Solucionario de Fisica(1)

7/25/2019 Solucionario de Fisica(1)

1/139

2dy

Solucionario de Fsica Bsica

0


2/139

INDICE

Vectores.2

Cinemtica.37

Dinmica89

Trabajo, otencia y Ener!a121

1


3/139

VECT"#ESEJERCICIO 4 pg 50 ejer 6

R=|V2-V1||V2-V1|2=V12+ V22-2V1V2COS60|V2-V1|2=2 V12- V1|V2-V1|2=|1|

!12=R2+!22 R"SE#$=%1"SE#90!12=102+102 &='RCSE#(RSE#90"!1)=45!1=14.14*g %1=(14.14*g135)

'=53,+0j-=(-1.76,-18.91j)

-= 484

|-|=22/

'=E E'E='+E 'E"E=EC"E='C" 'E=2E 'C=2E=C EC=E+C

E=2E

R=++++e

2


4/139

'=++eR=++R=2+

R=2+j-2(2)$C$=(42+2+R2)"4

R2='2+2+-2'37 R"e37="e&

R= 37cos10*3*21009 + =re(e37)"7.82R=7.82*g =50.32

R2= '2+2+-2'143 R"e143="e&R= 137cos10*3*21009 + =re(e143)"7.82R=12.53*g =re(e143)"12.53

=28.71R=(12.53*g28.71)

R12=2002+3002-230020075 R12= R12+1152-2R1(155)44.1R12=130000-1200075 R12122966.7-70024.85R1=314.55:g R=230.09

R1"e75=200"e r"e44.1=155"e=37.9 e=27.97&=44.1 ;=27.97+67.1+30

;=125.1

3


5/139

|'+2|= 22 4Ba +


6/139

EJERCICIO 5

COS30=!>"> =7.32#=23.8 !R=(7.3210)#

5


7/139

>=-60" =60.18" $=142.13

'?=100e53'?=79.86" R=(0.18,-0.14j)

'(60.1879.86)" R= 22 14.018.0 +C>=0 |R|=0.23"C?=-80"-=(0-80)"

Se40=!?"!!=80"e40=124.5#

!>=!60 !?=!& !2=!A!>=10060 !?=10045 !2=100120!>=50# !?=70.71# !2=-50#

!([email protected]@-50)#

6


8/139

R= 22 1510 + R2=102+152-21510120

R=18.03 R2=325+150R=21.8

!3>=!172 !12=!1>2+!1?2+!1B2 !2B=!2115

!1>=72 45

!1

2

=45-207

2

-5.36

2

!2B=115 45

!1>=2.09# !1= 01.3345 !2=(5.772.08-2.71)!2=(2.07-5.363.46) !1=3.46 !2=41-2.712-2.082

!2=5.77#

|!|= 222 75.028.38.7 ++|!|=8.5#C=7.8"8.5 &=0.75"8.5=23.42 &=84.9

'=(-4@8@5) =6"16.28|'|= 256416 ++ =68.37|'|=10.25

C&=15"16.28'=(3@5@0) &=48.74|'|= 141 ++|'|=2.45

7


9/139

R2=102-302-21030165 =45-3.73R2=1000+579.56 =41.26R=39.74

R"e165=10"e; &=90-41.26;=3.73 &=48.74

R-S=(1+4),+(7+2)j+(-3-3)*D S-R=(-4-1),+(-2-7)j+(3+3)*DR-S=5,+9j+6* S-R=(-5,-9j+6*)| R-S|= 368125 ++ | S-R|= 368125 ++

| R-S|=11.92/ | S-R|=11.92

C=5"11.92 =-5"11.92

=65.2 =114.8

&=9"11.92 &=-9"11.92&=40.97 &=139.03

A=-6"11.92 A=6"11.92A=120.22 A=59.78

EJERCICIO 6

8


10/139

!1=10015 !1>=96.5915 !2>=50330!1=96.59# !1>=68.3 !2>=43.3#

!2=10060 !1?=96.59e15 !2?=50e30!2=50# !1?=68.3 !2?=-25#

!1=(68.3,+68.3j)# !2=(43.3,-25j)#

'=+ |2|= 164 + $=2"''=(-2,-2j+4*) |2|=4.42 $==24.18|'|= 1644 +++ $=2"|2||'|=4.9/ $=26.51

'=(4.9,S26.54O)

|'|= 222 443 ++ =2"64

|'|=7.07/ =71.8

||= 222 621 ++ &=6"6.4

||=6.4/ &=20.36

'+=(2,+6j+*) A=1"64

|'+|= 222 621 ++ A=81.01|'+|=6.4/

9


11/139

'>=1070 $=B"C>B 152=5.752+9.962+?2

'>=3.42 B=5.75 ?2=92.74

F=9.63/'B=10130 $=C>B"|C|'B=-6.43 C>B=1540

C>B=11.5102=3.422+6.432+'?2 C>B2=B2+>2

'?2=47.34 11.525.752=>'?=6.9 >=9.96/

'([email protected]@-6.43) (-9.969.63-5.75)

2'--C=(6.84-5+9.96),+(13.8-4-9.63)j+(-12.86-+5.75)*D

2'--C=11.8,+8.17j-13.11*

|R|2=11.82+8.172+13.112

|R|=19.44/

)G1=H1-H=(0@2@4) ) GB=6.4:G2=H4-H3=(0-2@0) $=B" G>B

$=51.32

| G1|= 410 +| G2|=2 Hp=(5,+2j+0*)| G3|= 41104 =+

| G4|=2

| G


12/139

CA='B"' '>= 22 AzAxz

C11.7='B"13.5 '>= 22 )99.4(09.12 +

'B=-4.99 '>=11.01

'?=e26.4113.5'>B=12.09

R=(11.01+6j-4.99*)Se58=>"9.43 R'-=R-R>=7.99

g58=7.99"B R'-=11.01,+6j-4.99*B=4.99 7.99,+5.98j-4.99*?="51.96 e30=H?"60H>=44.99 H?=30

