2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy 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? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A 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 _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ à _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4à 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0à __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: 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. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy 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? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A 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 _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ à _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4à 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0à __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: 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. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

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ELEC153 Circuit Theory II M2A3 Lab: AC Series Circuits Introduction Previously you worked with two simple AC series circuits, R-C and R-L circuits. We continue that work in this experiment. Procedure 1. Setup the following circuit in MultiSim.The voltage source is 10 volts peak at 1000 Hz. Figure 1: Circuit for analysis using MultiSim 2. Change R1 to 1 k and C1 to 0.1 uF. Connect the oscilloscope to measure both the source voltage and the voltage across the resistor.You should have the following arrangement. Figure 2: Circuit of figure 1 connected to oscilloscope To color the wires, right click the desired wire and select “Color Segment…” and follow the instructions. Start the simulation and open the oscilloscope. You should get the following plot: Figure 3: Source voltage (red) and the voltage (blue) across the resistor The red signal is the voltage of the source and the blue is the voltage across the resistor. The colors correspond to the colors of the wires from the oscilloscope. 3. From the resulting analysis plotdetermine the peak current. To determine the peak current measure the peak voltage across the resistor and divide by the value of the resistor (1000 Ohms). Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5 Determine the phase shift between the current in the circuit and the source voltage. We look at the time between zero crossings to determine the phase shift between two waveforms. In our plot, the blue waveform (representing the circuit current or the voltage across the resistor) crosses zero before the red waveform (the circuit voltage). So, current is leading voltage in this circuit. This is exactly what should happen when we have a capacitive circuit. 6. To determine the phase shift, we first have to measure the time between zero crossings on the red and blue waveforms. This is done by moving the oscillator probes to the two zero crossing as is shown in the following figure Figure 4: Determining the phase shift between the two voltage waveforms We can see from the figure that the zero crossing difference (T2 – T1) is approximately 134 us. The ratio of the zero-crossing time difference to the period of the waveform determines the phase shift, as follows: Using our time values, we have: How do we know if this phase shift is correct? In step 4 when you did your manual calculations to find the peak current, you had to find the total impedance of the circuit, which was: Now, the current will be: Here, the positive angle on the current indicates it is leading the circuit voltage. 7. Change the frequency of the voltage source to 5000 Hz. Estimulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 8. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Writeup and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

ELEC153 Circuit Theory II M2A3 Lab: AC Series Circuits Introduction Previously you worked with two simple AC series circuits, R-C and R-L circuits. We continue that work in this experiment. Procedure 1. Setup the following circuit in MultiSim.The voltage source is 10 volts peak at 1000 Hz. Figure 1: Circuit for analysis using MultiSim 2. Change R1 to 1 k and C1 to 0.1 uF. Connect the oscilloscope to measure both the source voltage and the voltage across the resistor.You should have the following arrangement. Figure 2: Circuit of figure 1 connected to oscilloscope To color the wires, right click the desired wire and select “Color Segment…” and follow the instructions. Start the simulation and open the oscilloscope. You should get the following plot: Figure 3: Source voltage (red) and the voltage (blue) across the resistor The red signal is the voltage of the source and the blue is the voltage across the resistor. The colors correspond to the colors of the wires from the oscilloscope. 3. From the resulting analysis plotdetermine the peak current. To determine the peak current measure the peak voltage across the resistor and divide by the value of the resistor (1000 Ohms). Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5 Determine the phase shift between the current in the circuit and the source voltage. We look at the time between zero crossings to determine the phase shift between two waveforms. In our plot, the blue waveform (representing the circuit current or the voltage across the resistor) crosses zero before the red waveform (the circuit voltage). So, current is leading voltage in this circuit. This is exactly what should happen when we have a capacitive circuit. 6. To determine the phase shift, we first have to measure the time between zero crossings on the red and blue waveforms. This is done by moving the oscillator probes to the two zero crossing as is shown in the following figure Figure 4: Determining the phase shift between the two voltage waveforms We can see from the figure that the zero crossing difference (T2 – T1) is approximately 134 us. The ratio of the zero-crossing time difference to the period of the waveform determines the phase shift, as follows: Using our time values, we have: How do we know if this phase shift is correct? In step 4 when you did your manual calculations to find the peak current, you had to find the total impedance of the circuit, which was: Now, the current will be: Here, the positive angle on the current indicates it is leading the circuit voltage. 7. Change the frequency of the voltage source to 5000 Hz. Estimulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 8. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Writeup and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

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Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F  F = −kx x k m k x = 0 block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = -60 % s t = 0 s cm cm/s 0 = -2.09 rad Correct Part B What is the phase at ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: t = 0.5 s  = 0 rad t = 1.0 s  = 2.09 rad t = 1.5 s  = 4.19 rad Correct Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct g cm s 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 0.628 s 5.00 Nm -0.785 rad Part E The initial coordinate of the mass. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part F The initial velocity. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part G The maximum speed. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 1.41 cm 14.1 cms 20.0 cms Part H The total energy. Express your answer to one decimal place and include the appropriate units. ANSWER: Correct Part I The velocity at . Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? 1.0 mJ t = 0.40 s 1.46 cms N/m cm s Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum m = 110 g vmax = 49 cms A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. m L T T L T = 2 Lg −−  g T/2 T ‘2T 2T g/6 ANSWER: Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. T/6 T/’6 ‘6T 6T It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. g % s L = 19 cm m lmoon = 0.35 m m g 1.0 MHz Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 94.2%. You received 135.71 out of a possible total of 144 points. N amax = 6.6 μm vmax = 41 ms

Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F  F = −kx x k m k x = 0 block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = -60 % s t = 0 s cm cm/s 0 = -2.09 rad Correct Part B What is the phase at ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: t = 0.5 s  = 0 rad t = 1.0 s  = 2.09 rad t = 1.5 s  = 4.19 rad Correct Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct g cm s 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 0.628 s 5.00 Nm -0.785 rad Part E The initial coordinate of the mass. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part F The initial velocity. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part G The maximum speed. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 1.41 cm 14.1 cms 20.0 cms Part H The total energy. Express your answer to one decimal place and include the appropriate units. ANSWER: Correct Part I The velocity at . Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? 1.0 mJ t = 0.40 s 1.46 cms N/m cm s Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum m = 110 g vmax = 49 cms A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. m L T T L T = 2 Lg −−  g T/2 T ‘2T 2T g/6 ANSWER: Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. T/6 T/’6 ‘6T 6T It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. g % s L = 19 cm m lmoon = 0.35 m m g 1.0 MHz Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 94.2%. You received 135.71 out of a possible total of 144 points. N amax = 6.6 μm vmax = 41 ms

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

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

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PART 1: (Total 350 pts – 35pts per hazard x 10 hazards) Each identified hazard should contain the following elements (Element 1 ~ 7 below). Furthermore, each student will need to provide his/her responses in a pragraph format for each element by JUSTIFYING/SUPPORTING his/her responses: ELEMENT 1) Explain Hazard you identified. What kind of exposure does each hazard have on employee ? What is the hazard? What could go wrong? Think in terms of “What ifs?” or “What could happen?” In this section, you are to describe a situation(s) and discuss what could happen (5pts). ELEMENT 2) Who would be at risk? Be specific group of individuals who would be at risk meaning don’t just say “employees” or “students” are affected. Rather be sure to JUSTIFY your position/response. (5pts) ELEMENT 3) Identify Risk Level for each hazard you identified. When you determine risk level, it is critical that you JUSTIFY as to why you selected certain Frequency and Severity level. (5pts) ELEMENT 4) Citation. If you were a Compliance Safety and Health Officer (CSHO), which SPECIFIC standard/regulation would you cite this hazard under and WHY? You must provide exact standard (eg: 29CFR 1910.261(a)(1)(i)….) and state what it says AND relate your identified hazards with the standard/regulation. Eg: What was violated, etc. (5pts) ELEMENT 5) What is/are the abatement(s) or control measure(s) for each identified hazards and why? In other words, what or HOW would you correct this situation and WHY? This is where you must discuss “Two Stage Approach.” (5pts) It is important for you to select an appropriate corrective measure(s) to protect your employees. Again, we are here to protect human, property, and the environment. We can’t just say “just because.” We will need to have a good reason(s) or justification(s) as to WHY we take a certain approach or a corrective measure to protect human, propert, and the environment. Therefore, strong justification is critical in this section – when you do so, make sure to cite follow APA format. ELEMENT 6) Once you applied your control measure(s), you are to reassess Residual Risk to make sure that you have either eliminated or lowered your risk level to an acceptable level. ELEMENT 7) Supprting Resources: Each student must use at least two (2) “credible” resources PER HAZARD to support his/her responses. This EXCLUDE OSHA/citations. (5pts) seven (7) elements. NOTE 2: APA format needs to be followed for this Part 1. (See attached Sample) PART 2: (Total 15pts) Once you identified 10 hazards (two hazards/standard), you are to prioritize those hazards from most critical to least based on item 2 you did in Part 1. Furthermore, each student will need to prepare ONE PAGE, STAND ALONE document which outlines PRIORITIZATION of those hazards he/she identified and provide the information as as to which hazards need to be control the most. PART 3: (Total 20pts) Based on the above findings, you are to create 1 page report that includes above findings. Remember, one page does not necessary mean a vertical view of 8 1/2 by 11 paper. When you submit this REPORT, think in terms of you submitting this report to your boss. (This is a hands-on practice as to how you will compile a report. If you don’t know how to develop a report, I encourage you to research to determine types of report and come up with your own version. Remember, you will most likely to submit a report in a future that is not more than one page……

PART 1: (Total 350 pts – 35pts per hazard x 10 hazards) Each identified hazard should contain the following elements (Element 1 ~ 7 below). Furthermore, each student will need to provide his/her responses in a pragraph format for each element by JUSTIFYING/SUPPORTING his/her responses: ELEMENT 1) Explain Hazard you identified. What kind of exposure does each hazard have on employee ? What is the hazard? What could go wrong? Think in terms of “What ifs?” or “What could happen?” In this section, you are to describe a situation(s) and discuss what could happen (5pts). ELEMENT 2) Who would be at risk? Be specific group of individuals who would be at risk meaning don’t just say “employees” or “students” are affected. Rather be sure to JUSTIFY your position/response. (5pts) ELEMENT 3) Identify Risk Level for each hazard you identified. When you determine risk level, it is critical that you JUSTIFY as to why you selected certain Frequency and Severity level. (5pts) ELEMENT 4) Citation. If you were a Compliance Safety and Health Officer (CSHO), which SPECIFIC standard/regulation would you cite this hazard under and WHY? You must provide exact standard (eg: 29CFR 1910.261(a)(1)(i)….) and state what it says AND relate your identified hazards with the standard/regulation. Eg: What was violated, etc. (5pts) ELEMENT 5) What is/are the abatement(s) or control measure(s) for each identified hazards and why? In other words, what or HOW would you correct this situation and WHY? This is where you must discuss “Two Stage Approach.” (5pts) It is important for you to select an appropriate corrective measure(s) to protect your employees. Again, we are here to protect human, property, and the environment. We can’t just say “just because.” We will need to have a good reason(s) or justification(s) as to WHY we take a certain approach or a corrective measure to protect human, propert, and the environment. Therefore, strong justification is critical in this section – when you do so, make sure to cite follow APA format. ELEMENT 6) Once you applied your control measure(s), you are to reassess Residual Risk to make sure that you have either eliminated or lowered your risk level to an acceptable level. ELEMENT 7) Supprting Resources: Each student must use at least two (2) “credible” resources PER HAZARD to support his/her responses. This EXCLUDE OSHA/citations. (5pts) seven (7) elements. NOTE 2: APA format needs to be followed for this Part 1. (See attached Sample) PART 2: (Total 15pts) Once you identified 10 hazards (two hazards/standard), you are to prioritize those hazards from most critical to least based on item 2 you did in Part 1. Furthermore, each student will need to prepare ONE PAGE, STAND ALONE document which outlines PRIORITIZATION of those hazards he/she identified and provide the information as as to which hazards need to be control the most. PART 3: (Total 20pts) Based on the above findings, you are to create 1 page report that includes above findings. Remember, one page does not necessary mean a vertical view of 8 1/2 by 11 paper. When you submit this REPORT, think in terms of you submitting this report to your boss. (This is a hands-on practice as to how you will compile a report. If you don’t know how to develop a report, I encourage you to research to determine types of report and come up with your own version. Remember, you will most likely to submit a report in a future that is not more than one page……

