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8/8/2019 Typologio Fysikis a Lykeiou (2008)
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XX. .
, 2008, 2008
u
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2 .
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3
. .
Werner Heisenberg
() :2003 2008
GNU GPL
.
. 04.01
ad magorem Dei gloriam
1 /
TK 30020
, , :gpapadem @ sch .gr
. 3
mailto:gpapadem@sch.grmailto:gpapadem@sch.gr8/8/2019 Typologio Fysikis a Lykeiou (2008)
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(S.I.)
L meter m m Kilogram Kg
t second sec i Amperes A
T Kelvin K
mole mole I Candela cd
radian rad steredian sr
deka da = 101 deci d = 10-1
hecto h = 102 centi c = 10-2
Kilo K = 103 milli m = 10-3
Mega M = 106 micro = 10-6
Giga G = 109 nano n = 10-9
Terra T = 10 12 pico p = 10-12
Peta P = 1015 femto f = 10-15
Exa E = 1018 atto a = 10-18
:12 cm = 12 10-2 m = 0,12 m220 m = 22010-6 m15 KW = 15103 W200 nF = 20010-9 F
m2 m3. :
cm = 10-2 m (cm)2 = (10-2 m)2 cm2 = 10-4 m2
mm = 10-3 m (mm)3 = (10-2 m)3 mm3 = 10-6 m3
:1 L = 10-3 m3, 1 m3 = 103 L1 L = 103 mL, 1 mL = 10-3 L
4 .
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5
.
x , . x(t) . x=x(t) .
.
x y o x y .
x y, .
(x(t), y(t)) t.
.
x y
z o x y z .
r(t)=(x(t),y(t),z(t)) t.
x
. 2 1r r r= r1 r2 . x = x2-x1
S
. .
. 5
(x)i +- O
x
y
O
A
xA
yA A(x
A,y
A)
x
y
z
A(xA,y
A,z
A)
A
yA
xA
zA
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6
u (Velocity)
.r
ut
=r
r
.
x
ut
=r
2 12 1
x xu
t -t
= x
ut
=
m/sec2
:t 0
r
ut
=r
r(t)
:
Su u
t= =
: .
u = x = xo + u(t to) x = xo + ut x = ut ( xo=0)
xo ( to=0 sec)
( )
x-t ... .
u
t 0
u
t
=r
:u
t
=r
2 12 1
u u -u= =
t t -t m/sec2
u, :
6 .
20
U(m/sec)
t (sec)0
10
S (m)
t (sec)
0 2 4
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()
()
.
a .
-
.... (uo 0)
(>0) (
8/8/2019 Typologio Fysikis a Lykeiou (2008)
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= u=uo + t
x = uot +12t2
= u=uo - t
x = uot -12t2
.... (uo = 0)
(>0) (
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u
x
= 2 12 1
u ut t
. u= 2 12 1
x xt t
(Galileo Galilei 1600 ..)
t t t .
uox=uo
x : ux=uox=xo + uot
y : uy=gt
y=2
1gt2
. 9
t
5
0
-24
8
0
U
t
168
4 7 9
10
S (m)
t (sec)
0 2 4
hg
xux
ux
uy
u
y
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(Force) . Newton = Kg m/sec2
F=F2+F1
F=F2-F1
F = 2 21 2F F+
= 12
FF
F = 2 21 2 1 2F F 2FF+ +
= 12 1
FF F+
:
:
()
.
Hooke
.F=Kx, K : ,x : .
10 .
F1 F2 F F1 F2
F
F1
F2
F
F1
F2
F
F1
F1
-
F
y
Fx
=F
F
y=
F
x
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Newton
.
F = 0 . . .
Newton
F =
m
r F=m
:p
F =t
uuur( = )
x y :Fx=max Fy=may
: F = m
:
.... ...
Newton
FAB , FBA. :
AB BAF =-F
Newton:
1 22
mmF=G
rG : G = 6,673 10-11 m2Kgr-2
r :
:0 ,max T,max=Fk
: : Fk : . ()
< ,max
:
T= Fk () = Fk
. 11
F1
F2
m2
m1 r
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(Momentum)
p=mu
( ) .
F=0 p=p
(, ) .
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u .
! .
.
- : u= R
:
. u, , .
