MECET 423: Mechanics of Materials Chap. 7 HW Chap. 7 Homework Set 1. Consider the beam shown in the image below. Let F1 = 2 kN and F2 = 3 kN. Assume that points A, B and C represent pin connections and a wire rope connects points B and C. Consider the dimensions L1, L2, L3 and L4 to be 2 m, 4 m, 6 m, and 10 m, respectively. The beam is made from HSS 152 X 51 X 6.4 (Appendix A-9) and the longer side of the rectangle is vertical. What is the maximum normal stress (units: MPa) experienced by the beam? 2. Consider the beam and loading shown below. The beam has a total length of 12 ft. and a uniformly distributed load, w, of 125 lb./ft. The cross section of the beam is comprised of a standard steel channel (C6 X 13) which has a ½ in. plate of steel attached to its bottom. Determine the maximum normal stress in tension and compression that is experienced by this beam due to the described loading. MECET 423: Mechanics of Materials Chap. 7 HW 3. Consider the cantilever beam shown in the image below. The beam is experiencing a linearly varying distributed load with w1 = 50 lb./ft. and w2 = 10 lb./ft. The beam is to be made from ASTM A36 structural steel and is to be 8 ft. in length. Select the smallest standard schedule 40 steel pipe size (Appendix A-12) which will ensure a factor of safety of at least 3. 4. The beam shown below has been fabricated by combining two wooden boards into a T-section. The dimensions for these sizes can be found in Appendix A-4. The beam is 9 ft. in length overall and dimension L1 = 3 ft. Assume the beam is made from a wood which has an allowable bending stress of 1500 psi (in both tension and compression). What is the largest value of the force which can be applied? MECET 423: Mechanics of Materials Chap. 7 HW 5. The image below shows a hydraulic cylinder which is being utilized in a simple press-fit operation. As can be seen the cylinder is being suspended over the work piece using a cantilever beam. Note from the right view that there is a beam on either side of the cylinder. You may assume that each will be equally loaded by the cylinder. The beams are to be cut from AISI 1040 HR steel plate which has a thickness of 0.750 in. The proposed design includes the following dimensions (units: inch): H = 2.00, h = 1.00, r = 0.08, L1 = 8, and L2 = 18. Evaluate the design by calculating the resulting factor of safety with respect to the yield strength of the material at the location of the step if the total force generated by the cylinder is 1,000 lb. Also state whether or not yielding is predicted to occur. You may assume that bending in the thickness direction of the beams is negligible. 6. Consider the cantilever beam shown below. The beam has a length of 4 ft. and is made from a material whose design stress, σd, is equal to 10,000 psi. It is to carry a load of 200 lb. applied at its free end. The beam is to be designed as a beam of constant strength where the maximum normal stress experienced at each cross section is equal to the design normal stress. To achieve this the height will be held constant at 1.5 in. while the base will vary as a function of the position along the length of the beam. Determine the equation which describes the required length of the base as a function of the position along the length of the beam. For consistency, let the origin be located at point A and the positive x axis be directed toward the right. MECET 423: Mechanics of Materials Chap. 7 HW 7. Consider the overhanging beam shown in the image below. Assume that L = 5 ft. and L1 = 3 ft. The beam’s cross section is shown below. The centerline marks the horizontal centroidal axis. The moment of inertia about this axis is approx. 0.208 in4. Due to the geometry of the cross section and the material, the beam has different maximum allowable normal stresses in tension and compression. The design normal stress in tension is 24,000 psi while the design normal stress in compression is 18,000 psi. Using this data determine the maximum force, F, which can be applied to the beam.

MECET 423: Mechanics of Materials Chap. 7 HW Chap. 7 Homework Set 1. Consider the beam shown in the image below. Let F1 = 2 kN and F2 = 3 kN. Assume that points A, B and C represent pin connections and a wire rope connects points B and C. Consider the dimensions L1, L2, L3 and L4 to be 2 m, 4 m, 6 m, and 10 m, respectively. The beam is made from HSS 152 X 51 X 6.4 (Appendix A-9) and the longer side of the rectangle is vertical. What is the maximum normal stress (units: MPa) experienced by the beam? 2. Consider the beam and loading shown below. The beam has a total length of 12 ft. and a uniformly distributed load, w, of 125 lb./ft. The cross section of the beam is comprised of a standard steel channel (C6 X 13) which has a ½ in. plate of steel attached to its bottom. Determine the maximum normal stress in tension and compression that is experienced by this beam due to the described loading. MECET 423: Mechanics of Materials Chap. 7 HW 3. Consider the cantilever beam shown in the image below. The beam is experiencing a linearly varying distributed load with w1 = 50 lb./ft. and w2 = 10 lb./ft. The beam is to be made from ASTM A36 structural steel and is to be 8 ft. in length. Select the smallest standard schedule 40 steel pipe size (Appendix A-12) which will ensure a factor of safety of at least 3. 4. The beam shown below has been fabricated by combining two wooden boards into a T-section. The dimensions for these sizes can be found in Appendix A-4. The beam is 9 ft. in length overall and dimension L1 = 3 ft. Assume the beam is made from a wood which has an allowable bending stress of 1500 psi (in both tension and compression). What is the largest value of the force which can be applied? MECET 423: Mechanics of Materials Chap. 7 HW 5. The image below shows a hydraulic cylinder which is being utilized in a simple press-fit operation. As can be seen the cylinder is being suspended over the work piece using a cantilever beam. Note from the right view that there is a beam on either side of the cylinder. You may assume that each will be equally loaded by the cylinder. The beams are to be cut from AISI 1040 HR steel plate which has a thickness of 0.750 in. The proposed design includes the following dimensions (units: inch): H = 2.00, h = 1.00, r = 0.08, L1 = 8, and L2 = 18. Evaluate the design by calculating the resulting factor of safety with respect to the yield strength of the material at the location of the step if the total force generated by the cylinder is 1,000 lb. Also state whether or not yielding is predicted to occur. You may assume that bending in the thickness direction of the beams is negligible. 6. Consider the cantilever beam shown below. The beam has a length of 4 ft. and is made from a material whose design stress, σd, is equal to 10,000 psi. It is to carry a load of 200 lb. applied at its free end. The beam is to be designed as a beam of constant strength where the maximum normal stress experienced at each cross section is equal to the design normal stress. To achieve this the height will be held constant at 1.5 in. while the base will vary as a function of the position along the length of the beam. Determine the equation which describes the required length of the base as a function of the position along the length of the beam. For consistency, let the origin be located at point A and the positive x axis be directed toward the right. MECET 423: Mechanics of Materials Chap. 7 HW 7. Consider the overhanging beam shown in the image below. Assume that L = 5 ft. and L1 = 3 ft. The beam’s cross section is shown below. The centerline marks the horizontal centroidal axis. The moment of inertia about this axis is approx. 0.208 in4. Due to the geometry of the cross section and the material, the beam has different maximum allowable normal stresses in tension and compression. The design normal stress in tension is 24,000 psi while the design normal stress in compression is 18,000 psi. Using this data determine the maximum force, F, which can be applied to the beam.

