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proj3b - Project 3b Equilibrium Note This project is one...

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Project 3b: Equilibrium Note: This project is one option for the CMPSC 201 Simulation Project. This project is recommended for anyone who is currently taking or has taken the Statics course (E MCH 210 or 211), including, but not limited to, civil, aerospace, industrial, mechanical, and materials science students and physics majors with an interest in mechanics. This project was developed in conjunction with Christine Masters of the PSU Engineering Science and Mechanics department. Preliminary "Deadline": This project option requires you to derive an equation before you start coding. I'm happy to provide support with that, but you must ask questions pertaining to deriving the equation during the week of February 23-27. Out of fairness to your classmates waiting for support on later parts of the project, no support will be provided with the derivation afterward. Theory In this application, you'll work with the forces affecting a rigid body at equilibrium. A rigid body such as the one you'll work with in this project is at equilibrium when the following are true: The sum of the forces in the x direction is 0. The sum of the forces in the y direction is 0. The sum of the moments is 0. Thus, to solve a rigid body equilibrium problem, it is recommended that you draw a free-body diagram and then generate and solve a system of equations that satisfy the above conditions. The Application In this application, you'll work with the forces affecting a rigid body at equilibrium. Consider the following illustration (taken from Vector Mechanics for Engineers - Statics , 7th ed., by Beer, Johnston, and Eisenberg, McGraw-Hill, 2004, Problem 4.C1):

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The problem scenario (from the same source), is as follows: A slender rod AB of weight W is attached to blocks at A and B which can move freely in the guides shown. The constant of the spring is k , and the spring is unstretched when the rod is horizontal. Neglecting the weight of the blocks, derive an equation in terms of θ, W , l, and k which must be satisfied when the rod is in equilibrium. Begin solving this problem by deriving the equilibrium equations. Here are some hints: You'll need two force equations and one moment equation. (You can work with moments about A or moments about B; most find moments about A to be conceptually more straightforward.) You'll also need equations for the length of the spring and force of the spring. For the length, draw right triangles. For the force, the force of a spring is given by F = ks , where k is the spring constant and s is the distance from the unstretched length of the spring.
In applying the weight W in the moment equations, treat the weight as being located at the center of the rod. Thus, the moment arm (or torque arm) will be half the length of the rod.

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