C60=H"51.96 H>B=51.96HB=28.98

10.59,-25.08j+10.59*44.99,+30j-25.48*55.8,+30j-15.39*

Se45=>"14.99 e60=?"30S>=10.59 ?=25.98SB=10.59

g60=25.98"S>B

S=(10.59,-25.98j+10.59*)

11


13/139

C?=20e60 CB=C>B30C?=17.32 CB=1030C>B=2060 CB=8.66C>=C>e30 =(517.328.66)C>=10e30 +C=(-2+5,)+(17.32)j+(8.66-3):DC>=5 +C===3,+17.32j+5.66*

>B= m41.666.53 22 =+||=18.47

C$=>">B$=27.99

) C=(5,+17.32j+2.66*) KC=(5,+17.32j+2.66*)"20

|C|= 222

66.232.175 ++ KC=(0.25,+0.87j+0.43*)|C|=20

12


14/139

)V1=200/ #40O eLe.60 V1B=V1>B40

V2=160/ SE eLe.45 V1B=76.6/V1?=200e60 V1=(-64.28,+173.21j-76.6*)V1?173.21/

V2?=160e45V1>B=20060 V2?=113.14/V1>B=100/

V2>B=16045V1>=V1>Be40 V2>B=113.14/V1>=64.28/

V2>=V2>=V2>Be45 V2=(80,+113.14j+80*)V2>=80/ Vr=(80-64.28),+(173.21+113.14)j+(80-76.6)*D

Vr=(15.72,+286.35j+3.4*)

13


15/139

C=>" =5,+5j+7.07* ?=1"2(-2)>=1060 C=(C%-C,)=(2-0)+(2-4)+(1-5)D ?=-1>=5 C=2,-2j-4*||2=>2+?2+B2

B=7.07 '>+>-1"2C>+>=0 B=1"2(-4)-7.07-3

>=-14 B=-6.07=(-14,-j-6.07*)

|'|=100K 60 eLe45 30=>"50

||=50/ 30A75 >=43.3/

'?=|'|e45 75=B"50'?=70.71 B=12.94/

'>B=|'|45 502=43.32+12.92+?2

'>B=70.71/ ?=21.4/'>=70.71e60'>=-61.24/ '>+>+C>=0'=70.7160 C>=->-'>'B=-35.4/ C>=61.24-43.3'=(-61.24,+70.71j-35.4*) C>=17.94/ CB=-B+CB

C?-?-'? CB=35.4-12.94C?=-70.71-21 C=(17.94,-

92.11j+22.46*)C?=-92.11/C=(17.94,-92.11+22j.46*)

|'|=100/ ='>"' '2='>2+'?2+'B2

C=0.7 '>=70 'B2='2-'>2-'?2

C&=0.2 '?=1000.2 'B= 222 2070100

'?=20 'B=68.56'=(70,+20j+68.56*)

14


16/139

2'=10,-4j-3=-12,-15j R=-5,-16jC=-3,+3j

R='- e$=0.46|R|2=102+162-21016105 $=27.53+135|R|2=356+82.82 $=162.53R=20.9R"e105='"e$ R>=R162.53Se$=10e105"20.9 R>=-19.9

R?=Re162.5R?=6.27

15


17/139

'?='e50 '>=3.21'?=7.6 'B='>B30

'>B='50 'B='>B30

'>B=6.43 'B=-5.57'>='>=e30

'(3.21,+7.6j-5.57*)

'=4,-2j+6* 2'=-8,+4j-12* R1prLeL R1-2=2,-8j+2* 3=-3,+12j-3* R=24.54(0.42,+0.7j+0.57*)R1=6,-10j+8* R2=-11,+16j-15*

KR1=(6,-10j+8*) |R2|= 222 151611 ++

222 8106 + |R2|=24.54/

KR1=0.42,-0.7j+0.57*

'C=(2+5+7),+(1-1+2)j+(2+4+1)*D e$=2"15.8

'C=14,+2j+7* $=7.27

16


18/139

|'C|= 222 7214 ++ $"2=3.64

|'C|==15.8

Se$='C?"'C

) (12@6@-4) ) ||= 222 266 ++

(0@-6@-4) ||=8.72(-6@6@-2)

) ||= 222 4612 ++ A=-2"8.72

||=14/ A=-0.23

) K=(0,-6j-4*)" 22 46 + &=6"8.72

K==(0,-0.83j-0.55*) &=0.69

17


19/139

'?='e30 '>='>Be45 = 222 5.27155.30 ++

'?=20 '>=24.5 =43.7

'>B='30 'B='>B45


20/139

!2=(63.64+90),+(217.28)j+(150)*D !1=21.21,+72.43j-50!2=(51.21,+72.43j-50*):p !2=51.21,+72.43j-50*

!3=25.21,-0j-50*NNNN!r=(123.63,+144.86j-150*):p

'(20,+50j+40*) >B=4530 K=(0.6,-0.8j)?=45e30 >B=38.97?-22.5 C=(0.6,-0.8j)20

>=38.97e60 C=(12,-16j)>=33.75

+'=(33.75+20),B=38.9760 +(22.5+50)j+(19.5+40)*B=19.5=(33.75,-22.5j+19.5*) +'+C=(53.75+12),K=(3,-4j)" 169 + +(27.5-16)j+(59.5)*

?=e40 B=57.45 60 K+C=(0.11,+0.82j+0.56*)

?=48.21: B=28.73:

19


21/139

>B=#40 =(49.8,+48.21j+28.73*): =0.11>B=57.45: =83.7

K=(-5,+12j+9*)"15.81>=57.45e60 K=(-0.32,+0.76j+0.57*) &=0.82>=49.8: &=34.9

C=100(K) A=0.56C=(-32,+76j+57*): A=55.9

+C=(49.8-32),+(76+48.21)j+(28.73+57)*D:+C=(17.8,+124.21j+85.73*)*

K+C=(17.8,+124.21j+85.73*)"151.97

'?=8e30 'B=6.9360 >B=5'?=-4 'B=-3.47

>=5e45'>B=830 '=(6,-4j-3.47*) >=-3.54

'>B=6.93 ?=10e60 B=545'>=6.93e60 ?=-8.66 B=3.54'>=6

>B=1060 =(-3.54,-8.66j+3.54*)

=-' =-0.005=(-6-3.54),+(4-8.66)j+(3.47+3.54)*D =90.3=(-9.54,-4.66j+7.01*):

= 222 01.766.45.9 ++

=12.72:

20


22/139

24.

C>=12 245 '=5,-10j+7*C>=12, =9,+4j+2*C?=12 2e45 C=12,+12j+0*C?=12j R=26,+6j+9*

C=(12,+12j+0*)

EJERCICIO7

K=(24,+6j+8*)" 222 8624 ++ A=0.31

K=(0.92,+0.23j+0.31*) A=72

!=520 K A=!B"!!?=5200.23j !B=5200.31*!?=119.6j !?B=119.6j+161.2*

'+R= Kr=(0.41,+0.82j+0.41*) !=Kr|!|

R='- !=(32.8,+65.6j+32.8*)R=(,+2j+*)

21


23/139

'+R=sen

R

sen

A=

30

R=-' e$=15e308.06

'2=152+102-21030'2=325-260 e$=0.93'=8.06 $=68.52

C='>"' e60=?" >B=2060'>=1050 ?=20e60 >B=10'>=6.43 ?=-17.32

CA='B"' 60=>B" 50=B">B'B=10100 B=1050

22


24/139

'B=-1.74 B=6.43

102=6.432+1.742+'?2 e50=>">B>=10e50

'?= 63.55 >=7.66

'?=7.46=(7.99,-17.32j+6.43*)

'=(6.43,+7.46j-1.74*)

)'=' $

$=20*10

)74.1*43.6()46.7*32.17()43.6*66.7( ++'=(117.11)(

K')'=-5.86,-6.8j+1.59*

$=-0.46 |'|=9.12

$=117.11

K'=(6.43,+7.46j-1.74*)"10 '=74.146.743.6

43.632.1766.7

kji

K'=0.64,+0.75j-0.17*

'=17.83,-54.87j-168.52*

|'|=178.05

R=4,+3j r$ =(r')"' R'=(4,+3j)(0.5,+0.87j)( 0.5,+0.87j)R=R$K' r$=rK' R'=2.31,+4.01j

K'=60,+30j R'=r(K') K'DK'=0.5,+0.87j

23


25/139

'=(-3,+4j) 30= >B"|| K=-0.61,+0.5j-0.61*'=5 ||30=>B '=(' K) K

K'=-0.6,+0.8j '=(1.83+2)(-0.61,+0.5j&=?" 45="30|| -0.61*)e30=?"|| 4530=B" '=-2.34,+1.92j-2.34*0.5= ?"||

='=61.05.061.0

05.06.0

kji

=(-0.49,-0.37j+0.19*)10=(-4.9-3.7j+1.9*)

(2)

2

=

2

+

2

+

2

K>-B=( 2,+:)"

22

2 aa +

42=22+2 K>-B=(0.82,+0.88j)42-22=2

C= 22a =0.82,

C= 2 =0.58:

V=( 2,+j+*) &=0.5j

V>-2=( 2,+:)

=("3,+ 2j-*) )-'=-17,-1.19j-5*=C)|'|=5 (-')>?=-1.17,-1.19j=

24


26/139

C=C$|'>?|=3 $=(1.37+1.42)2

C30='?"3 (5.27)(1.67)3e30='?'>=1.5 $=2.79"8.80

$=71.52

'B2=(5)2-(1.5)2-(2.6)2 '-=1.17,+1.19j*+5*=E |E|=5.27'B2=252-9.012 Ke=(1.17,+1.19j+5*)"5.27

Ke=0.22,+0.23j+0.95*'B=4

C$=E>"E=1.19"5.27'=(1.5+2.6j+4*) $=76.95

K!=(-5,+7j-5*)"9.95K!=-0.5,+0.7j-0.5*

E%=(1.17,+1.19j+5*)K%D K%E%=(-0.59+0.83-2.5) K%E%=(-2.26) K%E%=(1.13,-1.58j+1.13*)

|!|= 222 21 Fz++ 60=10"5 25 Fz+

|!|= 25 Fz+ P=10"5 25 Fz+

|r|= 22 34 + !B2=16-5

|r|=5 !B=3.32#

!R=!R$

)C=60 )=90||= 251+ =0||=5.1 r=5B=0

K=(1j+5:)"5.1 5,+7j=(0+>),+(0.2C+?)j+(0.98C+B):K=0.2j+0.98* >=5

25


27/139

=C(0.2j+0.98*) ?+0.2C=7=0.02Cj+0.98C* C=-B"0.98

7=0.2(-B"0.98)+?70-0.2B+?

