Michael Jordan’s book.. Considering how the ending of the book was written, is it an effective ending? Did the ending surprise you? Why? Why not? Did the ending leave you with unanswered questions? Explain.

Michael Jordan’s book.. Considering how the ending of the book was written, is it an effective ending? Did the ending surprise you? Why? Why not? Did the ending leave you with unanswered questions? Explain.

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

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

info@checkyourstudy.com 2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm … Read More...
HI5004 Marketing Management Tri1 2014 Group Assignment Guidelines Written Report 20 marks Presentation 10 marks Written report Due Week 10 (Fri 5pm, both hard copy on lvl 6 and soft copy on…Macroeconomics 200 Online Topic Review / Class Quiz #2 Answer all Questions Each ‘Topic’ carries equal weighting (marks). This Quiz is worth 10% of your overall Mark for this Unit Submission D…BUACC2606 FINANCIAL ACCOUNTING RESEARCH ASSIGNMENT SEMESTER 1, 2014 RESEARCH TOPIC Assume that you are the chief financial officer of a listed company that provides printing services in Victoria. Th…Topic: Development of Management Theories from the Human Relations Movement to the Behavioural Science Approach General Framework Against a background of the prevailing wisdom of the early 1900s, in p…Case analysis – Nestlé Background Consumers have higher expectations than ever before. They want products to match these expectations. They also want accurate, up-to-date and useful informatio…Assessment_Questions_CIS8004_S1_2014 Assessment 1 with 1200 wordsAssessment Items Descriptions for CIS8004_S1_2014Simurino@hotmail.com Please help me to finalise attached assignment by Wednesday 21/05/14BUACC 2613 Management Accounting 1 Semester 1, 2014 Assignment Contribution to overall assessment: 25% Due date: Friday 30th May 2014 by 4.00pm • This assignment has two equally weighted parts: o …Assessment Items Descriptions for CIS8004_S1_2014 Description Marks out of Wtg(%) Due date Journals (written report) 100 50% Refer to study schedule This written assignment is to be electroni…font 12 heading 14 margin 2 centimetre from left and right author, surname, page -direct quotation author surname indirect quotation net present value should be in excel format. theory ethics:non fi…MAA 716 Financial Accounting WRITTEN ASSIGNMENT – TRIMESTER 1, 2014 PART 1 – QUESTION 3 Submission date and available mark Due date: Friday 23 May 2014 before 11.59 pm Marks: This Written Assig… The Faculty of Business BULAW 3731 Income Taxation Law & Practice Assignment: Semester 1/2014 INSTRUCTIONS 1. See the Instructions and Assessment Criteria in the Course Description and make sur…The Faculty of Business BUACC3741: Auditing Semester 1-2014 ASSIGNMENT This assignment is to be completed in groups of three and comprises twenty per-cent of the marks for this course. There are three…Task: Students are required to prepare a research Report on the topic shortlisted for Literature Review in Assessment 3. Research proposal would include information about the following: • Literature…ASSESSMENT 2: OVERSEAS MARKET ENTRY ACTIONS BRIEFING This assignment contributes 40% of the total marks for this module. The focus of this assignment is to draw upon your knowledge of international bu…Topic: Discuss: At the centre of many HRM approaches to organisational transformation and culture change is the concept of the HR professional as change agent. Discuss the role of HR in managing chang…CIS3003 2013 Assignment 3 Description Marks out of Wtg(%) Due date Assignment 3 100 30% Due Data 2 June 2014 There are two (2) parts to the third assignment. For part A (80%) need to write a single re…CIS3002 S1 2014 – Assignment 2 instructions All questions relate to the following Case Study which was used in Assignment 1. The national health insurance system “Medigood” that pays for patientâ…CIS3003 2013 Assignment 3 Description Marks out of Wtg(%) Due date Assignment 3 100 30% Due Data 2 June 2014 There are two (2) parts to the third assignment. For part A (80%) need to write a single re… ACCM 4200 Financial Accounting & Reporting 1 Assignment Trimester 1, 2014 VALUE: 25% of OVERALL ASSESSMENT DUE DATE: Monday, 26 May 2014 (11.00pm) SUBMISSION: The assignment will …Please check the attached file for CIS3008Assignment is Based on All topics Under macro EconomicsAssignment B Description Marks out of Wtg(%) Due date Assignment B (written report) 100 50% Refer to study schedule CIS8000 Global Information Systems Strategy 3000 words This written assignment is to…CIS8100 Assignment 4 PROJECT (FINAL) & REPORT Description Marks out of Wtg(%) Word limit Due date Assignment 4 100 55 5000 6 June 2014 Learning objectives and graduate skills tested This assignmen…ACC5502 – Accounting and Financial Management Assignment Two – Based on Modules 7-10 Due Date: 28 May, 2014. Weighting: 20% Question 1 25 marks Based on modules 7 & 8 – Budgeting and CVP The s…ITSMERD DIAGRAM SHOULD BE IN FRANKLIN METHOD 3.1.2 ASSESSMENT TASK 2: Research Report Individual formal research report based around any one of the current business issues discussed during LB5214 (executive summary; background; and aspects /issu…Research proposal 2 Due date: See your Study Desk Value: 40% Structure: Research paper Objectives The course objectives met by this assignment include: • Course specifications are available online… STUDENT GUIDE Diploma of Accounting (FNS50210) FNSACC403A: Make decisions in a legal context HBLAW – Business Law 1 HBLAW- Business Law Student Gui…Hi, This is another assignment of law. Per question 400 words and due date is 21st may.so please advise me the price. Thanks Task Read and consider Dollars & Sense Finance v Nathan [2008] N…ALL 4 TASKi need edit this.Hi there my topic is AUSTRALIAN DAIRY FARMERS and it should have 3 articles attached. you have to write on the basis on those articles. word length is 3000 excluding articles. send me the articles as…Any help with this Assignment please?please check thisPlease find the attach file Commercial Law (BULAW1503) Assignment 2014 Due: Friday Week 8 at 5 pm – MUST BE SUBMITTED ON MOODLE Weighting: 35% The purpose of the assignment is for you