1 / 20

CE 201 - Statics

CE 201 - Statics. Lecture 5. Contents. Position Vectors Force Vector Directed along a Line. z. B. y. A. x. POSITION VECTORS. If a force is acting between two points, then the use of position vector will help in representing the force in the form of Cartesian vector.

lynsey
Download Presentation

CE 201 - Statics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CE 201 - Statics Lecture 5

  2. Contents • Position Vectors • Force Vector Directed along a Line

  3. z B y A x POSITION VECTORS If a force is acting between two points, then the use of position vector will help in representing the force in the form of Cartesian vector. As discussed earlier, the right-handed coordinate system will be used throughout the course

  4. z A y x B Coordinates of a Point (x, y, and z) A coordinates are (2, 2, 6) B coordinates are (4, -4, -10)

  5. z A (x,y,z) r z k O y x i y j x Position Vectors • Position vector is a fixed vector that locates a point relative to another point. • If the position vector ( r ) is extending from the point of origin ( O ) to point ( A ) with x, y, and z coordinates, then it can be expressed in Cartesian vector form as: r = x i + y j + z k

  6. z A (xA,yA,zA) rBA B(xB, yB, zB) rA rB y x If a position vector extends from point B (xB, yB, zB) to point A(xA, yA, zA), then it can be expressed as rBA. By head – to – tail vector addition, we have: rB + rBA = rA then, rBA = rA - rB

  7. Substituting the values of rA and rB, we obtain rBA = (xAi + yAj + zAk) – (xBi + yBj + zBk) = (xA – xB) i + (yA – yB) j + (zA – zB) k So, position vector can be formed by subtracting the coordinates of the tail from those of the head.

  8. z B r u y A F x FORCE VECTOR DIRECTED ALONG A LINE If force F is directed along the AB, then it can be expressed as a Cartesian vector, knowing that it has the same direction as the position vector ( r ) which is directed from A to B. The direction can be expressed using the unit vector (u) u = (r / r) where, ( r ) is the vector and ( r ) is its magnitude. We know that: F = fu = f ( r / r)

  9. Procedure for Analysis When F is directed along the line AB (from A to B), then F can be expressed as a Cartesian vector in the following way: • Determine the position vector ( r ) directed from A to B • Determine the unit vector ( u = r / r ) which has the direction of both r and F • Determine F by combining its magnitude ( f ) and direction ( u ) F = f u

  10. Examples • Examples 2.12 – 2.15 • Problem 86 • Problem 98

More Related