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ME214StaticsWeek2_Chapter_2_11__2_15

# ME214StaticsWeek2_Chapter_2_11__2_15 - ME 214 Vector...

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ME 214 Vector Statics Lecture 4, Chapter 2.11-2.15 Instructor: A Rezaei Today’s Objective: Students will be able to: a) Represent a position vector in Cartesian coordinate form, from given geometry. b) Represent a force vector directed along a line. c) determine an angle between two vectors, and, d) determine the projection of a vector along a specified line. POSITION VECTOR The position vector directed from A to B , r AB , is defined as r AB = {( X B X A ) i + ( Y B Y A ) j + ( Z B Z A ) k }m Please note that B is the ending point and A is the starting point. So ALWAYS subtract the “tail” coordinates from the “tip” coordinates! FORCE VECTOR DIRECTED ALONG A LINE a) Find the position vector, r AB , along two points on that line. b) Find the unit vector describing the line’s direction, u AB = ( r AB /r AB ). c) Multiply the unit vector by the magnitude of the force, F = F u AB . EXAMPLE 1 Given: 400 lb force along the cable DA. Find: The force FDA in the Cartesian vector form.

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ME214StaticsWeek2_Chapter_2_11__2_15 - ME 214 Vector...

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