Primeiras provas fundamentos de mecânica

Prévia do material em texto

���������	��
���
	����� �����	����
��fiff�fl�ffi�
	��� ��ffi�
��"!#
��fi�$�&%$'��ffi��(%��*)�
+fl���� ����,-)��/.1032545076728254
9�:<;>=>?A@
)CB�DFEHG(I�J
K
EHG�LM4�N
K5O
I
K
G�P5,QPR2+N
K5O
I
K
N
K8SUT
DFEHG(I�J
V7K1WYX
�Z
V8O
I(E&[FE�\
V
[
V�V7]^S`_aVcb
\7J
V7K�O^V
G
T
D^EHG(I�J
K
EHG
V7deV
Zgf
K
P8\
K8S
)
S
Z h
VAV8T
DFEHi
V
G
T
D^E�EHGjIjZlk8E
S
E
_
E
S`S`V
[
K
EmL
_
EHG
_aK
G(E
VaV7]^SY_aV
IjZlk
V
EHG(IjZlk8E
S
\
K8S`S
E�I
V W
hjD^G(IjZ
]<T
DFE�\
K5_
GjD
V
G�N
V
i
V
k
S`V
G�n
Bo�7npfl
_aV
N
V7S
IHq
r
\�D^i
V
N
K
[FE+I(E
S
GjD
V
k8EHi
K
\�Zs[
V
[^E+k8E�I
K8S
Z
V
iC\
K5O
G(I
V8O
I(E8P
_
EHG
_oKAT
DFE
Ko_
q
K
[^D^i
K
[
V
k8EHi
K
\�Zs[
V
[FE�G(Eth
V
k
V7S
Z>q
V
k8EHiMn
�
V7]^S`_mV
IjZlk
V
EHG(I^q
V
��ffi�%+���+���u
v�"nw�
V7S`V
D
_
k8E�I
K8S
G(E
S
\
K5O
G(I
V8O
I(E8PxI
K
[
V
G
V
G�G`D
V
G�\
V7S`V
\/I(E
S
q
r
G(IjZy\
V
G�Pz\
K5_oK
GjD
V
G
\
K5_
N
K5O
E
O
I(EHG
O
D
_
GjZsG(I(E
_mV
[FE
S
E�{|E
S�'
E
O
\�Z
V
G
K
D}G(EHD
_
q
K
[^D^i
K
PQ[^Z
S
E
b
\7J
V7K
E�GjE
O
IjZs[
K
P1I
'
E
_
P
O
EH\/EHG`G
V7S
Z
V8_
E
O
I(E8P
T
D^E�G(E
S
\
K5O
G(I
V8O
I(EHG�n�!~E
V
il5D
_aV
[FEHi
V
G�k
V7S
Z
V7S
L€D
_aV
[
V
G	\
K5_
N
K5O
E
O
I(EHG
K
D
Ka_
q
K
[^D^i
K
PFN
K8S
E/f~E
_
N<i
K1W
P
K
k8E�I
K8S
k
V7S
Z
V
n
Bp6Qn!QE
K
G�N
SjK
[^DFI
K
G	EHGj\
V
i
V7S
EHGA‚
ƒ"„
‚
… E}‚
ƒ-„
‚
†
{
K8S
E
_
Zl5D
V
ZyG�P~N
K
[FE
_oK
G	
V7S`V8O
IjZ
S+T
D^E
‚
…	‡ ‚
†
n
�
V7]^S`_mV
IjZlk
V
EHG(I^q
V
��ffi�%	���+�+��
U�nˆ
�E
V
\
K8S
[
K
\
K5_�V
[FE
]<O
Z
b
\7J
V7K
[FE&N
SjK
[^DFI
K
EHGj\
V
i
V7S
P5I(E
_aK
G
T
DFE‚
ƒv„
‚
…�‡
ƒ
… \
K
Ge‰ˆŁY‹
EŒ‚
ƒ„
‚
†
‡
ƒQ†
\
K
Ge‰
Ł`Ž
P
K5O
[^Em‰ˆŁY‹qE
K'V8O
5D<i
K
E
O
I
S
E
K
G"k8E�I
K8S
EHG$‚
ƒ
E
‚
… E}‰
ŁYŽ
qE
K‘'V8O
5D^i
K
E
O
I
S
E
K
G-k8E�I
K8S
EHG$‚
ƒ
E’‚
†
n
�
O
I�J
V7K
P
ƒ
… \
K
Ge‰ˆŁY‹ ‡
ƒ1†
\
K
Ge‰ ŁYŽ E�N
K
[^E
_oK
Gu
V7SYV8O
IjZ
S�T
DFE … \
K
Ge‰ˆŁY‹ ‡
†
\
K
Ge‰ Ł`Ž n�!QE
K
G
'V8O
5D^i
K
G
O
J
V7K
{
K8S
E
_
Zl5D
V
ZyG�P
K
G�k8E�I
K8S
EHG
‚
… E}‚
†
G(E
S
J
V7K
[<Zl{“E
S
E
O
I(EHG"L
_mV
G	I(E
S
J
V7KmVm_
EHG
_aV
\
K5_
N
K5O
E
O
I(E
V7K
i
K5O

K
[FE}‚
ƒ W
n
Bp,Qnp�*6 � ” EHZc[FE�ffi+E�•+I
K5O
P1EHG`\
