물리ⅰ(핵심요약노트)

2 `

T H I N K M O R E A B O U T Y O U R F U T U R E

.

01.

1.

, .

,

.

2.

(v)(Ds)(Dt)

v=

(v) , Dt 0 .

-`` , .

m/s, km/h

(v)(Ds)(Dt)

v=

(v) , Dt 0 .

- , .

m/s, km/h

, (s)=_ s=v_t

Ds12Dt

limDt 0

Ds12Dt

Ds12Dt

limDt 0

Ds12Dt

, , , .

-A 1111-A 1111

(-) .

[ ]

0P

Q

s

s

t tt

0

R

s

s

t t

S

[ -`` ] [-`` ]

PQ = P = RS = S =

3.

, .

A B (v) . v=v-v (vA, vB) ,

,

,

.

4.

(a) . a .

(a) , (Dv) (Dt)

(a). a=

-``. (a)

, Dt 0 . a=

-``. m/s , cm/s

Dv12Dt

limDt 0

Dv12Dt

` 3

.

=() (

)

0

=

0

[-`` ] [()`-` ]

v

v

v+v

vv

v

vv-v

v

v

vv-v

[ ] [ ]

v

-v v

v

v-v

[ ]

0

v

vA

B

t' t t

AB =

=

[ ]

4 `

5.

, .

, , ,

6.

(a=) , .

v=v+at yy (v t, v, a, t)

s=vt+;2!;at yy `(s, .)

, 2as=v -v ( t.)

7.

-``

.

Rr

v

v

[] [ ]

[ ] [ ]

0

a

t

=

0

a

t

=

[a>0 ] [a

a>0(`=+at)a0a0v0 v}0 , v0 ] [a0 ] [a

6 `

.

. .

..

, .

. . .

..

.

-``

( )cm

3.02.52.01.51.00.50

[ ]

0.8 2.8 4.8 6.8 8.8 10.8

A B C D E F

{cm}

03.

1.

. 3, ,

.

N(), kgf() 1kgf=9.8N

2.

, . , .

F=F+F

F

F

F

.

A B C D E (cm/6)

0.8 2.8 4.8 6.8 8.8

(cm/(6) )

2.0 2.0 2.0 2.0

2.0cm/(6)

0

, 0

F

F

F

F=F-F

F F

F

` 7

.

04.

1. 1( )

0, .

, . , , 0 .

( 1) 0 , . ( 1).

.

..

. ,

.,

.

.

.

P A B C

D

[ ]

[ ]

.

()

[ ]

.

8 `

2. 2( )

, 0 ,

. aF

0 , , .

a

, , 0 , , .

aF_ , a=k

, 1kg 1m/s 1N k=1

a= , F=ma, 1N=1kgm/s

, F=ma . 2

, ,

3. 3( )

. , AB(), BA().

AB()F, BA()F, F=-F. , , 3()

.

,

., . , ,

., .

, , .

, , .

F15m

F15m

115m

115m

.

Fm

F

F

0

3a

2a

a

F 2F 3F

0

m 2m 3m

a

12a

13a

[ - ]

[ - ]

[ 2 ]

F=-F

F=-FF=0

AB

FF

F F

` 9

.

05.

1.

, F=ma .

, .

2.

.(, a=a)

.

., . (, m>m)

Fm

f

F-f=ma a=F-f1125m

T T Fm

f

m

f

T-f=ma, F-T-f=ma

a=

T=f+m_

T=F-f-m_ F-f-f111115m+m

F-f-f111115m+m

F-f-f111115m+m

m

f

m

T

T

m

T-f=ma, mg-T=ma

a=

T=f+m_

T=mg-m_ mg-f11115m+m

mg-f11115m+m

mg-f11115m+m

T

m

m

T

m

m

mg-T=ma, T-mg=ma

a= g

T=mg-m_ g

T=mg+m_ gm-m11115m+m

m-m11115m+m

m-m11115m+m

10 `

.

06.

1.

, .

, . , , g. g=9.8m/s

, F=mg

2.

. , .

, , , . .

, , . (N)

. . N=mg ( f ) , f=lN=

lmg. , .

(l) l , .

