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 _ ¥ _ ¥ Ã _ ¥ _ ¥ 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 _ ___ 4Ã 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__ _ 0Ã __ 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 _ ¥ _ ¥ Ã _ ¥ _ ¥ 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 _ ___ 4Ã 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__ _ 0Ã __ 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

info@checkyourstudy.com 2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm … Read More...
9. Which of the following statements is CORRECT? a. The ability of firms in competitive industries to voluntarily undertake socially beneficial but costly projects is constrained by competition and the need to attract capital. b. Any action that would maximize a firm’s stock price must be consistent with the maximization of social welfare. c. Decisions regarding social and ethical behavior have no effect, either positive or negative, on firms’ stock prices. d. In a competitive industry, if one group of firms is “socially conscious” and takes costly actions designed to improve social welfare, but other firms do not, then most investors will flock to the socially conscious firms, thus enhancing their ability to attract capital. Eventually, these firms must dominate the industry. e. Even if the government did not mandate some actions deemed to be socially responsible, such as those relating to fair hiring and environmentally sound practices, most firms in competitive markets would still pursue these policies.

## 9. Which of the following statements is CORRECT? a. The ability of firms in competitive industries to voluntarily undertake socially beneficial but costly projects is constrained by competition and the need to attract capital. b. Any action that would maximize a firm’s stock price must be consistent with the maximization of social welfare. c. Decisions regarding social and ethical behavior have no effect, either positive or negative, on firms’ stock prices. d. In a competitive industry, if one group of firms is “socially conscious” and takes costly actions designed to improve social welfare, but other firms do not, then most investors will flock to the socially conscious firms, thus enhancing their ability to attract capital. Eventually, these firms must dominate the industry. e. Even if the government did not mandate some actions deemed to be socially responsible, such as those relating to fair hiring and environmentally sound practices, most firms in competitive markets would still pursue these policies.