S
ZlI
V
[
V
{
K8S`_aV
‚
–z—|˜š™ ‡fi›
‚
ƒ
N
V7S`V
D
_
\
K8S
N
K
[FE
_aV
GjG
V
› P
O
J
V7K
k
V
ilE�[^EHGjG
V
{
K8S`_aV
P
T
D
V8O
[
KoVa_aV
GjG
V
[
K
\
K8S
N
K
E
_œT
DFEHG(I�J
V7K
qE"k
V7S
Z>q
V
k8EHiMn
�
V7]^SY_aV
IjZlk
V
EHGjI^q
V
%	���+���u
v�"nF�{
K8S`_mV
DFIjZsisZlž
V
[
V"V
\�Z
_aV
N
V7S`VAV
G(E�5D
O
[
V
ilEHZw[FE�ffi�E�•	I
K5O
G^q
K
k
V
ilE�G(E
VA_aV
GjG
V
[
K
\
K8S
N
K
{
K8S
\
K5O
GjI
V8O
I(E8nŒ�ŸE
T
D
Vcb
\7J
V7K
\
K8SjS
E�I
V
qE
X
‚
–
‡¡ 5¢
£
 (¤
‡
 
 (¤
L
›
‚
¥
W"T
DFE8P
OFK
\
V
G
K
[FE
_aV
GjG
V
G-k
V7S
ZHq
V
k8EHZsG�P¦G(E
EHGj\
S
E�k8E-\
K5_oK§X
‚
–
‡¨›
‚
ƒ�©
 jª
 (¤
‚
¥
n
9�:<;>=>?¬«
)��
S`K8d
ilE
_aV
GpL��H­aN
K5O
I
K
G�P<���
‡
­AN
K5O
I
K
G�®<��6-E��,
‡�¯
N
K5O
I
K
G
WYX
�+�Y° %
K5O
GjZs[^E
S
E
V
GjZlIjD
Vcb
\7J
V7K_oK
G(I
SYV
[
VmO^Va]
5D
S`VaV7K
i
V
[
K
P
K5O
[FE
V
G"\
K8S
[
V
G"GHJ
V7K
Zs[FE
V
ZsGaL€GjE
_±_aV
GjG
V
E-Z
O
E/f~I(E
O
GHq
r
k8EHZyG
W
EA²	q
VmV
I
S
ZsI
K
E
O
I
S
E
K³d
i
K
\
K
[^E
_mV
GjG
VA´
E
V
GjDFNwE
S
{�q
r
\�ZlE	²
K8S
Zlž
K5O
I
V
iMP~µ¶L
K
\
K
E/)
]
\�ZlE
O
I(E&[FE
V
I
S
ZsI
K
\�Z
O
qE�IjZs\
K
qE�Zs5D
V
i
V7K
EHG(I^q
V
IjZs\
K1W
n
�
'V8O
5D^i
K
‰�qE§{
K8S`O
EH\�Zs[
K
n‘ff
K8S`O
E
b
\
V
GjD
V
G
S
EHG()
N
K
G(I
V
G	E
_
I(E
S`_oK
G�[FEp‰FP
›
P
´
P^µE�·<n
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¸~¸~¸
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
¹~¹
T1
T1 T1
N1
N1Mg
Fa1
Fa1
mg
T2
T3
T3 T3
1 3
T2
2
T2
T3
T2
T1
θ
nó
n
�+�7n
V
°³ff
Vcb
\
VmK
G	[^Z
V

SYV8_aV
G	[FE�{
K8S8b
\
V
G	N
V7SYVK
G�[
K
ZsG
d
i
K
\
K
G�P
›
E
´
PFE�N
V7S`VoV
G�I
SH'
EHG+N
V7S
I(EHG	[
V
\
K8S
[
V
Pz�7P<6AE",Qn
�t[FE
O
IjZ
]<T
DFE
K
G�N
V7S
EHG	[FE
Vcb
\7J
V7K
E
S
E
Vcb
\7J
V7K
n
�+�7n
d
°}B�D
V
i
K
k
V
i
K8S+_
q
V
fFZ
_oK
[
Va_mV
GjG
V
›
N
V7S`VmT
DFE
K
GjZsG(I(E
_aV
\
K5O
IjZ
O
DFEpE
_ŸS
E�N
K
D<G
K1º
�+�7nR\Y°#B�D
V
ZsG
K
G	k
V
i
K8S
EHG	[
V
G�I(E
O
G�J
K
EHG
O^V
G	\
K8S
[
V
G�P~»U¼HP^»w½�E�»C¾7P
O
EHGjG
V
GjZlIjD
Vcb
\7J
V7K1º
�+�7nR[Q° !QE
K
k
V
i
K8S
[FE
›
{
K8S�Vm_
E�I
V
[FEA[
K
k
V
i
K8S
E
O
\
K5O
I
S`V
[
K}O^V
N
V7S
I(E���7n
d
P
T
D
V
i
K
k
V
i
K8S
[
V
{
K8S8b
\
V
[FE
V
I
S
ZlI
K
E
O
I
S
E
´
E
V
GjDFNwE
S
{�q
r
\�ZlE�²
K8S
Zlž
K5O
I
V
i
º
!
