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Biomechanics_6 - Lecture 6 BMEn 3001 Biomechanics 15...

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Lecture 6 BMEn 3001 Biomechanics 15 September 2008
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Last Lecture Review of Linear Equations
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Topics for Today Review of Linear Physics Newton's First and Second Laws Superposition and the additivity of forces – Equilibrium Review of Angular Physics Torque (moment) Newton's Third Law Moments and Reaction Moments
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Isaac Newton Possibly greatest scientist and mathematician ever. Contributions to – Calculus Solid-body mechanics Fluid mechanics – Optics Heat transfer
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Newton's First Law Corpus omne perseverare in statu suo Body every continues in state its quiescendi vel movendi uniformiter in of resting or of moving uniformly in directum, nisi quatenus a viribus impressis a direction, unless because of forces impressed cogitur statum illum mutare. it is compelled state that to change.
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Newton's Second Law Newton's Second Law says that the amount that the body's velocity changes is proportional to the force. That proportionality constant is the mass. Do you ever think about the fact that inertial mass (i.e., acceleration divided by force) is the same as gravitational mass (the thing that makes us have weight)? Note that thermal "mass," for example, is completely different.
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So, what is force? ON defines force as "mechanical disturbance or load." I like this definition because the word "disturbance" echoes well to Newton's First Law. Unfortunately, other than that, this definition tells you nothing. I prefer to think of force as the transfer of momentum. When you apply force to something, you cause its momentum to change, and if the net force on an object is zero, its momentum does not change (recall the Newton stamp!).
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F = ma
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a = 1 m F
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Superposition Under very few circumstances does an object experience only one force. Fortunately, acceleration and force are additive (the Principle of Superposition). This fact is so inherent to our lives that we rarely consider that it is not necessarily true: Why is it that equal forces acting in opposite directions on a given object should cancel out?
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a = 1 m F
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Thus . . . If we know the sum of all forces acting on an object, we know the amount and the direction in which it will accelerate. By integrating the acceleration, we can determine the velocity. By integrating the velocity, we can determine the position.
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A simple exercise • F 1 = 100 N, F 2 = 50 N, F 3 = 75 N, F 4 = 25 N. In what direction will the diamond accelerate? If the diamond has mass 5 kg, how quickly will it accelerate? F 1 F 2 F 3 F 4
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The Center of Mass Real objects, like the diamond on the previous slide, are not points. It would be nice, however, to be able to approximate them as points, and to be able to put that point in an appropriate place.
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