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Chapter 13 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Matter of Some Gravity Learning Goal: To understand Newton’s law of gravitation and the distinction between inertial and gravitational masses. In this problem, you will practice using Newton’s law of gravitation. According to that law, the magnitude of the gravitational force between two small particles of masses and , separated by a distance , is given by , where is the universal gravitational constant, whose numerical value (in SI units) is . This formula applies not only to small particles, but also to spherical objects. In fact, the gravitational force between two uniform spheres is the same as if we concentrated all the mass of each sphere at its center. Thus, by modeling the Earth and the Moon as uniform spheres, you can use the particle approximation when calculating the force of gravity between them. Be careful in using Newton’s law to choose the correct value for . To calculate the force of gravitational attraction between two uniform spheres, the distance in the equation for Newton’s law of gravitation is the distance between the centers of the spheres. For instance, if a small object such as an elephant is located on the surface of the Earth, the radius of the Earth would be used in the equation. Note that the force of gravity acting on an object located near the surface of a planet is often called weight. Also note that in situations involving satellites, you are often given the altitude of the satellite, that is, the distance from the satellite to the surface of the planet; this is not the distance to be used in the formula for the law of gravitation. There is a potentially confusing issue involving mass. Mass is defined as a measure of an object’s inertia, that is, its ability to resist acceleration. Newton’s second law demonstrates the relationship between mass, acceleration, and the net force acting on an object: . We can now refer to this measure of inertia more precisely as the inertial mass. On the other hand, the masses of the particles that appear in the expression for the law of gravity seem to have nothing to do with inertia: Rather, they serve as a measure of the strength of gravitational interactions. It would be reasonable to call such a property gravitational mass. Does this mean that every object has two different masses? Generally speaking, yes. However, the good news is that according to the latest, highly precise, measurements, the inertial and the gravitational mass of an object are, in fact, equal to each other; it is an established consensus among physicists that there is only one mass after all, which is a measure of both the object’s inertia and its ability to engage in gravitational interactions. Note that this consensus, like everything else in science, is open to possible amendments in the future. In this problem, you will answer several questions that require the use of Newton’s law of gravitation. Part A Two particles are separated by a certain distance. The force of gravitational interaction between them is . Now the separation between the particles is tripled. Find the new force of gravitational Fg m1 m2 r Fg = G m1m2 r2 G 6.67 × 10−11 N m2 kg2 r r rEarth F  = m net a F0 interaction . Express your answer in terms of . ANSWER: Part B A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite moves to a different orbit, so that its altitude is tripled. Find the new force of gravitational interaction . Express your answer in terms of . You did not open hints for this part. ANSWER: Part C A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite is brought back to the surface of the planet. Find the new force of gravitational interaction . Express your answer in terms of . ANSWER: F1 F0 F1 = F0 F2 F0 F2 = F0 F4 F0 Typesetting math: 81% Part D Two satellites revolve around the Earth. Satellite A has mass and has an orbit of radius . Satellite B has mass and an orbit of unknown radius . The forces of gravitational attraction between each satellite and the Earth is the same. Find . Express your answer in terms of . ANSWER: Part E An adult elephant has a mass of about 5.0 tons. An adult elephant shrew has a mass of about 50 grams. How far from the center of the Earth should an elephant be placed so that its weight equals that of the elephant shrew on the surface of the Earth? The radius of the Earth is 6400 . ( .) Express your answer in kilometers. ANSWER: The table below gives the masses of the Earth, the Moon, and the Sun. Name Mass (kg) Earth Moon Sun F4 = m r 6m rb rb r rb = r km 1 ton = 103 kg r = km 5.97 × 1024 7.35 × 1022 1.99 × 1030 Typesetting math: 81% The average distance between the Earth and the Moon is . The average distance between the Earth and the Sun is . Use this information to answer the following questions. Part F Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the new moon (when the moon is located directly between the Earth and the Sun). Express your answer in newtons to three significant figures. You did not open hints for this part. ANSWER: Part G Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the full moon (when the Earth is located directly between the moon and the sun). Express your answer in newtons to three significant figures. ANSWER: ± Understanding Newton’s Law of Universal Gravitation Learning Goal: To understand Newton’s law of universal gravitation and be able to apply it in two-object situations and (collinear) three-object situations; to distinguish between the use of and . 3.84 × 108 m 1.50 × 1011 m Fnet Fnet = N Fnet Fnet = N Typesetting math: 81% G g In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in the figure. Newton’s law of universal gravitation describes the magnitude of the attractive gravitational force between two objects with masses and as , where is the distance between the centers of the two objects and is the gravitational constant. The gravitational force is attractive, so in the figure it pulls to the right on (toward ) and toward the left on (toward ). The gravitational force acting on is equal in size to, but exactly opposite in direction from, the gravitational force acting on , as required by Newton’s third law. The magnitude of both forces is calculated with the equation given above. The gravitational constant has the value and should not be confused with the magnitude of the gravitational free-fall acceleration constant, denoted by , which equals 9.80 near the surface of the earth. The size of in SI units is tiny. This means that gravitational forces are sizeable only in the vicinity of very massive objects, such as the earth. You are in fact gravitationally attracted toward all the objects around you, such as the computer you are using, but the size of that force is too small to be noticed without extremely sensitive equipment. Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass and the sun has mass . They are separated, center to center, by . Part A What is the size of the gravitational force acting on the earth due to the sun? Express your answer in newtons. F  g m1 m2 Fg = G( ) m1m2 r2 r G m1 m2 m2 m1 m1 m2 G G = 6.67 × 10−11 N m2/kg2 g m/s2 G mearth = 5.98 × 1024 kg msun = 1.99 × 1030 kg r = 93 million miles = 150 million km Typesetting math: 81% You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F N Typesetting math: 81% This question will be shown after you complete previous question(s). Understanding Mass and Weight Learning Goal: To understand the distinction between mass and weight and to be able to calculate the weight of an object from its mass and Newton’s law of gravitation. The concepts of mass and weight are often confused. In fact, in everyday conversations, the word “weight” often replaces “mass,” as in “My weight is seventy-five kilograms” or “I need to lose some weight.” Of course, mass and weight are related; however, they are also very different. Mass, as you recall, is a measure of an object’s inertia (ability to resist acceleration). Newton’s 2nd law demonstrates the relationship among an object’s mass, its acceleration, and the net force acting on it: . Mass is an intrinsic property of an object and is independent of the object’s location. Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: , where is the weight of an object, is the mass of that object, and is the local acceleration due to gravity (in other words, the strength of the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the object and its location. Part A Which of the following quantities represent mass? Check all that apply. ANSWER: Fnet = ma w = mg w m g 12.0 lbs 0.34 g 120 kg 1600 kN 0.34 m 411 cm 899 MN Typesetting math: 81% Part B This question will be shown after you complete previous question(s). Using the universal law of gravity, we can find the weight of an object feeling the gravitational pull of a nearby planet. We can write an expression , where is the weight of the object, is the gravitational constant, is the mass of that object, is mass of the planet, and is the distance from the center of the planet to the object. If the object is on the surface of the planet, is simply the radius of the planet. Part C The gravitational field on the surface of the earth is stronger than that on the surface of the moon. If a rock is transported from the moon to the earth, which properties of the rock change? ANSWER: Part D This question will be shown after you complete previous question(s). Part E If acceleration due to gravity on the earth is , which formula gives the acceleration due to gravity on Loput? You did not open hints for this part. ANSWER: w = GmM/r2 w G m M r r mass only weight only both mass and weight neither mass nor weight g Typesetting math: 81% Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). ± Weight on a Neutron Star Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but a much smaller diameter. g 1.7 5.6 g 1.72 5.6 g 1.72 5.62 g 5.6 1.7 g 5.62 1.72 g 5.6 1.72 Typesetting math: 81% Part A If you weigh 655 on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 19.0 ? Take the mass of the sun to be = 1.99×1030 , the gravitational constant to be = 6.67×10−11 , and the acceleration due to gravity at the earth’s surface to be = 9.810 . Express your weight in newtons. You did not open hints for this part. ANSWER: ± Escape Velocity Learning Goal: To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass . The escape velocity is a function of the distance of the object from the center of the planet , but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question “How fast does my rocket have to go to escape from the surface of the planet?” Part A The key to making a concise mathematical definition of escape velocity is to consider the energy. If an object is launched at its escape velocity, what is the total mechanical energy of the object at a very large (i.e., infinite) distance from the planet? Follow the usual convention and take the gravitational potential energy to be zero at very large distances. You did not open hints for this part. ANSWER: N km ms kg G N m2/kg2 g m/s2 wstar wstar = N m M R Etotal Typesetting math: 81% Consider the motion of an object between a point close to the planet and a point very very far from the planet. Indicate whether the following statements are true or false. Part B Angular momentum about the center of the planet is conserved. ANSWER: Part C Total mechanical energy is conserved. ANSWER: Part D Kinetic energy is conserved. ANSWER: Etotal = true false true false Typesetting math: 81% Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). A Satellite in a Circular Orbit Consider a satellite of mass that orbits a planet of mass in a circle a distance from the center of the planet. The satellite’s mass is negligible compared with that of the planet. Indicate whether each of the statements in this problem is true or false. Part A The information given is sufficient to uniquely specify the speed, potential energy, and angular momentum of the satellite. You did not open hints for this part. ANSWER: true false m1 m2 r true false Typesetting math: 81% Part B The total mechanical energy of the satellite is conserved. You did not open hints for this part. ANSWER: Part C The linear momentum vector of the satellite is conserved. You did not open hints for this part. ANSWER: Part D The angular momentum of the satellite about the center of the planet is conserved. You did not open hints for this part. ANSWER: true false true false Typesetting math: 81% Part E The equations that express the conservation laws of total mechanical energy and linear momentum are sufficient to solve for the speed necessary to maintain a circular orbit at without using . You did not open hints for this part. ANSWER: At the Galaxy’s Core Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light years and an orbital speed of about 200 . Part A Determine the mass of the massive object at the center of the Milky Way galaxy. Take the distance of one light year to be . Express your answer in kilograms. You did not open hints for this part. true false R F = ma true false km/s M 9.461 × 1015 m Typesetting math: 81% ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Properties of Circular Orbits Learning Goal: To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth. M = kg Typesetting math: 81% The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit–a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass . For all parts of this problem, where appropriate, use for the universal gravitational constant. Part A Find the orbital speed for a satellite in a circular orbit of radius . Express the orbital speed in terms of , , and . You did not open hints for this part. ANSWER: Part B Find the kinetic energy of a satellite with mass in a circular orbit with radius . Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. ANSWER: Part C M G v R G M R v = K m R \texttip{K}{K} = Typesetting math: 81% This question will be shown after you complete previous question(s). Part D Find the orbital period \texttip{T}{T}. Express your answer in terms of \texttip{G}{G}, \texttip{M}{M}, \texttip{R}{R}, and \texttip{\pi }{pi}. You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F Find \texttip{L}{L}, the magnitude of the angular momentum of the satellite with respect to the center of the planet. Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. You did not open hints for this part. ANSWER: \texttip{T}{T} = Typesetting math: 81% Part G The quantities \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L} all represent physical quantities characterizing the orbit that depend on radius \texttip{R}{R}. Indicate the exponent (power) of the radial dependence of the absolute value of each. Express your answer as a comma-separated list of exponents corresponding to \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L}, in that order. For example, -1,-1/2,-0.5,-3/2 would mean v \propto R^{-1}, K \propto R^{-1/2}, and so forth. 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. \texttip{L}{L} = Typesetting math: 81%

