Due to all the Internet resources out there, this EC will be graded very strict. If you’re interested in doing the EC, the rules are below.Goal of EC: Derive the beam equation (assuming no friction) using very careful physics/engineering arguments. Assume your audience is a person who knows math but who is unfamiliar with physics beyond the most basic, thereby requiring a careful explanation of the physics in your write-up.Purpose: The derivation in class was purely intuitive and this EC is to show that rigorous derivations take a lot of time. The reason I chose intuitive/conceptual derivations in class is that often while doing rigorous derivations, you can lose touch with the physical situation, due to being caught up in the details of the rigor. You will probably experience this during your EC! Assumptions: The only physics you are allowed to take for granted are Newton’s three basic laws of motion (like force is proportional to acceleration); anything more you use, you must either carefully derive or you can explain the intuition behind the physics.Example: Suppose in your derivation of the beam equation you decide to use a certain equation relating “bending moment” to “strain”. 1) You must very carefully define these concepts; you should not use the words without carefully defining them.2) You must explain intuitively what the concepts are. For example, after giving a careful definition of the bending moment at a point x, you then explain intuitively what it measures. In particular, the bending moment involves a force and you need to explain what is causing the force.3) Finally, you cannot just state the equation relating bending moment to strain as a given. You should derive the equation relating the two and/or explain why the equation is intuitively obvious, referencing your very careful definitions in 1). Please be careful. I saw several youtube videos where various people state the definition of a variable used for strain. They then change the meaning of the variable for the purpose of deriving a bending moment equation. Finally, they go back to the original meaning, without explaining the switch between definitions. Your EC must be more careful.
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