Answer: a
Assignment 10 Due: 11:59pm on Wednesday, April 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.3 Part A The figure shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies to . Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: Ka Kc Correct Conceptual Question 12.6 You have two steel solid spheres. Sphere 2 has twice the radius of sphere 1. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: I2 I1 Correct Problem 12.2 A high-speed drill reaches 2500 in 0.59 . Part A What is the drill’s angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Through how many revolutions does it turn during this first 0.59 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct I2/I1 = 32 rpm s  = 440 rad s2 s  = 12 rev Constant Angular Acceleration in the Kitchen Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second. Hint 1. How to approach the problem Recall from your study of kinematics the three equations of motion derived for systems undergoing constant linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to work with the three analogous equations of motion. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find the angular acceleration . Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it What is the angular velocity of the salad spinner as Dario is spinning it? Express your answer numerically in degrees per second. Hint 1. Converting rotations to degrees When the salad spinner spins through one revolution, it turns through 360 degrees. ANSWER: Hint 3. Find the angular distance the salad spinner travels as it comes to rest Through how many degrees does the salad spinner rotate as it comes to rest? Express your answer numerically in degrees. Hint 1. Converting rotations to degrees  0 = 1440 degrees/s  =  − 0 One revolution is equivalent to 360 degrees. ANSWER: Hint 4. Determine which equation to use You know the initial and final velocities of the system and the angular distance through which the spinner rotates as it comes to a stop. Which equation should be used to solve for the unknown constant angular acceleration ? ANSWER: ANSWER: Correct Part B How long does it take for the salad spinner to come to rest? Express your answer numerically in seconds.  = 2160 degrees   = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0  = -480 degrees/s2 Hint 1. How to approach the problem Again, you will need the equations of rotational kinematics that apply to situations of constant angular acceleration. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find . Hint 2. Determine which equation to use You have the initial and final velocities of the system and the angular acceleration, which you found in the previous part. Which is the best equation to use to solve for the unknown time ? ANSWER: ANSWER: Correct ± A Spinning Electric Fan An electric fan is turned off, and its angular velocity decreases uniformly from 540 to 250 in a time interval of length 4.40 . Part A Find the angular acceleration in revolutions per second per second. Hint 1. Average acceleration Recall that if the angular velocity decreases uniformly, the angular acceleration will remain constant. Therefore, the angular acceleration is just the total change in angular velocity divided by t t  = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0 t = 3.00 s rev/min rev/min s  the total change in time. Be careful of the sign of the angular acceleration. ANSWER: Correct Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. Hint 1. Determine the correct kinematic equation Which of the following kinematic equations is best suited to this problem? Here and are the initial and final angular velocities, is the elapsed time, is the constant angular acceleration, and and are the initial and final angular displacements. Hint 1. How to chose the right equation Notice that you were given in the problem introduction the initial and final speeds, as well as the length of time between them. In this problem, you are asked to find the number of revolutions (which here is the change in angular displacement, ). If you already found the angular acceleration in Part A, you could use that as well, but you would end up using a more complex equation. Also, in general, it is somewhat favorable to use given quantities instead of quantities that you have calculated. ANSWER:  = -1.10 rev/s2 0  t  0   − 0  = 0 + t  = 0 + t+  1 2 t2 = + 2( − ) 2 20 0 − 0 = (+ )t 1 2 0 ANSWER: Correct Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? Hint 1. Finding the total time for spin down To find the total time for spin down, just calculate when the velocity will equal zero. This is accomplished by setting the initial velocity plus the acceleration multipled by the time equal to zero and then solving for the time. One can then just subtract the time it took to reach 250 from the total time. Be careful of your signs when you set up the equation. ANSWER: Correct Problem 12.8 A 100 ball and a 230 ball are connected by a 34- -long, massless, rigid rod. The balls rotate about their center of mass at 130 . Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units. ANSWER: 29.0 rev rev/min 3.79 s g g cm rpm g Correct Problem 12.10 A thin, 60.0 disk with a diameter of 9.00 rotates about an axis through its center with 0.200 of kinetic energy. Part A What is the speed of a point on the rim? Express your answer with the appropriate units. ANSWER: Correct Problem 12.12 A drum major twirls a 95- -long, 470 baton about its center of mass at 150 . Part A What is the baton’s rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 3.2 ms g cm J 3.65 ms cm g rpm K = 4.4 J Correct Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord’s weight can be ignored. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply. Hint 1. Conditions for equilibrium If the blocks had the same mass, the system would be in equilibrium. The blocks would have zero acceleration and the tension in each part of the cord would equal the weight of each block. Both parts of the cord would then pull with equal force on the pulley, resulting in a zero net torque and no rotation of the pulley. Is this still the case in the current situation where block B has twice the mass of block A? Hint 2. Rotational analogue of Newton’s second law The net torque of all the forces acting on a rigid body is proportional to the angular acceleration of the body net  and is given by , where is the moment of inertia of the body. Hint 3. Relation between linear and angular acceleration A particle that rotates with angular acceleration has linear acceleration equal to , where is the distance of the particle from the axis of rotation. In the present case, where there is no slipping or stretching of the cord, the cord and the pulley must move together at the same speed. Therefore, if the cord moves with linear acceleration , the pulley must rotate with angular acceleration , where is the radius of the pulley. ANSWER: Correct Part B What happens when block B moves downward? Hint 1. How to approach the problem To determine whether the tensions in both parts of the cord are equal, it is convenient to write a mathematical expression for the net torque on the pulley. This will allow you to relate the tensions in the cord to the pulley’s angular acceleration. Hint 2. Find the net torque on the pulley Let’s assume that the tensions in both parts of the cord are different. Let be the tension in the right cord and the tension in the left cord. If is the radius of the pulley, what is the net torque acting on the pulley? Take the positive sense of rotation to be counterclockwise. Express your answer in terms of , , and . net = I I  a a = R R a  = a R R The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. T1 T2 R net T1 T2 R Hint 1. Torque The torque of a force with respect to a point is defined as the product of the magnitude times the perpendicular distance between the line of action of and the point . In other words, . ANSWER: ANSWER: Correct Note that if the pulley were stationary (as in many systems where only linear motion is studied), then the tensions in both parts of the cord would be equal. However, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration. Problem 12.18 Part A In the figure , what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.  F  O F l F  O  = Fl net = R(T2 − T1 ) The left cord pulls on the pulley with greater force than the right cord. The left and right cord pull with equal force on the pulley. The right cord pulls on the pulley with greater force than the left cord. ANSWER: Correct Part B What is the direction of net torque about the axle? ANSWER: Correct Problem 12.22 An athlete at the gym holds a 3.5 steel ball in his hand. His arm is 78 long and has a mass of 3.6 . Assume the center of mass of the arm is at the geometrical center of the arm. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer to two significant figures and include the appropriate units.  = 0.20 Nm Clockwise Counterclockwise kg cm kg ANSWER: Correct Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Parallel Axis Theorem The parallel axis theorem relates , the moment of inertia of an object about an axis passing through its center of mass, to , the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is , where is the perpendicular distance from the center of mass to the axis that passes through point p, and is the mass of the object. Part A Suppose a uniform slender rod has length and mass . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . Find , the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the center of mass Find the distance appropriate to this problem. That is, find the perpendicular distance from the center of mass of the rod to the axis passing through one end of the rod.  = 41 Nm 45  = 29 Nm Icm Ip Ip = Icm + Md2 d M L m Icm = m 1 12 L2 Iend Iend m L d ANSWER: ANSWER: Correct Part B Now consider a cube of mass with edges of length . The moment of inertia of the cube about an axis through its center of mass and perpendicular to one of its faces is given by . Find , the moment of inertia about an axis p through one of the edges of the cube Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the axis Find the perpendicular distance from the center of mass axis to the new edge axis (axis labeled p in the figure). ANSWER: d = L 2 Iend = mL2 3 m a Icm Icm = m 1 6 a2 Iedge Iedge m a o p d ANSWER: Correct Problem 12.26 Starting from rest, a 12- -diameter compact disk takes 2.9 to reach its operating angular velocity of 2000 . Assume that the angular acceleration is constant. The disk’s moment of inertia is . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: d = a 2 Iedge = 2ma2 3 cm s rpm 2.5 × 10−5 kg m2 = 1.8×10−3  Nm Correct Problem 12.23 An object’s moment of inertia is 2.20 . Its angular velocity is increasing at the rate of 3.70 . Part A What is the total torque on the object? ANSWER: Correct Problem 12.31 A 5.1 cat and a 2.5 bowl of tuna fish are at opposite ends of the 4.0- -long seesaw. N = 48 rev kgm2 rad/s2 8.14 N  m kg kg m Part A How far to the left of the pivot must a 3.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass , length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance from the scapula. The deltoid muscle makes an angle of with the horizontal, as shown. Use throughout the problem. Part A kg d = 1.4 m M1 = 3.6 kg L = 0.66 m L1 = 0.33 m L2 = 0.15 m  = 17 g = 9.8 m/s2 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. Hint 1. Nature of the problem Remember that this is a statics problem, so all forces and torques are balanced (their sums equal zero). Hint 2. Origin of torque Calculate the torque about the point at which the arm attaches to the rest of the body. This allows one to balance the torques without having to worry about the undefined forces at this point. Hint 3. Adding up the torques Add up the torques about the point in which the humerus attaches to the body. Answer in terms of , , , , , and . Remember that counterclockwise torque is positive. ANSWER: ANSWER: Correct Part B Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). Express your answer in newtons, to the nearest integer. T L1 L2 M1 g T  total = 0 = L1M1g − Tsin()L2 T = 265 N Fy Hint 1. Total forces involved Recall that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body). ANSWER: Correct Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. Express your answer in newtons, to the nearest integer. ANSWER: Correct ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: , , and . Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). |Fy| = 42 N Fx |Fx| = 254 N F 1 F  2 F  3 Part A If and , what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. Hint 1. Finding torque about pivot from What is the magnitude of the torque | | provided by around the pivot point? Give your answer numerically in newton-meters to two significant figures. ANSWER: ANSWER: Correct Part B If the L-shaped rod has a moment of inertia , , , and again , how long a time would it take for the object to move through ( /4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures. F3 = 0 F1 = 12 N F 2 F 1   1 F  1 |  1 | = 0.36 N  m F2 = 4.5 N I = 9 kg m2 F1 = 12 N F2 = 27 N F3 = 0 t 45  Hint 1. Find the net torque about the pivot What is the magnitude of the total torque around the pivot point? Answer numerically in newton-meters to two significant figures. ANSWER: Hint 2. Calculate Given the total torque around the pivot point, what is , the magnitude of the angular acceleration? Express your answer numerically in radians per second squared to two significant figures. Hint 1. Equation for If you know the magnitude of the total torque ( ) and the rotational inertia ( ), you can then find the rotational acceleration ( ) from ANSWER: Hint 3. Description of angular kinematics Now that you know the angular acceleration, this is a problem in rotational kinematics; find the time needed to go through a given angle . For constant acceleration ( ) and starting with (where is angular speed) the relation is given by which is analogous to the expression for linear displacement ( ) with constant acceleration ( ) starting from rest, | p ivot| | p ivot| = 1.8 N  m    vot Ivot  pivot = Ipivot.  = 0.20 radians/s2    = 0   = 1  , 2 t2 x a . ANSWER: Correct Part C Now consider the situation in which and , but now a force with nonzero magnitude is acting on the rod. What does have to be to obtain equilibrium? Give a numerical answer, without trigonometric functions, in newtons, to two significant figures. Hint 1. Find the required component of Only the tangential (perpendicular) component of (call it ) provides a torque. What is ? Answer in terms of . You will need to evaluate any trigonometric functions. ANSWER: ANSWER: Correct x = 1 a 2 t2 t = 2.8 s F1 = 12 N F2 = 0 F3 F3 F 3 F  3 F3t F3t F3 F3t = 1 2 F3 F3 = 9.0 N Problem 12.32 A car tire is 55.0 in diameter. The car is traveling at a speed of 24.0 . Part A What is the tire’s rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units. ANSWER: cm m/s 833 rpm 48.0 ms 0 ms Correct Problem 12.33 A 460 , 8.00-cm-diameter solid cylinder rolls across the floor at 1.30 . Part A What is the can’s kinetic energy? Express your answer with the appropriate units. ANSWER: Correct Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? g m/s 0.583 J g ANSWER: Correct Part B What is the direction of the angular momentum of the bar ? ANSWER: Correct Problem 12.46 Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? 3.27 kgm2/s into the page out of the page kg ANSWER: Correct Part B What is its direction? ANSWER: Correct Problem 12.60 A 3.0- -long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.46. 3.66×10−2 kgm /s 2 x direction -x direction y direction -y direction z direction -z direction m Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.61 The 3.0- -long, 90 rigid beam in the following figure is supported at each end. An 70 student stands 2.0 from support 1.  = 47 m kg kg m Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 12.63 A 44 , 5.5- -long beam is supported, but not attached to, the two posts in the figure . A 22 boy starts walking along the beam. You may want to review ( pages 330 – 334) . For help with math skills, you may want to review: F1 = 670 N F2 = 900 N kg m kg The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture of the four forces acting on the beam, indicating both their direction and the place on the beam that the forces are acting. Choose a coordinate system with a direction for the axis along the beam, and indicate the position of the boy. What is the net force on the beam if it is stationary? Just before the beam tips, the force of the left support on the beam is zero. Using the zero net force condition, what is the force due to the right support just before the beam tips? For the beam to remain stationary, what must be zero besides the net force on the beam? Choose a point on the beam, and compute the net torque on the beam about that point. Be sure to choose a positive direction for the rotation axis and therefore the torques. Using the zero torque condition, what is the position of the boy on the beam just prior to tipping? How far is this position from the right edge of the beam? ANSWER: Correct d = 2.0 m Problem 12.68 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.6 diameter and a mass of 270 . Its maximum angular velocity is 1500 . Part A A motor spins up the flywheel with a constant torque of 54 . How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.2 . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: m kg rpm N  m t = 250 s = 1.1×106 E J s Correct Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.71 The 3.30 , 40.0-cm-diameter disk in the figure is spinning at 350 . Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2.10 ? P = 2.4×105 W  = 1800 Nm kg rpm s Express your answer with the appropriate units. ANSWER: Correct Problem 12.74 A 5.0 , 60- -diameter cylinder rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. Part A What is the magnitude of the cylinder’s initial angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: 5.76 N kg cm  = 22 rad s2 Correct Part B What is the magnitude of the cylinder’s angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.82 A 45 figure skater is spinning on the toes of her skates at 0.90 . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 , 20 average diameter, 160 tall) plus two rod-like arms (2.5 each, 67 long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 , 20- -diameter, 200- -tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Score Summary:  = 6.6 rad s kg rev/s kg cm cm kg cm kg cm cm 2 = Your score on this assignment is 95.7%. You received 189.42 out of a possible total of 198 points.