. . ( f ') ,

f '=l'N=l'mg . .

(l') l', .

3.

, .

, .

m

=m

{M}

.

F=

G M R

g= GM115R

GMm1115R

F=kx

x

0

[ ]

0

[ ]

msin

mcos

N=mcos

m

.() F=-kx ((-))

,

.F=kx=kx=kxx=x+x

= + = + ,

.

x=x=xF=kx+kx=kx k=k+k

4.

.

..

5.

.

..

115k

115k

115k

F15k

F15k

F15k

` 11

.

P:x=0

O:x=mk-

Q:x=2mk-

kx x

kF

[ ]

O

.

mg125k

k

k F

x

x

[ ]

--+++ -

[] []

N S N N S S

[] []

12 `


.

01.

1.

, ,

. , m

v p p=mv. .

. , . , ,

..,

. ,

.

2.

, ,

.

.

, , .I=Ft

-`` I=Ft -`` .

.

F

0 0 0t

F

t

= =

F

t

=

[ ] [ ] [ ]

, .

, .

` 13

.

F=ma=m FDt=mv-mv=Dp, .

, . ..., .

v-v111Dt

02.

1.

, A, B, .FDt=mv'-mv(FBA, v, v', A)FDt=mv'-mv(FAB, v, v', B)

F=-F, mv'-mv=-(mv'-mv), mv+mv=mv'+mv'. , , .

2.

, .

mv+mv=mv'+mv'

v v v'm m

mv mv

F F

BA

BABA

mv'

m

mv' mv'

[ ] [ ] [ ]

v v v'm m

mv mv

F F

BA

BABA

mv'

m

mv' mv'

[ ] [ ] [ ]

[ ]

[ ]

() , |v-v|=|v'-v'|

, |v-v|>|v'-v'|

, 0 .

14 `

.

mv+mv=(m+m)v'

, .

(m+m)v=mv'+mv'

v

m+mv'

v'

m

m+m m

m

v v' v'

m

03.

1.

, .

. (W)=_=Fscosh (h)J, Nm

W=Fs

h

F=Fcosh, F=FsinhW=Fs=Fscosh

F

s

m

F F F

F

sFx Fx

v v v'm m

mv mv

F F

BA

BABA

m m

{m+m}v'

[ ] [ ] [ ]

- - - - - - -

.

Fs=;2!;mv -;2!;mv

.

(F-f )s=;2!;mv -;2!;mv

` 15

.

2. `-`

-``.

W=Fs W=:)s F(s)ds3.

(P).

P= (W, t)

W(), J/s, HP()1W()1 1J(1W=1J/s, 1kW=1000W)1HP()(1HP=735W)

F, v,

P= = =Fv

. , F v.

4. ( )

, . .

Fs125t

W13t

W13t

0

F

Fs=

0

F

ss

s

[ ] [ ]

h P=Fv cosh

Fs

a

b

h w

F=w_ , s=h_

W=Fs={w_ }_{h_ }=wh, .

b1a

a1b

b1a

a1b

, mgDh.

,

mgDh+;2!;mv .

F=mh

m

0

W=Fh=mgh

hw

F=w, s=hW=Fs=wh, .

16 `

.

w

F

F

h

s

F=;2!;w, s=2hW=Fs=;2!;w_2h=wh, .

w

h

F

s

F=;4!;w, s=4hW=Fs=;4!;w_4h=wh

n

F= w, s=2nh

W=Fs= w_2nh=wh1122n

1122n

04.

1.

, . , .

. (E)m, v(v ).

E=;2!; mv -`` v F s

v,

. , .

2.

. , .

s

FF m

v v

[ 1 ]

[ 2 ]

A

m

v

s

A

m

B

M

B

M

A , B

f ;2!;mv =fs.v -v =2{ }s 2as=v -vF15m

v -v =2{ }sFs=;2!;mv -;2!;mv =W

F15m

` 17

.

.

h h

. m, g, h

, W=Fs=mgh.

x

x , .

k, x

, W=;2!;kx .

F=mh

m

0 0

m

h

W=mh

x

F

0

F=kx

x

12W= kx@

1

2Ep= kx@

0 x-x

[-`` ] [ -`` ]

05.

