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emechbk_2 - Concept of Force CHAPTER 2 Static Equilibrium...

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Concept of Force ENGINEERING MECHANICS FOR STRUCTURES 2.3 CHAPTER 2 Static Equilibrium Force and Moment 2.1 Concept of Force 2.1.1 Equilibrium of a Particle You are standing in an elevator, ascending at a constant velocity, what is the resultant force acting on you as a particle? The correct response is zero: For a particle at rest, or moving with constant velocity relative to an inertial frame, the resultant force acting on the isolated particle must be zero, must vanish. We usu- ally attribute this to the unquestionable authority of Newton. The essential phrases in the question are constant velocity, resultant force and particle. Other words like “standing”, “elevator”, “ascending”, and “you” seem less important, even distracting, but they are there for a reason: The world that you as an engineer will analyze, re-design, and systematize is filled with people and elevators, not isolated particles, velocity vectors, or resultant forces — or at least, not a first sight. The latter concepts are abstractions which you must learn to identify in the world around you in order to work effectively as an engineer, e.g., in order to design an elevator. The problems that appear in engineering text books are a kind of middle ground between abstract theory and everyday physical reality. We want you to learn to read and see through the superficial appearances, these descriptions which mask certain scientific concepts and principles, in order to grasp and appropriate the underlying forms that provide the basis for engineering analysis and design. The key phrase in Newton’s requirement is isolated particle : It is absolutely essential that you learn to abstract out of the problem statement and all of its relevant and irrelevant words and phrases, a vision of a particle as a point free in space. It’s best to render this vision, this abstraction “hard” by drawing it on a clean sheet of paper. Here is how it would look.
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Concept of Force 2.4 ENGINEERING MECHANICS FOR STRUCTURES This is a non-trivial step, akin to a one month old’s apprehension that there are other egos in the world. You are to take the dot drawn as the representation of a thing, all things, that can be thought of as an isolated particle. Now show all the forces acting on the particle. We have the force due to gravity, W = Mg , acting ver- tically down, toward the center of the earth .... (Who said the elevator was oriented vertically? Who said it was on the surface of the earth? This information is not given; indeed, you could press the point, arguing that the question is not well posed. But is this information essential? We return to this point at the end of this chapter). We have the reaction force of the elevator floor acting vertically upward on you, on you as an abstraction, as an isolated particle. This is how our particle looks with all forces acting upon it.
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