1) ED = ⎢ ⎢ ⎢ ⎣ ⎡ + 18- – 6 6 – 2) The cro a × b = = i(-3 ⋅ 2 = -15i – 2 ⎢ ⎢ ⎢ ⎣ ⎡ × = 3 b a 4 i + + + + – 2 16 3 0 4 -1 5 8 1 oss produc – 1 ⋅ 9) 2j + 39k ⎥ ⎥ ⎥ ⎦ ⎤ − 3 1 9 2 j k == + + + + + + 2 4 9 0 1 -3 5 2 3 1 t is – j(3 ⋅ 2 15i + 2j – ⎥ ⎥ ⎥ ⎦ ⎤ + + + + + 4 12 0 3 10 6

1) ED = ⎢ ⎢ ⎢ ⎣ ⎡ + 18- – 6 6 – 2) The cro a × b = = i(-3 ⋅ 2 = -15i – 2 ⎢ ⎢ ⎢ ⎣ ⎡ × = 3 b a 4 i + + + + – 2 16 3 0 4 -1 5 8 1 oss produc – 1 ⋅ 9) 2j + 39k ⎥ ⎥ ⎥ ⎦ ⎤ − 3 1 9 2 j k == + + + + + + 2 4 9 0 1 -3 5 2 3 1 t is – j(3 ⋅ 2 15i + 2j – ⎥ ⎥ ⎥ ⎦ ⎤ + + + + + 4 12 0 3 10 6

 
Name Car Fuel Economy Objectives: 1. Collect data from a reliable source 2. Create a chart of important values 3. Determine what type of graph best fits the available data (exponential, linear, logarithmic, polynomial… etc) 4. Create a plot using the correct values and determine which variable goes on which axis 5. Fit a line to the graph and show equation 6. Use the equation to predict a future value 7. Use the equation editor to display equations Your task: You want to determine whether the curb weight of the vehicle has any impact on the Highway MPG of the vehicle. In order to do this, go to a reliable source and select 10 of your favorite cars. It can be from any make, model or year and be different across the board. As a matter of fact, the more variety you have in the make, model and year the better. (Please follow the correct homework heading format and please record your answers in blue color on this sheet) General note: Whenever you create a graph, label the X-axis and the Y-axis. Give the graph an appropriate title and include units for the axes. Use the Equation Editor to type answers as equations. 1. On Excel, create a table by recording the make, model and year of the vehicle, the curb weight, and the highway MPG (Miles per gallon). Do this for all 10 cars. 2. Create/insert a scatter plot of the Curb weight (X-axis) vs. Highway MPG (Y-axis). 3. Select the data points by right clicking on the data point and select to add a linear trendline for the 10 cars you currently have. Make it a solid green line (format the line). 4. Select to display the equation on the chart. What is the equation? _______________________________ 5. Using your equation, predict the MPG of a Uhaul that has a curb weight of 12,600lbs (type in curb weight as x). What is that MPG (y)? ___________________________. Record the Uhaul’s curb weight and predicted MPG on the excel sheet. Label clearly with the equation used. Does that answer make sense? Why or why not? ___________________________________________________ ___________________________________________________________________________________________ 6. According to the Uhaul website, a typical truck will get about 10 MPG. Create another scatter plot (do not delete the original one) that shows the same data, but is fitted with an exponential trendline (dashed red line). 7. Select to display the equation on the chart. What is the equation? ________________________________ 8. Using your equation, predict the MPG of a Uhaul that has a curb weight of 12,600lbs. What is that MPG? ___________________________. Record the Uhaul’s curb weight and predicted MPG on the excel sheet. Label clearly with the equation used. Does that answer make sense? Why or why not? Is this prediction better or worse than the first equation? ___________________________________________________________________________________________ ___________________________________________________________________________________________ 9. Now create a third scatter plot of curb weight and highway MPG. Add both a linear and exponential trendline. Make the linear trendline a solid green line and the exponential trendline a dashed red line (just like the two previous graphs). 10. Include a legend for the third graph. 11. Organize the excel sheet to make it look professional. 12. Please upload both this document with all of your answers and the Excel sheet that you created in the assignment on eCampus.

