Physik Formelsammlung

Physik
Formelsammlung
Andreas Zimmer
WS 97/98
1.
Struktur der Materie
 Teilchen 
 mol 


Avogadro Konstante
N A = 6,022 ⋅ 10 23
Molvolumen
Vm = 22,414
Stoffmenge
n=
m
M
mol
Dichte
ρ=
m
V
 kg 
 3
m 
Masse des Elektrons
m e = 9,1091 ⋅ 10 −31
kg
Masse des Protons
m p = 1,6725 ⋅ 10 −27
kg
Elementarladung
e = 1,6021 ⋅ 10 −19
2.
l
As
Wechselwirkungen und Kräfte
Gravitationskraft
Coulombkraft
F=G
F=
m1 ⋅ m 2
r2
G = 6,670 ⋅ 10 −11
 m3 

2 
 kg ⋅ s 
ε 0 = 8,86 ⋅ 10 −12
 A⋅s
V ⋅ m


Q1 ⋅ Q 2
4 ⋅ π ⋅ ε0 ⋅ r
Kraft
F=m⋅g
Reibkraft
FR = FN ⋅ µ
Federkraft
FF = −k ⋅ x
2
vom Skript-Server der FH-Köln: http://skript.vt.fh-koeln.de/
m
g = 9,81  2 
s 
2
3.
Kinematik
Bewegungsgleichung
x = x0 + v0 ⋅ t +
Gleichförmige Bewegung
x =v⋅t
Beschleunigte Bewegung
x=
1
⋅ a ⋅ t2
2
v=
x
t
1
⋅ a ⋅ t2
2
v =a⋅t
v − v0
x=
2⋅a
t=
a=
a=
2⋅x
t
2
v
t
x
v
v = konst.
2⋅x
a
t=
t=
a = konst.
v
a
2
v = 2 ⋅ a ⋅ x + v0
2
Freier Fall
y = y 0 + v 0Y ⋅ t −
1
⋅ g ⋅ t2
2
Schiefer Wurf
x = x 0 + v 0X ⋅ t +
1
⋅ aX ⋅ t2
2
aX = 0
v 0 X = v 0 ⋅ cos α
y = y 0 + v 0Y ⋅ t +
1
⋅ aY ⋅ t2
2
a Y = −g
v 0 Y = v 0 ⋅ sin α
y = y 0 + v 0Y ⋅ t −
1
⋅ g ⋅ t2
2
v = v 0Y − g ⋅ t
a = −g
2
v
2 ⋅ y0
v 
= 0 Y +  0 Y  +
g
g
 g 
Wurfzeit
t 1/ 2
Steigzeit
tS =
v0
⋅ sin α
g
Wurfweite (Reichweite)
R=
v0
⋅ sin 2 α
g
2
2
Wurfhöhe
h max
v
= 0 ⋅ sin 2 α
2⋅g
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3
4.
Arbeit und Energie
[J = Nm = Ws]
Energie
E = E kin + E pot = konst.
Kinetische Energie
E kin =
Potentielle Energie
E pot = m ⋅ g ⋅ h
Arbeit
W = ∆E pot = ∆E kin = F ⋅ cos α ⋅ ∆x
1
⋅m ⋅ v2
2
∆E kin =
(
1
2
2
⋅ m ⋅ vE − v A
2
)
∆E pot = m ⋅ g ⋅ (h − x )
x2
∫
W = FX ⋅ dx =
x1
h
1 
1 2

 m − ⋅ h  ⋅ g ⋅ dh = m ⋅ h − ⋅ h
2 
4
0
∫
Reibarbeit
WR = −FN ⋅ µ ⋅ x
FN =
h
⋅g
0
FG
cos α
WR = ∆E kin + ∆E pot
W − WR = E kin
Federarbeit
WF =
W=
1
⋅ k ⋅ x2
2
1
⋅ k ⋅ x2 − m ⋅ g ⋅ h
2
W
F⋅x
= F⋅v =
t
t
Leistung
P=
Bremsleistung
E pot A = E kin B
v = 2⋅g⋅h

cos α 

v = 2 ⋅ g ⋅ h ⋅ 1 − µ ⋅
sin α 

vom Skript-Server der FH-Köln: http://skript.vt.fh-koeln.de/
ohne Re ibung
mit Re ibung
4
5.
Schwingungen
1
T
Frequenz
f=
f=
Kreisfrequenz
ω = 2⋅π⋅f
ω
2⋅π
f=
k
m
ω=
(Winkelgeschwindigkeit)
Schwingungsdauer
T=
1
f
Federkonstante
k=
m⋅g
x0
Anfangswinkel
ϕ = ω⋅ t
Amplitude
A=
T=
ω=
2⋅π
ω
1 −1 