to undertake independent research into …CIS3003 2013 Assignment 3 There are two (2) parts to the third assignment. For part A (80%) need to write a single report not more than 20 pages in the body. For part B (20%) you need to present the r…Assignment 2 – Case analysis – Nestlé Description Marks out of Wtg(%) Due date Assignment 2 100 50 2 June 2014 Background Consumers have higher expectations than ever before. They want pr…Assessment 2 Assessment Type: Research Exercise 2 – research and 1500 + 10% word report – individual assessment Purpose: In this assessment, students should use the feedback from the first assessm…Need 2 sets for this with 3000 words each and they needs to be totally differentNeed 1 set for this with 2400 wordsBUACC 2614 – Management Accounting 2 Semester 1, 2014 Group Assignment According to Martin and Steele (2010, p.13), “The two principal professional associations in Australia – CPA Australia (th…One more set required for Com14051117Deliverable 2: Data Cleansing & Conversion During software implementations data transfer and the set-up of periodic/permanent interfaces is one of the most costly and time-intensive work package…Hello Grace, Please I have my 3 assessment ,one is due on Sunday and are 5 Questios each question need to be answered with 300 to 400 words with 2 or 3 refferences. Question 1. Is the media complicit… NOTE: Learning Task 2: Individual assignment (Report) Due Date Week 10 – Monday 10:00am Weight 20% Length 3,000 words Purpose Learning task 2 continues and builds on the work undertaken for Lear… The Faculty of Business BULAW 3731 Income Taxation Law & Practice Assignment: Semester 1/2014 INSTRUCTIONS 1. See the Instructions and Assessment Criteria in the Course Description and make sur… Assignment BULAW2611 Organisations Law Semester 1, 2014 The Business School Purpose To enable you to apply problem solving skills; to research the nature of some of the duties owed by directors …Man14051126 ============ Commercial Law Assignment The purpose of the assignment is for you to undertake independent research into a particular aspect of law, to reflect on and consider particular le…please find this assingment and infrom me is it deal ok or not.18/05/2012 is last date.

HI5004 Marketing Management Tri1 2014 Group Assignment Guidelines Written Report 20 marks Presentation 10 marks Written report Due Week 10 (Fri 5pm, both hard copy on lvl 6 and soft copy on…Macroeconomics 200 Online Topic Review / Class Quiz #2 Answer all Questions Each ‘Topic’ carries equal weighting (marks). This Quiz is worth 10% of your overall Mark for this Unit Submission D…BUACC2606 FINANCIAL ACCOUNTING RESEARCH ASSIGNMENT SEMESTER 1, 2014 RESEARCH TOPIC Assume that you are the chief financial officer of a listed company that provides printing services in Victoria. Th…Topic: Development of Management Theories from the Human Relations Movement to the Behavioural Science Approach General Framework Against a background of the prevailing wisdom of the early 1900s, in p…Case analysis – Nestlé Background Consumers have higher expectations than ever before. They want products to match these expectations. They also want accurate, up-to-date and useful informatio…Assessment_Questions_CIS8004_S1_2014 Assessment 1 with 1200 wordsAssessment Items Descriptions for CIS8004_S1_2014Simurino@hotmail.com Please help me to finalise attached assignment by Wednesday 21/05/14BUACC 2613 Management Accounting 1 Semester 1, 2014 Assignment Contribution to overall assessment: 25% Due date: Friday 30th May 2014 by 4.00pm • This assignment has two equally weighted parts: o …Assessment Items Descriptions for CIS8004_S1_2014 Description Marks out of Wtg(%) Due date Journals (written report) 100 50% Refer to study schedule This written assignment is to be electroni…font 12 heading 14 margin 2 centimetre from left and right author, surname, page -direct quotation author surname indirect quotation net present value should be in excel format. theory ethics:non fi…MAA 716 Financial Accounting WRITTEN ASSIGNMENT – TRIMESTER 1, 2014 PART 1 – QUESTION 3 Submission date and available mark Due date: Friday 23 May 2014 before 11.59 pm Marks: This Written Assig… The Faculty of Business BULAW 3731 Income Taxation Law & Practice Assignment: Semester 1/2014 INSTRUCTIONS 1. See the Instructions and Assessment Criteria in the Course Description and make sur…The Faculty of Business BUACC3741: Auditing Semester 1-2014 ASSIGNMENT This assignment is to be completed in groups of three and comprises twenty per-cent of the marks for this course. There are three…Task: Students are required to prepare a research Report on the topic shortlisted for Literature Review in Assessment 3. Research proposal would include information about the following: • Literature…ASSESSMENT 2: OVERSEAS MARKET ENTRY ACTIONS BRIEFING This assignment contributes 40% of the total marks for this module. The focus of this assignment is to draw upon your knowledge of international bu…Topic: Discuss: At the centre of many HRM approaches to organisational transformation and culture change is the concept of the HR professional as change agent. Discuss the role of HR in managing chang…CIS3003 2013 Assignment 3 Description Marks out of Wtg(%) Due date Assignment 3 100 30% Due Data 2 June 2014 There are two (2) parts to the third assignment. For part A (80%) need to write a single re…CIS3002 S1 2014 – Assignment 2 instructions All questions relate to the following Case Study which was used in Assignment 1. The national health insurance system “Medigood” that pays for patientâ…CIS3003 2013 Assignment 3 Description Marks out of Wtg(%) Due date Assignment 3 100 30% Due Data 2 June 2014 There are two (2) parts to the third assignment. For part A (80%) need to write a single re… ACCM 4200 Financial Accounting & Reporting 1 Assignment Trimester 1, 2014 VALUE: 25% of OVERALL ASSESSMENT DUE DATE: Monday, 26 May 2014 (11.00pm) SUBMISSION: The assignment will …Please check the attached file for CIS3008Assignment is Based on All topics Under macro EconomicsAssignment B Description Marks out of Wtg(%) Due date Assignment B (written report) 100 50% Refer to study schedule CIS8000 Global Information Systems Strategy 3000 words This written assignment is to…CIS8100 Assignment 