A transformer has 300 turns in the primary coil and 50 turns in the secondary coil. If the RMS voltage in the primary is coil is 120 volts, find the power lost in the 20 Ohm resistor. 1) 0.5 watts 2) 1watts 3) 5 watts 4) 10 watts 5) 20 watts.

A transformer has 300 turns in the primary coil and 50 turns in the secondary coil. If the RMS voltage in the primary is coil is 120 volts, find the power lost in the 20 Ohm resistor. 1) 0.5 watts 2) 1watts 3) 5 watts 4) 10 watts 5) 20 watts.

   
On January 1, 2014, Rowley Company purchased a truck that cost $22,000. The truck had an expected useful life of 5 years and a $4,000 salvage value. The amount of depreciation expense recognized in 2014 assuming that Rowley uses the double declining balance method is:

On January 1, 2014, Rowley Company purchased a truck that cost $22,000. The truck had an expected useful life of 5 years and a $4,000 salvage value. The amount of depreciation expense recognized in 2014 assuming that Rowley uses the double declining balance method is:

Question 39   On January 1, 2014, Rowley Company purchased … Read More...
1 CEE 240 / MIE 210 Statics NAME: [Final] Exam #3 Version A — 100 points (120 minutes) SHOW YOUR WORK USING THE COURSE PROBLEM SOLVING GUIDELINES! CALCULATORS ONLY – NO OTHER REFERENCES! 1. (25 points) An underwater instrument is modeled as shown in the figure. Determine the coordinates of the centroid of this composite volume. Note: the mass center of a sphere = 4 π r3/3. No FBD is required for this problem. 2 2. (25 points) Determine the range of weights W for which the 100-lb block is in equilibrium. All wheels and pulleys have negligible friction. 3 3. (25 points) Determine the force in each member of the loaded truss. 4 4. (25 points) The 480-lb V-8 engine is supported on an engine stand and rotated 90o from its upright position so that its center of gravity G is in the position shown. Determine the vertical reaction at each roller of the stand. Neglect the weight of the stand itself. 5 BONUS. (5 points) The cargo box of the food-delivery truck for aircraft servicing has a loaded mass m and is elevated by the application of a torque M on the lower end of the link which is hinged to the truck frame. The horizontal slots allow the linkage to unfold as the cargo box is elevated. Express M as a function of h.

1 CEE 240 / MIE 210 Statics NAME: [Final] Exam #3 Version A — 100 points (120 minutes) SHOW YOUR WORK USING THE COURSE PROBLEM SOLVING GUIDELINES! CALCULATORS ONLY – NO OTHER REFERENCES! 1. (25 points) An underwater instrument is modeled as shown in the figure. Determine the coordinates of the centroid of this composite volume. Note: the mass center of a sphere = 4 π r3/3. No FBD is required for this problem. 2 2. (25 points) Determine the range of weights W for which the 100-lb block is in equilibrium. All wheels and pulleys have negligible friction. 3 3. (25 points) Determine the force in each member of the loaded truss. 4 4. (25 points) The 480-lb V-8 engine is supported on an engine stand and rotated 90o from its upright position so that its center of gravity G is in the position shown. Determine the vertical reaction at each roller of the stand. Neglect the weight of the stand itself. 5 BONUS. (5 points) The cargo box of the food-delivery truck for aircraft servicing has a loaded mass m and is elevated by the application of a torque M on the lower end of the link which is hinged to the truck frame. The horizontal slots allow the linkage to unfold as the cargo box is elevated. Express M as a function of h.

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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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Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

