Baixe euf2024 para estudar e outras Provas em PDF para Física, somente na Docsity!
M ω R ! a =
3 R
" ω !#
a
R
M
M
M
(^) ω =
q 3 GM a^3 $ ω =
q 3 GM 2 a^3
% ω =
q (^) √ 3 GM a^3 & ω =
q 2 GM 3 a^3
' (^) ω =
q GM 3 a^3
M ω R ! a =
3 R
" a ! !#
a
R
M
M
M
a =
( 3 GM
ω^2
$ a =
( 3 GM
2 ω^2
% a =
3 GM ω^2
& a =
( 2 GM
3 ω^2
' a =
( GM
3 ω^2
L = 30 cm ( ρ = 5,0 g/cm^3 M = 5,0 kg ) *+ 1 ,0 g/cm^3 , - . ( ) h " #
H 2 O
h
mercadoria
barra
L L
L = 40 cm ( ρ = 3,0 g/cm^3 M = 6,0 kg ) *+ 1 ,0 g/cm^3 , - . ( ) h " #
H 2 O
h
mercadoria
barra
L L
9 )9 L
M
)9 k ! L/ 3 . . 9 θ = 0 : g ; ; + 9 θ ≪ 1 cos θ ≈ 1 − 12 θ^2 sin θ ≈ θ
3
1 L
3
2 L
k
M
<< ! E = 12 M L^2
h θ˙^2 + (^ g L +^
k 9 M
θ^2
i
<<< ω =
q g L +^
k 9 M
" . #
; << <<< $ (^) 4 ( % (^) < & ; < <<< ' < <<
8 9 )9 L M ( ) )9 k ! 2 L/ 5 . . 9 θ = 0 : g ; ; + 9 θ ≪ 1 cos θ ≈ 1 − 12 θ^2 sin θ ≈ θ
5
2 L
5
3 L
k
M
<< ! E = 12 M L^2
h θ˙^2 +
( (^) g L +^
4 k 25 M
θ^2
i
<<< ω =
q g L +^
4 k 25 M
" . #
; << <<< $ 4 ( % (^) < & (^) ; < <<< ' (^) < <<
m 1 = 2M H *, . + 9 m 1 9 m 2 = M 9 + *,
H (^) h
m 1
m 2
(a) (b)
" . h H# % m 2 )9
h = 49 H $ h = 23 H
% h = 13 H & h = 19 H
' h = 89 H
m 1 = 3M H *, . + 9 m 1 9 m 2 = M 9 + *,
H (^) h
m 1
m 2
(a) (b)
" . h H# % m 2 )9
(^) h = 169 H $ (^) h = 34 H
% (^) h = 14 H & (^) h = 161 H
' (^) h = 163 H
E = κr^3 ˆr κ " ρ #
(^) ρ = 5κǫ 0 r^2 $ (^) ρ = 5πκǫ 0 r^2
% (^) ρ = 10κǫ 0 r^2 & (^) ρ = 10πκǫ 0 r^2
' (^) ρ = 4πκǫ 0 r^2
xy C R 1 R 2 > R 1 * , I 0 ( *R 2 , *z > 0 , 8 C
= μ^04 I 0 ( (^) R^11 + (^) R^12 )ˆz
$ = 0 % = − μ^04 I 0 ( (^) R^11 + (^) R^12 )ˆz
& = μ^04 I 0 ( (^) R^11 − (^) R^12 )ˆz ' (^) = μ^04 I 0 ( (^) R^12 − (^) R^11 )ˆz
xy C R 1 R 2 > R 1 * , I 0 ( *R 2 , *z > 0 , 8 C
(^) = μ^04 I 0 ( (^) R^12 − (^) R^11 )ˆz
$ (^) = 0 % = μ^04 I 0 ( (^) R^11 − (^) R^12 )ˆz
& = μ^04 I 0 ( (^) R^11 + (^) R^12 )ˆz
' = − μ^04 I 0 ( (^) R^11 + (^) R^12 )ˆz
9 (ρ,ϕ,z) = 12 C 0 ρ ϕˆ C 0 % (ρ,ϕ,z)C ' . #
(^) (ρ,ϕ,z) = C 0 ˆzC $ (^) (ρ,ϕ,z) = 14 C 0 ρ^2 ˆzC . 9 % (ρ,ϕ,z) = C 0 ϕˆC & (ρ,ϕ,z) = 12 C 0 ϕˆC . ' (ρ,ϕ,z) = C 0 ϕˆC .