4 PROJECT (FINAL) & REPORT Description Marks out of Wtg(%) Word limit Due date Assignment 4 100 55 5000 6 June 2014 Learning objectives and graduate skills tested This assignmen…ACC5502 – Accounting and Financial Management Assignment Two – Based on Modules 7-10 Due Date: 28 May, 2014. Weighting: 20% Question 1 25 marks Based on modules 7 & 8 – Budgeting and CVP The s…ITSMERD DIAGRAM SHOULD BE IN FRANKLIN METHOD 3.1.2 ASSESSMENT TASK 2: Research Report Individual formal research report based around any one of the current business issues discussed during LB5214 (executive summary; background; and aspects /issu…Research proposal 2 Due date: See your Study Desk Value: 40% Structure: Research paper Objectives The course objectives met by this assignment include: • Course specifications are available online… STUDENT GUIDE Diploma of Accounting (FNS50210) FNSACC403A: Make decisions in a legal context HBLAW – Business Law 1 HBLAW- Business Law Student Gui…Hi, This is another assignment of law. Per question 400 words and due date is 21st may.so please advise me the price. Thanks Task Read and consider Dollars & Sense Finance v Nathan [2008] N…ALL 4 TASKi need edit this.Hi there my topic is AUSTRALIAN DAIRY FARMERS and it should have 3 articles attached. you have to write on the basis on those articles. word length is 3000 excluding articles. send me the articles as…Any help with this Assignment please?please check thisPlease find the attach file Commercial Law (BULAW1503) Assignment 2014 Due: Friday Week 8 at 5 pm – MUST BE SUBMITTED ON MOODLE Weighting: 35% The purpose of the assignment is for you to undertake independent research into …CIS3003 2013 Assignment 3 There are two (2) parts to the third assignment. For part A (80%) need to write a single report not more than 20 pages in the body. For part B (20%) you need to present the r…Assignment 2 – Case analysis – Nestlé Description Marks out of Wtg(%) Due date Assignment 2 100 50 2 June 2014 Background Consumers have higher expectations than ever before. They want pr…Assessment 2 Assessment Type: Research Exercise 2 – research and 1500 + 10% word report – individual assessment Purpose: In this assessment, students should use the feedback from the first assessm…Need 2 sets for this with 3000 words each and they needs to be totally differentNeed 1 set for this with 2400 wordsBUACC 2614 – Management Accounting 2 Semester 1, 2014 Group Assignment According to Martin and Steele (2010, p.13), “The two principal professional associations in Australia – CPA Australia (th…One more set required for Com14051117Deliverable 2: Data Cleansing & Conversion During software implementations data transfer and the set-up of periodic/permanent interfaces is one of the most costly and time-intensive work package…Hello Grace, Please I have my 3 assessment ,one is due on Sunday and are 5 Questios each question need to be answered with 300 to 400 words with 2 or 3 refferences. Question 1. Is the media complicit… NOTE: Learning Task 2: Individual assignment (Report) Due Date Week 10 – Monday 10:00am Weight 20% Length 3,000 words Purpose Learning task 2 continues and builds on the work undertaken for Lear… The Faculty of Business BULAW 3731 Income Taxation Law & Practice Assignment: Semester 1/2014 INSTRUCTIONS 1. See the Instructions and Assessment Criteria in the Course Description and make sur… Assignment BULAW2611 Organisations Law Semester 1, 2014 The Business School Purpose To enable you to apply problem solving skills; to research the nature of some of the duties owed by directors …Man14051126 ============ Commercial Law Assignment The purpose of the assignment is for you to undertake independent research into a particular aspect of law, to reflect on and consider particular le…please find this assingment and infrom me is it deal ok or not.18/05/2012 is last date.

info@checkyourstudy.com HI5004 Marketing Management Tri1 2014 Group Assignment Guidelines Written … Read More...
After reading the supplement article on Business Analytics linked to the week 1 schedule, write an essay on how business analytics impacts you today, or its potential role in your chosen career path. Do research for your paper, or interview someone who works in your area. The goals of this paper are two-fold: (1) focus on high quality writing, using the COBE Writing Styles Guide for writing help and citations. (2) consider the importance of BI from a personal/work/career perspective.

After reading the supplement article on Business Analytics linked to the week 1 schedule, write an essay on how business analytics impacts you today, or its potential role in your chosen career path. Do research for your paper, or interview someone who works in your area. The goals of this paper are two-fold: (1) focus on high quality writing, using the COBE Writing Styles Guide for writing help and citations. (2) consider the importance of BI from a personal/work/career perspective.

  Business analytics importance and its potential     Introduction … Read More...
Book review The Shareholder Value Myth: How Putting Shareholders First Harms Investors, Corporations, and the Public by Lynn Stout Provide 1) a 900 word review of this book (word range 900-1,200) and 2) a 350 word reflection where you force yourself to relate the message of the book . As per the format of the review, I like the ones done by the folks of the WSJ. This is an example: http://forums.delphiforums.com/diversecity/messages?msg=17531.1264 or http://www.wsj.com/articles/book-review-how-adam-smith-can-change-your-life-by-russ-roberts-1413846808?KEYWORDS=book+reviews

Book review The Shareholder Value Myth: How Putting Shareholders First Harms Investors, Corporations, and the Public by Lynn Stout Provide 1) a 900 word review of this book (word range 900-1,200) and 2) a 350 word reflection where you force yourself to relate the message of the book . As per the format of the review, I like the ones done by the folks of the WSJ. This is an example: http://forums.delphiforums.com/diversecity/messages?msg=17531.1264 or http://www.wsj.com/articles/book-review-how-adam-smith-can-change-your-life-by-russ-roberts-1413846808?KEYWORDS=book+reviews

The Shareholder Value Myth: How Putting Shareholders First Harms Investors, … Read More...
