X-Men Exam: This Engineering Professor Tested His Students on Weapon X
Did you ever have a teacher that just knew how to make learning fun? Some teachers are great at improvising, going off the textbook and making the classroom feel more current, and less like it's a place where abstract concepts are slowly drilled into students' minds.
One professor at the University of Southern Maine in the U.S. recently did just that by testing his students on concepts such as bonding, crystal structures, solid imperfections, and diffusion via the Marvel Universe and X-Men.
Ph.D. Assistant Professor of Mechanical Engineering, Asheesh Lanba, shared his creative exam with us, which you can see below.
When Asheesh Lanba's students opened their exam papers, they were greeted with the following summary:
Marvel Comics fans will recognize Weapon X as the codename for the government genetic research facility responsible for injecting metal into individuals in order to turn them into weapons.
X-Men's Wolverine has this facility to thank for his abilities, though the character suffered from the traumatic events that occurred there.
Any Mechanical Engineers, or mere mortals, who want to test their mettle can have a look at the questions below.
Question 1. [10 points]
Prior to manufacture, you realize that Fe and Vi would form a passivation layer on the surface of Adamantium upon oxidation with Oxygen (O), with the oxides FeO and ViO2. There is a concern amongst your supervisors that the layer might be too hard (brittle) for practical purposes.
You recall that in general, ionic compounds are harder and more brittle than covalent compounds, and decide to quantify the percent ionic character of the bonding. Find the percent ionic character of the interatomic bonds for FeO and ViO2. Assume that Vi has the same electronegativity as Ti.
Question 2. [10 points]
Via X-ray crystallography, you discover that Vi in its native state has a face-centered cubic crystal structure and that this tight packing makes for a more dense, stronger metal. Your supervisor is not familiar with crystals structures in general and asks you to do some calculations. For the FCC crystal structure, show the atomic packing factor for FCC is 0.74.
Question 3. [10 points]
For Adamantium, determine if you would expect the alloy to exhibit complete solid solubility for system Fe-Vi. Explain your answer.
Question 4. [15 points]
Before manufacturing the alloy, you want to figure out some material properties, one of them being the density.
For the first pass of tests, you do not use carbon so as to better understand the Fe-Vi binary alloy system in Adamantium. You plan to use 85 wt% Fe and 15 wt% Vi. The atomic weight of Fe is 55.845 g/mol and of Vi is 48.948 g/mol. From the literature on Fe-Ti alloys, you find that the alloy is likely going to be BCC (you will have to recall or derive the number of atoms in a BCC unit cell). Assume a unit cell edge length of 0.312 nm, also found from literature.
Unfortunately, you cannot measure the density of Fe and Vi in order to find the average density. Find the theoretical density of the alloy with this composition with the information you have in g/cm3.
Question 5. [20 points]
You are tasked with establishing the temperature-diffusion relationship for Vi in Fe. You find that
Determine the values of D0 and the activation energy Qd, and write out the exponential relationship between the diffusion coefficient D and the temperature T.
You manufacture a cast polycrystalline alloy of 85 wt% Fe and 15 wt% Vi, and you make a cylindrical specimen with a diameter of 10 mm. You perform a tensile test on it till failure. You assume that the Poisson’s ratio for the alloy is 0.3.
(a) [10 points] You make the mistake of not measuring the longitudinal strain during the test, but accurately measure the elastic reduction in diameter of 1.8 10-4 mm at an applied load of 1000 N. Compute the modulus of elasticity for this alloy.
(b) [5 points] Your supervisor wants you to do an additional test in torsion to determine the elastic shear modulus of the alloy. You remember that the cast alloy is isotropic, and realize that you do not need another test. What is the shear modulus?
(c) [20 points] From the onset of plastic deformation on to necking, you want to establish the exponential relationship between the true stress and true strain. You find from your calculations that the engineering stress at two points on this portion of the curve are 550 and 600 MPa, and the respective engineering strains are 0.045 and 0.05. Find the K and n constants (with units) in the true stress and true strain relationship, and explicitly write out the equation of the relationship.
Thankfully, Professor Asheesh Lanba also provided the answers to the exam, which you can see below. If you took the test, be sure to add up your marks and let us know what you got!
A real-life Professor Xavier?
"The students' response was good!" Professor Asheesh Lanba told Interesting Engineering via email when we asked him how his students reacted to being tested as engineers for a top-secret government mutant project.
Lanba said that students took pictures of the exam as a memento and that one student had a long conversation with him about the Marvel Universe after the exam. Pop culture and comic books really are the mythology of our age.
Does Professor Lanba have any ideas for other comic-themed exams in the future?
"I do plan to write more comic or fantasy-based exams!" he tells us. "I feel it’s a great way to get a cohesive story together for the exam and makes things more fun for the students (and myself as I make the exam)."
"In fact, the second exam for the same course is coming up, and I am going to continue the story of the Materials Engineer at the Weapons X program!"
Professor Lanba said this approach helps students to get their minds off the stress of exams, helping them focus on the task. Most of all, it also makes learning enjoyable. The world needs more Professors like Asheesh Lanba.