## Assignment 10 Due: 11:59pm on Wednesday, April 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.3 Part A The figure shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies to . Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: Ka Kc Correct Conceptual Question 12.6 You have two steel solid spheres. Sphere 2 has twice the radius of sphere 1. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: I2 I1 Correct Problem 12.2 A high-speed drill reaches 2500 in 0.59 . Part A What is the drill’s angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Through how many revolutions does it turn during this first 0.59 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct I2/I1 = 32 rpm s  = 440 rad s2 s  = 12 rev Constant Angular Acceleration in the Kitchen Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second. Hint 1. How to approach the problem Recall from your study of kinematics the three equations of motion derived for systems undergoing constant linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to work with the three analogous equations of motion. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find the angular acceleration . Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it What is the angular velocity of the salad spinner as Dario is spinning it? Express your answer numerically in degrees per second. Hint 1. Converting rotations to degrees When the salad spinner spins through one revolution, it turns through 360 degrees. ANSWER: Hint 3. Find the angular distance the salad spinner travels as it comes to rest Through how many degrees does the salad spinner rotate as it comes to rest? Express your answer numerically in degrees. Hint 1. Converting rotations to degrees  0 = 1440 degrees/s  =  − 0 One revolution is equivalent to 360 degrees. ANSWER: Hint 4. Determine which equation to use You know the initial and final velocities of the system and the angular distance through which the spinner rotates as it comes to a stop. Which equation should be used to solve for the unknown constant angular acceleration ? ANSWER: ANSWER: Correct Part B How long does it take for the salad spinner to come to rest? Express your answer numerically in seconds.  = 2160 degrees   = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0  = -480 degrees/s2 Hint 1. How to approach the problem Again, you will need the equations of rotational kinematics that apply to situations of constant angular acceleration. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find . Hint 2. Determine which equation to use You have the initial and final velocities of the system and the angular acceleration, which you found in the previous part. Which is the best equation to use to solve for the unknown time ? ANSWER: ANSWER: Correct ± A Spinning Electric Fan An electric fan is turned off, and its angular velocity decreases uniformly from 540 to 250 in a time interval of length 4.40 . Part A Find the angular acceleration in revolutions per second per second. Hint 1. Average acceleration Recall that if the angular velocity decreases uniformly, the angular acceleration will remain constant. Therefore, the angular acceleration is just the total change in angular velocity divided by t t  = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0 t = 3.00 s rev/min rev/min s  the total change in time. Be careful of the sign of the angular acceleration. ANSWER: Correct Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. Hint 1. Determine the correct kinematic equation Which of the following kinematic equations is best suited to this problem? Here and are the initial and final angular velocities, is the elapsed time, is the constant angular acceleration, and and are the initial and final angular displacements. Hint 1. How to chose the right equation Notice that you were given in the problem introduction the initial and final speeds, as well as the length of time between them. In this problem, you are asked to find the number of revolutions (which here is the change in angular displacement, ). If you already found the angular acceleration in Part A, you could use that as well, but you would end up using a more complex equation. Also, in general, it is somewhat favorable to use given quantities instead of quantities that you have calculated. ANSWER:  = -1.10 rev/s2 0  t  0   − 0  = 0 + t  = 0 + t+  1 2 t2 = + 2( − ) 2 20 0 − 0 = (+ )t 1 2 0 ANSWER: Correct Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? Hint 1. Finding the total time for spin down To find the total time for spin down, just calculate when the velocity will equal zero. This is accomplished by setting the initial velocity plus the acceleration multipled by the time equal to zero and then solving for the time. One can then just subtract the time it took to reach 250 from the total time. Be careful of your signs when you set up the equation. ANSWER: Correct Problem 12.8 A 100 ball and a 230 ball are connected by a 34- -long, massless, rigid rod. The balls rotate about their center of mass at 130 . Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units. ANSWER: 29.0 rev rev/min 3.79 s g g cm rpm g Correct Problem 12.10 A thin, 60.0 disk with a diameter of 9.00 rotates about an axis through its center with 0.200 of kinetic energy. Part A What is the speed of a point on the rim? Express your answer with the appropriate units. ANSWER: Correct Problem 12.12 A drum major twirls a 95- -long, 470 baton about its center of mass at 150 . Part A What is the baton’s rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 3.2 ms g cm J 3.65 ms cm g rpm K = 4.4 J Correct Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord’s weight can be ignored. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply. Hint 1. Conditions for equilibrium If the blocks had the same mass, the system would be in equilibrium. The blocks would have zero acceleration and the tension in each part of the cord would equal the weight of each block. Both parts of the cord would then pull with equal force on the pulley, resulting in a zero net torque and no rotation of the pulley. Is this still the case in the current situation where block B has twice the mass of block A? Hint 2. Rotational analogue of Newton’s second law The net torque of all the forces acting on a rigid body is proportional to the angular acceleration of the body net  and is given by , where is the moment of inertia of the body. Hint 3. Relation between linear and angular acceleration A particle that rotates with angular acceleration has linear acceleration equal to , where is the distance of the particle from the axis of rotation. In the present case, where there is no slipping or stretching of the cord, the cord and the pulley must move together at the same speed. Therefore, if the cord moves with linear acceleration , the pulley must rotate with angular acceleration , where is the radius of the pulley. ANSWER: Correct Part B What happens when block B moves downward? Hint 1. How to approach the problem To determine whether the tensions in both parts of the cord are equal, it is convenient to write a mathematical expression for the net torque on the pulley. This will allow you to relate the tensions in the cord to the pulley’s angular acceleration. Hint 2. Find the net torque on the pulley Let’s assume that the tensions in both parts of the cord are different. Let be the tension in the right cord and the tension in the left cord. If is the radius of the pulley, what is the net torque acting on the pulley? Take the positive sense of rotation to be counterclockwise. Express your answer in terms of , , and . net = I I  a a = R R a  = a R R The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. T1 T2 R net T1 T2 R Hint 1. Torque The torque of a force with respect to a point is defined as the product of the magnitude times the perpendicular distance between the line of action of and the point . In other words, . ANSWER: ANSWER: Correct Note that if the pulley were stationary (as in many systems where only linear motion is studied), then the tensions in both parts of the cord would be equal. However, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration. Problem 12.18 Part A In the figure , what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.  F  O F l F  O  = Fl net = R(T2 − T1 ) The left cord pulls on the pulley with greater force than the right cord. The left and right cord pull with equal force on the pulley. The right cord pulls on the pulley with greater force than the left cord. ANSWER: Correct Part B What is the direction of net torque about the axle? ANSWER: Correct Problem 12.22 An athlete at the gym holds a 3.5 steel ball in his hand. His arm is 78 long and has a mass of 3.6 . Assume the center of mass of the arm is at the geometrical center of the arm. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer to two significant figures and include the appropriate units.  = 0.20 Nm Clockwise Counterclockwise kg cm kg ANSWER: Correct Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Parallel Axis Theorem The parallel axis theorem relates , the moment of inertia of an object about an axis passing through its center of mass, to , the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is , where is the perpendicular distance from the center of mass to the axis that passes through point p, and is the mass of the object. Part A Suppose a uniform slender rod has length and mass . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . Find , the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the center of mass Find the distance appropriate to this problem. That is, find the perpendicular distance from the center of mass of the rod to the axis passing through one end of the rod.  = 41 Nm 45  = 29 Nm Icm Ip Ip = Icm + Md2 d M L m Icm = m 1 12 L2 Iend Iend m L d ANSWER: ANSWER: Correct Part B Now consider a cube of mass with edges of length . The moment of inertia of the cube about an axis through its center of mass and perpendicular to one of its faces is given by . Find , the moment of inertia about an axis p through one of the edges of the cube Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the axis Find the perpendicular distance from the center of mass axis to the new edge axis (axis labeled p in the figure). ANSWER: d = L 2 Iend = mL2 3 m a Icm Icm = m 1 6 a2 Iedge Iedge m a o p d ANSWER: Correct Problem 12.26 Starting from rest, a 12- -diameter compact disk takes 2.9 to reach its operating angular velocity of 2000 . Assume that the angular acceleration is constant. The disk’s moment of inertia is . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: d = a 2 Iedge = 2ma2 3 cm s rpm 2.5 × 10−5 kg m2 = 1.8×10−3  Nm Correct Problem 12.23 An object’s moment of inertia is 2.20 . Its angular velocity is increasing at the rate of 3.70 . Part A What is the total torque on the object? ANSWER: Correct Problem 12.31 A 5.1 cat and a 2.5 bowl of tuna fish are at opposite ends of the 4.0- -long seesaw. N = 48 rev kgm2 rad/s2 8.14 N  m kg kg m Part A How far to the left of the pivot must a 3.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass , length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance from the scapula. The deltoid muscle makes an angle of with the horizontal, as shown. Use throughout the problem. Part A kg d = 1.4 m M1 = 3.6 kg L = 0.66 m L1 = 0.33 m L2 = 0.15 m  = 17 g = 9.8 m/s2 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. Hint 1. Nature of the problem Remember that this is a statics problem, so all forces and torques are balanced (their sums equal zero). Hint 2. Origin of torque Calculate the torque about the point at which the arm attaches to the rest of the body. This allows one to balance the torques without having to worry about the undefined forces at this point. Hint 3. Adding up the torques Add up the torques about the point in which the humerus attaches to the body. Answer in terms of , , , , , and . Remember that counterclockwise torque is positive. ANSWER: ANSWER: Correct Part B Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). Express your answer in newtons, to the nearest integer. T L1 L2 M1 g T  total = 0 = L1M1g − Tsin()L2 T = 265 N Fy Hint 1. Total forces involved Recall that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body). ANSWER: Correct Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. Express your answer in newtons, to the nearest integer. ANSWER: Correct ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: , , and . Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). |Fy| = 42 N Fx |Fx| = 254 N F 1 F  2 F  3 Part A If and , what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. Hint 1. Finding torque about pivot from What is the magnitude of the torque | | provided by around the pivot point? Give your answer numerically in newton-meters to two significant figures. ANSWER: ANSWER: Correct Part B If the L-shaped rod has a moment of inertia , , , and again , how long a time would it take for the object to move through ( /4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures. F3 = 0 F1 = 12 N F 2 F 1   1 F  1 |  1 | = 0.36 N  m F2 = 4.5 N I = 9 kg m2 F1 = 12 N F2 = 27 N F3 = 0 t 45  Hint 1. Find the net torque about the pivot What is the magnitude of the total torque around the pivot point? Answer numerically in newton-meters to two significant figures. ANSWER: Hint 2. Calculate Given the total torque around the pivot point, what is , the magnitude of the angular acceleration? Express your answer numerically in radians per second squared to two significant figures. Hint 1. Equation for If you know the magnitude of the total torque ( ) and the rotational inertia ( ), you can then find the rotational acceleration ( ) from ANSWER: Hint 3. Description of angular kinematics Now that you know the angular acceleration, this is a problem in rotational kinematics; find the time needed to go through a given angle . For constant acceleration ( ) and starting with (where is angular speed) the relation is given by which is analogous to the expression for linear displacement ( ) with constant acceleration ( ) starting from rest, | p ivot| | p ivot| = 1.8 N  m    vot Ivot  pivot = Ipivot.  = 0.20 radians/s2    = 0   = 1  , 2 t2 x a . ANSWER: Correct Part C Now consider the situation in which and , but now a force with nonzero magnitude is acting on the rod. What does have to be to obtain equilibrium? Give a numerical answer, without trigonometric functions, in newtons, to two significant figures. Hint 1. Find the required component of Only the tangential (perpendicular) component of (call it ) provides a torque. What is ? Answer in terms of . You will need to evaluate any trigonometric functions. ANSWER: ANSWER: Correct x = 1 a 2 t2 t = 2.8 s F1 = 12 N F2 = 0 F3 F3 F 3 F  3 F3t F3t F3 F3t = 1 2 F3 F3 = 9.0 N Problem 12.32 A car tire is 55.0 in diameter. The car is traveling at a speed of 24.0 . Part A What is the tire’s rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units. ANSWER: cm m/s 833 rpm 48.0 ms 0 ms Correct Problem 12.33 A 460 , 8.00-cm-diameter solid cylinder rolls across the floor at 1.30 . Part A What is the can’s kinetic energy? Express your answer with the appropriate units. ANSWER: Correct Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? g m/s 0.583 J g ANSWER: Correct Part B What is the direction of the angular momentum of the bar ? ANSWER: Correct Problem 12.46 Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? 3.27 kgm2/s into the page out of the page kg ANSWER: Correct Part B What is its direction? ANSWER: Correct Problem 12.60 A 3.0- -long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.46. 3.66×10−2 kgm /s 2 x direction -x direction y direction -y direction z direction -z direction m Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.61 The 3.0- -long, 90 rigid beam in the following figure is supported at each end. An 70 student stands 2.0 from support 1.  = 47 m kg kg m Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 12.63 A 44 , 5.5- -long beam is supported, but not attached to, the two posts in the figure . A 22 boy starts walking along the beam. You may want to review ( pages 330 – 334) . For help with math skills, you may want to review: F1 = 670 N F2 = 900 N kg m kg The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture of the four forces acting on the beam, indicating both their direction and the place on the beam that the forces are acting. Choose a coordinate system with a direction for the axis along the beam, and indicate the position of the boy. What is the net force on the beam if it is stationary? Just before the beam tips, the force of the left support on the beam is zero. Using the zero net force condition, what is the force due to the right support just before the beam tips? For the beam to remain stationary, what must be zero besides the net force on the beam? Choose a point on the beam, and compute the net torque on the beam about that point. Be sure to choose a positive direction for the rotation axis and therefore the torques. Using the zero torque condition, what is the position of the boy on the beam just prior to tipping? How far is this position from the right edge of the beam? ANSWER: Correct d = 2.0 m Problem 12.68 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.6 diameter and a mass of 270 . Its maximum angular velocity is 1500 . Part A A motor spins up the flywheel with a constant torque of 54 . How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.2 . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: m kg rpm N  m t = 250 s = 1.1×106 E J s Correct Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.71 The 3.30 , 40.0-cm-diameter disk in the figure is spinning at 350 . Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2.10 ? P = 2.4×105 W  = 1800 Nm kg rpm s Express your answer with the appropriate units. ANSWER: Correct Problem 12.74 A 5.0 , 60- -diameter cylinder rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. Part A What is the magnitude of the cylinder’s initial angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: 5.76 N kg cm  = 22 rad s2 Correct Part B What is the magnitude of the cylinder’s angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.82 A 45 figure skater is spinning on the toes of her skates at 0.90 . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 , 20 average diameter, 160 tall) plus two rod-like arms (2.5 each, 67 long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 , 20- -diameter, 200- -tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Score Summary:  = 6.6 rad s kg rev/s kg cm cm kg cm kg cm cm 2 = Your score on this assignment is 95.7%. You received 189.42 out of a possible total of 198 points.