1.

. , .

, , , .

. .

mgh-mgh=;2!;mv -;2!;mv

mhv=0

O

A

B

v

m

vh

h

h

mh

mh

mv@21

mv@21

[ ]

18 `

.

,

mgh+;2!;mv =mgh+;2!;mv =. , , .

()

..

;2!;mv -;2!;mv =;2!;kx -;2!;kx,

;2!;kx +;2!;mv =;2!;kx +;2!;mv. , . .

()

.

;2!;mv -;2!;mv =mgh-mgh-{;2!;kx -;2!;kx },

;2!;kx +;2!;mv +mgh=;2!;kx +;2!;mv +mgh=. , . .

xkx=mgx= .

0,

mg(x+y)=;2!;k(x+y) , mg=;2!;k(x+y), ;2!;kx=;2!;ky{x= }, y=x.

mg125k

mg125k

kx

kxvx

x F=kx

P

Q

O

x

x xx

F

0

kx@- kx@21

21

F=kx

v

x=0,`h=h,`v=v

x:21-kx@

v:21-mv@

v:21-mv@

h:mhh:mh

x:21-kx@

[ ]

` 19


.

01.

1.

.

(+) .1

, I= C/s, A.

. X(), 1X 1V

1A ..

. ,

.

I= , V=IRV1R

Q1t

, (+)(-) .

C , . 1C 6.02_10 .

0

=1

[-`` ]

0

=

[-`` ]

{-} {+}{-} {+} {-}{+} +

++

+

+ ++

Cl

Cl

Cl

Cl

Na

Na

Na NaNa

[ ]

(-) .

[ ]

(+) (-), (-) (+) .

[ ] (-) , (+) (+) .

:

0

[ ]

02.

1. ,

, . , . (R)(S), (l).

R=ql1S

l

2S S S21-

R=2Sl- R=

Sl- R= S

2l-

20 `

.

q, . 1m, 1m . Xm.

, , , . , ,

, . ,

. ,

2.

R=R(1+aT)

(RT(), R0, a)

.(Pb), (Cu)

. (Ge), (Si)

, ,

, 0 , 0 .

(T) 0. 0,

.,

S S S

l

2l3lR=

Sl-

R=S2l-

R=S3l-

0(K)T

HgT=4.2K

{ }

[ -`` ]

{

m`}

{K}0

10*

10$

10*

10@1

1200400 800

Si

CuGePb

[, , ]

03.

1.

, .

. I=I=I=I

V

I

VI

V V

R R Ra b a b

V

VV=V+V+V

I=I=I=I

R

I I

` 21

.

.V=V+V+V

.VVV=IRIRIR=RRR

.

V=V+V+V

IR=IR+IR+IR R=R+R+R2.

, .

.V=V=V=V

.I=I+I+I

.

III= =

.

I=I+I+I

= + + = + + R=

3.

, .

.

RRR111111111RR+RR+RR

113R

113R

113R

113R

V13R

V13R

V13R

V13R

113R

113R

113R

V13R

V13R

V13R

.R=R+R+R+y+R>R(R>R>R>y>R)

.

= + + +y+ >

(R>R>R>y>R) R

22 `

.

R, V ,

I, 1E.

E=VIt=I Rt= t

J()1J1V 1A .

, 1cal 4.2J . .

Q= = VIt= I Rt= t (J=4.2J/cal)

2.

A, B, C.

A, B, C.

A, B, C.

A, B, C.

V15R

11J

11J

11J

E15J

V12R

.

.

.

.PPP=RRR

.

V VV

A B C

30V

5 10 15

[ ]

A

30V

5

10

15

C

B

A

A

A

[ ]

15

10

5

0

{

V}

C

B

A

21

19

17

150

{

C}

C

B

A

6

32

0

{

A}

A

BC

21

1817

150

{

C}

A

BC

.

PRP= 112R112R112R

` 23

.

, , .

3.

. , .

4.

` . ` .

` . ` ,

.

, .

, .

. , . .

, .

, . .

.

0

+-

.

0

05.

1.

1 .

P= =VI=I R=

W() . W=J/s .