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ield ENGL 2110-01 Midterm You must write an essay for each of the following prompts. Part I: Write a 1500 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Many of the readings that we have covered up to this point in the class have considered the native population that explorers encountered when they came to the “New World.” For this essay, you should examine the readings from any two of the explorers that we have encountered to this point to compare and contrast the similarities and differences between the ways that these two explorers interacted with the indigenous peoples. The thesis for this essay should make an argumentative claim as to which approach was/is more effective, and the writer should use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument the writer is making. Please note that you should avoid summarizing the texts. Instead, your focus should be on making an argument about the ways that these explorers deal with the indigenous populations. Part II: Write a 1000 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Now that you have considered how the explorers interacted with the indigenous populations that they encountered, it then becomes necessary to examine how the native population viewed the explorers. Choose one of the readings that we covered in the creation/emergence accounts from Native American authors. You will then make an argumentative claim for your thesis statement about the way that this writer presents the relationship between the indigenous peoples and the European explorers. Is this a positive relationship, according to this writer? Does the writer think this is a negative relationship? You should also use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument you are making. Please note that you should only discuss one text, and that you should avoid summarizing the text and instead focus on building and supporting an argument about the way that the author views the effect that the explorers have had or will have on the native population. Due: A typed Midterm Exam is due at the beginning of class on Wednesday, September 30th. Format: The exam should be formatted according to MLA guidelines, and it should be stapled in the upper left hand corner. It has to be from the book: The Concise Health Anthology of American Literature!!!!!!

ield ENGL 2110-01 Midterm You must write an essay for each of the following prompts. Part I: Write a 1500 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Many of the readings that we have covered up to this point in the class have considered the native population that explorers encountered when they came to the “New World.” For this essay, you should examine the readings from any two of the explorers that we have encountered to this point to compare and contrast the similarities and differences between the ways that these two explorers interacted with the indigenous peoples. The thesis for this essay should make an argumentative claim as to which approach was/is more effective, and the writer should use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument the writer is making. Please note that you should avoid summarizing the texts. Instead, your focus should be on making an argument about the ways that these explorers deal with the indigenous populations. Part II: Write a 1000 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Now that you have considered how the explorers interacted with the indigenous populations that they encountered, it then becomes necessary to examine how the native population viewed the explorers. Choose one of the readings that we covered in the creation/emergence accounts from Native American authors. You will then make an argumentative claim for your thesis statement about the way that this writer presents the relationship between the indigenous peoples and the European explorers. Is this a positive relationship, according to this writer? Does the writer think this is a negative relationship? You should also use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument you are making. Please note that you should only discuss one text, and that you should avoid summarizing the text and instead focus on building and supporting an argument about the way that the author views the effect that the explorers have had or will have on the native population. Due: A typed Midterm Exam is due at the beginning of class on Wednesday, September 30th. Format: The exam should be formatted according to MLA guidelines, and it should be stapled in the upper left hand corner. It has to be from the book: The Concise Health Anthology of American Literature!!!!!!

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MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 Homework #8 Due: Wednesday, April 8, in or before class. Note: Problems 2 (extra credit) and 3 have to be solved by hand. Problems 1 and 5 require MATLAB. The item 1(a) must be shown by hand. Problem 4 can be done either in Matlab or by hand. 1. Consider the following ODE: d y d x = ?8 y with y(0) = 3 on 0 < x < 5, (a) Calculate the largest step size required to maintain stability of the numerical solution to this equation using explicit Euler method. (b) Choose a step size two times smaller than this value. Solve the ODE with explicit Euler method using this step size. (c) Choose a step size two times larger than this value. Solve the ODE with explicit Euler method using this step size. (d) Now repeat parts (b) and (c) with implicit Euler method. (e) Plot all the solutions, including the analytical solution to this problem, on the same plot. Discuss your results. 2. Extra credit. Investigate the stability of the following numerical schemes on the example of an ODE d y d x = ? y with > 0. Show whether the scheme is conditionally or unconditionally stable. Derive the stability threshold if the scheme is conditionally stable. (a) The semi-implicit trapezoidal method: yi+1 = yi + 1 2 (f(xi; yi) + f(xi+1; yi+1)) h (b) The explicit midpoint method: yi+1 = yi + f  xi+1=2; yi + f(xi; yi) h 2  h 3. Solve Problem 25.1 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:5. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. 4. Solve Problem 25.2 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:25. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. There is a typo in this problem. The interval should be from t=0 to 1, not x=0 to 1. 5. For the following rst-order ODE d y d t = t2 ? 2 y t with y(1) = 2, the purpose will be to write MATLAB functions that solve this equation from t = 1 to t = 4 with 1 of 2 MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 (a) Third-order Runge-Kutta (page 734) (b) Fourth-order Runge-Kutta (page 735) For each method, (a) Write the MATLAB function that solves the ODE by using the number of intervals N as an input argument. (b) Solve the ODE using your MATLAB function for N equal to 8, 16, 32, 64. Calculate the step size h inside the function. (c) Calculate the EL2 errors between the true solution and the numerical solution for each N (consult HW6 for the true solution). The following plots should be presented: 1. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 8. Do not print out the values at your grid points. 2. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 32. Do not print out the values at your grid points. 3. Plot the values of EL2 errors for the methods (a), (b), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot. What do you observe? 4. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 5. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of N, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 6. Discuss whether your convergence results for each method correspond to the known order of accuracy for each method. Explain why or why not. 2 of 2

MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 Homework #8 Due: Wednesday, April 8, in or before class. Note: Problems 2 (extra credit) and 3 have to be solved by hand. Problems 1 and 5 require MATLAB. The item 1(a) must be shown by hand. Problem 4 can be done either in Matlab or by hand. 1. Consider the following ODE: d y d x = ?8 y with y(0) = 3 on 0 < x < 5, (a) Calculate the largest step size required to maintain stability of the numerical solution to this equation using explicit Euler method. (b) Choose a step size two times smaller than this value. Solve the ODE with explicit Euler method using this step size. (c) Choose a step size two times larger than this value. Solve the ODE with explicit Euler method using this step size. (d) Now repeat parts (b) and (c) with implicit Euler method. (e) Plot all the solutions, including the analytical solution to this problem, on the same plot. Discuss your results. 2. Extra credit. Investigate the stability of the following numerical schemes on the example of an ODE d y d x = ? y with > 0. Show whether the scheme is conditionally or unconditionally stable. Derive the stability threshold if the scheme is conditionally stable. (a) The semi-implicit trapezoidal method: yi+1 = yi + 1 2 (f(xi; yi) + f(xi+1; yi+1)) h (b) The explicit midpoint method: yi+1 = yi + f  xi+1=2; yi + f(xi; yi) h 2  h 3. Solve Problem 25.1 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:5. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. 4. Solve Problem 25.2 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:25. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. There is a typo in this problem. The interval should be from t=0 to 1, not x=0 to 1. 5. For the following rst-order ODE d y d t = t2 ? 2 y t with y(1) = 2, the purpose will be to write MATLAB functions that solve this equation from t = 1 to t = 4 with 1 of 2 MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 (a) Third-order Runge-Kutta (page 734) (b) Fourth-order Runge-Kutta (page 735) For each method, (a) Write the MATLAB function that solves the ODE by using the number of intervals N as an input argument. (b) Solve the ODE using your MATLAB function for N equal to 8, 16, 32, 64. Calculate the step size h inside the function. (c) Calculate the EL2 errors between the true solution and the numerical solution for each N (consult HW6 for the true solution). The following plots should be presented: 1. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 8. Do not print out the values at your grid points. 2. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 32. Do not print out the values at your grid points. 3. Plot the values of EL2 errors for the methods (a), (b), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot. What do you observe? 4. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 5. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of N, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 6. Discuss whether your convergence results for each method correspond to the known order of accuracy for each method. Explain why or why not. 2 of 2

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Chapter 8 Practice Problems (Practice – no credit) Due: 12:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Circular Launch A ball is launched up a semicircular chute in such a way that at the top of the chute, just before it goes into free fall, the ball has a centripetal acceleration of magnitude 2 . Part A How far from the bottom of the chute does the ball land? Your answer for the distance the ball travels from the end of the chute should contain . You did not open hints for this part. ANSWER: g R Normal Force and Centripetal Force Ranking Task A roller-coaster track has six semicircular “dips” with different radii of curvature. The same roller-coaster cart rides through each dip at a different speed. Part A For the different values given for the radius of curvature and speed , rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each dip. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: D = R v Two Cars on a Curving Road Part A A small car of mass and a large car of mass drive along a highway. They approach a curve of radius . Both cars maintain the same acceleration as they travel around the curve. How does the speed of the small car compare to the speed of the large car as they round the curve? You did not open hints for this part. m 4m R a vS vL ANSWER: Part B Now assume that two identical cars of mass drive along a highway. One car approaches a curve of radius at speed . The second car approaches a curve of radius at a speed of . How does the magnitude of the net force exerted on the first car compare to the magnitude of the net force exerted on the second car? You did not open hints for this part. ANSWER: ± A Ride on the Ferris Wheel A woman rides on a Ferris wheel of radius 16 that maintains the same speed throughout its motion. To better understand physics, she takes along a digital bathroom scale (with memory) and sits on it. When she gets off the ride, she uploads the scale readings to a computer and creates a graph of scale reading versus time. Note that the graph has a minimum value of 510 and a maximum value of 666 . vS = 1 4 vL vS = 1 2 vL vS = vL vS = 2vL vS = 4vL m 2R v 6R 3v F1 F2 F1 = 1 3 F2 F1 = 3 4 F2 F1 = F2 F1 = 3F2 F1 = 27F2 m N N Part A What is the woman’s mass? Express your answer in kilograms. You did not open hints for this part. ANSWER: ± Mass on Turntable A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated in the diagram . The small metal cylinder has a mass of 0.20 , the coefficient of static friction between the cylinder and the turntable is 0.080, and the cylinder is located 0.15 from the center of the turntable. Take the magnitude of the acceleration due to gravity to be 9.81 . m = kg kg m m/s2 Part A What is the maximum speed that the cylinder can move along its circular path without slipping off the turntable? Express your answer numerically in meters per second to two significant figures. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. vmax vmax = m/s

