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Notes for Week of January 18

by: Macen Notetaker

Notes for Week of January 18 BME1030

Marketplace > University of Cincinnati > Biomedical Sciences > BME1030 > Notes for Week of January 18
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About this Document

These are the notes from the week of January 18.
Statics and Basic Strengths of Materials
Dr. Dimov
Class Notes
Statics and Basic Strengths of Materials




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This 3 page Class Notes was uploaded by Macen Notetaker on Friday January 22, 2016. The Class Notes belongs to BME1030 at University of Cincinnati taught by Dr. Dimov in Spring 2016. Since its upload, it has received 45 views. For similar materials see Statics and Basic Strengths of Materials in Biomedical Sciences at University of Cincinnati.


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Date Created: 01/22/16
BME1030 Statics and Basic Strengths of Materials Notes for Week of January 18 End of Chapter 2 Equilibrium of Particles When the resultant of all forces acting on a particle is equal to zero, the particle is said to be in equilibrium. Above, the rigid body is in equilibrium due to the two forces acting on it being equal in magnitude, but opposite in direction. Polygon Rule When arranged as such, these vectors start and end at the same point. This means that their resultant vector is equal to zero. Algebraically R x ΣF x R y ΣF y 2 2 ???? = √???????? + ???????? = 0 Newton’s First Law of Motion – A body at rest will remain at rest unless acted on by a resultant force. It is Newton’s First Law being satisfied that causes a body to be in static equilibrium. Free Body Diagrams To solve engineering mechanics problems: 1. Identify all external forces acting on the “body of interest” 2. Prepare a sketch of this “body of interest”, known as a free body diagram 3. Show all forces exerted, known or to be determined 4. Choose coordinate axes to be used and what directions/dimensions are needed Chapter 3 Forces acting on rigid bodies are separated into 2 groups: 1. External – Either causes the body to move or remain at rest a. Gravitational forces, lift, drag, buoyancy 2. Internal – Holds the body together a. Tension, compression Vector Product of Two Vectors Concept of the moment of a force about a point is the vector product, also known as the cross product, of the two vectors. In plain English, this means that the cross product of two vectors is perpendicular to the plane on which the two vectors exists. Therefore, any problem involving a vector product is in three dimensions. The general form of a vector product is as follows: ???? × ???? = ???? C is the resulting vector in this case, and has a magnitude equal to C = A*B*sin (θ). Its direction is determined according to the right hand rule, in that if one places their hand along the direction of vector A and curls their fingers toward vector B, the direction of the thumb is the direction of vector C. Cross Products are not commutative ???? × ???? ≠ ???? × ???? ???? × ???? = −(???? × ????) Cross Products are not associate (???? × ????) × ???? ≠ ???? × (???? × ????) Cross Products are distributive ???? × (???? + ???? ) = ???????? + ???????? 1 2 1 2


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