=2u
R
:
. :
F=m F=2mu
R
Newton :
FR=F =2mu
R
-
W=FS:
F: S: : F S.
Joule ( J = Newton m)
. 13
S
uR
u
FS
uR
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F=(x) F=(x) x.
W = F=(x) .
:
( x1 x2) :
W =12
x12 -12
x22
T x1, x2 . (...)
( )
(Energy)
, . . ,, . Joule, J = Newton m
m =mc2 (Einstein 1905). , . ( ) (..
). (Potential Energy)
UAB
U = - W
UB = mg(hh) UB = mgh
UE=12
x2
14 .
F
F1
x x
ST
W=TS180 W=-TS
=90
. .
x2x1
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To x .
(Kinetic Energy)
=12
mu2
(Conservative)
,
.
:, (Coulomb), ,
:, , ,
= + U
( ) ,
= 1 + U1 = K2 + U2
E=WF- (= Q)
( , ....)
= WF
= WF1+WF2+
(To .... , )
:
P = Wt = t P = E/t
. 15
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() F : P =Fu():
u F u
: Watt, W=Joule/sec HP =750 W (Horse Power = )
:
,
16 .
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=
, =
=
, =
2+2 = 1 =
=1
(2k+)=(2k+)=
(k+)=(k+)=
(-)=(-)=-
(-)=-(-)=-
(+)=-(+)=-
(+)=(+)= /2
/2
(2
-)=
(2
-)=
(2
-)=
( 2-)=
(2
+)=
(2
+)=-
(2
+)=-
( 2+)=-
(-)=-
(-)=
(-)=-
(-)=-
. 17
0
1
1-1
-1
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0 30 45 60 90 180270
360
06
4
3
2
32
2
0 12
22
32
1 0 -1 0
132
22
12
0 -1 0 1
033
1 3 + 0 - 0
+ 3 133
0 - 0 +
x=
x=2k+
x=2k+-
x= x=k+
x= x=2k
x= x=k+
-1 x 1, -1 x 1, - x , - x ,
18 .
()=()=
()=1m
()= 1
m
2=2
2=2-2=22-1=1-22
2= 22
1-
2=2 -1
2
. 3=3-43
3=43
-33=
3
2
3-1 3
3=3
2
-33 -1
2=12
2
2=12
2+
2=1-21+2
2=1+21-2
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()2=22+()=3+3()4 =44+64+4
:
. Pascal
:
(+)n=
0
nn+
1
nn-1+
2
nn-22++
1n
nn-1+
n
nn
n
k
=n!
k!(n k)!( ) n!=1 2 3 (n-1) n (
)
-=(-)(+) ( )-=(-)(++)4-4=(-)(+++)-=(-)(-1+-2+-3++-2+-1)
-=(+)(-)4-4=(+)(-+-)2-2=(+)(2-1-2-2+2-32-+2-2-2-1)
+=(+)(-+)5+5=(+)(4-+-+4)2+1+2+1=(+)(2-2-1+2-22--2-1+2)( 2+2)
=
... 1 4 2 4 3
=+
-
=
()=
=
-= 1- =
( ) =
x+x+=0 =-4 >0
=0
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x + x + = 0 x1 x2
S
=
P
=
S P 1 2 1 2 :
x - Sx + P = 0
20 .
x+x+
>0 x1 x2
=0 x
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B
vgyt
u (a.m.u.) 1.66054 10-27 Kg
931.434 MeV/c2
Avogadro NA6.022136 1023(g
mol)-1
Bohr =2
2em ekh
0,52918 10-10 m
Boltzmann k=R/NA 1.3807 10-23 J/K
me9.10939 10-31 Kg5.485799 10-4 u0.51099906 MeV/c2
eV 1.602177 10-19
J e 1.602177 10-19 C R 8.314510 J/Kmol
G
6.67259 10-11
Nm/Kg
=
4e2 2
me8 h
13,605698 eV
mn1.674928 10-27 Kg1.008664904 u
939.56563 MeV/c2
4 10-7 /
= 2
1 c
8,85187817 10-12
C/Nm
Planckh
h2
=h6.626075 10-34 Js
1.05457266 10-34 Js
mp1.672623 10-27Kg1.007276470 u938.2723 MeV/c2
c 2.99792458 10
8 m/s
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