Chapter 8 Practice Problems (Practice – no credit) Due: 12:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Circular Launch A ball is launched up a semicircular chute in such a way that at the top of the chute, just before it goes into free fall, the ball has a centripetal acceleration of magnitude 2 . Part A How far from the bottom of the chute does the ball land? Your answer for the distance the ball travels from the end of the chute should contain . You did not open hints for this part. ANSWER: g R Normal Force and Centripetal Force Ranking Task A roller-coaster track has six semicircular “dips” with different radii of curvature. The same roller-coaster cart rides through each dip at a different speed. Part A For the different values given for the radius of curvature and speed , rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each dip. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: D = R v Two Cars on a Curving Road Part A A small car of mass and a large car of mass drive along a highway. They approach a curve of radius . Both cars maintain the same acceleration as they travel around the curve. How does the speed of the small car compare to the speed of the large car as they round the curve? You did not open hints for this part. m 4m R a vS vL ANSWER: Part B Now assume that two identical cars of mass drive along a highway. One car approaches a curve of radius at speed . The second car approaches a curve of radius at a speed of . How does the magnitude of the net force exerted on the first car compare to the magnitude of the net force exerted on the second car? You did not open hints for this part. ANSWER: ± A Ride on the Ferris Wheel A woman rides on a Ferris wheel of radius 16 that maintains the same speed throughout its motion. To better understand physics, she takes along a digital bathroom scale (with memory) and sits on it. When she gets off the ride, she uploads the scale readings to a computer and creates a graph of scale reading versus time. Note that the graph has a minimum value of 510 and a maximum value of 666 . vS = 1 4 vL vS = 1 2 vL vS = vL vS = 2vL vS = 4vL m 2R v 6R 3v F1 F2 F1 = 1 3 F2 F1 = 3 4 F2 F1 = F2 F1 = 3F2 F1 = 27F2 m N N Part A What is the woman’s mass? Express your answer in kilograms. You did not open hints for this part. ANSWER: ± Mass on Turntable A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated in the diagram . The small metal cylinder has a mass of 0.20 , the coefficient of static friction between the cylinder and the turntable is 0.080, and the cylinder is located 0.15 from the center of the turntable. Take the magnitude of the acceleration due to gravity to be 9.81 . m = kg kg m m/s2 Part A What is the maximum speed that the cylinder can move along its circular path without slipping off the turntable? Express your answer numerically in meters per second to two significant figures. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. vmax vmax = m/s