Name Car Fuel Economy Objectives: 1. Collect data from a reliable source 2. Create a chart of important values 3. Determine what type of graph best fits the available data (exponential, linear, logarithmic, polynomial… etc) 4. Create a plot using the correct values and determine which variable goes on which axis 5. Fit a line to the graph and show equation 6. Use the equation to predict a future value 7. Use the equation editor to display equations Your task: You want to determine whether the curb weight of the vehicle has any impact on the Highway MPG of the vehicle. In order to do this, go to a reliable source and select 10 of your favorite cars. It can be from any make, model or year and be different across the board. As a matter of fact, the more variety you have in the make, model and year the better. (Please follow the correct homework heading format and please record your answers in blue color on this sheet) General note: Whenever you create a graph, label the X-axis and the Y-axis. Give the graph an appropriate title and include units for the axes. Use the Equation Editor to type answers as equations. 1. On Excel, create a table by recording the make, model and year of the vehicle, the curb weight, and the highway MPG (Miles per gallon). Do this for all 10 cars. 2. Create/insert a scatter plot of the Curb weight (X-axis) vs. Highway MPG (Y-axis). 3. Select the data points by right clicking on the data point and select to add a linear trendline for the 10 cars you currently have. Make it a solid green line (format the line). 4. Select to display the equation on the chart. What is the equation? _______________________________ 5. Using your equation, predict the MPG of a Uhaul that has a curb weight of 12,600lbs (type in curb weight as x). What is that MPG (y)? ___________________________. Record the Uhaul’s curb weight and predicted MPG on the excel sheet. Label clearly with the equation used. Does that answer make sense? Why or why not? ___________________________________________________ ___________________________________________________________________________________________ 6. According to the Uhaul website, a typical truck will get about 10 MPG. Create another scatter plot (do not delete the original one) that shows the same data, but is fitted with an exponential trendline (dashed red line). 7. Select to display the equation on the chart. What is the equation? ________________________________ 8. Using your equation, predict the MPG of a Uhaul that has a curb weight of 12,600lbs. What is that MPG? ___________________________. Record the Uhaul’s curb weight and predicted MPG on the excel sheet. Label clearly with the equation used. Does that answer make sense? Why or why not? Is this prediction better or worse than the first equation? ___________________________________________________________________________________________ ___________________________________________________________________________________________ 9. Now create a third scatter plot of curb weight and highway MPG. Add both a linear and exponential trendline. Make the linear trendline a solid green line and the exponential trendline a dashed red line (just like the two previous graphs). 10. Include a legend for the third graph. 11. Organize the excel sheet to make it look professional. 12. Please upload both this document with all of your answers and the Excel sheet that you created in the assignment on eCampus.

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MCE 260 Fall 2015 Homework 9, due November 12, 2015. PRESENT CLEARLY HOW YOU DEVELOPED THE SOLUTION TO THE PROBLEMS Each problem is worth up to 5 points. Points are given as follows: 5 points: Work was complete and presented clearly, the answer is correct 4 points: Work was complete, but not clearly presented or some errors in calculation 3 points: Some errors or omissions in methods or presentation 2 points: Major errors or omissions in methods or presentation 1 point: Problem was understood but incorrect approach was used 1. The radial compressor shown above (with dimensions) has a crank that rotates at 120 RPM. What is the maximal acceleration of each piston? 2. Design a follower displacement profile for a double-dwell (RDFD) cam, with these performance specifications: Machine cycle is 5 seconds. Rise from 0 to 22 mm in 45 degrees. Dwell for 45 degrees. Fall from 22 mm back to zero in 90 degrees. Dwell for the remainder of the machine cycle. You may use any profile that satisfies the fundamental law of cam design. Write equations for follower displacement (s) as a function of cam angle (θ) for each of the four segments of the cam. 3. (10% extra credit) What is the maximal acceleration of the follower? At which point in the cycle does it occur? Page 1 of 1

