Lecture 4 _Sections 2.7-2.8.pptx

7/29/2019 Lecture 4 _Sections 2.7-2.8.pptx

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ES 201 Statics

Lecture 4

POSITION VECTORS & FORCE

VECTORS

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a) Represent a 3-D vector in a Cartesian coordinate system.

b) Find the magnitude and coordinate angles of a 3-D vector

c) Add vectors (forces) in 3-D space

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Review


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EXAMPLE

G

Given: Two forcesF1 andF2 are

applied to a hook.

Find: The resultant force in

Cartesian vector form.

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4

Homework #2

5090-

FR

FB=6kN


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Homework #2


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Todays Objectives:

a) Represent a position vector in Cartesian coordinate form,

from given geometry.

b) Represent a force vector directed along a line.

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CARTESIAN VECTORS AND

THEIR ADDITION & SUBTRACTION

(Section 2.72.8)


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POSITION VECTOR

(Section 2.7)

Consider two points, A and B, in 3-D space. Let their

coordinates be (XA, YA, ZA) and (XB, YB, ZB ),respectively.

A position vector is

defined as a fixed

vector that locates a

point in space relativeto another point.

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POSITION VECTOR

The position vector directed from A to B, rAB , is defined as

rAB

= {( XB 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.

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ALWAYS subtract the tail coordinates from the tip

coordinates!


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FORCE VECTOR DIRECTED ALONG A LINE

(Section 2.8)

If a force is directed along a line,

we can represent the force vector

in Cartesian coordinates by using

a unit vector and the forces

magnitude:

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a) Find the position vector,rAB, along two points on that

line.

b) Find the unit vector describing the lines direction,

uAB

= (rAB

/rAB

).

c) Multiply the unit vector by the magnitude of the force,

F = F uAB = F (rAB/rAB) =

F {( XB XA )i + ( YB YA )j + ( ZB ZA )k }/

{( XB XA )2

+ ( YB YA )2

+ ( ZB ZA )2

)}


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CONCEPT QUIZ

1. A position vector,rPQ, is obtained by

A) Coordinates of Q minus coordinates of P

B) Coordinates of P minus coordinates of Q

C) Coordinates of Q minus coordinates of the origin

D) Coordinates of the origin minus coordinates of P

2. A force of magnitude F, directed along a unit

vector U, is given byF = ______ .

A) F (U)

B) U/ FC) F /U

D) F + U

E) FU

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EXAMPLE


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EXAMPLE

Plan:

1. Find the position vectorrACand the unit vector uAC.

2. Obtain the force vector asFAC= 420 N uAC.

Given: The 420 N forcealong the cable AC.

Find: The forceFACin the

Cartesian vector form.

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CONCEPT QUIZ

P and Q are two points in a 3-D space. How are the position

vectorsrPQ andrQPrelated?

A)rPQ = rQP B)rPQ = - rQP

C)rPQ = 1/rQP D)rPQ = 2rQP

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GROUP PROBLEM SOLVING

Plan:

1) Find the forces along CA and CB in the Cartesian vector form.

2) Add the two forces to get the resultant force,FR.

3) Determine the magnitude and the coordinate angles ofFR.

Given: Two forces are acting

on a pipe as shown in

the figure.

Find: The magnitude and the

coordinate direction

angles of the resultant

force.

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ATTENTION QUIZ

1. Two points in 3D space have coordinates of P (1, 2, 3)

and Q (4, 5, 6) meters. The position vectorrQP is given by

A) {3 i + 3j + 3 k}m

B) {3i 3j 3k}m

C) {5i + 7 j + 9k} m

D) {3 i + 3j + 3k} m

E) {4i + 5j + 6k} m

2. Force vector,F, directed along a line PQ is given by

A) (F/ F)rPQ B)rPQ/rPQ

C) F(rPQ/rPQ) D) F(rPQ/rPQ)

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EXAMPLE


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Homework 4: 2-90, 2-95

Due on Jan 31, 2013

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Lecture 4 _Sections 2.7-2.8.pptx