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Assignment 1 Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 1.6 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. ANSWER: Correct Positive Negative Negative Positive Part C Determine the sign (positive or negative) of the acceleration for the particle in the figure. ANSWER: Correct Conceptual Question 1.7 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: Positive Negative Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. ANSWER: Correct Part C Determine the sign (positive or negative) of the acceleration for the particle in the figure. ANSWER: Correct Enhanced EOC: Problem 1.18 The figure shows the motion diagram of a drag racer. The camera took one frame every 2 . Positive Negative Positive Negative Negative Positive s You may want to review ( pages 16 – 19) . For help with math skills, you may want to review: Plotting Points on a Graph Part A Make a position-versus-time graph for the drag racer. Hint 1. How to approach the problem Based on Table 1.1 in the book/e-text, what two observables are associated with each point? Which position or point of the drag racer occurs first? Which position occurs last? If you label the first point as happening at , at what time does the next point occur? At what time does the last position point occur? What is the position of a point halfway in between and ? Can you think of a way to estimate the positions of the points using a ruler? ANSWER: t = 0 s x = 0 m x = 200 m Correct Motion of Two Rockets Learning Goal: To learn to use images of an object in motion to determine velocity and acceleration. Two toy rockets are traveling in the same direction (taken to be the x axis). A diagram is shown of a time-exposure image where a stroboscope has illuminated the rockets at the uniform time intervals indicated. Part A At what time(s) do the rockets have the same velocity? Hint 1. How to determine the velocity The diagram shows position, not velocity. You can’t find instantaneous velocity from this diagram, but you can determine the average velocity between two times and : . Note that no position values are given in the diagram; you will need to estimate these based on the distance between successive positions of the rockets. ANSWER: Correct t1 t2 vavg[t1, t2] = x(t2)−x(t1) t2−t1 at time only at time only at times and at some instant in time between and at no time shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 Part B At what time(s) do the rockets have the same x position? ANSWER: Correct Part C At what time(s) do the two rockets have the same acceleration? Hint 1. How to determine the acceleration The velocity is related to the spacing between images in a stroboscopic diagram. Since acceleration is the rate at which velocity changes, the acceleration is related to the how much this spacing changes from one interval to the next. ANSWER: at time only at time only at times and at some instant in time between and at no time shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 at time only at time only at times and at some instant in time between and at no time shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 Correct Part D The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________. ANSWER: Correct Part E The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________. ANSWER: Correct Part F At what time(s) is rocket A ahead of rocket B? and nonzero acceleration velocity displacement time and nonzero acceleration velocity displacement time Hint 1. Use the diagram You can answer this question by looking at the diagram and identifying the time(s) when rocket A is to the right of rocket B. ANSWER: Correct Dimensions of Physical Quantities Learning Goal: To introduce the idea of physical dimensions and to learn how to find them. Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the same dimension–length. Part A In classical mechanics there are three base dimensions. Length is one of them. What are the other two? Hint 1. MKS system The current system of units is called the International System (abbreviated SI from the French Système International). In the past this system was called the mks system for its base units: meter, kilogram, and second. What are the dimensions of these quantities? ANSWER: before only after only before and after between and at no time(s) shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 Correct There are three dimensions used in mechanics: length ( ), mass ( ), and time ( ). A combination of these three dimensions suffices to express any physical quantity, because when a new physical quantity is needed (e.g., velocity), it always obeys an equation that permits it to be expressed in terms of the units used for these three dimensions. One then derives a unit to measure the new physical quantity from that equation, and often its unit is given a special name. Such new dimensions are called derived dimensions and the units they are measured in are called derived units. For example, area has derived dimensions . (Note that “dimensions of variable ” is symbolized as .) You can find these dimensions by looking at the formula for the area of a square , where is the length of a side of the square. Clearly . Plugging this into the equation gives . Part B Find the dimensions of volume. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for volume You have likely learned many formulas for the volume of various shapes in geometry. Any of these equations will give you the dimensions for volume. You can find the dimensions most easily from the volume of a cube , where is the length of the edge of the cube. ANSWER: acceleration and mass acceleration and time acceleration and charge mass and time mass and charge time and charge l m t A [A] = l2 x [x] A = s2 s [s] = l [A] = [s] = 2 l2 [V ] l m t V = e3 e [V ] = l3 Correct Part C Find the dimensions of speed. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for speed Speed is defined in terms of distance and time as . Therefore, . Hint 2. Familiar units for speed You are probably accustomed to hearing speeds in miles per hour (or possibly kilometers per hour). Think about the dimensions for miles and hours. If you divide the dimensions for miles by the dimensions for hours, you will have the dimensions for speed. ANSWER: Correct The dimensions of a quantity are not changed by addition or subtraction of another quantity with the same dimensions. This means that , which comes from subtracting two speeds, has the same dimensions as speed. It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time. You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert both quantities to the same set of units before you actually compute the sum. You can use this rule to check your answers to any physics problem you work. If the answer involves the sum or difference of two quantities with different dimensions, then it must be incorrect. This rule also ensures that the dimensions of any physical quantity will never involve sums or differences of the base dimensions. (As in the preceeding example, is not a valid dimension for a [v] l m t v d t v = d t [v] = [d]/[t] [v] = lt−1 v l + t physical quantitiy.) A valid dimension will only involve the product or ratio of powers of the base dimensions (e.g. ). Part D Find the dimensions of acceleration. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for acceleration In physics, acceleration is defined as the change in velocity in a certain time. This is shown by the equation . The is a symbol that means “the change in.” ANSWER: Correct Consistency of Units In physics, every physical quantity is measured with respect to a unit. Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. Knowing the units of physical quantities will help you solve problems in physics. Part A Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The force of gravitational attraction is represented by the equation , where is the magnitude of the gravitational attraction on either body, and are the masses of the bodies, is the distance between them, and is the gravitational constant. In SI units, the units of force are , the units of mass are , and the units of distance are . For this equation to have consistent units, the units of must be which of the following? Hint 1. How to approach the problem To solve this problem, we start with the equation m2/3 l2 t−2 [a] l m t a a = v/t  [a] = lt−2 F = Gm1m2 r2 F m1 m2 r G kg  m/s2 kg m G . For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for . ANSWER: Correct Part B One consequence of Einstein’s theory of special relativity is that mass is a form of energy. This mass-energy relationship is perhaps the most famous of all physics equations: , where is mass, is the speed of the light, and is the energy. In SI units, the units of speed are . For the preceding equation to have consistent units (the same units on both sides of the equation), the units of must be which of the following? Hint 1. How to approach the problem To solve this problem, we start with the equation . For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for . ANSWER: F = Gm1m2 r2 m1 kg G kg3 ms2 kgs2 m3 m3 kgs2 m kgs2 E = mc2 m c E m/s E E = mc2 m kg E Correct To solve the types of problems typified by these examples, we start with the given equation. For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for the units of the unknown variable. Problem 1.24 Convert the following to SI units: Part A 5.0 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B 54 Express your answer to two significant figures and include the appropriate units. kgm s kgm2 s2 kgs2 m2 kgm2 s m kg in 0.13 m ft/s ANSWER: Correct Part C 72 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D 17 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 1.55 The figure shows a motion diagram of a car traveling down a street. The camera took one frame every 10 . A distance scale is provided. 16 ms mph 32 ms in2 1.1×10−2 m2 s Part A Make a position-versus-time graph for the car. ANSWER: Incorrect; Try Again ± Moving at the Speed of Light Part A How many nanoseconds does it take light to travel a distance of 4.40 in vacuum? Express your answer numerically in nanoseconds. Hint 1. How to approach the problem Light travels at a constant speed; therefore, you can use the formula for the distance traveled in a certain amount of time by an object moving at constant speed. Before performing any calculations, it is often recommended, although it is not strictly necessary, to convert all quantities to their fundamental units rather than to multiples of the fundamental unit. km Hint 2. Find how many seconds it takes light to travel the given distance Given that the speed of light in vacuum is , how many seconds does it take light to travel a distance of 4.40 ? Express your answer numerically in seconds. Hint 1. Find the time it takes light to travel a certain distance How long does it take light to travel a distance ? Let be the speed of light. Hint 1. The speed of an object The equation that relates the distance traveled by an object with constant speed in a time is . ANSWER: Correct Hint 2. Convert the given distance to meters Convert = 4.40 to meters. Express your answer numerically in meters. Hint 1. Conversion of kilometers to meters Recall that . 3.00 × 108 m/s km r c s v t s = vt r  c r c c r d km 1 km = 103 m ANSWER: Correct ANSWER: Correct Now convert the time into nanoseconds. Recall that . ANSWER: Correct Score Summary: Your score on this assignment is 84.7%. You received 50.84 out of a possible total of 60 points. 4.40km = 4400 m 1.47×10−5 s 1 ns = 10−9 s 1.47×104 ns