Chapter 13 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Matter of Some Gravity Learning Goal: To understand Newton’s law of gravitation and the distinction between inertial and gravitational masses. In this problem, you will practice using Newton’s law of gravitation. According to that law, the magnitude of the gravitational force between two small particles of masses and , separated by a distance , is given by , where is the universal gravitational constant, whose numerical value (in SI units) is . This formula applies not only to small particles, but also to spherical objects. In fact, the gravitational force between two uniform spheres is the same as if we concentrated all the mass of each sphere at its center. Thus, by modeling the Earth and the Moon as uniform spheres, you can use the particle approximation when calculating the force of gravity between them. Be careful in using Newton’s law to choose the correct value for . To calculate the force of gravitational attraction between two uniform spheres, the distance in the equation for Newton’s law of gravitation is the distance between the centers of the spheres. For instance, if a small object such as an elephant is located on the surface of the Earth, the radius of the Earth would be used in the equation. Note that the force of gravity acting on an object located near the surface of a planet is often called weight. Also note that in situations involving satellites, you are often given the altitude of the satellite, that is, the distance from the satellite to the surface of the planet; this is not the distance to be used in the formula for the law of gravitation. There is a potentially confusing issue involving mass. Mass is defined as a measure of an object’s inertia, that is, its ability to resist acceleration. Newton’s second law demonstrates the relationship between mass, acceleration, and the net force acting on an object: . We can now refer to this measure of inertia more precisely as the inertial mass. On the other hand, the masses of the particles that appear in the expression for the law of gravity seem to have nothing to do with inertia: Rather, they serve as a measure of the strength of gravitational interactions. It would be reasonable to call such a property gravitational mass. Does this mean that every object has two different masses? Generally speaking, yes. However, the good news is that according to the latest, highly precise, measurements, the inertial and the gravitational mass of an object are, in fact, equal to each other; it is an established consensus among physicists that there is only one mass after all, which is a measure of both the object’s inertia and its ability to engage in gravitational interactions. Note that this consensus, like everything else in science, is open to possible amendments in the future. In this problem, you will answer several questions that require the use of Newton’s law of gravitation. Part A Two particles are separated by a certain distance. The force of gravitational interaction between them is . Now the separation between the particles is tripled. Find the new force of gravitational Fg m1 m2 r Fg = G m1m2 r2 G 6.67 × 10−11 N m2 kg2 r r rEarth F  = m net a F0 interaction . Express your answer in terms of . ANSWER: Part B A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite moves to a different orbit, so that its altitude is tripled. Find the new force of gravitational interaction . Express your answer in terms of . You did not open hints for this part. ANSWER: Part C A satellite revolves around a planet at an altitude equal to the radius of the planet. The force of gravitational interaction between the satellite and the planet is . Then the satellite is brought back to the surface of the planet. Find the new force of gravitational interaction . Express your answer in terms of . ANSWER: F1 F0 F1 = F0 F2 F0 F2 = F0 F4 F0 Typesetting math: 81% Part D Two satellites revolve around the Earth. Satellite A has mass and has an orbit of radius . Satellite B has mass and an orbit of unknown radius . The forces of gravitational attraction between each satellite and the Earth is the same. Find . Express your answer in terms of . ANSWER: Part E An adult elephant has a mass of about 5.0 tons. An adult elephant shrew has a mass of about 50 grams. How far from the center of the Earth should an elephant be placed so that its weight equals that of the elephant shrew on the surface of the Earth? The radius of the Earth is 6400 . ( .) Express your answer in kilometers. ANSWER: The table below gives the masses of the Earth, the Moon, and the Sun. Name Mass (kg) Earth Moon Sun F4 = m r 6m rb rb r rb = r km 1 ton = 103 kg r = km 5.97 × 1024 7.35 × 1022 1.99 × 1030 Typesetting math: 81% The average distance between the Earth and the Moon is . The average distance between the Earth and the Sun is . Use this information to answer the following questions. Part F Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the new moon (when the moon is located directly between the Earth and the Sun). Express your answer in newtons to three significant figures. You did not open hints for this part. ANSWER: Part G Find the net gravitational force acting on the Earth in the Sun-Earth-Moon system during the full moon (when the Earth is located directly between the moon and the sun). Express your answer in newtons to three significant figures. ANSWER: ± Understanding Newton’s Law of Universal Gravitation Learning Goal: To understand Newton’s law of universal gravitation and be able to apply it in two-object situations and (collinear) three-object situations; to distinguish between the use of and . 3.84 × 108 m 1.50 × 1011 m Fnet Fnet = N Fnet Fnet = N Typesetting math: 81% G g In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in the figure. Newton’s law of universal gravitation describes the magnitude of the attractive gravitational force between two objects with masses and as , where is the distance between the centers of the two objects and is the gravitational constant. The gravitational force is attractive, so in the figure it pulls to the right on (toward ) and toward the left on (toward ). The gravitational force acting on is equal in size to, but exactly opposite in direction from, the gravitational force acting on , as required by Newton’s third law. The magnitude of both forces is calculated with the equation given above. The gravitational constant has the value and should not be confused with the magnitude of the gravitational free-fall acceleration constant, denoted by , which equals 9.80 near the surface of the earth. The size of in SI units is tiny. This means that gravitational forces are sizeable only in the vicinity of very massive objects, such as the earth. You are in fact gravitationally attracted toward all the objects around you, such as the computer you are using, but the size of that force is too small to be noticed without extremely sensitive equipment. Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass and the sun has mass . They are separated, center to center, by . Part A What is the size of the gravitational force acting on the earth due to the sun? Express your answer in newtons. F  g m1 m2 Fg = G( ) m1m2 r2 r G m1 m2 m2 m1 m1 m2 G G = 6.67 × 10−11 N m2/kg2 g m/s2 G mearth = 5.98 × 1024 kg msun = 1.99 × 1030 kg r = 93 million miles = 150 million km Typesetting math: 81% You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F N Typesetting math: 81% This question will be shown after you complete previous question(s). Understanding Mass and Weight Learning Goal: To understand the distinction between mass and weight and to be able to calculate the weight of an object from its mass and Newton’s law of gravitation. The concepts of mass and weight are often confused. In fact, in everyday conversations, the word “weight” often replaces “mass,” as in “My weight is seventy-five kilograms” or “I need to lose some weight.” Of course, mass and weight are related; however, they are also very different. Mass, as you recall, is a measure of an object’s inertia (ability to resist acceleration). Newton’s 2nd law demonstrates the relationship among an object’s mass, its acceleration, and the net force acting on it: . Mass is an intrinsic property of an object and is independent of the object’s location. Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: , where is the weight of an object, is the mass of that object, and is the local acceleration due to gravity (in other words, the strength of the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the object and its location. Part A Which of the following quantities represent mass? Check all that apply. ANSWER: Fnet = ma w = mg w m g 12.0 lbs 0.34 g 120 kg 1600 kN 0.34 m 411 cm 899 MN Typesetting math: 81% Part B This question will be shown after you complete previous question(s). Using the universal law of gravity, we can find the weight of an object feeling the gravitational pull of a nearby planet. We can write an expression , where is the weight of the object, is the gravitational constant, is the mass of that object, is mass of the planet, and is the distance from the center of the planet to the object. If the object is on the surface of the planet, is simply the radius of the planet. Part C The gravitational field on the surface of the earth is stronger than that on the surface of the moon. If a rock is transported from the moon to the earth, which properties of the rock change? ANSWER: Part D This question will be shown after you complete previous question(s). Part E If acceleration due to gravity on the earth is , which formula gives the acceleration due to gravity on Loput? You did not open hints for this part. ANSWER: w = GmM/r2 w G m M r r mass only weight only both mass and weight neither mass nor weight g Typesetting math: 81% Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). ± Weight on a Neutron Star Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but a much smaller diameter. g 1.7 5.6 g 1.72 5.6 g 1.72 5.62 g 5.6 1.7 g 5.62 1.72 g 5.6 1.72 Typesetting math: 81% Part A If you weigh 655 on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 19.0 ? Take the mass of the sun to be = 1.99×1030 , the gravitational constant to be = 6.67×10−11 , and the acceleration due to gravity at the earth’s surface to be = 9.810 . Express your weight in newtons. You did not open hints for this part. ANSWER: ± Escape Velocity Learning Goal: To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass . The escape velocity is a function of the distance of the object from the center of the planet , but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question “How fast does my rocket have to go to escape from the surface of the planet?” Part A The key to making a concise mathematical definition of escape velocity is to consider the energy. If an object is launched at its escape velocity, what is the total mechanical energy of the object at a very large (i.e., infinite) distance from the planet? Follow the usual convention and take the gravitational potential energy to be zero at very large distances. You did not open hints for this part. ANSWER: N km ms kg G N m2/kg2 g m/s2 wstar wstar = N m M R Etotal Typesetting math: 81% Consider the motion of an object between a point close to the planet and a point very very far from the planet. Indicate whether the following statements are true or false. Part B Angular momentum about the center of the planet is conserved. ANSWER: Part C Total mechanical energy is conserved. ANSWER: Part D Kinetic energy is conserved. ANSWER: Etotal = true false true false Typesetting math: 81% Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). A Satellite in a Circular Orbit Consider a satellite of mass that orbits a planet of mass in a circle a distance from the center of the planet. The satellite’s mass is negligible compared with that of the planet. Indicate whether each of the statements in this problem is true or false. Part A The information given is sufficient to uniquely specify the speed, potential energy, and angular momentum of the satellite. You did not open hints for this part. ANSWER: true false m1 m2 r true false Typesetting math: 81% Part B The total mechanical energy of the satellite is conserved. You did not open hints for this part. ANSWER: Part C The linear momentum vector of the satellite is conserved. You did not open hints for this part. ANSWER: Part D The angular momentum of the satellite about the center of the planet is conserved. You did not open hints for this part. ANSWER: true false true false Typesetting math: 81% Part E The equations that express the conservation laws of total mechanical energy and linear momentum are sufficient to solve for the speed necessary to maintain a circular orbit at without using . You did not open hints for this part. ANSWER: At the Galaxy’s Core Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light years and an orbital speed of about 200 . Part A Determine the mass of the massive object at the center of the Milky Way galaxy. Take the distance of one light year to be . Express your answer in kilograms. You did not open hints for this part. true false R F = ma true false km/s M 9.461 × 1015 m Typesetting math: 81% ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Properties of Circular Orbits Learning Goal: To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth. M = kg Typesetting math: 81% The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit–a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass . For all parts of this problem, where appropriate, use for the universal gravitational constant. Part A Find the orbital speed for a satellite in a circular orbit of radius . Express the orbital speed in terms of , , and . You did not open hints for this part. ANSWER: Part B Find the kinetic energy of a satellite with mass in a circular orbit with radius . Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. ANSWER: Part C M G v R G M R v = K m R \texttip{K}{K} = Typesetting math: 81% This question will be shown after you complete previous question(s). Part D Find the orbital period \texttip{T}{T}. Express your answer in terms of \texttip{G}{G}, \texttip{M}{M}, \texttip{R}{R}, and \texttip{\pi }{pi}. You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F Find \texttip{L}{L}, the magnitude of the angular momentum of the satellite with respect to the center of the planet. Express your answer in terms of \texttip{m}{m}, \texttip{M}{M}, \texttip{G}{G}, and \texttip{R}{R}. You did not open hints for this part. ANSWER: \texttip{T}{T} = Typesetting math: 81% Part G The quantities \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L} all represent physical quantities characterizing the orbit that depend on radius \texttip{R}{R}. Indicate the exponent (power) of the radial dependence of the absolute value of each. Express your answer as a comma-separated list of exponents corresponding to \texttip{v}{v}, \texttip{K}{K}, \texttip{U}{U}, and \texttip{L}{L}, in that order. For example, -1,-1/2,-0.5,-3/2 would mean v \propto R^{-1}, K \propto R^{-1/2}, and so forth. 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. \texttip{L}{L} = Typesetting math: 81%