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Light takes 1.28 seconds to travel from the moon to the Earth. What is the distance between them?

## Light takes 1.28 seconds to travel from the moon to the Earth. What is the distance between them?

Solution: Time taken to travel, t = 1.28 s Speed … Read More...
Question 22 1 / 1 point Echo sounding (sonar) is used to measure ocean depths by measuring the time it takes for a sound pulse to travel to the seafloor and back. measuring the time it takes for radar waves to travel between satellites. measuring the angle at which sound waves intersect the seafloor. measuring the time it takes to lower a weight to the seafloor and haul it back.Question 22 1 / 1 point Echo sounding (sonar) is used to measure ocean depths by measuring the time it takes for a sound pulse to travel to the seafloor and back. measuring the time it takes for radar waves to travel between satellites. measuring the angle at which sound waves intersect the seafloor. measuring the time it takes to lower a weight to the seafloor and haul it back.

## Question 22 1 / 1 point Echo sounding (sonar) is used to measure ocean depths by measuring the time it takes for a sound pulse to travel to the seafloor and back. measuring the time it takes for radar waves to travel between satellites. measuring the angle at which sound waves intersect the seafloor. measuring the time it takes to lower a weight to the seafloor and haul it back.Question 22 1 / 1 point Echo sounding (sonar) is used to measure ocean depths by measuring the time it takes for a sound pulse to travel to the seafloor and back. measuring the time it takes for radar waves to travel between satellites. measuring the angle at which sound waves intersect the seafloor. measuring the time it takes to lower a weight to the seafloor and haul it back.

If one cooks rice on top of a mountain, it takes a longer time for the rice to cook than that it takes at sea level. Discuss this in terms of boiling point, phase changes etc.

## If one cooks rice on top of a mountain, it takes a longer time for the rice to cook than that it takes at sea level. Discuss this in terms of boiling point, phase changes etc.

In general, if you are making something that needs to … Read More...
INEN 415 Simulation Lab 6 Fall 2015 Due Date: November 24th, 2015 (Submit via Blackboard) Description A small pizza delivery outlet in a busy metro area opens only for the lunch and dinner hours; for lunch from 11AM to 4PM and for dinner from 6PM to 11PM. Orders for single pizzas (no other orders are accepted) arrive with an inter-arrival time that is exponentially distributed with a mean of 3.25 minutes. (Need to create a rate table, see lab 5) The inside operations are handled by an OrderTaker, two IronChef, and an OvenMeister named Cruz. The outlet has one oven with a capacity of five pizzas. Two drivers driving Mustangs handle the deliveries. Timmy takes orders (for order-taking assume a triangular distribution with parameters 1, 2, 3 minutes). The IronChefs make the pizza including adding of toppings (assume a triangular distribution with parameters 2, 2.5, 3 minutes). When the pizza is made (but not cooked), the IronChefs places it in a Load Area in front of the oven. Cruz picks up the pizza from the Load Area and places the pizza in the oven (assume a triangular distribution with parameters 10, 15, 20 seconds) (Cruz is a worker) The cook time in the oven requires 15 minutes (fixed), and does not require any supervision; a buzzer alerts Cruz whenever any pizza has completed its oven time. When the pizza has cooked in the oven, Cruz takes the pizzas out of the oven (assume a triangular distribution with parameters 10, 15, 20 seconds). He carries the pizza to the Box Area. Where Cruz boxes the pizza (assume a triangular distribution with parameters 30, 45, 60 seconds) and leaves it in an area for the delivery people, who can transport a maximum of 5 pizzas (Triangular 10,20,30). Note: Cruz moves between Load Area, Oven, and Box Area. Assume travel times are negligible. Drivers take the pizza to the sink. Run model for 16 hours to ensure all pizzas are made. Simulate operations for one day using two scenarios: 1. The data as given above. 2. Inter-arrival rate decreases to 3 minutes.   Deliverable(s) I. Objectives a. Clearly define the objective(s) of the project. II. System Description / Modeling Approach a. Describe the model (personnel, processes, etc.) III. Input Data Requirements a. Describe the data collected to be used in the model. IV. Simulation Model a. Simulation Model (Screen shot of SIMIO model) V. Results / Conclusions Compare the following statististics for the two scenarios in a table. 1. Number of pizzas delivered. 2. Utilization of the all three personnel types. 3. Time in System for an order. VI. Discussion a. Based on the data provided, will the system have issues? b. As the IE professional, suggest possible changes to the system and clearly explain why such changes may improve the process. Tutorials/Simbits 1. Workers using work schedule (Simbit) 2. Single Vehicle Usage (Simbit) 3. Check on YouTube, they have many videos that can help!

## INEN 415 Simulation Lab 6 Fall 2015 Due Date: November 24th, 2015 (Submit via Blackboard) Description A small pizza delivery outlet in a busy metro area opens only for the lunch and dinner hours; for lunch from 11AM to 4PM and for dinner from 6PM to 11PM. Orders for single pizzas (no other orders are accepted) arrive with an inter-arrival time that is exponentially distributed with a mean of 3.25 minutes. (Need to create a rate table, see lab 5) The inside operations are handled by an OrderTaker, two IronChef, and an OvenMeister named Cruz. The outlet has one oven with a capacity of five pizzas. Two drivers driving Mustangs handle the deliveries. Timmy takes orders (for order-taking assume a triangular distribution with parameters 1, 2, 3 minutes). The IronChefs make the pizza including adding of toppings (assume a triangular distribution with parameters 2, 2.5, 3 minutes). When the pizza is made (but not cooked), the IronChefs places it in a Load Area in front of the oven. Cruz picks up the pizza from the Load Area and places the pizza in the oven (assume a triangular distribution with parameters 10, 15, 20 seconds) (Cruz is a worker) The cook time in the oven requires 15 minutes (fixed), and does not require any supervision; a buzzer alerts Cruz whenever any pizza has completed its oven time. When the pizza has cooked in the oven, Cruz takes the pizzas out of the oven (assume a triangular distribution with parameters 10, 15, 20 seconds). He carries the pizza to the Box Area. Where Cruz boxes the pizza (assume a triangular distribution with parameters 30, 45, 60 seconds) and leaves it in an area for the delivery people, who can transport a maximum of 5 pizzas (Triangular 10,20,30). Note: Cruz moves between Load Area, Oven, and Box Area. Assume travel times are negligible. Drivers take the pizza to the sink. Run model for 16 hours to ensure all pizzas are made. Simulate operations for one day using two scenarios: 1. The data as given above. 2. Inter-arrival rate decreases to 3 minutes.   Deliverable(s) I. Objectives a. Clearly define the objective(s) of the project. II. System Description / Modeling Approach a. Describe the model (personnel, processes, etc.) III. Input Data Requirements a. Describe the data collected to be used in the model. IV. Simulation Model a. Simulation Model (Screen shot of SIMIO model) V. Results / Conclusions Compare the following statististics for the two scenarios in a table. 1. Number of pizzas delivered. 2. Utilization of the all three personnel types. 3. Time in System for an order. VI. Discussion a. Based on the data provided, will the system have issues? b. As the IE professional, suggest possible changes to the system and clearly explain why such changes may improve the process. Tutorials/Simbits 1. Workers using work schedule (Simbit) 2. Single Vehicle Usage (Simbit) 3. Check on YouTube, they have many videos that can help!