MCE 260 Fall 2015 Homework 9, due November 12, 2015. PRESENT CLEARLY HOW YOU DEVELOPED THE SOLUTION TO THE PROBLEMS Each problem is worth up to 5 points. Points are given as follows: 5 points: Work was complete and presented clearly, the answer is correct 4 points: Work was complete, but not clearly presented or some errors in calculation 3 points: Some errors or omissions in methods or presentation 2 points: Major errors or omissions in methods or presentation 1 point: Problem was understood but incorrect approach was used 1. The radial compressor shown above (with dimensions) has a crank that rotates at 120 RPM. What is the maximal acceleration of each piston? 2. Design a follower displacement profile for a double-dwell (RDFD) cam, with these performance specifications: Machine cycle is 5 seconds. Rise from 0 to 22 mm in 45 degrees. Dwell for 45 degrees. Fall from 22 mm back to zero in 90 degrees. Dwell for the remainder of the machine cycle. You may use any profile that satisfies the fundamental law of cam design. Write equations for follower displacement (s) as a function of cam angle (θ) for each of the four segments of the cam. 3. (10% extra credit) What is the maximal acceleration of the follower? At which point in the cycle does it occur? Page 1 of 1

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The solubility of Ar in water at 25°C is 1.6 × 10-3 M when the pressure of the Ar above the solution is 1.0 atm. The solubility of Ar at a pressure of 2.5 atm is __________ M. A) 1.6 × 103 B) 6.4 × 10-4 C) 4.0 × 10-3 D) 7.5 × 10-2 E) 1.6 × 10-3

The solubility of Ar in water at 25°C is 1.6 × 10-3 M when the pressure of the Ar above the solution is 1.0 atm. The solubility of Ar at a pressure of 2.5 atm is __________ M. A) 1.6 × 103 B) 6.4 × 10-4 C) 4.0 × 10-3 D) 7.5 × 10-2 E) 1.6 × 10-3

COMP 4440/5440 – Dr. Erdemir Mobile Robotics Project (DUE 12/02/2015) HONOR CODE I pledge my honor that I have neither given nor received aid on this work. Do not sign until after you have completed your assignment. Name: Signature: 1. (Prerequisite) Given the asset package (it is in mytsu under assignments folder) download it, open a new project (don’t double click on the file, it won’t open), go to Assets/Import Package/Custom Package, select the asset package given to you (project.unitypackage). After the import is completed, you will see main scene in the assets folder of your project. Double click on it, and choose “Don’t Save” option if it asks for save. 2. Print this page and attach it to your code and your snapshot of your final scene (5 points) 3. After the class starts, instructor will come next to you and you are supposed to show him your code running (10 points) 4. When you run the code you will see, your robot (red cube that we used in the class) is trying to reach the targets but it can’t due to an obstacle between your robot and the targets. Write a code that makes this robot to avoid from the obstacles and reach the targets. Your code will read the collision and intelligently avoid from other moving robots and fixed obstacles and get the three targets. (50 points) 5. Maximum time is 2 minutes, your robot shall get the targets in 2 minutes (10 points) 6. Your robot shall escape from the blue robot and not collide them. (10 Points) 7. Anything extra (up to 20 points) ? Moving objects, new sensor, Artificial Intelligence or other techniques. 8. YOU CAN NOT USE TRANSLATE FUNCTION. USE ONLY AddRelativeForce FUNCTION IN THE FORWARD DIRECTION AS ALL THE MOBILE ROBOTS WORK.

COMP 4440/5440 – Dr. Erdemir Mobile Robotics Project (DUE 12/02/2015) HONOR CODE I pledge my honor that I have neither given nor received aid on this work. Do not sign until after you have completed your assignment. Name: Signature: 1. (Prerequisite) Given the asset package (it is in mytsu under assignments folder) download it, open a new project (don’t double click on the file, it won’t open), go to Assets/Import Package/Custom Package, select the asset package given to you (project.unitypackage). After the import is completed, you will see main scene in the assets folder of your project. Double click on it, and choose “Don’t Save” option if it asks for save. 2. Print this page and attach it to your code and your snapshot of your final scene (5 points) 3. After the class starts, instructor will come next to you and you are supposed to show him your code running (10 points) 4. When you run the code you will see, your robot (red cube that we used in the class) is trying to reach the targets but it can’t due to an obstacle between your robot and the targets. Write a code that makes this robot to avoid from the obstacles and reach the targets. Your code will read the collision and intelligently avoid from other moving robots and fixed obstacles and get the three targets. (50 points) 5. Maximum time is 2 minutes, your robot shall get the targets in 2 minutes (10 points) 6. Your robot shall escape from the blue robot and not collide them. (10 Points) 7. Anything extra (up to 20 points) ? Moving objects, new sensor, Artificial Intelligence or other techniques. 8. YOU CAN NOT USE TRANSLATE FUNCTION. USE ONLY AddRelativeForce FUNCTION IN THE FORWARD DIRECTION AS ALL THE MOBILE ROBOTS WORK.