Assignment 5 Due: 11:59pm on Wednesday, March 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 6.13 A hand presses down on the book in the figure. Part A Is the normal force of the table on the book larger than, smaller than, or equal to ? ANSWER: Correct mg Equal to Larger than Smaller than mg mg mg Problem 6.2 The three ropes in the figure are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. Part A What is the magnitude of the tension in the third rope? Express your answer using two significant figures. ANSWER: Correct Part B What is the direction of the tension in the third rope? Express your answer using two significant figures. T  3 T3 = 94 N T  3 Typesetting math: 100% ANSWER: Correct The Normal Force When an object rests on a surface, there is always a force perpendicular to the surface; we call this the normal force, denoted by . The two questions to the right will explore the normal force. Part A A man attempts to pick up his suitcase of weight by pulling straight up on the handle. However, he is unable to lift the suitcase from the floor. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man pulls upward on the suitcase? Hint 1. How to approach this problem First, identify the forces that act on the suitcase and draw a free-body diagram. Then use the fact that the suitcase is in equilibrium, , to examine how the forces acting on the suitcase relate to each other. Hint 2. Identify the correct free-body diagram Which of the figures represents the free-body diagram of the suitcase while the man is pulling on the handle with a force of magnitude ? = 58   below horizontal n ws n F = 0 fpull Typesetting math: 100% ANSWER: ANSWER: Correct Part B A B C D The magnitude of the normal force is equal to the magnitude of the weight of the suitcase. The magnitude of the normal force is equal to the magnitude of the weight of the suitcase minus the magnitude of the force of the pull. The magnitude of the normal force is equal to the sum of the magnitude of the force of the pull and the magnitude of the suitcase’s weight. The magnitude of the normal force is greater than the magnitude of the weight of the suitcase. Typesetting math: 100% Now assume that the man of weight is tired and decides to sit on his suitcase. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man is sitting on the suitcase? Hint 1. Identify the correct free-body diagram. Which of the figures represents the free-body diagram while the man is sitting atop the suitcase? Here the vector labeled is a force that has the same magnitude as the man’s weight. ANSWER: wm n wm Typesetting math: 100% ANSWER: Correct Recognize that the normal force acting on an object is not always equal to the weight of that object. This is an important point to understand. Problem 6.5 A construction worker with a weight of 880 stands on a roof that is sloped at 18 . Part A What is the magnitude of the normal force of the roof on the worker? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct A B C D The magnitude of the normal force is equal to the magnitude of the suitcase’s weight. The magnitude of the normal force is equal to the magnitude of the suitcase’s weight minus the magnitude of the man’s weight. The magnitude of the normal force is equal to the sum of the magnitude of the man’s weight and the magnitude of the suitcase’s weight. The magnitude of the normal force is less than the magnitude of the suitcase’s weight. N  n = 840 N Typesetting math: 100% Problem 6.6 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B For diagram the part A, find the value of the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: kg ax x ax = -0.67 m s2 ay, y Typesetting math: 100% Correct Part C For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D For diagram the part C, find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: ay = 0 m s2 ax x ax = 0.67 m s2 ay y Typesetting math: 100% Correct Problem 6.7 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay = 0 m s2 kg ax x ax = 0.99 m s2 Typesetting math: 100% Part B Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay y ay = 0 m s2 ax x ax = -0.18 m s2 ay y ay = 0 m s2 Typesetting math: 100% Problem 6.10 A horizontal rope is tied to a 53.0 box on frictionless ice. What is the tension in the rope if: Part A The box is at rest? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B The box moves at a steady = 4.80 ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C The box = 4.80 and = 4.60 ? Express your answer to three significant figures and include the appropriate units. ANSWER: kg T = 0 N vx m/s T = 0 N vx m/s ax m/s2 Typesetting math: 100% Correct Problem 6.14 It takes the elevator in a skyscraper 4.5 to reach its cruising speed of 11 . A 60 passenger gets aboard on the ground floor. Part A What is the passenger’s weight before the elevator starts moving? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the passenger’s weight while the elevator is speeding up? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the passenger’s weight after the elevator reaches its cruising speed? T = 244 N s m/s kg w = 590 N w = 730 N Typesetting math: 100% Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Block on an Incline A block lies on a plane raised an angle from the horizontal. Three forces act upon the block: , the force of gravity; , the normal force; and , the force of friction. The coefficient of friction is large enough to prevent the block from sliding . Part A Consider coordinate system a, with the x axis along the plane. Which forces lie along the axes? ANSWER: w = 590 N  F  w F n F  f Typesetting math: 100% Correct Part B Which forces lie along the axes of the coordinate system b, in which the y axis is vertical? ANSWER: Correct only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w Typesetting math: 100% Usually the best advice is to choose coordinate system so that the acceleration of the system is directly along one of the coordinate axes. If the system isn’t accelerating, then you are better off choosing the coordinate system with the most vectors along the coordinate axes. But now you are going to ignore that advice. You will find the normal force, , using vertical coordinate system b. In these coordinates you will find the magnitude appearing in both the x and y equations, each multiplied by a trigonometric function. Part C Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the y-axis is also , as shown in the figure. ANSWER: F  n Fn Fn Ff Fw  F n Fny F  n Fn  F  n  Typesetting math: 100% Hint 2. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the x-axis is also , as shown in the figure. ANSWER: ANSWER: Fny = Fncos() F f Ffy F f Ff  F  f  Ffy = Ffsin() Fy = 0 = Fncos() + Ffsin() − Fw Typesetting math: 100% Correct Part D Because the block is not moving, the sum of the x components of the forces acting on the block must be zero. Find an expression for the sum of the x components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the x component of Write an expression for , the x component of the force , using coordinate system b. Express your answer in terms of and . ANSWER: ANSWER: Correct Part E To find the magnitude of the normal force, you must express in terms of since is an unknown. Using the equations you found in the two previous parts, find an expression for involving and but not . Hint 1. How to approach the problem From your answers to the previous two parts you should have two force equations ( and ). Combine these equations to eliminate . The key is to multiply the Fn Ff Fw  F n Fnx F  n Fn  Fnx = −Fnsin() Fx = 0 = −Fnsin() + Ffcos() Fn Fw Ff Fn Fw  Ff Typesetting math: 100% Fy = 0 Fx = 0 Ff equation for the y components by and the equation for the x components by , then add or subtract the two equations to eliminate the term . An alternative motivation for the algebra is to eliminate the trig functions in front of by using the trig identity . At the very least this would result in an equation that is simple to solve for . ANSWER: Correct Congratulations on working this through. Now realize that in coordinate system a, which is aligned with the plane, the y-coordinate equation is , which leads immediately to the result obtained here for . CONCLUSION: A thoughtful examination of which coordinate system to choose can save a lot of algebra. Contact Forces Introduced Learning Goal: To introduce contact forces (normal and friction forces) and to understand that, except for friction forces under certain circumstances, these forces must be determined from: net Force = ma. Two solid objects cannot occupy the same space at the same time. Indeed, when the objects touch, they exert repulsive normal forces on each other, as well as frictional forces that resist their slipping relative to each other. These contact forces arise from a complex interplay between the electrostatic forces between the electrons and ions in the objects and the laws of quantum mechanics. As two surfaces are pushed together these forces increase exponentially over an atomic distance scale, easily becoming strong enough to distort the bulk material in the objects if they approach too close. In everyday experience, contact forces are limited by the deformation or acceleration of the objects, rather than by the fundamental interatomic forces. Hence, we can conclude the following: The magnitude of contact forces is determined by , that is, by the other forces on, and acceleration of, the contacting bodies. The only exception is that the frictional forces cannot exceed (although they can be smaller than this or even zero). Normal and friction forces Two types of contact forces operate in typical mechanics problems, the normal and frictional forces, usually designated by and (or , or something similar) respectively. These are the components of the overall contact force: perpendicular to and parallel to the plane of contact. Kinetic friction when surfaces slide cos  sin  Ff cos() sin() Fn sin2() + cos2 () = 1 Fn Fn = Fwcos() Fy = Fn − FW cos() = 0 Fn F = ma μn n f Ffric n f Typesetting math: 100% When one surface is sliding past the other, experiments show three things about the friction force (denoted ): The frictional force opposes the relative motion at the 1. point of contact, 2. is proportional to the normal force, and 3. the ratio of the magnitude of the frictional force to that of the normal force is fairly constant over a wide range of speeds. The constant of proportionality is called the coefficient of kinetic friction, often designated . As long as the sliding continues, the frictional force is then (valid when the surfaces slide by each other). Static friction when surfaces don’t slide When there is no relative motion of the surfaces, the frictional force can assume any value from zero up to a maximum , where is the coefficient of static friction. Invariably, is larger than , in agreement with the observation that when a force is large enough that something breaks loose and starts to slide, it often accelerates. The frictional force for surfaces with no relative motion is therefore (valid when the contacting surfaces have no relative motion). The actual magnitude and direction of the static friction force are such that it (together with other forces on the object) causes the object to remain motionless with respect to the contacting surface as long as the static friction force required does not exceed . The equation is valid only when the surfaces are on the verge of sliding. Part A When two objects slide by one another, which of the following statements about the force of friction between them, is true? ANSWER: Correct Part B fk fk μk fk = μkn μsn μs μs μk fs ! μsn μsn fs = μsn The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μkn μkn μkn Typesetting math: 100% When two objects are in contact with no relative motion, which of the following statements about the frictional force between them, is true? ANSWER: Correct For static friction, the actual magnitude and direction of the friction force are such that it, together with any other forces present, will cause the object to have the observed acceleration. The magnitude of the force cannot exceed . If the magnitude of static friction needed to keep acceleration equal to zero exceeds , then the object will slide subject to the resistance of kinetic friction. Do not automatically assume that unless you are considering a situation in which the magnitude of the static friction force is as large as possible (i.e., when determining at what point an object will just begin to slip). Whether the actual magnitude of the friction force is 0, less than , or equal to depends on the magnitude of the other forces (if any) as well as the acceleration of the object through . Part C When a board with a box on it is slowly tilted to larger and larger angle, common experience shows that the box will at some point “break loose” and start to accelerate down the board. The box begins to slide once the component of gravity acting parallel to the board just begins to exceeds the maximum force of static friction. Which of the following is the most general explanation for why the box accelerates down the board? ANSWER: The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μsn μsn μsn μsn μsn fs = μsn μsn μsn F = ma Fg The force of kinetic friction is smaller than that of maximum static friction, but remains the same. Once the box is moving, is smaller than the force of maximum static friction but larger than the force of kinetic friction. Once the box is moving, is larger than the force of maximum static friction. When the box is stationary, equals the force of static friction, but once the box starts moving, the sliding reduces the normal force, which in turn reduces the friction. Fg Fg Fg Fg Typesetting math: 100% Correct At the point when the box finally does “break loose,” you know that the component of the box’s weight that is parallel to the board just exceeds (i.e., this component of gravitational force on the box has just reached a magnitude such that the force of static friction, which has a maximum value of , can no longer oppose it.) For the box to then accelerate, there must be a net force on the box along the board. Thus, the component of the box’s weight parallel to the board must be greater than the force of kinetic friction. Therefore the force of kinetic friction must be less than the force of static friction which implies , as expected. Part D Consider a problem in which a car of mass is on a road tilted at an angle . The normal force Select the best answer. ANSWER: Correct The key point is that contact forces must be determined from Newton’s equation. In the problem described above, there is not enough information given to determine the normal force (e.g., the acceleration is unknown). Each of the answer options is valid under some conditions ( , the car is sliding