9 (ρ,ϕ,z) = −C 0 ln (ρ/a)ˆz C 0 a % (ρ,ϕ,z)C ' . #
(ρ,ϕ,z) = C ρ^0 ϕˆC . 9
$ (^) (ρ,ϕ,z) = C 0 ( a ρ ) ˆϕC . 9
% (ρ,ϕ,z) = C ρ^0 ϕˆC .
& (ρ,ϕ,z) = C 0 ( a ρ )ˆzC
' (ρ,ϕ,z) = C 0 ρˆzC
zˆ *μ = μ 0 , ( 8 . (z,t) = E 0 exp[i(kz − ωt)](ˆx + 3ˆy) k = 1, 8 × 107 −^1 ω = 3, 6 × 1015 D) E 0 % E vf C 9 n C (z,t) ) c = 3, 0 × 108 F
(^) vf = 2, 0 × 108 FC n = 1, 5 C (z,t) = − kE ω 0 exp[i(kz − ωt)](3ˆx − ˆy) $ (^) vf = 2, 0 × 108 FC n = 1, 5 C (z,t) = kE ω 0 exp[i(kz − ωt)](3ˆx + ˆy) % vf = 5, 0 × 108 FC n = 6, 0 C (z,t) = − kE ω 0 exp[i(kz − ωt)](3ˆx − ˆy) & vf = 5, 0 × 108 FC n = 6, 0 C (z,t) = kE ω 0 exp[i(kz − ωt)](3ˆx + ˆy) ' vf = 1, 5 × 108 FC n = 2, 0 C (z,t) = kE ω 0 exp[i(kz − ωt)](ˆx − 3ˆy)
zˆ *μ = μ 0 , ( 8 . (z,t) = E 0 exp[i(kz − ωt)](2ˆx − yˆ) k = 1, 2 × 107 −^1 ω = 3, 0 × 1015 D) E 0 % E vf C 9 n C (z,t) ) c = 3, 0 × 108 F
(^) vf = 2, 5 × 108 FC n = 1, 2 C (z,t) = kE ω 0 exp[i(kz − ωt)](ˆx + 2ˆy) $ vf = 2, 5 × 108 FC n = 1, 2 C (z,t) = kE ω 0 exp[i(kz − ωt)](ˆx − 2ˆy) % vf = 4, 0 × 108 FC n = 7, 5 C (z,t) = − kE ω 0 exp[i(kz − ωt)](ˆx + 2ˆy) & vf = 4, 0 × 108 FC n = 7, 5 C (z,t) = − kE ω 0 exp[i(kz − ωt)](ˆx − 2ˆy) ' vf = 7, 5 × 108 FC n = 4, 0 C (z,t) = kE ω 0 exp[i(kz − ωt)](2ˆx + ˆy)
D
L a (a ≪ L) 8 . 8 N I(t) = I 0 cos ωt " ) ε ) #
(^) ε = ωμ^0 I^0 N D
2 L sin^ ωt $ ε = ωμ^0 I^0 N D
2 L cos^ ωt % ε = μ^0 I^0 N^
(^2) D 2 L^2 sin^ ωt & ε = μ^0 I^0 N^ (πa
(^2) ) L cos^ ωt ' (^) ε = μ^0 I^0 N^
(^2) (πa (^2) ) L^2 sin^ ωt
T 0 v 0 . G +
u = RcT − a v
R a c 8 ) v 0 vf = 3v 0 Tf 8 ( W ) Tf
W = 0 Tf = T 0 − (^3) v^20 aRc $ (^) W = 0 Tf = T 0 + (^3) v^20 aRc
% (^) W = RT ln
3 v 0 −b v 0 −b
& W = 0 Tf = T 0
' (^) W = RT ln
3 v 0 −b v 0 −b