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1 | P a g e Lecture #2: Abortion (Warren) While studying this topic, we will ask whether it is morally permissible to intentionally terminate a pregnancy and, if so, whether certain restrictions should be placed upon such practices. Even though we will most often be speaking of terminating a fetus, biologists make further classifications: the zygote is the single cell resulting from the fusion of the egg and the sperm; the morula is the cluster of cells that travels through the fallopian tubes; the blastocyte exists once an outer shell of cells has formed around an inner group of cells; the embryo exists once the cells begin to take on specific functions (around the 15th day); the fetus comes into existence in the 8th week when the embryo gains a basic structural resemblance to the adult. Given these distinctions, there are certain kinds of non-fetal abortion—such as usage of RU-486 (the morning-after “abortion pill”)—though most of the writers we will study refer to fetal abortions. So now let us consider the “Classical Argument against Abortion”, which has been very influential: P1) It is wrong to kill innocent persons. P2) A fetus is an innocent person. C) It is wrong to kill a fetus. (Note that this argument has received various formulations, including those from Warren and Thomson which differ from the above. For this course, we will refer to the above formulation as the “Classical Argument”.) Before evaluating this argument, we should talk about terminology: A person is a member of the moral community; i.e., someone who has rights and/or duties. ‘Persons’ is the plural of ‘person’. ‘Person’ can be contrasted with ‘human being’; a human being is anyone who is genetically human (i.e., a member of Homo sapiens). ‘People’ (or ‘human beings’) is the plural of ‘human being’. Why does this matter? First, not all persons are human beings. For example, consider an alien from another planet who mentally resembled us. If he were to visit Earth, it would be morally reprehensible to kick him or to set him on fire because of the pain and suffering that these acts would cause. And, similarly, the alien would be morally condemnable if he were to propagate such acts on us; he has a moral duty not to act in those ways (again, assuming a certain mental resemblance to us). So, even though this alien is not a human being, he is nevertheless a person with the associative rights and/or duties. 2 | P a g e And, more controversially, maybe not all human beings are persons. For example, anencephalic infants—i.e., ones born without cerebral cortexes and therefore with severely limited cognitive abilities—certainly do not have duties since they are not capable of rational thought and autonomous action. Some philosophers have even argued that they do not have rights. Now let us return to the Classical Argument. It is valid insofar as, if the premises are true, then the conclusion has to be true. But maybe it commits equivocation, which is to say that it uses the same word in multiple senses; equivocation is an informal fallacy (i.e., attaches to arguments that are formally valid but otherwise fallacious). Consider the following: P1) I put my money in the bank. P2) The bank borders the river. C) I put my money somewhere that borders the river. This argument equivocates since ‘bank’ is being used in two different senses: in P1 it is used to represent a financial institution and, in P2, it is used to represent a geological feature. Returning to the classical argument, it could be argued that ‘person’ is being used in two different senses: in P1 it is used in its appropriate moral sense and, in P2, it is inappropriately used instead of ‘human being’. The critic might suggest that a more accurate way to represent the argument would be as follows: P1) It is wrong to kill innocent persons. P2) A fetus is a human being. C) It is wrong to kill a fetus. This argument is obviously invalid. So one way to criticize the Classical Argument is to say that it conflates two different concepts—viz., ‘person’ and ‘human being’—and therefore commits equivocation. However, the more straightforward way to attack the Classical Argument is just to deny its second premise and thus contend that the argument is unsound. This is the approach that Mary Anne Warren takes in “On the Moral and Legal Status of Abortion”. Why does Warren think that the second premise is false? Remember that we defined a person as “a member of the moral community.” And we said that an alien, for example, could be afforded moral status even though it is not a human being. Why do we think that this alien should not be tortured or set on fire? Warren thinks that, intuitively, we think that membership in the moral community is based upon possession of the following traits: 3 | P a g e 1. Consciousness of objects and events external and/or internal to the being and especially the capacity to feel pain; 2. Reasoning or rationality (i.e., the developed capacity to solve new and relatively complex problems); 3. Self-motivated activity (i.e., activity which is relatively independent of either genetic or direct external control); 4. Capacity to communicate (not necessarily verbal or linguistic); and 5. Possession of self-concepts and self-awareness. Warren then admits that, though all of the items on this list look promising, we need not require that a person have all of the items on this list. (4) is perhaps the most expendable: imagine someone who is fully paralyzed as well as deaf, these incapacities, which preclude communication, are not sufficient to justify torture. Similarly, we might be able to imagine certain psychological afflictions that negate (5) without compromising personhood. Warren suspects that (1) and (2) are might be sufficient to confer personhood, and thinks that (1)-(3) “quite probably” are sufficient. Note that, if she is right, we would not be able to torture chimps, let us say, but we could set plants on fire (and most likely ants as well). However, given Warren’s aims, she does not need to specify which of these traits are necessary or sufficient for personhood; all that she wants to observe is that the fetus has none of them! Therefore, regardless of which traits we want to require, Warren thinks that the fetus is not a person. Therefore she thinks that the Classical Argument is unsound and should be rejected. Even if we accept Warren’s refutation of the second premise, we might be inclined to say that, while the fetus is not (now) a person, it is a potential person: the fetus will hopefully mature into a being that possesses all five of the traits on Warren’s list. We might then propose the following adjustment to the Classical Argument: P1) It is wrong to kill all innocent persons. P2) A fetus is a potential person. C) It is wrong to kill a fetus. However, this argument is invalid. Warren grants that potentiality might serve as a prima facie reason (i.e., a reason that has some moral weight but which might be outweighed by other considerations) not to abort a fetus, but potentiality alone is insufficient to grant the fetus a moral right against being terminated. By analogy, consider the following argument: 4 | P a g e P1) The President has the right to declare war. P2) Mary is a potential President. C) Mary has the right to declare war. This argument is invalid since the premises are both true and the conclusion is false. By parity, the following argument is also invalid: P1) A person has a right to life. P2) A fetus is a potential person. C) A fetus has a right to life. Thus Warren thinks that considerations of potentiality are insufficient to undermine her argument that fetuses—which are potential persons but, she thinks, not persons—do not have a right to life.