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Problem 5: Physical Fitness versus Weight. You may have noticed from your analysis in Problem 4 that height does not explain 100% of the variation that we have observed in students’ heights. Is it possible that the amount of time students devote to physical fitness each week may help us to better understand their weights? a. Question 12 of the survey asked students, “About how much time per week (on average) do you devote to physical fitness?” We have named this variable FITNESS. Create a suitable graph to display the distribution of FITNESS and insert it here. b. What is the mode of this distribution? (Please underline one option.) Between 0 & 2 hours Between 2 & 5 hours Between 5 & 9 hours Between 9 & 15 hours Over 15 hours c. Create side-by-side boxplots to display students’ weights for the different levels of FITNESS. (Go to Graph > Boxplot > One Y with Groups > OK. Select WEIGHT for the “Graph variables” slot and FITNESS for the “Categorical variables for grouping” slot.) Insert your graph here. d. Use Minitab to calculate the basic statistics of WEIGHT for each level of FITNESS. Copy and paste the output here. e. With regard to FITNESS levels, which group of students has the lowest mean weight? (Please underline one option.) Between 0 & 2 hours Between 2 & 5 hours Between 5 & 9 hours Between 9 & 15 hours Over 15 hours f. Discuss the results: Describe the distributions of WEIGHT for the different levels of FITNESS as well as draw comparisons (i.e., What do they have in common?) and contrasts (i.e., How are they different?) between these distributions. Are there any surprises in the results? Explain why you think so, or why not. Problem 6 (Even): If your E number ends in an even number (0, 2, 4, 6, or 8) then do this question. (Omit this page/problem if your E# ends with an odd number.) Gender and Nuclear Safety. Question 5 in the survey asked students “How safe would you feel if a nuclear energy plant were built near where you live?” (Students could choose one of these options: Extremely safe, Very Safe, Moderately safe, Slightly safe, or Not at all safe.) Is there a relationship between gender and students’ opinions about nuclear safety? a. Create an appropriate graph to display the relationship between GENDER and NUCLEAR SAFETY. You don’t want to display information for students that didn’t answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside “Include missing as a group” and “Include empty cells.” Insert your graph here. b. Create an appropriate two-way table to summarize the data. Click on Options > Display missing values for… and put a dot in the circle beside “No variables.” Insert your table here. c. SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.) i. What is the probability that this student is a female and feels “very safe”? P = ii. What is the probability that this student is either a male or that he/she feels “very safe”? P = iii. What is the probability that this student feels “not at all safe” given that the student selected is a female? P = iv. What is the probability that this student is a male given that the student selected feels “not at all safe”? P = d. Do you think there may be an association between GENDER and NUCLEAR SAFETY? Why or why not? Explain your reasoning based on what you see in your graph.

Problem 5: Physical Fitness versus Weight. You may have noticed from your analysis in Problem 4 that height does not explain 100% of the variation that we have observed in students’ heights. Is it possible that the amount of time students devote to physical fitness each week may help us to better understand their weights? a. Question 12 of the survey asked students, “About how much time per week (on average) do you devote to physical fitness?” We have named this variable FITNESS. Create a suitable graph to display the distribution of FITNESS and insert it here. b. What is the mode of this distribution? (Please underline one option.) Between 0 & 2 hours Between 2 & 5 hours Between 5 & 9 hours Between 9 & 15 hours Over 15 hours c. Create side-by-side boxplots to display students’ weights for the different levels of FITNESS. (Go to Graph > Boxplot > One Y with Groups > OK. Select WEIGHT for the “Graph variables” slot and FITNESS for the “Categorical variables for grouping” slot.) Insert your graph here. d. Use Minitab to calculate the basic statistics of WEIGHT for each level of FITNESS. Copy and paste the output here. e. With regard to FITNESS levels, which group of students has the lowest mean weight? (Please underline one option.) Between 0 & 2 hours Between 2 & 5 hours Between 5 & 9 hours Between 9 & 15 hours Over 15 hours f. Discuss the results: Describe the distributions of WEIGHT for the different levels of FITNESS as well as draw comparisons (i.e., What do they have in common?) and contrasts (i.e., How are they different?) between these distributions. Are there any surprises in the results? Explain why you think so, or why not. Problem 6 (Even): If your E number ends in an even number (0, 2, 4, 6, or 8) then do this question. (Omit this page/problem if your E# ends with an odd number.) Gender and Nuclear Safety. Question 5 in the survey asked students “How safe would you feel if a nuclear energy plant were built near where you live?” (Students could choose one of these options: Extremely safe, Very Safe, Moderately safe, Slightly safe, or Not at all safe.) Is there a relationship between gender and students’ opinions about nuclear safety? a. Create an appropriate graph to display the relationship between GENDER and NUCLEAR SAFETY. You don’t want to display information for students that didn’t answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside “Include missing as a group” and “Include empty cells.” Insert your graph here. b. Create an appropriate two-way table to summarize the data. Click on Options > Display missing values for… and put a dot in the circle beside “No variables.” Insert your table here. c. SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.) i. What is the probability that this student is a female and feels “very safe”? P = ii. What is the probability that this student is either a male or that he/she feels “very safe”? P = iii. What is the probability that this student feels “not at all safe” given that the student selected is a female? P = iv. What is the probability that this student is a male given that the student selected feels “not at all safe”? P = d. Do you think there may be an association between GENDER and NUCLEAR SAFETY? Why or why not? Explain your reasoning based on what you see in your graph.

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A small object of mass m starts from rest at the position shown and slide along the frictionless loop-the-loop track of radius R. what is the smallest value of y such that object will slide without losing contact with the track ? (1) R/2, (2) R/4, (3) R, (4) 2R, (5) zero

A small object of mass m starts from rest at the position shown and slide along the frictionless loop-the-loop track of radius R. what is the smallest value of y such that object will slide without losing contact with the track ? (1) R/2, (2) R/4, (3) R, (4) 2R, (5) zero

In Figure 14.1, which structure is the primary site for digestion and absorption of food? Select one: a. 1 b. 2 c. 3 d. 4 e. 5

In Figure 14.1, which structure is the primary site for digestion and absorption of food? Select one: a. 1 b. 2 c. 3 d. 4 e. 5

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