Assignment 1 Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 1.6 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. ANSWER: Correct Positive Negative Negative Positive Part C Determine the sign (positive or negative) of the acceleration for the particle in the figure. ANSWER: Correct Conceptual Question 1.7 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: Positive Negative Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. ANSWER: Correct Part C Determine the sign (positive or negative) of the acceleration for the particle in the figure. ANSWER: Correct Enhanced EOC: Problem 1.18 The figure shows the motion diagram of a drag racer. The camera took one frame every 2 . Positive Negative Positive Negative Negative Positive s You may want to review ( pages 16 – 19) . For help with math skills, you may want to review: Plotting Points on a Graph Part A Make a position-versus-time graph for the drag racer. Hint 1. How to approach the problem Based on Table 1.1 in the book/e-text, what two observables are associated with each point? Which position or point of the drag racer occurs first? Which position occurs last? If you label the first point as happening at , at what time does the next point occur? At what time does the last position point occur? What is the position of a point halfway in between and ? Can you think of a way to estimate the positions of the points using a ruler? ANSWER: t = 0 s x = 0 m x = 200 m Correct Motion of Two Rockets Learning Goal: To learn to use images of an object in motion to determine velocity and acceleration. Two toy rockets are traveling in the same direction (taken to be the x axis). A diagram is shown of a time-exposure image where a stroboscope has illuminated the rockets at the uniform time intervals indicated. Part A At what time(s) do the rockets have the same velocity? Hint 1. How to determine the velocity The diagram shows position, not velocity. You can’t find instantaneous velocity from this diagram, but you can determine the average velocity between two times and : . Note that no position values are given in the diagram; you will need to estimate these based on the distance between successive positions of the rockets. ANSWER: Correct t1 t2 vavg[t1, t2] = x(t2)−x(t1) t2−t1 at time only at time only at times and at some instant in time between and at no time shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 Part B At what time(s) do the rockets have the same x position? ANSWER: Correct Part C At what time(s) do the two rockets have the same acceleration? Hint 1. How to determine the acceleration The velocity is related to the spacing between images in a stroboscopic diagram. Since acceleration is the rate at which velocity changes, the acceleration is related to the how much this spacing changes from one interval to the next. ANSWER: at time only at time only at times and at some instant in time between and at no time shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 at time only at time only at times and at some instant in time between and at no time shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 Correct Part D The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________. ANSWER: Correct Part E The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________. ANSWER: Correct Part F At what time(s) is rocket A ahead of rocket B? and nonzero acceleration velocity displacement time and nonzero acceleration velocity displacement time Hint 1. Use the diagram You can answer this question by looking at the diagram and identifying the time(s) when rocket A is to the right of rocket B. ANSWER: Correct Dimensions of Physical Quantities Learning Goal: To introduce the idea of physical dimensions and to learn how to find them. Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the same dimension–length. Part A In classical mechanics there are three base dimensions. Length is one of them. What are the other two? Hint 1. MKS system The current system of units is called the International System (abbreviated SI from the French Système International). In the past this system was called the mks system for its base units: meter, kilogram, and second. What are the dimensions of these quantities? ANSWER: before only after only before and after between and at no time(s) shown in the figure t = 1 t = 4 t = 1 t = 4 t = 1 t = 4 Correct There are three dimensions used in mechanics: length ( ), mass ( ), and time ( ). A combination of these three dimensions suffices to express any physical quantity, because when a new physical quantity is needed (e.g., velocity), it always obeys an equation that permits it to be expressed in terms of the units used for these three dimensions. One then derives a unit to measure the new physical quantity from that equation, and often its unit is given a special name. Such new dimensions are called derived dimensions and the units they are measured in are called derived units. For example, area has derived dimensions . (Note that “dimensions of variable ” is symbolized as .) You can find these dimensions by looking at the formula for the area of a square , where is the length of a side of the square. Clearly . Plugging this into the equation gives . Part B Find the dimensions of volume. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for volume You have likely learned many formulas for the volume of various shapes in geometry. Any of these equations will give you the dimensions for volume. You can find the dimensions most easily from the volume of a cube , where is the length of the edge of the cube. ANSWER: acceleration and mass acceleration and time acceleration and charge mass and time mass and charge time and charge l m t A [A] = l2 x [x] A = s2 s [s] = l [A] = [s] = 2 l2 [V ] l m t V = e3 e [V ] = l3 Correct Part C Find the dimensions of speed. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for speed Speed is defined in terms of distance and time as . Therefore, . Hint 2. Familiar units for speed You are probably accustomed to hearing speeds in miles per hour (or possibly kilometers per hour). Think about the dimensions for miles and hours. If you divide the dimensions for miles by the dimensions for hours, you will have the dimensions for speed. ANSWER: Correct The dimensions of a quantity are not changed by addition or subtraction of another quantity with the same dimensions. This means that , which comes from subtracting two speeds, has the same dimensions as speed. It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time. You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert both quantities to the same set of units before you actually compute the sum. You can use this rule to check your answers to any physics problem you work. If the answer involves the sum or difference of two quantities with different dimensions, then it must be incorrect. This rule also ensures that the dimensions of any physical quantity will never involve sums or differences of the base dimensions. (As in the preceeding example, is not a valid dimension for a [v] l m t v d t v = d t [v] = [d]/[t] [v] = lt−1 v l + t physical quantitiy.) A valid dimension will only involve the product or ratio of powers of the base dimensions (e.g. ). Part D Find the dimensions of acceleration. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for acceleration In physics, acceleration is defined as the change in velocity in a certain time. This is shown by the equation . The is a symbol that means “the change in.” ANSWER: Correct Consistency of Units In physics, every physical quantity is measured with respect to a unit. Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. Knowing the units of physical quantities will help you solve problems in physics. Part A Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The force of gravitational attraction is represented by the equation , where is the magnitude of the gravitational attraction on either body, and are the masses of the bodies, is the distance between them, and is the gravitational constant. In SI units, the units of force are , the units of mass are , and the units of distance are . For this equation to have consistent units, the units of must be which of the following? Hint 1. How to approach the problem To solve this problem, we start with the equation m2/3 l2 t−2 [a] l m t a a = v/t  [a] = lt−2 F = Gm1m2 r2 F m1 m2 r G kg  m/s2 kg m G . For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for . ANSWER: Correct Part B One consequence of Einstein’s theory of special relativity is that mass is a form of energy. This mass-energy relationship is perhaps the most famous of all physics equations: , where is mass, is the speed of the light, and is the energy. In SI units, the units of speed are . For the preceding equation to have consistent units (the same units on both sides of the equation), the units of must be which of the following? Hint 1. How to approach the problem To solve this problem, we start with the equation . For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for . ANSWER: F = Gm1m2 r2 m1 kg G kg3 ms2 kgs2 m3 m3 kgs2 m kgs2 E = mc2 m c E m/s E E = mc2 m kg E Correct To solve the types of problems typified by these examples, we start with the given equation. For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for the units of the unknown variable. Problem 1.24 Convert the following to SI units: Part A 5.0 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B 54 Express your answer to two significant figures and include the appropriate units. kgm s kgm2 s2 kgs2 m2 kgm2 s m kg in 0.13 m ft/s ANSWER: Correct Part C 72 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D 17 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 1.55 The figure shows a motion diagram of a car traveling down a street. The camera took one frame every 10 . A distance scale is provided. 16 ms mph 32 ms in2 1.1×10−2 m2 s Part A Make a position-versus-time graph for the car. ANSWER: Incorrect; Try Again ± Moving at the Speed of Light Part A How many nanoseconds does it take light to travel a distance of 4.40 in vacuum? Express your answer numerically in nanoseconds. Hint 1. How to approach the problem Light travels at a constant speed; therefore, you can use the formula for the distance traveled in a certain amount of time by an object moving at constant speed. Before performing any calculations, it is often recommended, although it is not strictly necessary, to convert all quantities to their fundamental units rather than to multiples of the fundamental unit. km Hint 2. Find how many seconds it takes light to travel the given distance Given that the speed of light in vacuum is , how many seconds does it take light to travel a distance of 4.40 ? Express your answer numerically in seconds. Hint 1. Find the time it takes light to travel a certain distance How long does it take light to travel a distance ? Let be the speed of light. Hint 1. The speed of an object The equation that relates the distance traveled by an object with constant speed in a time is . ANSWER: Correct Hint 2. Convert the given distance to meters Convert = 4.40 to meters. Express your answer numerically in meters. Hint 1. Conversion of kilometers to meters Recall that . 3.00 × 108 m/s km r c s v t s = vt r  c r c c r d km 1 km = 103 m ANSWER: Correct ANSWER: Correct Now convert the time into nanoseconds. Recall that . ANSWER: Correct Score Summary: Your score on this assignment is 84.7%. You received 50.84 out of a possible total of 60 points. 4.40km = 4400 m 1.47×10−5 s 1 ns = 10−9 s 1.47×104 ns