Hz = s = 1 


1
k
⋅
2⋅π
m
ϕ
t
ω=
m
k
T =2⋅π⋅
v
r
T=
t
n
x 0 ⇒ Auslenkung aus der Ruhelage
v0
ω ⋅ x0
cos ϕ =
v0
ω ⋅ sin ϕ
A=
tan ϕ =
x0
cos ϕ
A=
x0
A
a
ω ⋅ cos ϕ
2
A ⇒ max . Auslenkung
Auslenkung
x = A ⋅ cos (ω ⋅ t + ϕ)
x 0 = A ⋅ cos ϕ
Geschwindigkeit
v = − A ⋅ ω ⋅ sin (ω ⋅ t + ϕ)
v 0 = − A ⋅ ω ⋅ sin ϕ
Beschleunigung
a = − A ⋅ ω2 ⋅ cos (ω ⋅ t + ϕ)
a0 = − A ⋅ ω2 ⋅ cos ϕ
a = −ω2 ⋅ x
Energiebilanz
Eges =
1
⋅ k ⋅ A2
2
Epot = Eges ⋅ cos2 (ω ⋅ t + ϕ)
Epot =
1
⋅ k ⋅ x2
2
Ekin = Eges ⋅ sin2 (ω ⋅ t + ϕ)
Ekin =
1
⋅ m ⋅ v2
2
Max. Geschwindigkeit
v max =
Mathematisches Pendel
ϕ=
ω=
s
l
2 ⋅ E ges
v max = ω ⋅ A
m
für kleine Winkel
g
l
T =2⋅π⋅
; FT = −m ⋅ g ⋅ sin ϕ
l
g
l=
T2 ⋅ g
4 ⋅ π2
s = A ⋅ cos ϕ
vom Skript-Server der FH-Köln: http://skript.vt.fh-koeln.de/
5
6.
Elektrische Felder
Feldstärke
E=
U
d
E=
F
Q
E=
E pot =
Q
4 ⋅ π ⋅ ε0 ⋅ r
2
=
2⋅Q
ε0 ⋅ A
e2
V
m 
 
[J = Nm]
Potentielle Energie
E pot = Q ⋅ ϕ
Potentielle Arbeit
W = ∆E pot = E pot 2 − E pot 2 = Q ⋅ ϕ 2 − Q ⋅ ϕ1 = Q ⋅ (ϕ 2 − ϕ1 ) = Q ⋅ U
4 ⋅ π ⋅ ε0 ⋅ r
∆E pot = e ⋅ U
Energiebilanz
∆E pot = E kin
e⋅U =
Spannung
U=
(
1
2
2
⋅ m ⋅ ve − va
2
(
m
2
2
⋅ ve − va
⋅
2 e
)
)
2⋅ e ⋅U
m
v=
Elementarladung
e = 1,6021 ⋅ 10 −19
m
2
⋅ ve
⋅
2 e
Nm J 

 V = As = C 


U=E⋅d
Geschwindigkeit
UBrems =
ve =
2⋅e⋅U
2
+ va
m
As
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6
7.
Atomphysik
Photon Energie
E=
h⋅c
1
= h ⋅ υ = ⋅ m ⋅ v 2 + WA
λ
2
Frequenz
υ=
E 2 − E1 c
=
λ
h
Wellenlänge
λ=
h⋅c c
h
= =
υ m⋅υ
E
Austrittsarbeit
WA = E −
Austrittsgeschwindigkeit
v=
Max. Bremsspannung
U 0 max =
2
⋅ (E − W A )
m
U 0 max
UV-Laser
1
h⋅c 1
⋅m ⋅ v2 =
− ⋅m ⋅ v2
λ
2
2
E kin
e
h⋅c

− WA 

e⋅λ

=
e
E ion = 2 ⋅ E = 2 ⋅ h ⋅ υ =
λ=
2⋅h⋅c
e⋅λ
2⋅h⋅c
e ⋅ E ion
Lichtgeschwindigkeit
c = 2,9979 ⋅ 10 8
Plancksche Konstante
h = 6,6256 ⋅ 10−34
m 
s
 
Js
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7