K
isD
b
\7J
V7K
�+�7n
V
°m�¦Eth
VoV-]
5D
S`V
P
K5O
[FE
K
G�\
K8S
N
K
G�E
V
G�\
K8S
[
V
G�{
K8S`V8_
G(E�N
V7S`V
[
K
G�P~N
V7S`V
{
V
\�ZsisZlI
V7S�V
Zs[FE
O
IjZ
]
\
Vcb
\7J
V7K
[
V
G�{
K8S8b
\
V
G�n
��IjD
V8_œO^Kod
i
K
\
K
[FE
_aV
GjG
V
›
L|E
_
\�Z
_aV
[
Vo_
EHG
V¿W
�7n
K
G(EHD#NwEHG
K´
·<P<\
V
D^G
V
[
K
NwEHi
V
zE
S`S`V
P
T
DFEpG
K
{
S
E
VAS
E
Vcb
\7J
V7K
6Qn
V
{
K8S8b
\
V
[
V
\
K8S
[
V
PF»
¼
P
T
DFE�G
K{
S
E
VAS
E
Vcb
\7J
V7K
L
S
E�N
S
EHG(E
O
I
V
[
VoO^V
\
K8S
[
V
��E�isZl
V
[
V
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHis²
V¿W
,Qn
V
{
K8S8b
\
VO^K8S`_aV
i�[
V_
EHG
V
P&À
¼
P
T
DFE§G
K
{
S
E
VÁS
E
Vcb
\7J
V7K
L
S
E�N
S
EHG(E
O
I
V
[
VO^V_
EHG
V
E§isZl
V
[
V
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHis²
V¿W
.Fn
V
{
K8S8b
\
V
[^E
V
I
S
ZlI
K
–
�tÂÄÃ
¼
Pz\
V
D^G
V
[
V
NwEHi
V}_
EHG
V#T
DFEoG
K
{
S
E
V}S
E
Vcb
\7J
V7K
L
S
E�N
S
EHG(E
O
I
V
[
V§O^V}_
EHG
V
EaiyZl
V
[
V
N
K8S
D
_aV
isZ
O
²
V
I
SYV
\/Eth
V
[
V
k8E
S`_
EHis²
V¿W
ffi
Kmd
i
K
\
K
[FE
_aV
GjG
V
› L|NcE
O
[^D
S`V
[
K1W�V
IjD
V8_
�7n
K
G(EHD#NwEHG
K
› ·<Pe\
V
D^G
V
[
K
NwEHi
V
UE
SjS`V
P
T
DFEpG
K
{
S
E
VoS
E
Vcb
\7J
V7K
6Qn
V
{
K8S8b
\
V
[
V
\
K8S
[
V
PF» ½ P
T
DFE�G
K
{
S
E
VAS
E
Vcb
\7J
V7K
L
S
E�N
S
EHG(E
O
I
V
[
VoO^V
\
K8S
[
V
6-E�isZl
V
[
V
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHis²
V¿W
n
ffi
V
\
K8S
[
V
�mL€²
K8S
Zlž
K5O
I
V
i
W�V
IjD
V8_
�7n
V}S
E
Vcb
\7J
V7K
[
V
{
K8S8b
\
V T
DFE
V
\
K8S
[
V
�A{
V
ž
O^V§_mV
GjG
V§´
Px» ¼ PUisZl
V
[
V³V7K
G(EHDN
V7S
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHis²
V
6Qnp\
K5_oKpV
\
K8S
[
V
qE	Zs[^E
V
iMP
O
J
V7K
N
K
GjGjD^Z
_aV
GjG
V
E8P5N
K8S
I
V8O
I
K
P
O
J
V7K
N
K
[^E&G
K
{
S
E
S
{
K8S8b
\
V
išq
r T
D^Zy[
V�S
EHGjD<ilI
V8O
I(E8n¦�
O
I�J
V7K
P
I(E
_ÅT
DFEG
K
{
S
E
S
D
_aV
{
K8S5b
\
V
» ¼ [
K$K
DFI
SjK
i
V
[
K
n ��GjG
V
{
K8S8b
\
V
qE³\
V
D^G
V
[
V
NwEHi
KÇÆ(O
q
K5È
P
T
D^EG
K
{
S
E
V$S
E
Vcb
\7J
V7K
L€isZl
V
[
VoV
EHGjG
V
{
K8S5b
\
V
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHiy²
V¿W
n
ffi
V
\
K8S
[
V
6§L|k8E
S
IjZy\
V
i
W�V
IjD
V8_
�7n
V#S
E
Vcb
\7J
V7K
[
V
{
K8S8b
\
V T
DFE
V
\
K8S
[
V
6#{
V
ž
O^V§_aV
GjG
V
› PU» ½ P�isZl
V
[
V§V7K
G(EHDŒN
V7S
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHis²
V
6Qnp\
K5_oKpV
\
K8S
[
V
qE	Zs[^E
V
iMP
O
J
V7K
N
K
GjGjD^Z
_aV
GjG
V
E8P5N
K8S
I
V8O
I
K
P
O
J
V7K
N
K
[^E&G
K
{
S
E
S
{
K8S8b
\
V
išq
r T
D^Zy[
V�S
EHGjD<ilI
V8O
I(E8n¦�
O
I�J
V7K
P
I(E
_ÅT
DFEG
K
{
S
E
S
D
_aV
{
K8S5b
\
V
» ½ [
K$K
DFI
SjK
i
V
[
K
n ��GjG
V
{
K8S8b
\
V
qE³\
V
D^G
V
[
V
NwEHi
KÇÆ(O
q
K5È
P
T
D^EG
K
{
S
E
V$S
E
Vcb
\7J
V7K
L€isZl
V
[
VoV
EHGjG
V
{
K8S5b
\
V
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHiy²