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Prepare a five page (minimum) paper along with a cover page, a summary (as noted below) and reference page, on a Landmark Supreme Court Case that dealt with Aboriginal rights in Canada within the past 25 years (e.g. choose from those covered in Oct. 22rd class or another one if you find one that was not addressed but fits the criteria of a Supreme Court case that dealt with Aboriginal rights in Canada within the past 25 years). You can complete the assignment as a written paper (1.5 space/12 point font Times New Roman x 4 pages) or you can use points. In either method, provide a detailed response to each of the questions listed below. In addition to the paper that you will submit for grading, prepare a one page summary/cover page that you will present in class on November 12th and share with the other ANIS3006 students (handout, there are 18 students registered in the course). Frame your paper within the context of the following quotes: “Even when we win we lose.” (Chief Dean Sayers, Batchewana First Nation, commenting on Anishinabe experience in Canadian courts). “For the master’s tools will never dismantle the master’s house. They may allow us to temporarily beat him at his own game, but they will never enable us to bring about genuine change. Racism and homophobia are real conditions of all our lives in this place and time. I urge each one of us here to reach down into that deep place of knowledge inside herself [himself] and touch that terror and loathing of any difference that lives here. See whose face it wears. Then the personal as the political can begin to illuminate all our choices.” (Audre Lorde, feminist) In your paper, answer this broader question: How has the case you’ve selected served to advance Anishinabe rights in Canada? Describe what was gained and consider at what cost (“Even when we win, we lose.”) Address the following, and add anything that you find significant about the case, its process, its outcome and subsequent impact: • What was the basis of the court case? • What happened (e.g. Anishinabe people charged, by who, what charge)? • Who took the issue to court (who was the claimant, against who)? • What was the basis of the claim (be specific)? How was the issue framed/presented? • Who supported the court case (locally, regionally, nationally)? How did they support it? What was the impact of their support (e.g. political, financial, public awareness, protests, etc.)? • How long did it take from initiating the claim to decision (specific dates, chronology)? • What happened? What was the lower court’s decision? How did the case move through to the Supreme Court? What was the final Supreme Court decisions? • What did the Supreme Court’s decision mean in terms of Aboriginal rights in Canada? (What was gained, what was lost)? • Anything else of note relating to the case, its process or outcome. • Answer if and how the Supreme Court decision formed the basis for changes in Canadian government policies or practice concerning Aboriginal Peoples in Canada. In other words, what has the outcome of the Supreme Court decision been to date?

Prepare a five page (minimum) paper along with a cover page, a summary (as noted below) and reference page, on a Landmark Supreme Court Case that dealt with Aboriginal rights in Canada within the past 25 years (e.g. choose from those covered in Oct. 22rd class or another one if you find one that was not addressed but fits the criteria of a Supreme Court case that dealt with Aboriginal rights in Canada within the past 25 years). You can complete the assignment as a written paper (1.5 space/12 point font Times New Roman x 4 pages) or you can use points. In either method, provide a detailed response to each of the questions listed below. In addition to the paper that you will submit for grading, prepare a one page summary/cover page that you will present in class on November 12th and share with the other ANIS3006 students (handout, there are 18 students registered in the course). Frame your paper within the context of the following quotes: “Even when we win we lose.” (Chief Dean Sayers, Batchewana First Nation, commenting on Anishinabe experience in Canadian courts). “For the master’s tools will never dismantle the master’s house. They may allow us to temporarily beat him at his own game, but they will never enable us to bring about genuine change. Racism and homophobia are real conditions of all our lives in this place and time. I urge each one of us here to reach down into that deep place of knowledge inside herself [himself] and touch that terror and loathing of any difference that lives here. See whose face it wears. Then the personal as the political can begin to illuminate all our choices.” (Audre Lorde, feminist) In your paper, answer this broader question: How has the case you’ve selected served to advance Anishinabe rights in Canada? Describe what was gained and consider at what cost (“Even when we win, we lose.”) Address the following, and add anything that you find significant about the case, its process, its outcome and subsequent impact: • What was the basis of the court case? • What happened (e.g. Anishinabe people charged, by who, what charge)? • Who took the issue to court (who was the claimant, against who)? • What was the basis of the claim (be specific)? How was the issue framed/presented? • Who supported the court case (locally, regionally, nationally)? How did they support it? What was the impact of their support (e.g. political, financial, public awareness, protests, etc.)? • How long did it take from initiating the claim to decision (specific dates, chronology)? • What happened? What was the lower court’s decision? How did the case move through to the Supreme Court? What was the final Supreme Court decisions? • What did the Supreme Court’s decision mean in terms of Aboriginal rights in Canada? (What was gained, what was lost)? • Anything else of note relating to the case, its process or outcome. • Answer if and how the Supreme Court decision formed the basis for changes in Canadian government policies or practice concerning Aboriginal Peoples in Canada. In other words, what has the outcome of the Supreme Court decision been to date?