V13R

E15t

24 `

.

.

. ,

I= = R= =

II=11VV=RR=12

PP=VIVI=1_12_1=12

II= =21

VV=11

PP=VIVI=1_21_1=21

2.

. .

W=Pt (t.)Wh(), kWh() . 1Wh1W 1 1Wh=1W_3600s=1J/s_3600s=3600J

, .

3.

.

.

P=I _r={ }2_r(P, r, V)

P12V

112R

112R

V13P

P15I

P13R

P13V

P=VI=I R

P=VI= V13R

V

A{R}

2I

B{2R}

I

V

A{R} B{2R}

I I

[ ]

` 25

.

.

. {I= } n

. . .

110V 220V . (P=VI),

.

113n

11n

P12V

06.

1.

. (.) . , , .

2.

VVV= 211III=312PPP=612

VVV= 112III=112PPP=114

V

A{R} B{2R}

A{R} B{2R}

.

.

A{R}

A{R}

V

1-3V

B{2R}

2-3V

110V ,220V .

.

.

A{4}B{6}

C{3}

4 2A{1} B{1}

C{1}

2

1

26 `

.

VV=12= V V, PP=12=

V=V 3P= , 9

.

3.

...A , B .

A, B....A ,B .A, B.

...AB.A , B .

...AB.A ,B .

V12R

4V1259R

V1259R

213

113

220V

I

A{R} B{r}

220V

A{R}

B{r}

R, r R=R+r

P=

V= V

V= Vr112R+r

R112R+r

V112R+r

R, r

R=

P={ }VV=V=V

R+r112Rr

Rr112R+r

` 27


.

01.

1.

,

., NS.

,

. .

.

.

N.

.

N S , SN.

, .

. .

2.

( U) Wb().U=BS(Wb)

( B)(1m )()

B= (Wb/m =T())U1S

[ ]

N S, N.

.

=BS

S

B

N S

NS

NS

28 `

.

02.

1.

.

. ,

. I, r.

B=k (k=2_10 N/A )

2.

.

, ..

I r.

B=k' (k'=2p_10 N/A )

3.

, , .

, .N, S

. I

n.B=k''nI(k''=4p_10 N/A )

4.

.

.

I1r

I1r

r N

S

={I}

={B}

N S

[]

[ ]

[ ]

[ ]

` 29

.

03.

1. ()

() , .

, , .

,

,

.

F, F I B, l.F=BIlsinh(h)

, .

, . A, B I, I ,

r , I I

B=k , B B

.

F=BIl=k l

2.

.

, .

II112r

I12r

N S N S N S

IB

IB I

B

ll

lsin

[ ] [ ] [ ]

[ ] [ ]

F=BIl ( h=90) F=0 ( h=0) F=BIl sinh

r

I I

A B

FF FFr

ff

ff

f

l

S

F F

[ ]

30 `

.

, .

()

, , , , ,

.

{-} {+}

B C

( )

A D

{-}

B

C

A

D

{-} {+}

C B

D A

{+}

04.

1.

( ) .

, . ,

, .

2.

. ( ) E

N .

E=N =N (V)D(BS)1111Dt

DU125Dt

DU125Dt

F

.

N.

.

N

S

N

S

S.

G G

.

.

S

N

S

N

N.

S.

G G

[N ] [S ] [N ] [S ]

[ ]

` 31

.

05.

1.

,

(AC).

2.

1 2.

1=2 P=VI=VI=P = = = I12

IN12N

V12V

N12N

V12V

, .

v, l ,E.

E=-N =- =- =- =-Blv(V) (N=1)

() ,

, .

F=BIl.

BlvDt1112Dt

BDS1112Dt

D(BS)1111Dt

DU12Dt

N

(( ))

b

aB

FR

S

tc

d avv

v

l

S

b

( )

[ ]

N S

R

2

1

NI IN

V V

[]

[ ]

32 `


.

01.

1.

, .

2.

(A)(k)(T)

( f )1, f=

v

v= =kf { f= }. ,

11T

k1T

11T

[] []

[] []

{}

O

A

-A

{A}

[-`` ]

A

-A

{T}

O

{A}

[-`` ]

A

B

C

A'

A A'

B'

B B'

C'

C C'

[] []

` 33

.