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– 1 – Laboratory 1 Introduction: In this lab you will look at two problems that are at the heart of calculus. Each of these experiments illustrates a core calculus concept. You should perform each experiment taking notes and pictures. You will use these to write up your results. You are expected to use a word processor to produce the laboratory. Graphing software should be used to draw your graphs and illustrations. You can also include pictures you have taken. Equations should be written using “equation editor” software. In short, the laboratory should have a professional look and feel to it. It should be of publishable quality. You report should be printed on 8.5 x 11 inch paper and include a title page (format will be discussed in class). Each page should be numbered. You can work in groups of 3 on this laboratory. If you do this, you must include a page right after the title page and before the report that includes a list of the contributions of each member of the group has made. Question 1 Suppose you start 10 feet away from a wall and walk 5 feet toward the wall and stop. Now walk 2.5 feet toward the wall and stop. Keep going each time walking half the distance of your previous walk toward the wall. 1. Where are you after three walks? 2. Where are you after 2, 3, 4, 5, 10 walks? 3. Create a function where n is the number of the walk and f(n) is the distance from the wall. 4. Graph this function. 5. Using your modeling skills find a model for this function. 6. If you walk forever, were will you end up? For this one write a paragraph defending your location. 7. If instead of walking one half as far as the previous walk, walk one third. That is start 9 feet away from the wall and walk 3 feet, then 1 foot, then 1/3 of a foot, etc. Where do you end up this time? Again write a paragraph. 8. Discuss you experiment in relation Zeno’s Paradox called Achilles and Tortoise. – 2 – Question 2 Here you are going to find the circumference and area of a circle by approximating it with polygons. 1. Start by drawing a circle with radius 3” on a sheet of paper. (You should include your drawings in laboratory report. You should be able to get two per page.) 2. Divide the circle into 3 equal parts. 3. Now connect adjacent points on the circumference to form 3 triangles as shown below. You need to find the area of these isosceles triangles and the length of the bases (red lines). 4. In a table keep track of the following: a. The number of triangles. b. The sum of the lengths of the bases. This is your approximation for the circumference. Label this column, C. c. The sum of the areas of the triangles. This is your approximation for the area of the circle. Label this column , A. d. In a column divide your approximation for the circumference by 2*r. This value should be 6 since r is the radius of your circle is 3. Label this column P1 e. In a column divide your approximation for the area by r2 or 9. Label this column P2. – 3 – 5. Repeat this process for n = 4 … 15 recording your results in the correct columns. 6. Create the two functions described below. You should the graph for each of these functions separately. a. C(n) which associates n to the corresponding approximation of the circumference. b. A(n) which associates n to the corresponding approximation of the area. 7. For the two functions created in step 6 find a model for each function. 8. If we were to continue this experiment — let n grow larger without bound then what values do C and A will approach. Write a paragraph for each variable explaining your reasoning. 9. Then examine the P1 and P2 columns of your table. Write a paragraph on what you if n is allowed to grow larger without bound.