?0-5(-1.35)-?-5B=0 ?=6.75?-0.2B=7-5.2B=7 C=-(-1.35)"0.98

C=1.38B0-1.35*

=(5,+6.75j-1.35*) C=(0.28j+1.35*)

)122=2+92+0.04 )2'-3=(6,+4j+110*)-(11.4+34.2j+0.63*)144-0.04=102 R=-5.4,-30.2j+9.37*2=3.8

2-4=(8,-6j+24*)-(15.2,+45.6j+0.84*)=3.8,+11.4j+0.21* R2=-7.2,-51.6j+23.16*

RR2=16.236.512.7

37.92.304.5

kji

=-215.93,+57.64j+61.2:

Rr2=(RKR2) KR2 Rr2=(0.68+27.48+3.84)KR1

KR2= 222 23.1651.6-7.2

23.16k51.6j-7.2i

+

+

Rr2032KR2

KR2=-0.13,-0.91j+0.41* Rr20-4.03,-29.12j+13.12*

52=(50.3)2+(50.2)2+52 Rr20(0.68+27.48+3.84)KR225-2.25-1=25 2 Rr2032KR2C2=0.87 Rr20=-4.03,-29.12j+13.12*

C=0.93

26


28/139

V=(1.5,-j+4.55*)Se30='?"''?=15e30'?=7.5C30='>B"'

'>B=13

64=(80.3)2+(8)2+(80.46)2

642=64-5.76-13.54 50=">B |R|=17.47C=0.84 B=9.4"50 5"2'=-23,+18.75j-23*

'=2.4,+6.72-3.68* e50=>">BSe20=?"|| >=9.4"e50?=10"e20 >=7.2?=3.42

=7.2,+3.42j-6.04*C20=>B"||>B=1020>B=9.4 3'=7.2,+20.16j-1104*

-=-(3.6,+1.71j-3.02*)R=16.74j-5*

'E=(4,-3j+6*) 'E!=('EK!) K!|'E|=7.81 'E!=(2.04-1.14-4.62) K!!=(4,+3j-6*) 'E!=-1.89,-1.41j+2.86*K!0.5,+0.38j-0.77*

27


29/139

Se45=V?"V 25=32+(5)2+4V?=30e45 25-9-4=252

V?=21.21"2 =(3,+3.45j-2*)"2

C$=(')"'V>B=21.21" $=(-31.83+73.17+36.74)"150

$=58.63

C30=VB"V>BVB=21.2130VB=-18.37"2

Se30=V>"V>BV>=21.21e30V>=-10.61"2

V=(-10.61,+21.21j-18.37*)"2

K=(3,-j+*)" 11 '='B'/K=0.9,-0.3j+0.3* '/=(,+4*)-(1.62,-0.54j+0.54*)

'/=-0.62,+1.54j+3.46*'F='B'B=('K') K''B=1.62,-0.54j+0.54*

28


30/139

'=2,+j+2*=,-2j+3*

'=('K) K'=(1.61)(0.27,-0.53j+0.8*)()

K=(,-2j-3*)" 14 '=0.43,-0.85j+1.29*K=0.27,-0.53j+0.8*

'=,+j+* 20= 222 14.029.004.0 ++ V

=,+8j-4* 20=0.32V||=9 V= 3

K=0.11,+0.89j-0.44* K'=0.58,+0.58j+0.58*K=(0.06,+0.52j-0.26*)V(K) V=V0.58,+V0.58j+V0.58*K=(0.04,+0.29j-0.14*) V=35.8,+35.8j+35.8*

|V|=20/ |-'|=17.83 E=-C='+V K-'=-0.28,-0.11j+0.95* E=-2,+4j-7*V='+V V=-11.2,-4.4j-38*V=-' |E|=8.31

V=-5,-2j-17* KE=-0.24,+0.48j-0.84*

VE=(VKE) KEVE=(2.69-2.11+5.88) KEVE=6.46(-0.24,+0.48j-0.48*)VE=-1.55,+3.1j-5.43*

29


31/139

EJERCICIO 8

=(2,+3j-6*)-(-2,+6j+3*-(4,-2j-3*))=(2+2-4),+(3-6+2)j-(6+3-3)*

=-1 '=(-4,+3j+9*)

=-1 H'=(-3,+4j+10*)=-1 |H'|=11.2

=-2,+6j+3* H=(-1@-1@-1) 'H=-3,-4j+5*

-'=-2,-3j+6* '=111

362

632

C=4,-2j-3*NN=j+6* '=34.5/2

0=2+2-41=3-6+26=-6-3+3

=(-2@10@-20) 'C= 20102020620

kji

E=(-20@0@0) K'C=0.37,+0.92j+0.09*KE=-,E=(KE) KE V=7.4,+18.4j+1.8*E=20(,)E=-20,=V'C=(-20@6@20)

30


32/139

'=([email protected]) 'B=('KC') KC''C=(4-3@0) 'B=(3.2+4.8)(0.8I-0.6J)

KC'=(4,-3j)"5

KC'=0.8,-0.6j 'C'=1"2034

884

kji

'C'=12,+16j+10*

'=(4,+2j-7*) 'C=1"2577

724

kji

'C=(.7,+7j-5*) 'C=19.5,+34.5j+21*C=(-11,+5j+2*) K''C=(19.5,+34.5j+21*)"44.85

=0.43,+0.77j+0.47*|'|=8.3|'C|=11.09|C|=12.24 V=(6.8,+12.018j+7.48*)

'=4,-9j+* =1"2(99,+16*+9j+81*-4,+44j)'C=9,+4j-11* ''C=47.5,+26.5j+48.5*=RC=5,+3j-12* KR=(47.5,+26.5j+48.5*)"72.87

KR=0.65,+0.36j+0.67*

''C=1"21149

194

kji

E=15/

E=9.75,+5.4j+10.05*KC=(5,+13j-12*)"18.38

31


33/139

KC=0.27,+0.71j-0.65*

'C=('KC) KC=(1.08-6.39-0.65) KC=-5.96(0.27,+0.71j-0.65*)

=-1.61,-4.23j+3.87*|'|=5.95

'=(,-j+2*) E=-15,-16j+35*'=(3,+5j-*) |E|=41.3

'C=(4,-5j+4*) KE=0.36,-0.39j+0.85*'C=(4,-5j+4*)

