lecture 4 _sections 2.7-2.8.pptx
TRANSCRIPT
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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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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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