V¿W
n
ffi
V
\
K8S
[
V
,§L€Z
O
\�isZ
O^V
[
V¿W�V
IjD
V8_
�7n
VAS
E
Vcb
\7J
V7K
[
V
{
K8S8b
\
VmT
DFE
V
\
K8S
[
V
,A{
V
ž
OFKή(O
q
K5È
PcisZl
V
[
VAV7K
G(EHD#N
V7S
N
K8S
D
_mV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
SY_
EHis²
V
6Qnp\
K5_oKpV
\
K8S
[
V
qE	Zs[^E
V
iMP
O
J
V7K
N
K
GjGjD^Z
_aV
GjG
V
E8P5N
K8S
I
V8O
I
K
P
O
J
V7K
N
K
[^E&G
K
{
S
E
S
{
K8S8b
\
V
išq
r
T
D^Zy[
V�S
EHGjD<ilI
V8O
I(E8n¦�
O
I�J
V7K
P
I(E
_ÉT
DFEAG
K
{
S
E
S
D
_aV
{
K8S5b
\
V
»
½
[
KK
D^I
SjK
i
V
[
K
n��uGjG
V
{
K8S8b
\
V
qEa\
V
D^G
V
[
V
NwEHi
V
N
V7S
EH[FE8P
T
DFEoG
K
{
S
E
V³S
E
Vcb
\7J
V7K
L€isZl
V
[
VoV
EHGjG
V
{
K8S5b
\
V
N
K8S
D
_aV
isZ
O
²
V
I
S`V
\/Eth
V
[
V
k8E
S`_
EHiy²
V¿W
n
�+�7n
d
°¬�ÊGjZsGjI(E
_aV
k
V
Z
]
\
V7S
E
_
E
T
D<Zsišq
r
d^S
Z
K
E
O^T
D
V8O
I
K#V
G�{
K8S8b
\
V
G
O^V
G
_aV
GjG
V
G
´
E
›
[FE
S
E
_ËS
EHG`D^ilI
V8O
I(EHG
O
D^i
V
GHn
�
O
I�J
V7K
P
O
EHGjG
V
GjZlIjD
Vcb
\7J
V7K
P<N
K
[FE
_oK
G�\
K5O
\�isD^Z
S	T
DFE8P
O^Vo_mV
GjG
V
NwE
O
[^D
S`V
[
V
P
V
G	{
Kwb
\
V
G+G
K5_aV8_
ž�E
SjK
E
»
½�̏›
·
‡
2
ÌeÍ
»
½+‡fi›
·<Î L��
W
%
K5_oK$Kޮ(O
q
K5ȬO
J
V7K
N
K
G`GjD^Z
_mV
GjG
V
P
V S
EHGjD^ilI
V8O
I(EG
K8d<S
EmEHilEI(E
_ÏT
DFE³G(E
S
ž�E
SjK
P¦I
V8O
I
KO^V
²
K8S
Zlž
K5O
I
V
iu\
K5_aKÁO<V
k8E
S
IjZs\
V
iMn��
O
I�J
V7K
P^N
K
[FE
_aK
G�EHGj\
S
E�k8E
SHX
k8E
S
IjZs\
V
i »v¼
à Ð
©
»C½
à Ð
©
»C¾
à Ð
‡
2
©
L
Ì�›
·
W
©
»w¾CG(E
O
‰
‡
2
ÌcÍ
»C¾
‡
›
·
G(E
O
‰
LM6
W
²
K8S
Zlž
K5O
I
V
i »
¼
à Ñ
©
»
½
à Ñ
©
»
¾
à Ñ
‡ Ì
»
¼
©
2
©
»
¾
\
K
Ge‰
‡
2
ÌcÍ
»
¼�‡
»
¾
\
K
G<‰FÎ LM,
W
!~D
d
GjIjZlIjD^Z
O
[
KuK
k
V
i
K8S
[
V
�
T
nˆLM6
WwO^V
LM,
W
P7E
O
\
K5O
I
S`V8_oK
Gz»
¼&‡fi›
·�\
K
Ie‰^P>N
V7S`V+V
GjZlIjD
Vcb
\7J
V7K
[FEÒE
T
D^Zsišq
r
d<S
Z
K
nC��\
K5O
I(EH\/E8P
N
K8S
qE
_
P
T
DFE
K
\
K8S
N
K
G
K8d^S
E
Vm_
EHG
V
I
V8_d
qE
_
I(E
_ÓT
DFE"EHGjI
V7S
E
_
E
T
D<Zsišq
r
d^S
Z
K
P~I
V8O
I
K}O^V
k8E
S
IjZs\
V
i�L|NwE
S
NwE
O
[^Zy\�D^i
V7S
Ô
V
GjDFNwE
S
{�q
r
\�ZlE�[
Va_
EHG
V¿W�T
D
V8O
[
KoO^V
²
K8S
Zlž
K5O
I
V
i�L|N
V7S`V
ilEHi
K1W
n��Gj\
S
E�k8E
O
[
K
ZsGjG
KFX
NwE
S
NwE
O
[^Zs\�D^i
V7S
À
¼
©
2
©
L
Ì
´
·
W
©
2
‡
2
ÌeÍ
À
¼&‡
´
· L|.
W
N
V7SYV
ilEHi
K
2
©
L
Ì
–
�tÂÕÃ
¼
W
©
2
©
»
¼Ö‡
2
Ìe͖
�tÂÕÃ
¼�‡
»
¼
Î L
¯
W
fl�G
V8O
[
K³K
k
V
i
K8S
E
O
\
K5O
I
S`V
[
K
N
V7S`V
»
¼
V
\�Z
_mV³O<V
�
T
n>L
¯
W
PxE
O
\
K5O
I
S`V8_aK
G
K
k
V
i
K8S
[
V
{
K8S5b
\
V
[^E
V
I
S
ZlI
K³O
EH\/EHGjG^q
V7S
Z
V
N
V7S`V
G(E�5D
S`V7S	Kad
i
K
\
K
[FE
_mV
GjG
Vm´
E
_
E
T
D^Zsišq
r
d^S
Z
KFX
–
�tÂÕÃ
¼
‡
»v¼
‡fi›
·&\
K
I<‰^Î LM­
W
�
V7S`V
EHGjG(EAk
V
i
K8S
GjE
S�K
k
V
i
K8S�_
q
V
fFZ
_oK
[
V
{
K8S8b
\
V
[FE
V
I
S
ZlI
K
EHG(I^q
V
IjZy\
K
PxEHilE-I(E
_ÉT
DFEAG(E
S
Zl5D
V
i
V
µxÀm¼/npfl�G
V8O
[
K³V
G
�
T
G�n>LM­
W
EL|.