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I. Autobiography: Please submit an autobiography (not to exceed 300 words) telling me about yourself, why you are taking this course, and why online. This is part of your assignment for this week! II. “Nature of the Law” Question: Explain how a statute, the Restatement Second, and the common law affect legal decisions. IMPORTANT: Before Sending Your Answer, please carefully review and then strictly follow the required formatting procedures for homework assignments as outlined in your Syllabus as well as under the Required Format – Homework button located to the left of this screen under “Course Home”. For example: You are not permitted to copy word for word, or to cut-and-paste. You must also provide citations for all of your answers. a) A statute . . . . . . . . . . . . b) The Restatement Second . . . . . c) The Common Law. . . . . . . . .

I. Autobiography: Please submit an autobiography (not to exceed 300 words) telling me about yourself, why you are taking this course, and why online. This is part of your assignment for this week! II. “Nature of the Law” Question: Explain how a statute, the Restatement Second, and the common law affect legal decisions. IMPORTANT: Before Sending Your Answer, please carefully review and then strictly follow the required formatting procedures for homework assignments as outlined in your Syllabus as well as under the Required Format – Homework button located to the left of this screen under “Course Home”. For example: You are not permitted to copy word for word, or to cut-and-paste. You must also provide citations for all of your answers. a) A statute . . . . . . . . . . . . b) The Restatement Second . . . . . c) The Common Law. . . . . . . . .