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GLG 110: Dangerous World Assignment #2: Landslides Part 1: Disasters in the News On March 22nd 2014, a large landslide occurred near Oso, Washington. As of July 23rd, 2014, all remains had been recovered and the death toll stood at 43 people. Lots of information about the landslide can be found on the American Geophysical Union’s Landslide blog. Read about the landslide here (don’t worry, each entry is quite short): http://blogs.agu.org/landslideblog/2014/03/23/oso-landslide-1/ http://blogs.agu.org/landslideblog/2014/03/24/oso-landslip-useful-resources/ http://blogs.agu.org/landslideblog/2014/03/25/the-steelhead-landslide-1/ http://blogs.agu.org/landslideblog/2014/03/28/oso-mechanisms-1/ http://blogs.agu.org/landslideblog/2014/04/02/steelhead-landslide-in-washington/ Answer the following questions: 1) Describe the factors that led to this landslide: What type of material was involved- how cohesive/prone to failure is it? Was the cause primarily due to a change in slope, a change in friction/cohesion, or addition of mass? What was this cause? 2) Was the cause of this slide natural, man-made, or a combination of both? 3) Discuss the hazard assessment/mitigation efforts in effect before the slide. What evidence in the surrounding geology/geography suggests an existing landslide hazard? Was anything being to done to reduce the risk of a damaging landslide? For questions 4 & 5, use the photo of the Oso Landslide below: 4) What type of slide do you think this is (rotational or translational)? What visual evidence in the photo above supports your choice? 5) On the image above and using diagrams from the lecture and your textbook, label the different parts of the slide. Terms you can include, but are not limited to, are: scarp, original surface, toe, head, foot. 6) When the failed material entered the river, it created another type of mass movement; what is this mass movement and why did it make the slide more damaging? Part 2: A little physics (it is a science class after all) We discussed in class how whether or not a slope will fail is based on the balance of gravitational vs. frictional forces using the following diagram and equations: For simplicity, we will ignore FR, the force of the base of the slope supporting the upper slope. In the case shown above, for the slope to be stable, the frictional resistance force, Ff, must be larger than the gravitational force acting down the slope, Fll: Fll < Ff 7) For a slope with angle θ = 30o and coefficient of friction μ = 0.6, is the slope stable? Please show your work, partial credit will be given. Please put a box around your answer. 8) For a slope with θ = 15o, for what values of μ will the slope be unstable? In other words, at what value of μ does, Fll = Ff, such that any decrease in μ will result in a slope failure? Please show your work, partial credit will be given. Please put a box around your answer. 9) For a slope where the cohesion of the vegetation and soil leads to a coefficient of friction of μ = 0.75, above what slope angle θ will the slope fail? Note: please answer in degrees, not radians. Please show your work, partial credit will be given. Please put a box around your answer. 10) Describe why the mass of a potential slide, in the slope force balance used above, does not affect whether or not the slope will fail.

GLG 110: Dangerous World Assignment #2: Landslides Part 1: Disasters in the News On March 22nd 2014, a large landslide occurred near Oso, Washington. As of July 23rd, 2014, all remains had been recovered and the death toll stood at 43 people. Lots of information about the landslide can be found on the American Geophysical Union’s Landslide blog. Read about the landslide here (don’t worry, each entry is quite short): http://blogs.agu.org/landslideblog/2014/03/23/oso-landslide-1/ http://blogs.agu.org/landslideblog/2014/03/24/oso-landslip-useful-resources/ http://blogs.agu.org/landslideblog/2014/03/25/the-steelhead-landslide-1/ http://blogs.agu.org/landslideblog/2014/03/28/oso-mechanisms-1/ http://blogs.agu.org/landslideblog/2014/04/02/steelhead-landslide-in-washington/ Answer the following questions: 1) Describe the factors that led to this landslide: What type of material was involved- how cohesive/prone to failure is it? Was the cause primarily due to a change in slope, a change in friction/cohesion, or addition of mass? What was this cause? 2) Was the cause of this slide natural, man-made, or a combination of both? 3) Discuss the hazard assessment/mitigation efforts in effect before the slide. What evidence in the surrounding geology/geography suggests an existing landslide hazard? Was anything being to done to reduce the risk of a damaging landslide? For questions 4 & 5, use the photo of the Oso Landslide below: 4) What type of slide do you think this is (rotational or translational)? What visual evidence in the photo above supports your choice? 5) On the image above and using diagrams from the lecture and your textbook, label the different parts of the slide. Terms you can include, but are not limited to, are: scarp, original surface, toe, head, foot. 6) When the failed material entered the river, it created another type of mass movement; what is this mass movement and why did it make the slide more damaging? Part 2: A little physics (it is a science class after all) We discussed in class how whether or not a slope will fail is based on the balance of gravitational vs. frictional forces using the following diagram and equations: For simplicity, we will ignore FR, the force of the base of the slope supporting the upper slope. In the case shown above, for the slope to be stable, the frictional resistance force, Ff, must be larger than the gravitational force acting down the slope, Fll: Fll < Ff 7) For a slope with angle θ = 30o and coefficient of friction μ = 0.6, is the slope stable? Please show your work, partial credit will be given. Please put a box around your answer. 8) For a slope with θ = 15o, for what values of μ will the slope be unstable? In other words, at what value of μ does, Fll = Ff, such that any decrease in μ will result in a slope failure? Please show your work, partial credit will be given. Please put a box around your answer. 9) For a slope where the cohesion of the vegetation and soil leads to a coefficient of friction of μ = 0.75, above what slope angle θ will the slope fail? Note: please answer in degrees, not radians. Please show your work, partial credit will be given. Please put a box around your answer. 10) Describe why the mass of a potential slide, in the slope force balance used above, does not affect whether or not the slope will fail.

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

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

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