W
P
–
�tÂÄÃ
¼�‡fi›
·�\
K
I<‰
‡
µ
´
·
Ì<Í ›Ó‡
µ
´
·
·&\
K
Ie‰
‡
µ
´
I
V8O
‰FÎ Lš×
W
�+�7nR\Y°#ffi
V
GjZsIjD
Vcb
\7J
V7KV
\�Z
_mV
P^[FEpE
T
D^Zsišq
r d<S
Z
K
P
V
G	I(E
O
G�J
K
EHG	k
V
ilE
_
P<E
_Ø_
q
K
[^D^i
KFX
» ¼&‡ › ·&\
K
I<‰ ‡ µ
´
· LMÙ
W
» ½+‡ › · ‡ µ
´
·uI
V8O
‰ LM4
W
» ¾+‡ Ú
L › ·
W
½
©
L › ·&\
K
Ie‰
W
½
‡fi› ·~Û �
©
\
K
I
½
‰ ‡fi› ·
¼
™|˜šÜ�Ý
‡fi› ·�\
K
G(EH\z‰ ‡ßÞ7à-á
âšã
™HÝ
ΠL���2
W
�+�7nR[Q°ffi
V
�
T
n>LM­
W
E
O
\
K5O
I
S`V8_aK
G
K
k
V
i
K8S
[
V
{
K8S8b
\
V
[FE
V
I
S
ZsI
KaO
EH\/EHGjG^q
V7S
Z
V
N
V7S`Vo_aV8O
I(E
S+K
GjZyG(I(E
_aV
E
_
E
T
D^Zsišq
r d^S
Z
K
P
E
_
{|D
O�b
\7J
V7K
[
V�_aV
GjG
V
› P8E
O<V
�
T
n>Lš×
W
E
O
\
K5O
I
SYV8_oK
G
K
k
V
i
K8SÒ_
q
V
fFZ
_oK
[FE › P5N
V7S`V�K
GjZyG(I(E
_aV�]
\
V7S
E
_
E
T
D^Zsišq
r d^S
Z
K
n
�
V
G(I
V
GjD
d
G(IjZlIjD^Z
S`_oK
G
_
E�I
V
[FE"[
K
k
V
i
K8S
[
V
�
T
n>Lš×
W�O^V
�
T
n>LM­
W
–
�tÂÕÃ
¼&‡�䓛#ågæ ·�\
K
Ic‰ ‡èç
�
6
µ
´
I
V8O
‰8éo·&\
K
Ie‰ ÌcÍ –
�tÂÄÃ
¼�‡
�
6
µ
´
· L��8�
W
��6>°¶%
K5O
G`Zs[FE
S
E
K
GjZyG(I(E
_aV
[
V ]
5D
S`V V7K
i
V
[
K
nÁ�
_aV
GjG
V
› EHGjI^q
V
N
S
EHG
V
N
K8S
[<D
V
G	\
K8S
[
V
G�Zs[FE
V
ZyG"L
_aV
GjG
V
G�[FEHG(N
S
E�ž5q
r
k8EHZsG+EZ
O
E/f~I(E
O
GHq
r
k8EHZsG
W&V
D
_aV
²
V
G(I(E
k8E
S
IjZs\
V
i
T
DFEo5Z
S`V
\
K5_
k8EHi
K
\�Zy[
V
[FE
V8O
5D^i
V7S�ê
na��G\
K8S
[
V
G�EHG(I�J
V7K
N
S
EHG
V
G
Ô
V
²
V
G(I(EA[FEp{
K8S`_aV³V
{
V
ž�E
S
D
_
I
S
Z
'V8O
5D^i
K
E
T
D^Zsi>q
V
I(E
SjK
n��ëG`ZsG(I(E
_aV
5Z
S`V
[^E
{
K8S`_aV+T
DFE
V
GU\
K8S
[
V
G
]eT
DFE
_
G(E
_
N
S
EuEHG(IjZs\
V
[
V
G�P
_aV
G
V
Gv\
K8S
[
V
GvGjDFN
K8S
I
V8_
D
_aV
I(E
O
G�J
V7Km_
q
V
f~Z
_mV
»cì
�tí
n
��6Qns�Y°¬ff
Vcb
\
V§K
[^Z
V

SYV8_aV
[FEo{
K8S5b
\
V
G
O^V#_aV
GjG
V
› PxE
O^V
G�[^D
V
G�\
K8S
[
V
G�P��AEm6QP
E
O<T
D
V8O
I
K
²	q
Va_aK
k~Z
_
E
O
I
K
nÒ�t[^E
O
IjZ
]eT
DFE
K
G+N
V7S
EHG	[FE
Vcb
\7J
V7K
E
S
E
Vcb
\7J
V7K
n
��6Qnî6>°#
�E�I(E
SY_
Z
O
E
V
I(E
O
G�J
V7KmO^V
G	[<D
V
G	\
K8S
[
V
GHP^E
_
I(E
S`_oK
G�[FE�·<P › P
ê
E"ï	n
��6Qnî,>°§
�E�I(E
S`_
Z
O
E
V
k8EHi
K
\�Zs[
V
[FE
V8O
5D<i
V7S�ðŸñ
:Fòzó
ð
:
Pc[FE"{
K8S`_aV³T
DFE
V
G�\
K8S
[
V
G
V
Z
O
[
V¬]<T
DFE
_
EHG(IjZs\
V
[
V
G$L
K
GjZyG(I(E
_aV
N
S
EHGjE
S
k8E
V
{
K8S`_aV¿W
P
_aV
G
T
DFE
O
J
V7K
V7S`S
E
d
E
O
I(E
_
L€\
K5O
GjZs[FE
S
E
T
D
V
iC\
K8S
[
V
[FE�k8E
V7SjS
E
d
E
O
I
V7S
N
S
Z
_
EHZ
SjK
n
W
L
ω
mgT2
T2
T2
T1
T1
T1
1
2
L
L
30
30o
o
!