(I)

, (A)( f). I=A f

02.

1.

.

, ,

.

.(i)(i ')

, . .. ()()

180 ()()

2.

.

,

i i '

.

[ ] [ ]

[] []

i=i'[ ]

34 `

.

3.

() .

., .

v, v. 2v.

;2!;.4.

, .

( .)F.F..

( .) F'

.F'..

OF

OF'

O:F:

O:F':

[ ] [ ]

a= 2f

` 35

.

03.

1.

. r.

1 2 , 1 , , , v, k, n, i, 2 , , , v, k, n, r.

n= = = =

2.

, .

. c, 1, v, n

.

n=

1 n, v, 2 n, v, 12.

n= = = =

( )

n= = = = = nsin i=nsinr

.

3.

. . .

n13n

k13k

v13v

sin i113sinr

n13n

113n11113n

v13c11v13c

v13v

c1v

k13k

v13v

sin i113sinr

. . , .

sini= =

sinr= =

= = k15k

v15v

sini115sinr

vt115BA'

BB'115BA'

vt115BA'

AA'115BA'

i`1

`2

A'

A

B

B'r

r

vt

vt

i

.

.

.

[ ]

36 `

.

.. C... C.

FF

F'F'

CC

[ ] [ ]

a= 2f

` 37

.

05.

1.

, y y, y. y=y+y

.

2.

.,

D= = (2m)(m=0, 1, 2, 3, y)

.

D= = (2m+1)(m=0, 1, 2, 3, y)

Dx= k= dDx113L

Lk12d

k12

dx12L

k12

dx12L

y y yy

y

y yy

A

B

A+B

A

B

A+B

[ ] [ ]

D=|SP-SP|=dsinh?d x1L

m=2 m=2 m=1 m=1 m=0 m=0 m=0 m=1 m=1 m=2 m=2

S

P

OS

S

dsin

L

xL

dL

[ ]

38 `

.

3.

.

. D=D'C+CD=D'E=2ndcosr

2ndcosr= (2m+1)`(m=0, 1, 2, y)

2ndcosr= (2m)`(m=1, 2, 3, y)k12

k12

{n}

E

A'A

B

B' D' D

C

d

i

r r r

r

06.

1.

,

.

..

2.

, .

,

, .

dsinh= = (2m+1)`(m=1, 2, y)

dsinh= = (2m)`(m=1, 2, y)k12

dx12L

k12

dx12L

.

[ ] [ ]

O

P

L

d

A

B

d`sin

x

m=2 m=2 m=1 m=1 m=1 m=1 m=2 m=2

[ ]

[ ]

` 39

.

07.

1.

, , , .

,

.

. , . l, k, f.

k= , f= = n (n=1, 2, 3 y)

()

;2!;. l, k, f.

k= , f= = n (n=1, 2, 3 y)

,

.

l, k, f.

k= , f= = (2n-1) (n=1, 2, 3 y)v134l

v112k

4l1112n-1

114

v132l

v13k

2l12n

v132l

v13k

2l12n

3 {= l}2-32 {=l} {=2l}

l

3 {= l}2-32 {=l} {=2l}

l

5 {= l}4-53 {= l}4-3

{=4l}

l

[ ]

1cm

[ ]

40 `

.

08.

1.

. K. .P. P K (-)

, V , EV . E=eV

2.

hf

( W) , E.

E= mv =eV=hf-W=hf-hf=h -h (V)

(W) .

W=hf=h ( f, k)

( f), . ,

., , ,

c1k

c1k

c1k

112

[ ] [ ]

0-V

0-V-V

. .

.

Of

EK=hf-W

-W

{EK}

{

hf}

{

W}

hfv

W

VA

---

P ()K ()

[ ]

` 41

.

09.

1.

() , () .

m, v k.

k= =

, .

.

2.

X. ,

.

V m, e,

V E= mv =eV.

k= , mv='2meV, k= .

. .

(E), (p) E=( f ), (k) v=fk

p112m

h1111'2meVh11mv

112

h1p

h12mv

[X ] [ ]

.

.

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