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Lab Description: Follow the instructions in the lab tasks below to complete Problems 3 and 4 of Project 10 from the Digilent Real Digital website. These are two design problems involving finite state machine design and interfacing with seven-segment display. First start by analyzing the block diagram for Problem 3 of Project 10. Then, use VHDL to design each of the system components. You will need to use four separate design modules and instantiate each of these within a fifth design module for the overall system. For Problem 4 of Project 10, carefully read through the problem and the “Seven-Segment Display” section of the FPGA board’s user guide before carefully planning the design of this system. Lab Tasks: 1. Complete Problem 3 of Project 10 (a single-digit stopwatch): a. Pay particular attention to the block diagram displayed for this problem. Create each of the four components to this system: i. Seven-segment decoder: You will be able to reuse your design from Lab 2 ii. 4-bit counter: I recommend taking a look at the behavior binary counter illustrated in “Binary counters in VHDL” from Module 10 iii. Clock divider: You will be able to reuse your design from Lab 5. However, you will have to revise this design for task 2. For more information, I recommend taking a look at “Binary counters in VHDL” from Module 10 for information about clock dividers. Note: The stopwatch circuit will increment the digit once every second. Design your clock divider accordingly in order to meet this timing specification. Remember, the clock on the lab FPGA board (Spartan 3) has a frequency of 50 MHz. If you purchased your board, the FPGA Basys 3 or Nexys 4 DDR FPGA board has a frequency of 100 MHz. iv. Controller: This is the main component you will design using a finite state machine b. Use VHDL test benches to verify the correct operation of your 4-bit counter, clock divider (I suggest you use a small divider value for simulating so you do not have to simulate for a long duration), controller, and overall system (again, I suggest you use a small divider value for simulating) c. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit 2. Complete Problem 4 of Project 10 (a multi-digit stopwatch): a. Note: The least-significant digit should change at a rate of once per millisecond. However, for our design, the most-significant bit will not change once per second since each digit will count from 0-F. b. For more information about the timing and pinouts of the seven-segment display, please refer to your board’s user guide from Digilent’s website. Or use this direct link to our lab’s Spartan 3 FPGA board’s user guide. Look for a heading named “Seven-Segment Display” for more information about the timing requirements. c. Use VHDL test benches to verify the correct operation of your system and its components (again, I suggest you use a small divider value for simulating) d. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit 3. If you complete both of the tasks above, then you may continue and complete one or both of the following extra credit tasks: a. Decimal, Multi-Digit Stopwatch (extra credit task) You may complete this extra credit task instead of the hexadecimal, multi-digit stopwatch (lab task 2), or you may complete lab task 2 first, then complete this task i. Modify/create a multi-digit stopwatch so that only decimal numbers are displayed. The least-significant digit should change at a rate of once per millisecond and the most-significant bit will change once per second. This will now act like a real stopwatch. ii. Use VHDL test benches to verify the correct operation of your system and its components (again, I suggest you use a small divider value for simulating) iii. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit iv. Answer the extra credit lab task A questions on the cover sheet. In addition, list any references you use for this extra credit task. b. A Blinking, Multi-Digit Stopwatch (extra credit task) You may complete this extra credit task by altering your design of the hexadecimal or decimal multidigit stopwatch i. Modify your multi-digit stopwatch so the seven-segment display will blink rapidly once the most-significant digit is 9 or greater (to signal the stopwatch is close to the maximum value). This is your chance to design the system you described in the discussion question on the cover sheet. You may choose an appropriate rate at which the seven-segment display will blink. ii. Use VHDL test benches to verify the correct operation of your system and its components (again, I suggest you use a small divider value for simulating) iii. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit iv. Answer the extra credit lab task B questions on the cover sheet. In addition, list any references you use for this extra credit task.