## 1 | P a g e Lecture #2: Abortion (Warren) While studying this topic, we will ask whether it is morally permissible to intentionally terminate a pregnancy and, if so, whether certain restrictions should be placed upon such practices. Even though we will most often be speaking of terminating a fetus, biologists make further classifications: the zygote is the single cell resulting from the fusion of the egg and the sperm; the morula is the cluster of cells that travels through the fallopian tubes; the blastocyte exists once an outer shell of cells has formed around an inner group of cells; the embryo exists once the cells begin to take on specific functions (around the 15th day); the fetus comes into existence in the 8th week when the embryo gains a basic structural resemblance to the adult. Given these distinctions, there are certain kinds of non-fetal abortion—such as usage of RU-486 (the morning-after “abortion pill”)—though most of the writers we will study refer to fetal abortions. So now let us consider the “Classical Argument against Abortion”, which has been very influential: P1) It is wrong to kill innocent persons. P2) A fetus is an innocent person. C) It is wrong to kill a fetus. (Note that this argument has received various formulations, including those from Warren and Thomson which differ from the above. For this course, we will refer to the above formulation as the “Classical Argument”.) Before evaluating this argument, we should talk about terminology: A person is a member of the moral community; i.e., someone who has rights and/or duties. ‘Persons’ is the plural of ‘person’. ‘Person’ can be contrasted with ‘human being’; a human being is anyone who is genetically human (i.e., a member of Homo sapiens). ‘People’ (or ‘human beings’) is the plural of ‘human being’. Why does this matter? First, not all persons are human beings. For example, consider an alien from another planet who mentally resembled us. If he were to visit Earth, it would be morally reprehensible to kick him or to set him on fire because of the pain and suffering that these acts would cause. And, similarly, the alien would be morally condemnable if he were to propagate such acts on us; he has a moral duty not to act in those ways (again, assuming a certain mental resemblance to us). So, even though this alien is not a human being, he is nevertheless a person with the associative rights and/or duties. 2 | P a g e And, more controversially, maybe not all human beings are persons. For example, anencephalic infants—i.e., ones born without cerebral cortexes and therefore with severely limited cognitive abilities—certainly do not have duties since they are not capable of rational thought and autonomous action. Some philosophers have even argued that they do not have rights. Now let us return to the Classical Argument. It is valid insofar as, if the premises are true, then the conclusion has to be true. But maybe it commits equivocation, which is to say that it uses the same word in multiple senses; equivocation is an informal fallacy (i.e., attaches to arguments that are formally valid but otherwise fallacious). Consider the following: P1) I put my money in the bank. P2) The bank borders the river. C) I put my money somewhere that borders the river. This argument equivocates since ‘bank’ is being used in two different senses: in P1 it is used to represent a financial institution and, in P2, it is used to represent a geological feature. Returning to the classical argument, it could be argued that ‘person’ is being used in two different senses: in P1 it is used in its appropriate moral sense and, in P2, it is inappropriately used instead of ‘human being’. The critic might suggest that a more accurate way to represent the argument would be as follows: P1) It is wrong to kill innocent persons. P2) A fetus is a human being. C) It is wrong to kill a fetus. This argument is obviously invalid. So one way to criticize the Classical Argument is to say that it conflates two different concepts—viz., ‘person’ and ‘human being’—and therefore commits equivocation. However, the more straightforward way to attack the Classical Argument is just to deny its second premise and thus contend that the argument is unsound. This is the approach that Mary Anne Warren takes in “On the Moral and Legal Status of Abortion”. Why does Warren think that the second premise is false? Remember that we defined a person as “a member of the moral community.” And we said that an alien, for example, could be afforded moral status even though it is not a human being. Why do we think that this alien should not be tortured or set on fire? Warren thinks that, intuitively, we think that membership in the moral community is based upon possession of the following traits: 3 | P a g e 1. Consciousness of objects and events external and/or internal to the being and especially the capacity to feel pain; 2. Reasoning or rationality (i.e., the developed capacity to solve new and relatively complex problems); 3. Self-motivated activity (i.e., activity which is relatively independent of either genetic or direct external control); 4. Capacity to communicate (not necessarily verbal or linguistic); and 5. Possession of self-concepts and self-awareness. Warren then admits that, though all of the items on this list look promising, we need not require that a person have all of the items on this list. (4) is perhaps the most expendable: imagine someone who is fully paralyzed as well as deaf, these incapacities, which preclude communication, are not sufficient to justify torture. Similarly, we might be able to imagine certain psychological afflictions that negate (5) without compromising personhood. Warren suspects that (1) and (2) are might be sufficient to confer personhood, and thinks that (1)-(3) “quite probably” are sufficient. Note that, if she is right, we would not be able to torture chimps, let us say, but we could set plants on fire (and most likely ants as well). However, given Warren’s aims, she does not need to specify which of these traits are necessary or sufficient for personhood; all that she wants to observe is that the fetus has none of them! Therefore, regardless of which traits we want to require, Warren thinks that the fetus is not a person. Therefore she thinks that the Classical Argument is unsound and should be rejected. Even if we accept Warren’s refutation of the second premise, we might be inclined to say that, while the fetus is not (now) a person, it is a potential person: the fetus will hopefully mature into a being that possesses all five of the traits on Warren’s list. We might then propose the following adjustment to the Classical Argument: P1) It is wrong to kill all innocent persons. P2) A fetus is a potential person. C) It is wrong to kill a fetus. However, this argument is invalid. Warren grants that potentiality might serve as a prima facie reason (i.e., a reason that has some moral weight but which might be outweighed by other considerations) not to abort a fetus, but potentiality alone is insufficient to grant the fetus a moral right against being terminated. By analogy, consider the following argument: 4 | P a g e P1) The President has the right to declare war. P2) Mary is a potential President. C) Mary has the right to declare war. This argument is invalid since the premises are both true and the conclusion is false. By parity, the following argument is also invalid: P1) A person has a right to life. P2) A fetus is a potential person. C) A fetus has a right to life. Thus Warren thinks that considerations of potentiality are insufficient to undermine her argument that fetuses—which are potential persons but, she thinks, not persons—do not have a right to life.

The light reactions take place in the _________ and the Calvin cycle takes place in the _________.

## The light reactions take place in the _________ and the Calvin cycle takes place in the _________.

thylakoids; stroma