damage. C. In general, as long as regions get either steady fall or downpours most things will stay the same. D. Downpours are always more beneficial to crop growth than steady rain. E. Steady rain is always more beneficial to crop growth than downpours. Climate Change Threatens Kona Coffee What is unique about the climate in Hawaii, making it a good place to grow coffee? A. The elevation is high, the nights are cool and the days are humid. B. The elevation is low, the nights are warm and the days are dry. C. The elevation is high, the nights are warm and the days are dry. D. The elevation is low, the nights are cool and the days are dry. E. The elevation is high, the nights are warm and the days are humid. What specific temperature pattern have experts noted about the region where Kona coffee is grown in Hawaii? A. There has been no significant change but the bean production has dropped. B. The nights have warmed up, even though the days have cooled. C. There has been an increase in bean production with the change in climate. D. The nights have cooled even more so than before. E. There has been universally hot days all the way around.

http://www.econlib.org/library/Smith/smWN1.html#B.I,%20Ch.1,%20Of%20the%20Division%20of%20Labor What does Smith mean by division of labor, and … Read More...
Perceptual ________ refers to the process whereby the perceptual system filters out information that might make the individual uncomfortable or distressed. defense screening distortion bias

Perceptual ________ refers to the process whereby the perceptual system filters out information that might make the individual uncomfortable or distressed. defense screening distortion bias

Perceptual ________ refers to the process whereby the perceptual system … Read More...