'=('KE) KE

E='C'=153

454

kji

=(0.36+0.39+1.7) KE

'E=0.88,-9.56j+2.08*

==-20,+10j-20* )'=2j-20*E=-20, =-20,+10j-20*|E|=20

'=201020

2020

kji

E=(KE) KE

=20(-,) !=-40,+400j+40*+200,E=-20, !=160,+400j+40*

|!|=423.67K!=0.37,+0.92j+0.09*V= K!(|E|)V=7.4,+18.4j+1.84*

32


34/139

'+=11,-j+5* |'|=9.11'-=-5,+11j+9* )'(')='(')"$2'=6,+10j+14* $045.52'=3,+5j+7*

'('+)=5111

753

kji

=25,-3*+7j-55*+7,+15j

'+=11,-j+5*-'+=5,-11j-9* '('+)=32,+62j-58*2=16,-12j-4*=8,-6j-2*

Se40='?"15 =7.5,-125.5j+25*'?=9.64 252=7.52+11.52+252

2=0.66C40='>B"15 =0.81'>B=11.5

C=7.5,-12.5j+20.25*Se60='"11.5 3'-5C=(28.98-37.5),+(28.92+62.5)j+(-17.25-101.25)*'>=9.96 =-8.52,+91.42j-118.5*

C60='B"11.5 7+5=(28+35),+(14+75)j+(-21-150)*'B=-5.75 =63,+89j-171*

'=9.66,+9.64j-5.75*

Q=1718963

5.11842.9152.8

kji

Q=-5096.58,-8922.42j-6475.14*

33


35/139

)R=R-=(,-j) '=1"2

112

121

123

=1"2(-2)

HR= 22 )21()31( ++ '=1

HR=2.24)H=H-=(2,-4j)

C18='?"' '=006.5754.18

045.449.22

kji

'?=-57.06 '=2130.77:

Se18='>"' '"'=$'>=-18.54 $=134.74

'=-18.54,-57.06j

'=05.499.22

006.5754.18

kji

=-824.1:-1306.67:'=-2130.77:

C='"' '2='>2+'?2+'B2 60=>B"'=1050 '?2=100-(6.43)2-(1.71) >B=2060'=6.43 '?=7.46 >B=10

CA='B"' '=(6.43,+7.46j-1.74*) e50=">B'B=10100 e60=?" >=7.66'B=-1.74 ?=20e60 50=B">B

?=-17.32 B=6.43

34


36/139

=(7.66,-17.32j+6.43*)

K'='"10

K'=0.64,+0.75j-0.17* '=

43.632.1766.7

74.146.743.6

kji

K="20 |'>|=178.05K=0.38,-0.87j+0.52*

) '='$ K'='K'>$=(49.25-129.21-11.19)"200 K'>=0.1,-0.31j-0.95*$=117.1

)'=20117.1K' V=' K'>'=-5.83,-6.83j+1.55* V=9.11(0.1,-0.31j-0.95*)

|'|=9.11 V=0.91,-2.82j-8.65*

) '=-'=-,-j-2* ''C=1"211

211

i

kji

) |'|=2.45 =1"2(,+3*-2j+2*-6,-j)) 'C=C-'=,-3j-* |'C|=3.32

)''C=$ '=1"2 222 435 ++

'CC$=4"2453.32 '=3.54/

2

$=60.5

=(-1.74,+7.66j+6.19*)

C=>" =425

19.666.774.1

kji

35


37/139

>=10100>=-1.74

C&=?"?=1040

?=7.66

102=1.742+7.66,2+B2 |'|=67.08B2=100-61.7 K'=0.64,+0.57j-0.52*B=6.19 K'=-0.64,-0.57j+0.52*

V=|"2|=K''=(43.12,+37.97j-34.82*) V=(-5.3,-4.7j+4.3*)2'=10,-4j+8*-=1.74,-7.66j-6.19*C=11.74,-11.66j+1.89*

"2=5.87,-5.83j+0.97*|"2|=8.32

CINEMATICA

EJERCICIO 9

1.-Encont! "! #$"oci%!% &$%i! ' "! osicin in!"+ s!,i$n%o $ n!

!t/c"! !t$ %$" nto (201)& ' s$ %$&o! 5s !! ""$! ! $ $st!

!" E %$ . $ s!,$ $ $" &%"o %$" %$s"!!&i$nto $s 20&

36


38/139

o(201) &%t

:5s &205

%200& &4&s

;20&E ;-oCos4520 s$n45 t) * t%10(8>2) 10(2> t)12.5* t

%100& t812.5&s

37

)37( jiV =


39/139

4.-

% t t t %444.44 %$

8002 %800-20 %< %(800-444.44)& %$

32&s4032

800 xx

%355.56 %$

3200720.083

55B&A t12855 :t2.713A

18&in0.3A t2.33A

5&in0.083A

&128B&2.73A &47.18B&A

6.-%os i"$s s$ %$s"!!n 1.6B& $n "! &is&! %i$ccin. E" i&$o con

n! #$"oci%!% %$ 5.2&s ' $" s$n%o con 4.5&s. E" i" &Ds Di%o

%! n #$nt!j! !" &Ds "$nto o%D !!nc! so"o %$ss %$ $ $" &Ds "$nto

!s$ o ci$to nto &!c!%o $n "! ist!.

Fon%$ %$,$ $st! $s! &!c! !! $ ""$$n "os %os i"$s !" &is&oti$&o

5.0 &s :AV

r

AV

r:

BV

xr

4.5&s : :7200832-5.2t2:o' ;t1.41>3.46

:(14.14j)&s ;t4.87s

:1.41

L&!o't-9t2

L&!