Lab Description: Follow the instructions in the lab tasks below to complete Problems 3 and 4 of Project 10 from the Digilent Real Digital website. These are two design problems involving finite state machine design and interfacing with seven-segment display. First start by analyzing the block diagram for Problem 3 of Project 10. Then, use VHDL to design each of the system components. You will need to use four separate design modules and instantiate each of these within a fifth design module for the overall system. For Problem 4 of Project 10, carefully read through the problem and the “Seven-Segment Display” section of the FPGA board’s user guide before carefully planning the design of this system. Lab Tasks: 1. Complete Problem 3 of Project 10 (a single-digit stopwatch): a. Pay particular attention to the block diagram displayed for this problem. Create each of the four components to this system: i. Seven-segment decoder: You will be able to reuse your design from Lab 2 ii. 4-bit counter: I recommend taking a look at the behavior binary counter illustrated in “Binary counters in VHDL” from Module 10 iii. Clock divider: You will be able to reuse your design from Lab 5. However, you will have to revise this design for task 2. For more information, I recommend taking a look at “Binary counters in VHDL” from Module 10 for information about clock dividers. Note: The stopwatch circuit will increment the digit once every second. Design your clock divider accordingly in order to meet this timing specification. Remember, the clock on the lab FPGA board (Spartan 3) has a frequency of 50 MHz. If you purchased your board, the FPGA Basys 3 or Nexys 4 DDR FPGA board has a frequency of 100 MHz. iv. Controller: This is the main component you will design using a finite state machine b. Use VHDL test benches to verify the correct operation of your 4-bit counter, clock divider (I suggest you use a small divider value for simulating so you do not have to simulate for a long duration), controller, and overall system (again, I suggest you use a small divider value for simulating) c. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit 2. Complete Problem 4 of Project 10 (a multi-digit stopwatch): a. Note: The least-significant digit should change at a rate of once per millisecond. However, for our design, the most-significant bit will not change once per second since each digit will count from 0-F. b. For more information about the timing and pinouts of the seven-segment display, please refer to your board’s user guide from Digilent’s website. Or use this direct link to our lab’s Spartan 3 FPGA board’s user guide. Look for a heading named “Seven-Segment Display” for more information about the timing requirements. c. Use VHDL test benches to verify the correct operation of your system and its components (again, I suggest you use a small divider value for simulating) d. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit 3. If you complete both of the tasks above, then you may continue and complete one or both of the following extra credit tasks: a. Decimal, Multi-Digit Stopwatch (extra credit task) You may complete this extra credit task instead of the hexadecimal, multi-digit stopwatch (lab task 2), or you may complete lab task 2 first, then complete this task i. Modify/create a multi-digit stopwatch so that only decimal numbers are displayed. The least-significant digit should change at a rate of once per millisecond and the most-significant bit will change once per second. This will now act like a real stopwatch. ii. Use VHDL test benches to verify the correct operation of your system and its components (again, I suggest you use a small divider value for simulating) iii. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit iv. Answer the extra credit lab task A questions on the cover sheet. In addition, list any references you use for this extra credit task. b. A Blinking, Multi-Digit Stopwatch (extra credit task) You may complete this extra credit task by altering your design of the hexadecimal or decimal multidigit stopwatch i. Modify your multi-digit stopwatch so the seven-segment display will blink rapidly once the most-significant digit is 9 or greater (to signal the stopwatch is close to the maximum value). This is your chance to design the system you described in the discussion question on the cover sheet. You may choose an appropriate rate at which the seven-segment display will blink. ii. Use VHDL test benches to verify the correct operation of your system and its components (again, I suggest you use a small divider value for simulating) iii. Ask the instructor to check your designs, simulation waveforms, and FPGA board implementation for your circuit iv. Answer the extra credit lab task B questions on the cover sheet. In addition, list any references you use for this extra credit task.

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