3 Movimento em Duas e Três Dimensões -...
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6/4/2008 1 3 – Movimento em Duas e Três Dimensões x y r
Transcript of 3 Movimento em Duas e Três Dimensões -...
6/4/2008
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3 – Movimento em Duas e Três Dimensões
x
y
r
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1 3 m 4 mr i j
1r2r
2 5 m 3 mr i j©2002 by John Wiley & Sons
x yr r rx yr rr i j
x
y
r
x
y
rry
rxx
y
rry
i rxj
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x y zr r rr i j k
x y zr r r r
x
y
z
rry
rx
rz
ik
j
x
y
z
rry
rx
rz
x
y
z
r
x y zr r r r x
y
z
r
ry
rx
rz
x y zr i j k
©2004 by Pearson Education
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A AB Br r r
AB B Ar r r
x
yA
B
x
yrAB
x
y
rA
rB
x
y
rA
rB
rAB
,AB B A
m AB
AB B At t t
r r rv
mt
rv
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mt
rv
©2004 by Pearson Education
0lim t t t
t
d dx y z
t dt dt
r r rv i j k
d
dt
r
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0lim t t t
t
d
t dt
r r rv
©2002 by John Wiley & Sons
tany
x
v
v
2 2 2
x y zv v v vv
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,AB B A
m AB
AB B At t t
v v va
mt
va
2
20lim t t t
t
d d
t dt dt
v v v ra
d
dt
v
2
2
d
dt
r
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0lim t t t
t
d
t dt
v v va
©2002 by John Wiley & Sons
0lim
t
d
t dt
v vam
t
va 2 1vv v
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a
a
©2004 by Pearson Education
©2004 by Pearson Education
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©2004 by Pearson Education
©2004 by Pearson Education
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ga j
©2004 by Pearson Education
©2004 by Pearson Education
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0 0cosx v t
2
0 2 2
0 0
tan2 cos
gy x x
v2
0 0
1sen
2y v t gt
2
0 0
1
2yy y v t gt
0 xx x v t
©2004 by Pearson Education
©2004 by Pearson Education
©2004 by Pearson Education
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0 0cosR v t2
00sen 2
vR
g2
0 0
10 sen
2v t gt
2
0 0
1
2yy y v t gt
0 0xx x v t0
0
0 0 0
0 0 0
0
0
0
cos
sen
x
y
x R
x
y
y
v v
v v
x
y
v0
Rv0x
v0y
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1 2R R
x
y
v02
R
v01
| | | |v01 = v02
2 2
0 01 2sen 2 sen 2
v v
g g
1 2sen 2 sen 2
1 22 2
o1 2 452 4
o1 2 452
©2002 by John Wiley & Sons
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0 0A Ptr v
2
0 0
1
2P P Pt tr r v g
2
0 0
1
2A A At tr r v g
2
0
10
2P Pt tr v g
2
0
10
2A A tr r g
P Ar r
P Ar r
x
y
v0P
r0A
rA = rP
½ gt2
A = Alvo
P = Projétil
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©2004 by Pearson Education
©2004 by Pearson Education
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v2
r
v1O
P1
P2
s
rt
vsen
2 2
vv
v2 v1
v
v2
rv1
O
P1
P2
v
22 sen sen2 2
2
m
vv v
art r
v
2
0 0 0
sen2lim lim lim
2
mt t t
v va a
t r
2va
r
cos senru i j
vv u
sen cosu i j
dv ddv
dt dt dt
u uva
sen cos
cos sen
r
d d d
dt dt dt
d d
dt dt
d
dt
ui j
i j
u
r
dv
dta u
2
2
d v
rdt t r
v
2
r
v
ra u
r
u
O
y
x
j
i
ura
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cos senru i j
vv u
sen cosu i j
dv dd dvv
dt dt dt dt
u uva u r r ta aa u u
sen cos
cos sen
r
d d d
dt dt dt
d d
dt dt
d
dt
ui j
i j
u
r
u
O
y
x
j
i
ur
a
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PA PB BAx x x
©2002 by John Wiley & Sons
PA BA PBr r r
PA PB BAx x x
PA PB BAdx dx dx
dt dt dt
PA PB BAv v v
©2004 by Pearson Education
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©2002 by John Wiley & Sons
©2004 by Pearson Education
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