64/139

;'-44.1&

H44&

L


65/139


66/139

o 22 VoyVox +

o 2530.16 2 +

o17.11&s

'o-t'16.36-9.8*3

'-13.03&s

LtM


67/139

o-t

:40j10&s 2ot-t22

:#8s 2(240i>320j)*320

L6.19

22 senVo

19.6'o2s$n2M t!n-1(4529.77)-45

26.19 senVO=M29.72 11.56

O


68/139

!t3.42&s2 'o'>!'t

29.24s$n(-70)o'>(-10)(4.48)

o'17.32&s

o10i>17.32j(&s)

2

3.92 2250

29.24&s

'os$n53t-5jt2 1.50

:1.12s

67


69/139

8.43j)(0.5i>0.86j) 7.25 '692.82&s

!t9.7&s2

@#0.5i>0.86j

200&

68


70/139

:sos$nM tsos$n

:s0.05o ts0.08o

ot!0.05 o(ts)0.08

0.08:s0.05:s :!:,

:sP:s

o


71/139

200ocos30t o12!12t2

-300os$n30t>12t2 -300o'(9.12)>12(-10)(9.12)2

-300(230.94t)s$n30t>12(-10)t2 o'12.7j&s

:9.12

'o'>t

'12.7-10*9.12

'-78.5j&s

(21.93i-78.5j)&s

A!o't-12t2

A!25*1.7-4.9*1.72 AA-H

A28.34& A28.34-22.65

A5.69&

Ao't-4.9t2

A21.6*1.7-4.9*1.72 o


72/139

H22.65& o


73/139

1240.041A

!cQ2*R Q2!%t2240.26!%A

!c430.95k&A2

#Q*R

(6375)(0.26)

1668.97B&A

750#$"t!s 2!% 1&in 78.53!%s

2.5&in 1#$"t! 60s

%M*R

%(4712.38)(0.7)3298.67&

!cQ2*R

!c(4712.3810)0.7 #Q*R

!c329.86&s2 (78.53)(0.7)54.97&s2

72


74/139

#Q*R3k*515B 5k()-0.6i>0.8j

!c Q2*R9B2*545 B2 (-9i>12j)&s

!c45 B2(-0.6i>0.8j)

!c(-27i>36j)&s2

1200$#125.66!%s

:2!%Q0.05s Q*

(125.66)(2)SMt 251.32&s

M (125.66)(10)1256.6!%

!cQ2*R

!c(1256.66)2*2

!c31580.87&s

ct$72B&A20&s S*R !cQ2*R

M 300.52!% 20S*160 !c(18)2*160

150& S18 !c2.5&s2

73


75/139

S80& MQ*t 29.7j)&s2

S4!%sR0.25&

74


76/139

1&s

c2R

c4&s2

EJERCICIO 15

;Mts1s30 30 !%s

Q*R4!%s 0.5&2&s2

75


77/139

oSo* !cQ2*

So22 12.52Q2

So1!%s Q2.5!%s

SSo>t !t*t

2.51>*3 !t0.5*2

0.5!%s !t1&s2

S2So2>2;M T45>59.2104.2

(2.5)21>2*0.5;M T255.81

;M300.8R-0.49i-1.94j


78/139

smacR 71.64515*3* ===

SooR3.531.67!%s SR6.7132.24!%sU(S-So)t(2.24-1.67)50.11!%s$

! 22 atac + 22 33.015 +

!15&s

M315*18074

(cos152.44i>s$n152.44j)

3&(-2.66i>1.34j)

Vt!n-1!c!t150.3388.74

t* Q 2So2>2 ;M Q*

210 Q 22*0.2*73 1.71(9.66i>2.585j)

0.2!%s2 S1.71!%s$ 16.52i>4.43j

!t

2.58j) !t28.32i>7.6j

!c28.32i>7.6j 1.932i>0.51j

'10s$n15

'2.58j !t(3025i>8.12j)

77


79/139

SSo>t Q*

S2!%s>2!%s2*s 4!%s*&

S4!%s 4&s

;M tWoWf

*2

0 (1.49i-3.71j)&s

;M(4>2)2

;M9!%171.89

M171.89>30

M01.89

t :#

12.562 6.28*3*2

12.56!% 37.68&s

n;M212.562 Q* S 2 So2>2;M

n1.99#$"t!s S37.682 (8.8)22*6.28;M

S18.84!%s ;M28.26!%

Q2Qo2>2; M

(12.56)

2

2*6.28; M; M12.56!% A!st! t2s----n2#$"t!s

78


80/139

A!st! t3s----n4.5#$"t!s

GM*R ;MS,*t>12t2 SSo>!t

M 4!%*10& 24 S2*2


81/139

;MSot>Ut ;MSot>Ut

220*t-20t22 ;M20*2-20*4 2

20t2-40 t> 2 ;M2 oi 360

;MSot>Ut2

;M20*2

;M10

% tWoWf

*2

+

o>!t !c 2t

% t*2

105+!t(10-5)5 !c100100

!t1&s2 !t1 &s2

!: 22 acat +

!:

22

11 +!: 12 &s2

80


82/139

SooR4150.27!%s SSo>Ut

;MSo*t>Ut22 S0.27>10.50*34

U-2.940.28s3 S8.15&s

U10.50!%s !t0.27>10.50*2

S1So>U !t157.5&sS110.77!%s S221.27!%s

!c 22 atac + !c 22 atac +

!c 22 5.1571739389 + !c 22 5.15799.7108 +

!c17.47&s2 !c7110.73&s2

U (S-So);t30!%s !c900*(cos116.64>s$n116.64)

So*R30!%s !c(403.54i-804.46j)&s2

!t U*R> Ut22 !t5(s$n116.64i>cos116.64j)

!c 22 atac + 22 5900 + 900&s !t(-4.47-2.24j)&s2

;M90!%*M*116.64

!(-4.47i-2.24j)>(403.54i-804.46j)

!(399.07i-806.24j)&s

!