- (^32) va 0 Tf = T 0 − (^3) v^20 aRc
*CV = 32 R , ) 9
(^) Wciclo = P 0 V 0 (ln 4 − 1) $ Wciclo = P 0 V 0 (ln 4 + 1) % Wciclo = P 0 V 0 (ln 4 − 2) & Wciclo = P 0 V 0 ' Wciclo = −P 0 V 0
*CV = 32 R , ) 9
Wciclo = P 0 V 0 (ln 27 − 2) $ Wciclo = P 0 V 0 (ln 27 + 2) % (^) Wciclo = P 0 V 0 (ln 9 − 2) & (^) Wciclo = 2P 0 V 0 ' (^) Wciclo = − 2 P 0 V 0
% ) * ( , P 0 Pf > P 0 : N,V S U F H ! D ( ) 9 ) E
( ∂T
∂P
S,N
( ∂T
∂P
V,N
( ∂T
∂P
U,N
( ∂T
∂P
F,N
( ∂T
∂P
H,N
* ( , V 0
Vf > V 0 : N,P S U F H ! D ( ) 9 ) E
( ∂T
∂V
S,N
( ∂T
∂V
P,N
( ∂T
∂V
U,N
( ∂T
∂V
F,N
( ∂T
∂V
H,N
' /I % "
3 J ^2 # %
103 G $ 102 G % 101 G & 100 G ' 10 −^1 G
5 S ; x = −a x = +a . x . S′ ) . x S v x < ; S′E
< 8 .; S′ << ! 2 a/
p 1 − v^2 /c^2 c ) <<< x = +a . x = −a
<<< $ ; << <<< % < & << ' ; < <<
5 S ; x = −a x = +a . x . S′ ) . x S v x < ; S′E
< 8 .; S′ << ! 2 a
p 1 − v^2 /c^2 c ) <<< x = +a . x = −a
; << <<< $ < % (^) << & (^) <<< ' (^) ; < << <<<
H K ( 60 ◦ " . # *8 E h/mc = 2 h 52 m c ) ,
(^) 300 2 L $ (^) 30 2 L % (^) 10 2 L & (^) I0 2 L ' (^) K00 2 L
H 7 ( 60 ◦ " . # *8 E h/mc = 2 h 52 m c ) ,
700 2 L $ 30 2 L % 10 2 L & I0 2 L ' K00 2 L
: + |n〉 *n = 0, 1 , 2 ,..., n ( @ H D H|n〉 = ℏω(n + 1/2)|n〉 ω 9 : 1 , 5 ℏω . *L, *M,
- , 8 n = 1
- , 8 ) n = 1
- , 8 (1/
L M L M
$ L M M M
% M L M M
& L L L M
' M M M L
: + |n〉 *n = 0, 1 , 2 ,..., n ( @ H D H|n〉 = ℏω(n + 1/2)|n〉 ω 9 : 1 , 5 ℏω . *L, *M,
- , 8 n = 1
- , 8 ) n = 1
- , 8 (1/
M M L L
$ L M L L
% M M L M
& M M M L
' L L L M
) Sα *α = x,y,z, " 9 3F7 Sz Sα = (ℏ/2)σα σα ) 5 M :( 9 3F7 + z 8 9 t
1 2
( (^) iωt/ 2 √ 3 −iωt/^2
ω 8 x z 〈Sx〉 〈Sz 〉 .
8 〈"〉 ! 〈Sz 〉 $ 8 〈"〉 . x ! x 〈Sx〉 % 8 〈"〉 〈Sz 〉 −ℏ/ 2 +ℏ/ 2 & 8 〈"〉 +ℏ/ 2 ' 8 〈"〉 +ℏ/ 2 . x