K
isD
b
\7J
V7K
��6Qns�Y°#��IjD
V8_œOFK
\
K8S
N
K
[^E
_aV
GjG
V
›
�7npG(EHD#NwEHG
K
P
›
·<P<\
V
D<G
V
[
K
NwEHi
V
UE
SjS`V
P
T
DFEpG
K
{
S
E
VAS
E
Vcb
\7J
V7K
P
6Qn
V
{
K8S8b
\
V
»
¼
P<\
V
D<G
V
[
V
NwEHi
V
\
K8S
[
V
[FEp\�Z
_aV
P
T
DFEpG
K
{
S
E
VoS
E
Vcb
\7J
V7K
P<E
,Qn
V
{
K8S8b
\
V
»
½
P<\
V
D<G
V
[
V
NwEHi
V
\
K8S
[
V
[FE
d<V
Zgf
K
P
T
D^EpG
K
{
S
E
VAS
E
Vcb
\7J
V7K
n
ffi
V
G�\
K8S
[
V
G�[FE+\�Z
_aV
E+[FE
d<V
Zlf
K
PQ\
K5_oK
EHi
V
G�G�J
V7K
Zy[FE
V
ZsG�E
O
J
V7K
N
K
GjGjDFE
_ë_mV
GjG
V
P
O
J
V7K
N
K
[^E
V
IjD
V7S�O
E
O
²1D
_mV
{
K8S8b
\
V
S
EHGjD^isI
V8O
I(E8n+��G�{
K8S5b
\
V
G
T
DFE
V
IjD
V8_ÓO
EHGjG
V
G�\
K8S`V
G�EHG(I�J
V7K³S
E�N
S
EHG(E
O
I
V
[
V
G
O^Vm]
5D
S`V
PcE
K
G�N
V7S
EHG�[FE
Vcb
\7J
V7K
E
S
E
Vcb
\7J
V7K
EHG(I�J
V7K
iyZl
V
[
K
G�N
K8S
isZ
O
²
V
G&I
S`V
\/Eth
V
[
V
G	k8E
_
EHis²
V
G�n
��6Qnî6>°’��\
K8S
N
K
[FE
_aV
G`G
V
›
E/f~EH\�DFI
V
D
_ô_oK
k~Z
_
E
O
I
K
\�Z
S
\�D<i
V7S
N<D
S`V8_
E
O
I(Ea²
K8S
Zlž
K5O
I
V
išPU[FE
S`V
Z
K õ
n%
K5_oK§K
\
K5_
N
S
Z
_
E
O
I
K
[
V
G�\
K8S
[
V
GqEpïöE�EHi
V
G�{
K8SY_aV8_
D
_
I
S
Z
'V8O
5D<i
K
E
T
D^Zsi>q
V
I(E
SjK
P~N
K
[FE
_oK
G�\
V
is\�D<i
V7S�T
DFE
õ
‡Ÿ÷
¾(ø
½
nÒffi
V
[^Z
S
E
b
\7J
V7K
k8E
S
IjZs\
V
i�L|ù
W
P
V$S
EHGjD^ilI
V8O
I(Em[
V
G{
K8S8b
\
V
G
T
DFE
V
IjD
V8_ÅO<V _aV
GjG
V
›
I(E
_úT
D^EG(E
SAO
D<i
V
PzE
O^T
D
V8O
I
K¬T
DFE
V
\
K5_
N
K5O
E
O
I(E-[FEHG`G
V
{
K8S8b
\
VS
EHGjD^isI
V8O
I(E
O^V
[<Z
S
E
b
\7J
V7K
²
K8S
Zlž
K5O
I
V
i�L|û
W
GjE
S
q
VV
{
K8S8b
\
V
\/E
O
I
S
q
r
NwE�I
V
P
–
â
˜šÜ
Â
—“üþý
‡›
ê
½
õ
‡
›
ê
½
÷
¾(ø
½
n¦�uGj\
S
E�k8E
O
[
K
ZyGjG
K
P1\
K5O
GjZs[FE
S`V8O
[
KpT
D^E
K
EHZgf
K
ù
V
N
K5O
I
V
N
V7S`V
\�Z
_aV
P
T
DFE
K
EHZgf
K
û
V
N
K5O
I
V
N
V7S`V"V
²
V
G(I(E
E
T
D^EK$'V8O
5D^i
K
‰
‡
,725ß3P
k8E
S
IjZs\
V
i »v¼
à Ð
©
»w½
à Ð
©��
Ð
‡
»v¼FGjE
O
,72
ß
©
L
Ì
»C½
W
G(E
O
,72
ß
©
L
Ì�›
·
W
‡
2 L��H6
W
²
K8S
Zlž
K5O
I
V
i »v¼
à Ñ
©
»w½
à Ñ
©��
¾
à Ñ
‡
»v¼F\
K
Gc,72
ß
©
»C½w\
K
Ge,72
ß
©
2
‡
–
â
˜ÄÜ
Â
—|üþý‡fi›
ê
½
õ
ΠL��H,
W
”
E
_d^S`V8O
[
KaT
DFEpGjE
O
,725ß
‡
¼
½
E
T
DFE"\
K
Gc,725ß
‡
÷
¾
½
P
k8E
S
IjZs\
V
i »U¼<G(E
O
,72
ß
Ì
»w½CGjE
O
,72
ß
‡fi›
·
ÌeÍ
»U¼
Ì
»C½
‡
6
›
· L��/.