down an icy incline, or the car is going around a banked turn), but in fact none is likely to be correct if there are other forces on the car or if the car is accelerating. Do not memorize values for the normal force valid in different problems–you must determine from . Problem 6.17 Bonnie and Clyde are sliding a 323 bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 375 of force while Bonnie pulls forward on a rope with 335 of force. μsn μsn μkn μsn μk < μs M  is found using n = Mg n = Mg cos() n = Mg cos() F  = Ma  = 0 n F = ma kg N N Typesetting math: 100% Part A What is the safe's coefficient of kinetic friction on the bank floor? ANSWER: Correct Problem 6.19 A crate is placed on a horizontal conveyor belt. The materials are such that and . Part A Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: 0.224 10 kg μs = 0.5 μk = 0.3 Typesetting math: 100% Correct Part B Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Part C What is the maximum acceleration the belt can have without the crate slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct amax = 4.9 m s2 Typesetting math: 100% Problem 6.28 A 1100 steel beam is supported by two ropes. Part A What is the tension in rope 1? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. ANSWER: kg T1 = 7000 N Typesetting math: 100% Correct Problem 6.35 The position of a 1.4 mass is given by , where is in seconds. Part A What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.39 T2 = 4800 N kg x = (2t3 − 3t2 )m t t = 0 s F = -8.4 N t = 1 s F = 8.4 N Typesetting math: 100% A rifle with a barrel length of 61 fires a 8 bullet with a horizontal speed of 400 . The bullet strikes a block of wood and penetrates to a depth of 11 . Part A What resistive force (assumed to be constant) does the wood exert on the bullet? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How long does it take the bullet to come to rest after entering the wood? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.45 You and your friend Peter are putting new shingles on a roof pitched at 21 . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0 away, asks you for the box of nails. Rather than carry the 2.0 box of nails down to Peter, you decide to give the box a push and have it slide down to him. Part A If the coefficient of kinetic friction between the box and the roof is 0.55, with what speed should you push the box to have it gently come to rest right at the edge of the roof? Express your answer to two significant figures and include the appropriate units. cm g m/s cm fk = 5800 N = 5.5×10−4 t s  m kg Typesetting math: 100% ANSWER: Correct Problem 6.54 The 2.0 wood box in the figure slides down a vertical wood wall while you push on it at a 45 angle. Part A What magnitude of force should you apply to cause the box to slide down at a constant speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct v = 3.9 ms kg  F = 23 N Typesetting math: 100% Score Summary: Your score on this assignment is 98.8%. You received 114.57 out of a possible total of 116 points. Typesetting math: 100%

Assignment 5 Due: 11:59pm on Wednesday, March 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 6.13 A hand presses down on the book in the figure. Part A Is the normal force of the table on the book larger than, smaller than, or equal to ? ANSWER: Correct mg Equal to Larger than Smaller than mg mg mg Problem 6.2 The three ropes in the figure are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. Part A What is the magnitude of the tension in the third rope? Express your answer using two significant figures. ANSWER: Correct Part B What is the direction of the tension in the third rope? Express your answer using two significant figures. T  3 T3 = 94 N T  3 Typesetting math: 100% ANSWER: Correct The Normal Force When an object rests on a surface, there is always a force perpendicular to the surface; we call this the normal force, denoted by . The two questions to the right will explore the normal force. Part A A man attempts to pick up his suitcase of weight by pulling straight up on the handle. However, he is unable to lift the suitcase from the floor. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man pulls upward on the suitcase? Hint 1. How to approach this problem First, identify the forces that act on the suitcase and draw a free-body diagram. Then use the fact that the suitcase is in equilibrium, , to examine how the forces acting on the suitcase relate to each other. Hint 2. Identify the correct free-body diagram Which of the figures represents the free-body diagram of the suitcase while the man is pulling on the handle with a force of magnitude ? = 58   below horizontal n ws n F = 0 fpull Typesetting math: 100% ANSWER: ANSWER: Correct Part B A B C D The magnitude of the normal force is equal to the magnitude of the weight of the suitcase. The magnitude of the normal force is equal to the magnitude of the weight of the suitcase minus the magnitude of the force of the pull. The magnitude of the normal force is equal to the sum of the magnitude of the force of the pull and the magnitude of the suitcase’s weight. The magnitude of the normal force is greater than the magnitude of the weight of the suitcase. Typesetting math: 100% Now assume that the man of weight is tired and decides to sit on his suitcase. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man is sitting on the suitcase? Hint 1. Identify the correct free-body diagram. Which of the figures represents the free-body diagram while the man is sitting atop the suitcase? Here the vector labeled is a force that has the same magnitude as the man’s weight. ANSWER: wm n wm Typesetting math: 100% ANSWER: Correct Recognize that the normal force acting on an object is not always equal to the weight of that object. This is an important point to understand. Problem 6.5 A construction worker with a weight of 880 stands on a roof that is sloped at 18 . Part A What is the magnitude of the normal force of the roof on the worker? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct A B C D The magnitude of the normal force is equal to the magnitude of the suitcase’s weight. The magnitude of the normal force is equal to the magnitude of the suitcase’s weight minus the magnitude of the man’s weight. The magnitude of the normal force is equal to the sum of the magnitude of the man’s weight and the magnitude of the suitcase’s weight. The magnitude of the normal force is less than the magnitude of the suitcase’s weight. N  n = 840 N Typesetting math: 100% Problem 6.6 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B For diagram the part A, find the value of the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: kg ax x ax = -0.67 m s2 ay, y Typesetting math: 100% Correct Part C For diagram , find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D For diagram the part C, find the value of , the -component of the acceleration. Express your answer to two significant figures and include the appropriate units. ANSWER: ay = 0 m s2 ax x ax = 0.67 m s2 ay y Typesetting math: 100% Correct Problem 6.7 In each of the two free-body diagrams, the forces are acting on a 3.0 object. Part A Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay = 0 m s2 kg ax x ax = 0.99 m s2 Typesetting math: 100% Part B Find the value of , the component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Find the value of , the component of the acceleration in diagram (b). Express your answer to two significant figures and include the appropriate units. ANSWER: Correct ay y ay = 0 m s2 ax x ax = -0.18 m s2 ay y ay = 0 m s2 Typesetting math: 100% Problem 6.10 A horizontal rope is tied to a 53.0 box on frictionless ice. What is the tension in the rope if: Part A The box is at rest? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B The box moves at a steady = 4.80 ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C The box = 4.80 and = 4.60 ? Express your answer to three significant figures and include the appropriate units. ANSWER: kg T = 0 N vx m/s T = 0 N vx m/s ax m/s2 Typesetting math: 100% Correct Problem 6.14 It takes the elevator in a skyscraper 4.5 to reach its cruising speed of 11 . A 60 passenger gets aboard on the ground floor. Part A What is the passenger’s weight before the elevator starts moving? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the passenger’s weight while the elevator is speeding up? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the passenger’s weight after the elevator reaches its cruising speed? T = 244 N s m/s kg w = 590 N w = 730 N Typesetting math: 100% Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Block on an Incline A block lies on a plane raised an angle from the horizontal. Three forces act upon the block: , the force of gravity; , the normal force; and , the force of friction. The coefficient of friction is large enough to prevent the block from sliding . Part A Consider coordinate system a, with the x axis along the plane. Which forces lie along the axes? ANSWER: w = 590 N  F  w F n F  f Typesetting math: 100% Correct Part B Which forces lie along the axes of the coordinate system b, in which the y axis is vertical? ANSWER: Correct only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w only only only and and and and and F  f F  n F  w F  f F  n F  f F  w F  n F w F  f F  n F w Typesetting math: 100% Usually the best advice is to choose coordinate system so that the acceleration of the system is directly along one of the coordinate axes. If the system isn’t accelerating, then you are better off choosing the coordinate system with the most vectors along the coordinate axes. But now you are going to ignore that advice. You will find the normal force, , using vertical coordinate system b. In these coordinates you will find the magnitude appearing in both the x and y equations, each multiplied by a trigonometric function. Part C Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the y-axis is also , as shown in the figure. ANSWER: F  n Fn Fn Ff Fw  F n Fny F  n Fn  F  n  Typesetting math: 100% Hint 2. Find the y component of Write an expression for , the y component of the force , using coordinate system b. Express your answer in terms of and . Hint 1. Some geometry help – a useful angle The smaller angle between and the x-axis is also , as shown in the figure. ANSWER: ANSWER: Fny = Fncos() F f Ffy F f Ff  F  f  Ffy = Ffsin() Fy = 0 = Fncos() + Ffsin() − Fw Typesetting math: 100% Correct Part D Because the block is not moving, the sum of the x components of the forces acting on the block must be zero. Find an expression for the sum of the x components of the forces acting on the block, using coordinate system b. Express your answer in terms of some or all of the variables , , , and . Hint 1. Find the x component of Write an expression for , the x component of the force , using coordinate system b. Express your answer in terms of and . ANSWER: ANSWER: Correct Part E To find the magnitude of the normal force, you must express in terms of since is an unknown. Using the equations you found in the two previous parts, find an expression for involving and but not . Hint 1. How to approach the problem From your answers to the previous two parts you should have two force equations ( and ). Combine these equations to eliminate . The key is to multiply the Fn Ff Fw  F n Fnx F  n Fn  Fnx = −Fnsin() Fx = 0 = −Fnsin() + Ffcos() Fn Fw Ff Fn Fw  Ff Typesetting math: 100% Fy = 0 Fx = 0 Ff equation for the y components by and the equation for the x components by , then add or subtract the two equations to eliminate the term . An alternative motivation for the algebra is to eliminate the trig functions in front of by using the trig identity . At the very least this would result in an equation that is simple to solve for . ANSWER: Correct Congratulations on working this through. Now realize that in coordinate system a, which is aligned with the plane, the y-coordinate equation is , which leads immediately to the result obtained here for . CONCLUSION: A thoughtful examination of which coordinate system to choose can save a lot of algebra. Contact Forces Introduced Learning Goal: To introduce contact forces (normal and friction forces) and to understand that, except for friction forces under certain circumstances, these forces must be determined from: net Force = ma. Two solid objects cannot occupy the same space at the same time. Indeed, when the objects touch, they exert repulsive normal forces on each other, as well as frictional forces that resist their slipping relative to each other. These contact forces arise from a complex interplay between the electrostatic forces between the electrons and ions in the objects and the laws of quantum mechanics. As two surfaces are pushed together these forces increase exponentially over an atomic distance scale, easily becoming strong enough to distort the bulk material in the objects if they approach too close. In everyday experience, contact forces are limited by the deformation or acceleration of the objects, rather than by the fundamental interatomic forces. Hence, we can conclude the following: The magnitude of contact forces is determined by , that is, by the other forces on, and acceleration of, the contacting bodies. The only exception is that the frictional forces cannot exceed (although they can be smaller than this or even zero). Normal and friction forces Two types of contact forces operate in typical mechanics problems, the normal and frictional forces, usually designated by and (or , or something similar) respectively. These are the components of the overall contact force: perpendicular to and parallel to the plane of contact. Kinetic friction when surfaces slide cos  sin  Ff cos() sin() Fn sin2() + cos2 () = 1 Fn Fn = Fwcos() Fy = Fn − FW cos() = 0 Fn F = ma μn n f Ffric n f Typesetting math: 100% When one surface is sliding past the other, experiments show three things about the friction force (denoted ): The frictional force opposes the relative motion at the 1. point of contact, 2. is proportional to the normal force, and 3. the ratio of the magnitude of the frictional force to that of the normal force is fairly constant over a wide range of speeds. The constant of proportionality is called the coefficient of kinetic friction, often designated . As long as the sliding continues, the frictional force is then (valid when the surfaces slide by each other). Static friction when surfaces don’t slide When there is no relative motion of the surfaces, the frictional force can assume any value from zero up to a maximum , where is the coefficient of static friction. Invariably, is larger than , in agreement with the observation that when a force is large enough that something breaks loose and starts to slide, it often accelerates. The frictional force for surfaces with no relative motion is therefore (valid when the contacting surfaces have no relative motion). The actual magnitude and direction of the static friction force are such that it (together with other forces on the object) causes the object to remain motionless with respect to the contacting surface as long as the static friction force required does not exceed . The equation is valid only when the surfaces are on the verge of sliding. Part A When two objects slide by one another, which of the following statements about the force of friction between them, is true? ANSWER: Correct Part B fk fk μk fk = μkn μsn μs μs μk fs ! μsn μsn fs = μsn The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μkn μkn μkn Typesetting math: 100% When two objects are in contact with no relative motion, which of the following statements about the frictional force between them, is true? ANSWER: Correct For static friction, the actual magnitude and direction of the friction force are such that it, together with any other forces present, will cause the object to have the observed acceleration. The magnitude of the force cannot exceed . If the magnitude of static friction needed to keep acceleration equal to zero exceeds , then the object will slide subject to the resistance of kinetic friction. Do not automatically assume that unless you are considering a situation in which the magnitude of the static friction force is as large as possible (i.e., when determining at what point an object will just begin to slip). Whether the actual magnitude of the friction force is 0, less than , or equal to depends on the magnitude of the other forces (if any) as well as the acceleration of the object through . Part C When a board with a box on it is slowly tilted to larger and larger angle, common experience shows that the box will at some point “break loose” and start to accelerate down the board. The box begins to slide once the component of gravity acting parallel to the board just begins to exceeds the maximum force of static friction. Which of the following is the most general explanation for why the box accelerates down the board? ANSWER: The frictional force is always equal to . The frictional force is always less than . The frictional force is determined by other forces on the objects so it can be either equal to or less than . μsn μsn μsn μsn μsn fs = μsn μsn μsn F = ma Fg The force of kinetic friction is smaller than that of maximum static friction, but remains the same. Once the box is moving, is smaller than the force of maximum static friction but larger than the force of kinetic friction. Once the box is moving, is larger than the force of maximum static friction. When the box is stationary, equals the force of static friction, but once the box starts moving, the sliding reduces the normal force, which in turn reduces the friction. Fg Fg Fg Fg Typesetting math: 100% Correct At the point when the box finally does “break loose,” you know that the component of the box’s weight that is parallel to the board just exceeds (i.e., this component of gravitational force on the box has just reached a magnitude such that the force of static friction, which has a maximum value of , can no longer oppose it.) For the box to then accelerate, there must be a net force on the box along the board. Thus, the component of the box’s weight parallel to the board must be greater than the force of kinetic friction. Therefore the force of kinetic friction must be less than the force of static friction which implies , as expected. Part D Consider a problem in which a car of mass is on a road tilted at an angle . The normal force Select the best answer. ANSWER: Correct The key point is that contact forces must be determined from Newton’s equation. In the problem described above, there is not enough information given to determine the normal force (e.g., the acceleration is unknown). Each of the answer options is valid under some conditions ( , the car is sliding down an icy incline, or the car is going around a banked turn), but in fact none is likely to be correct if there are other forces on the car or if the car is accelerating. Do not memorize values for the normal force valid in different problems–you must determine from . Problem 6.17 Bonnie and Clyde are sliding a 323 bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 375 of force while Bonnie pulls forward on a rope with 335 of force. μsn μsn μkn μsn μk < μs M  is found using n = Mg n = Mg cos() n = Mg cos() F  = Ma  = 0 n F = ma kg N N Typesetting math: 100% Part A What is the safe's coefficient of kinetic friction on the bank floor? ANSWER: Correct Problem 6.19 A crate is placed on a horizontal conveyor belt. The materials are such that and . Part A Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: 0.224 10 kg μs = 0.5 μk = 0.3 Typesetting math: 100% Correct Part B Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Part C What is the maximum acceleration the belt can have without the crate slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct amax = 4.9 m s2 Typesetting math: 100% Problem 6.28 A 1100 steel beam is supported by two ropes. Part A What is the tension in rope 1? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. ANSWER: kg T1 = 7000 N Typesetting math: 100% Correct Problem 6.35 The position of a 1.4 mass is given by , where is in seconds. Part A What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the net horizontal force on the mass at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.39 T2 = 4800 N kg x = (2t3 − 3t2 )m t t = 0 s F = -8.4 N t = 1 s F = 8.4 N Typesetting math: 100% A rifle with a barrel length of 61 fires a 8 bullet with a horizontal speed of 400 . The bullet strikes a block of wood and penetrates to a depth of 11 . Part A What resistive force (assumed to be constant) does the wood exert on the bullet? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How long does it take the bullet to come to rest after entering the wood? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 6.45 You and your friend Peter are putting new shingles on a roof pitched at 21 . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0 away, asks you for the box of nails. Rather than carry the 2.0 box of nails down to Peter, you decide to give the box a push and have it slide down to him. Part A If the coefficient of kinetic friction between the box and the roof is 0.55, with what speed should you push the box to have it gently come to rest right at the edge of the roof? Express your answer to two significant figures and include the appropriate units. cm g m/s cm fk = 5800 N = 5.5×10−4 t s  m kg Typesetting math: 100% ANSWER: Correct Problem 6.54 The 2.0 wood box in the figure slides down a vertical wood wall while you push on it at a 45 angle. Part A What magnitude of force should you apply to cause the box to slide down at a constant speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct v = 3.9 ms kg  F = 23 N Typesetting math: 100% Score Summary: Your score on this assignment is 98.8%. You received 114.57 out of a possible total of 116 points. Typesetting math: 100%

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On January 1, 2014, equipment was purchased for $80,000; the equipment’s estimated residual value is $15,000, and its estimated useful life is 10 years. For 2014, the depreciation expense under the double-declining balance method is $13,000.

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