typologio fysikis a lykeiou (2008)

8/8/2019 Typologio Fysikis a Lykeiou (2008)

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XX. .

, 2008, 2008

u


2/21

2

2 .


3/21

3

. .

Werner Heisenberg

() :2003 2008

GNU GPL

.

. 04.01

ad magorem Dei gloriam

1 /

TK 30020

, , :gpapadem @ sch .gr

. 3
mailto:[email protected]:[email protected]


4/21

4

(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 .


5/21

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


6/21

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


7/21

7

()

()

.

a .

-

.... (uo 0)

(>0) (


8/21

8

= u=uo + t

x = uot +12t2

= u=uo - t

x = uot -12t2

.... (uo = 0)

(>0) (


9/21

9

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


10/21

10

(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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11

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


12/21

12

(Momentum)

p=mu

( ) .

F=0 p=p

(, ) .


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13

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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14

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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15

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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16

() F : P =Fu():

u F u

: Watt, W=Joule/sec HP =750 W (Horse Power = )

:

,

16 .


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17

=

, =

=

, =

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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18

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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20

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


21/21

21

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

typologio fysikis a lykeiou (2008)

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