W
²
K8S
Zlž
K5O
I
V
i »U¼^\
K
Ge,72
ß
©
»w½w\
K
Gc,72
ß
‡fi›
ê
½
Û
,7ï
6
ÌeÍ
»v¼
©
»w½
‡¨›
ê
½
ï+Î L��
¯
W
�	EHG
K
isk8E
O
[
K
P
»v¼
‡fi›
�
·
©
ê
½
ï
6��
E »C½
‡fi›
�
ê
½
ï
6
Ì
·
�
L��H­
W
��6Qnî,>°a� I(E
O
G�J
V7K
»v¼oqE�GjE
_
N
S
E
_aV
Z��
K8S�T
DFE
V
I(E
O
GHJ
V7K
»C½7PQ\
K5_aK
N
K
[FE+G(E
S
kQZyG(I
K
NwEHi
V
G��
T
G�n>L��H­
W
n&!QE
V
k8EHi
K
\�Zs[
V
[^E
V8O
5D^i
V7S�ê
{
K8S�V
D
_
E
O
I
V8O
[
K
Pc» ¼ k
V
Z
V
IjZ
O
5Z
S
N
S
Z
_
EHZ
SjKoK
k
V
i
K8S
[FE
S
D^N^IjD
S`V
[
V
\
K8S
[
V
n	»wì
�tí
n�� k
V
i
K8S�_
q
V
f~Z
_aK
[FE
ê
G(E
S
q
V
P<E
O
I�J
V7K
P
T
D
V8O
[
K
» ¼&‡ »cì
�tí
X
» ¼&‡fi›
�
·
©
ê
½
ì
�tí
ï
6 �
‡ »cì
�tí
ÌeÍ
ê
ì
�tí
‡	�
6FL“»cì
�tí
̏› ·
W
› ï
L��>×
W
��,>°fifl
_ S
Z�
^E[^ZsG(N
V7SYV deV
i
V
G
T
D^EŒG
V
E
_
[FEŒG`D
V
dwK
\
V
\
K5_
k8EHi
K
\�Zy[
V
[FE
���&E
_ S
EHi
Vcb
\7J
V7KpV7K
G
K
i
K
n
�
V
IjZ
S`V
[
K8S&T
D^E
S�V
\/E
S
I
V7S
D
_ V
isk
KT
DFE	EHG(I^q
V-V
D
_aV
[^ZsG(I
'V8O
\�Z
V
²
K8S
Zsž
K5O
I
V
i�� L|N
V7S`V§V
[<Z
S
EHZg)
I
V¿W
E Ô
Vo_
EHG
_aVAV
ilIjD
S`V
[
V-dwK
\
V
[
VAV7S`_mV
L€[FE
K5O
[FE
V"d<V
i
V
G
V
Z
W
PQ\
K5_aK-_oK
GjI
S`V
[
KAO^Vp]
5D
S`V
n
�EHG(N
S
E�ž
V8O
[
K�V+S
EHG`ZsG(I
'
E
O
\�Z
V
[
K�V7S
P5\
V
is\�D^ilE�E
_
I(E
SY_oK
G	[FE�� � PF·mE��$n
��,Qns�Y°
VoV
ilIjD
S`V��$V
\�Z
_aV
[
KaV
ilk
K
P^N
V7S`VoVmT
D
V
i
VAd<V
i
V
[FE�k8E"GjE
S�V
N
K5O
I
V
[
V
P<[FE�{
K8S`_aVoVaV
\/E
S
I
V7S�KaV
ilk
K
®
��,Qnî6>°
K
I(E
_
N
KmT
D^E
Vod<V
i
VA]
\
VoO^KaV7S
P^N
V7S`V
Z
S
[
VAdwK
\
V
[
VoV7S`_aVaV
IQqE
KV
ilk
K
n
D
V0
h
!