– 1 – Laboratory 1 Introduction: In this lab you will look at two problems that are at the heart of calculus. Each of these experiments illustrates a core calculus concept. You should perform each experiment taking notes and pictures. You will use these to write up your results. You are expected to use a word processor to produce the laboratory. Graphing software should be used to draw your graphs and illustrations. You can also include pictures you have taken. Equations should be written using “equation editor” software. In short, the laboratory should have a professional look and feel to it. It should be of publishable quality. You report should be printed on 8.5 x 11 inch paper and include a title page (format will be discussed in class). Each page should be numbered. You can work in groups of 3 on this laboratory. If you do this, you must include a page right after the title page and before the report that includes a list of the contributions of each member of the group has made. Question 1 Suppose you start 10 feet away from a wall and walk 5 feet toward the wall and stop. Now walk 2.5 feet toward the wall and stop. Keep going each time walking half the distance of your previous walk toward the wall. 1. Where are you after three walks? 2. Where are you after 2, 3, 4, 5, 10 walks? 3. Create a function where n is the number of the walk and f(n) is the distance from the wall. 4. Graph this function. 5. Using your modeling skills find a model for this function. 6. If you walk forever, were will you end up? For this one write a paragraph defending your location. 7. If instead of walking one half as far as the previous walk, walk one third. That is start 9 feet away from the wall and walk 3 feet, then 1 foot, then 1/3 of a foot, etc. Where do you end up this time? Again write a paragraph. 8. Discuss you experiment in relation Zeno’s Paradox called Achilles and Tortoise. – 2 – Question 2 Here you are going to find the circumference and area of a circle by approximating it with polygons. 1. Start by drawing a circle with radius 3” on a sheet of paper. (You should include your drawings in laboratory report. You should be able to get two per page.) 2. Divide the circle into 3 equal parts. 3. Now connect adjacent points on the circumference to form 3 triangles as shown below. You need to find the area of these isosceles triangles and the length of the bases (red lines). 4. In a table keep track of the following: a. The number of triangles. b. The sum of the lengths of the bases. This is your approximation for the circumference. Label this column, C. c. The sum of the areas of the triangles. This is your approximation for the area of the circle. Label this column , A. d. In a column divide your approximation for the circumference by 2*r. This value should be 6 since r is the radius of your circle is 3. Label this column P1 e. In a column divide your approximation for the area by r2 or 9. Label this column P2. – 3 – 5. Repeat this process for n = 4 … 15 recording your results in the correct columns. 6. Create the two functions described below. You should the graph for each of these functions separately. a. C(n) which associates n to the corresponding approximation of the circumference. b. A(n) which associates n to the corresponding approximation of the area. 7. For the two functions created in step 6 find a model for each function. 8. If we were to continue this experiment — let n grow larger without bound then what values do C and A will approach. Write a paragraph for each variable explaining your reasoning. 9. Then examine the P1 and P2 columns of your table. Write a paragraph on what you if n is allowed to grow larger without bound.

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Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi

Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi

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SITUATIONAL ASSESSMENTS Directions: Given the following situations, make assessments of how to prepare for each presentation. Include in your assessment the following: a) topic, b) length, c) amount of detail needed, d) appropriate room set up, e) equipment needs, f) visual aids needed, g) type of presentation to me made, and other pertinent information. Also, identify those things that need to be answered prior to the presentation and how you would go about finding it out. Situation 1: Dr. Jenson has called to have you speak to his college class about job opportunities in your field. His class meets from 1-4pm. He has asked you to speak for about 30 minutes. Situation 2: Ms. Jenkins, the office manager for one of the larger companies in town, has asked you to do a “Dress for Success” workshop for her employees. She wants to improve the image of her employees. She would like you to present your workshop in next month. Situation 3: You have been asked to speak to the local Toastmasters. The group of professionals meets weekly at the a local restaurant. You have been asked to talk for about 10 minutes at this week’s meeting. Situation 4: Your boss has left a message for you, letting you know he wants you to talk to the plant supervisors next week about ways to improve productivity.

SITUATIONAL ASSESSMENTS Directions: Given the following situations, make assessments of how to prepare for each presentation. Include in your assessment the following: a) topic, b) length, c) amount of detail needed, d) appropriate room set up, e) equipment needs, f) visual aids needed, g) type of presentation to me made, and other pertinent information. Also, identify those things that need to be answered prior to the presentation and how you would go about finding it out. Situation 1: Dr. Jenson has called to have you speak to his college class about job opportunities in your field. His class meets from 1-4pm. He has asked you to speak for about 30 minutes. Situation 2: Ms. Jenkins, the office manager for one of the larger companies in town, has asked you to do a “Dress for Success” workshop for her employees. She wants to improve the image of her employees. She would like you to present your workshop in next month. Situation 3: You have been asked to speak to the local Toastmasters. The group of professionals meets weekly at the a local restaurant. You have been asked to talk for about 10 minutes at this week’s meeting. Situation 4: Your boss has left a message for you, letting you know he wants you to talk to the plant supervisors next week about ways to improve productivity.

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