81


83/139

oSo

So4!%s$

!t*!t(-3)(1)

!t-3!%s2

;MSot>t22 S1So>t S 2 So2>2;M

S2(120-3*8)4 24!%s3*t 016>2(3);M

S124!%s t8s ;M77.74

H7.642

H1.22#$"t!s

;M ;M ;M2 V30-11.84

;M77.47-65.9 V-18.16341.84

;M11.84

R


84/139

!c 22 93.85143.8 +

!c851.97&s2

!) R3002 150& SSo>t !c30150

120&20&s*t !c(25-15)t !c6&s2

:6s !t1061.67&s2 ! 22 atac +

! 22 67.136 +

!6.23&s2

,) o>!t

t(-o)!t(30-15)1.678.98s So151500.1!%s

;MSot>t22 !tR1.671500.01 !%s

;M0.1!%*8.98>0.01*8.9822

;M1.30!%

;MSot>t22 S1So>t S 2 So2>2;M

S2(120-3*8)4 24!%s3*t 016>2(3);MS124!%s t8s ;M77.74

83


85/139

;MSot>t22 ;*t

7 420t>100 t22 ;t

200 t2>80t-20 100.01

t0.0425 100&s

SSo>t M tWoWf

*2

+

St1!%s>1!%s2t M(3>1)2*2

S3!%s ;M4!%229.18

S*R3&s ;M M W M

229.18 M-45

M274.18

??(cos4.18i>s$n4.18j)

(2.99i>0.22j)

84


86/139

S200&20.94!%s$ S*R

2!%s R(20.94)(0)

!,

(S*R)

R10c&0.1& R(6.98!%s)

R30c&0.3&

SSo>t6.98*2:

:4.445s

85


87/139

%R*M M1.56!%89.38 2R!c

%2*2 !tR 2*1

% & 1!%s -1.41j

SoR SSo-t

So42!%s S2-1*1.5

So2!%s S0.5!%s

S*R!c M tWoWf

*2

+

(0.5)22!c M(0.5>2)21.5!%107.43

!c0.5&s

!t

1!%s n ;M282 1.27#$"t!s

n ;M2182 2.86#$"t!s

oSo ;MSot>12t

86


88/139

So4!%s ;M12(1)(36)

o>!t nt1.27>2.86

04>(-1)t nt4.13#$"t!s

:4s

87


89/139

Dinmica

1.- "!s sii$nt$s $!s X1(-6i>4j)+ X2(9i-5j)+ X3(17i) s$ !"ic!n

so,$ n o,j$to o%ci$n%o n! !c$"$!cin %$ 3+5 &s2

!) YCD" $s "! %i$ccin %$ "! !c$"$!cin Z ,) YCD" $s "! &!s! %$" o,j$to Z

c)i $" o,j$to $st! inici!"&$nt$ $n $oso c!"c"!"! #$"oci%!% %$ss %$

20s

[ F F 1> F 2> F 3 !) ?[ F ?&*!

F 1-6i>4j @@!

F29i-5j @

+

02+2002+20

20 ji

F 317i

[ F 20i-j @0+99i-0+05j

?[ F ? 1202 + ,) ?[ F ?&*3+5&s2

?[ F ?20.02 m=5+3

02+205+7B

c) 0>!t

(3+5)(20)70&s

2.- ! #$"oci%!% o&$%io %$ n! &o"c"! %$ nit$no $n $" !i$ $s %$

!o


90/139

6+721 !t2 A11+64&

3+27&s ;'2

1(3+27)*12

A21>1+642+64&

;'1+64

:1(3+27>9+8)13+07

4.- os inst&$ntos %$ n "o,o &$t$oo"ico ti$n$ n &!s! %$ 1B. !) $"

"o,o s$ s$"t! ' $j$c$ n! $! A!ci! !i,! %$ 50 so,$ "os

inst&$ntos YCD" $s "! !c$"$!cin %$" "o,o ' %$ "os inst&$ntosZ %)F$ss %$ $ $" "o,o A! !c$"$!%o %!nt$ 10 s$n%os + "os

89


91/139

inst&$ntos s$ s$"t!n YCD" $s #$"oci%!% %$ "os inst&$ntos $n $"

&o&$nto $n $ s$ s$"t!nZ %) YC!" $s "! $! n$t! $ !ct]! so,$ "os

inst&$ntos %$ $ s$ s$"t!nZ %) En $ &o&$nto "! %i$ccin %$ s

#$"oci%!% co&i$n! A!ci! !,!joZ

&1B !)X&*!

X5 50.125*!

!40&s2 !40&s2

t10s

,) 0>!t c) X10

40*10

400&s

5.- n tin$o %$ 50B %$ &!s! s$ $&j! ! "o "!o %$ n! s$ici$ "!n!

c,i$t! %$ ni$#$. E" co$ici$nt$ %$ o!&i$nto $stDtico $s %$ 0.3 ' $" %$

o!&i$nto cintico $s %$ 0.1 !) YCD" $s $" $so %$" tin$oZ ) YT $!

s$ $i$$ !! $ $" tin$o co&i$nc$ ! &o#$s$Z c)YT $! s$

$i$$ !! $ $" tin$o s$ &$#! con n #$"oci%!% const!nt$Z F) n!

#$ $n &o#i&i$nto YT $! %$,$ !"icDs$"$ !" tin$o !! !c$"$!"o !