K
isD
b
\7J
V7K
SYV
I
V
)ÄG(E[FED
_Ø_oK
kQZ
_
E
O
I
K
[^EpN
SjK
h1qE�IjZsiMP
K5O
[^E
VmV
\/EHilE
S`Vcb
\7J
V7K
qE\
K5O
GjI
V8O
I(E8PwZl5D
V
i
V
ž�E
SjKmO^V
[<Z
S
E
b
\7J
V7K
²
K8S
Zlž
K5O
I
V
i
EpZl5D
V
i
V
·³N
V7S`VodeV
Zgf
KaO<V
[^Z
S
E
b
\7J
V7K
k8E
S
IjZy\
V
iMnu��G�E
T
D
Vcb
\7J
K
EHG
T
DFE
S
E�8E
_
EHGjG(EpIjZlN
K
[FE
_aK
k~Z
_
E
O
I
K
G�J
V7K
²
K8S
Zlž
K5O
I
V
i
X
û
‡
û
�
©
�
�
à ��
�
Ñ
‡
�
�
à Ñ
L��HÙ
W
k8E
S
IjZy\
V
i
X
ù
‡
ù
�
©
�
�
à ��
©
¼
½
ƒ
��
½
�
Ð
‡
�
�
à Ð
©ƒ
��
L��H4
W
��,Qns�Y°#�UEHi
V
8E
K5_
E�I
S
Z
V
[
VA]
5D
S`V
PFN
K
[FE
_oK
G�k8E
S�T
DFE
�
�
‡
I
V8O
‰
K
D
�
‡
� I
V8O
‰FÎ LM672
W
ffi"J
V7K
\
K5O
²FEH\/E
_oK
G�P
V
Z
O
[
V
P
K$'V8O
5D^i
K
‰Fnu%
K5O
G`Zs[FE
S`V8O
[
KK
EHZgf
K
ùmN
K
GjZlIjZlk
K
N
V7S`V
\�Z
_aV
E
K
EHZlf
K
û§N
K
GjZlIjZsk
K
N
V7SYV-V
[^Z
S
EHZsI
VaO^V]
5D
S`V
PcN
K
[FE
_aK
G�D^G
V7S�V
N
S
Z
_
EHZ
S`V
[
V
G��
T
G�nˆL��HÙ
W
PCN
V7S`V
ûUn��
K
\`²FE�
V7SpV7K#V
ilk
K
P
K}V
ilk
K
GjE-[FEHG`i
K
\
K
D
D
_aV
[^ZsG(I
'V8O
\�Z
V
û
Ì
û
��‡
�
O^V
[^Z
S
E
b
\7J
V7K
²
K8S
Zlž
K5O
I
V
iMPw\
K5_
D
_aV
k8EHi
K
\�Zs[
V
[FE\
K5O
GjI
V8O
I(EoZl5D
V
i
V
�
�
à Ñ
‡
�
�
\
K
G<‰^P
K5O
[FE
K#'V8O
5D<i
K
‰
V
Z
O
[
V
qE�[FEHG`\
K5O
²FEH\�Zs[
K
nÒ�
deV
i
V
NwE
S
\
K8SjS
EHDmEHGjG
V
[^ZyG(I�J
V8O
\�Z
VO
D
_
\/E
S
I
K
I(E
_
N
K
» L€G
K
isZy\�ZlI
V
[
KO<V
N
V7S
I(Ep�&,Qnî6
W
n��
O
I�J
V7K
û
Ì
û
�	‡
�
‡
�
�
\
K
G<‰7»
ÌeÍ
»
‡
�
�
�
\
K
G^‰
LM6~�
W
!
V7d
E
O
[
K§T
DFE8P
V7K
\`²^E�
V7SAV7K$V
ilk
K
P
K§d
i
K
\
K
N
K
GjGjD^Zvù
‡
ù��3P
K5O
[^Eaù��’qEGjD
V V
ilIjD
S`V#V7K
N
V7S
IjZ
S
[
V#dwK
\
V
[
V
V7S`_aV
P
T
D^E
]
\
K
D‘G
K8d
D
_aVV
\/EHilE
S`Vcb
\7J
V7K
ƒ
Ð
‡ Ì
· E
T
DFE#N
V7S
IjZsDö\
K5_
G`D
V
k8EHi
K
\�Zs[
V
[FE#{
V
ž�E
O
[
K
D
_Ö'V8O
5D^i
K
‰
L€[FEHGj\
K5O
²^EH\�Zs[
K1W
\
K5_œV
²
K8S
Zlž
K5O
I
V
i
X
ù
‡
ù
�	‡
ù
�
©
�
�
à Ð
»
©
�
6
L
Ì
·
W
»
½
ÌcÍ
2
‡
�
�
G(E
O
‰8»
Ì
�
6
·5»
½
K
D »
‡
6��
�
GjE
O
‰
·
LM686
W
�Õ5D
V
i
V8O
[
KaV
G	�
T
GHn>LM6~�
W
ELM686
W
�
�
�
\
K
G<‰
‡
6��
�
G(E
O
‰
·
K
D 6�G(E
O
‰¦\
K
Ge‰
‡
�m·
�
½
�
Î LM68,
W
�ôI(E
S`_oK
6�G(E
O
‰¦\
K
Ge‰ëqED
_aV S
EHi
Vcb
\7J
V7K
I
S
Zs
K5OFK5_
qE�I
S
Zs\
V
\
K5O
²^EH\�Zs[
V
E$k
V
ilEÁG(E
O
LM67‰
W
E
V
�
T
n>LM68,
W
GjE
S
EH[^DFž
Ô
V
\
K5O
²FEH\�Zs[
V
E
T
D
Vcb
\7J
V7K
[
KaV
is\
V8O
\/E
X
G(E
O
LM67‰
W
‡
�a·
�
½
�
E ‰
‡
�
6
V7S
\�G(E
O
ç
�m·
�
½
�
é
Î LM63.
W
%
K5_oK
E
O
\
K5O
I
S`V8_oK
G
K¬'V8O
5D<i
K
‰FPF�
T
nˆLM63.
W
P<N
K
[FE
_oK
G�\
K
i
K
\Cq
V
)Äi
KmO<V
�
T
n>LM672
W
EpE
O
\
K5O
I
S`V7Sff�
n
��,Qnî6>° %
K5O
²FEH\/E
O
[
K
‰FPF�
T
nˆLM63.
W
Pe\
K
i
K
\
V8_oK
G+EHGjG(Epk
V
i
K8S+O^V
�
T
n3LM6~�
W&K
D
O^V
�T
n>LM686
W
EpE
O
\
K5O
I
S`V8_oK
G	»"n