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F = ma
F12
F21
F21 = F12
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F = 0
Fx = 0
Fy = T Fg = 0 T = Fg
Fy = n Fg = 0 n = Fg
Fy = T = max ax =
T
m
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Fy = mg R
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x = g kv2v2
mx = mg mkv2 x = g kv2
v dvdx
= g kv2v
gkv2dv =
dx
12k ln(g kv2) = x + C,
v2 = gk
(1 e2kx)
v =
gk
(1 e2kh)
v2 = U2 2gR2( 1R 1
x)
9.8ms2
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a =dv
dt= k
x2
g = kR2 k = gR2
dv
dt
=
gR2
x2
vdv
dx= gR
2
x2
vdv = gR
2
x2dx
v2
2= gR2
1
x
+ C
U2
2= gR2( 1
R) + C C = U
2
2+ gR
v2 = U2 2gR2( 1R 1
x)
U2 = 2gR2(1
R 1
x)
x =2gR2
2gR
U2
x
2gR U2 0
U =
2gR 11.2kms1
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a = k(1
v2), k > 0
v210 ms2U ms1
v =10U
10+Ut ms1x = 10ln(1 + Ut10 ) m
v + v3
x = arctan( Qv1+Qv )
t = 12 ln(Q2(1+v2)v2(1+Q2) v
2
t
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Fx = Fcos
Fy = Fsin
= ddt
v = r at = ddt =
dd
12
2 = dd
=
ac = r2 = v2
r
Fc = m v2
r = mr T = 2
T = mv2
r= (3)(
16
2) = 8 N
mv2
r= 147 v =
147
r
m= 7
2
v = r = 7
2 = 722
rad/s
=7
2
4rev/s
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P F = 0
mg N =mv2
r
N = mg mv2
r= 3400 N
mg =mv2
r v2 = gr
ms2
F = kmM
r2
mg = kmM
R2 k = gR
2
M
F =mgR2
r2= mr2
=2
T 7.3 105 rad/s
r3 =gR2
2=
(9.8)(6.4 106)2(7.3 105)2 = 7.53 10
22 r = 4.22 107 m
v = r = (4.22 107)(7.3 105) = 3000 ms1
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Horizontally : Tsin = mr2
V ertically : Tcos = mg
l2 = r2 + h2
r = lsinh = lcos
T = ml2 tam = r2
g= v
2
gr
tan = rh
=
gh
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F + mgsin =mv2
rcos
Nmgcos = mv2
rsin
mv2
r= Fcos + Nsin
mg = Ncos Fsin
F = 0
tan =v2
gr
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F + mgsin =
mv2
r cos
tan =v2
gr=
13.42
(9.8)(50) = 20.1
T = 2
hg
40