3&s2Z

&50k !) [X'0 ,) [X0.10.4

Xt @t*

[X


92/139

6.- n! $son! %$ &!s! %$ 78B. $ $nc$nt! $n n !sc$nso. !! "!s

sii$nt$s sit!cion$s %$t$&in$ "! $! $ $" iso $j$c$ so,$ "! $son!

c!n%o

!) E" !sc$nso !sci$n%$ con #$"oci%!% nio&$

,) E" !sc$nso ,!j! con #$"oci%!% nio&$c) E" !sc$nso !c$"$! A!ci! !i,! ! 2.5&s2

%) E" !sc$nso !c$"$! A!ci! !,!jo ! 2.5&s2

$) E" c!,"$ s$ o&$ ' $" !sc$nso c!$ "i,$&$nt$

&78B

!) !X&: ,) !X&: c) !X&:

78078 78078 2.5*78

780 780 780

$) 780-7800

7.-n! $$`! $s$! %$ 1B s$ s$"t! !" t$cAo %$ n n o &$%io %$

n Ai"o. C!n%o $" n !c$"$! nio&$&$nt$ $" o,j$to s$ %$s"!!

%$s%$ s osicin #$tic!" %$ t!" &!n$! $ !" !"c!n! $" $i"i,io $"

Dn"o $ o&! $" Ai"o con "! #$tic!" $s %$ 15 YCD" $s "! !c$"$!cin %$"nZ

!) [X


93/139

@k0+30 !! "! &!s! ' @s0+50 ' @k0+40. Inici!"&$nt$ !&,os

,"o$s s$ $nc$nt!n $n cont!cto ' son %$j!%os $n "i,$t!% !) $nc$nt$ "!

!c$"$!cin %$ c!%! ,"o$ ' "! $! %$ cont!cto $nt$ !&,os.

,)Enc$nt$ "! !c$"$!cin %$ c!%! ,"o$ ' "! $! %$ cont!cto $nt$

!&,os si int$c!&,i!n ss osicion$s.

[X'0

-&**cos300

&**cos30

[X


94/139

@0.27

10.-H!""! "! $! n$c$s!i! !! inici! ! &o#$ A!ci! "! %$$cA! $"

c$o %$ 200B $ s$ &$st! $n "! i!. E" co$ici$nt$ %$ o!&i$nto

$stDtico $s @0.35

&1100B - @- @0

&2200B -(0.35)!-(0.35),0

@0.35 :cos30- @!0

[X'0 :cos30-0.35(@!-:cos35)0

-0 :35.65

!100-33.65(n30)

1960 !83+17

[X


95/139

C$o1

[X


96/139

:1-2! 19.6 29.4s$n30-29.4cos30-t1>t2&*!

10.76-:1>:2&*!

:2>10.76-:13!

:1>:2>3!-10.76

c$o 3[X


97/139

&1&22 B

c$o &1 C$o2 &2[XQcos&* S'Scos

!*t!n

16.- Fos c$os %$ 15 ' 30 $stDn con$ct!%os o n! c$%! ' so,$ n"!no inc"in!%o %$ 45 C!n%o "os c$os son so"t!%os !)YCD" s$D "!

t$nsin %$ "! c$%!Z ) YCD" $s "! !c$"$!cin $ !%i$$nZ

96


98/139

C$o1 c$o2 !4.19&s2

S15 Q30 :0.88

[X


99/139

c$oC c$o

[X(:2-15)&*!

[X'0

'

0

19.- F!%o $" sist$&!. Enc$nt$ "!s !c$"$!cion$s con $ s$ &$#$n "os

,"o$s

C$o &3 c$o &1

S200*9.8 [X


100/139

[X'&*! :2-


101/139

Q200&*!20.41B

S200&20.41B

S


102/139

K!30B %ot>12!t2

S!2.49 !0.32&s2

@0.2 [X24.5

t2t 15!C

[X15!c !4.9&s2

:!49-5!9-20!15!C !C0!2.45&s2

101


103/139

&!&!>&C!C

&!40!>15!C

24.- F$t$&in! "! !c$"$!cin con "! c!" s$ &$#$ "os c$os $n "! i!

!) ' ,) :!&,in "! t$nsion$s $n "! c$%!s. bn$ $ "so c$os s$%$s"i!n sin iccin &1200 &2180 30 V60

!

S0.98

S12!t2ot>4t2[X


104/139

26.-H!""! "! !c$"$!cin ' "! $! X A!D $ $" ,"o$ %$ $so S+ $st$4 !

nto %$ %$s"i!s$ so,$ "! s$ici$ inc"in!%! t!" co&o s$ &$st! "!

i!

E" co$ici$nt$ %$ o!&i$nto $n $" "!no inc"in!%o $s 1 ' $nt$ "! c`! ' $"

s$"o $s 2

[XQ1)(!> @2) [X


105/139

:1702.176>100!1

-t1-980>100\2!1>!22.78

:18873!22.78

!20.93

!11.87

28.-E" ti!nt$ %$ n! to$ $st! !s$!%o $n &$%i!nt$ n $no+ "! t$nsin

$n $" c!,"$ $s %$ 2500 F$t$&in! !)"!s co&on$nt$s X


106/139

4i>j-7k

()9

@-0.44>0.44-0.77

$! $n -00i>200j-350B()

30.- n! c!! S $stD ss$n%i%! %$ 3 c!,"$s+ co&o s$ &$st! $n "!

i!. F$t$&in! $" #!"o %$ Q+ si "! t$nsin $n $" c!,"$ F $s %$ 975

F975 FC9i>12j

F'-F(12j-5k) @Fc0.6i>0.8j

F13 F-6i>12j>4k

@F0.92j-0.38k @F-0.43i>0.86j>0.29k

X$! F897j-370.5B

0.6C-0.43!0-370.5>0.29!0 '>C'>'Q

0.6c0.43\*0.29\370.5 897>735.89>1098.73C919.861277.59 Q273.62

105


107/139

31.- !,i$n%o $ "! t$nsin $n $" c!,"$ 450. C!"c"! "!s

co&on$nt$s %$ "!s $!s $ s$ $j$c$ so,$ "! "!c! $n

-4i>3j-5k

()7.07 X-256i>189j-318k

@-0.57i>0.42j>0.71k

32.-n! c!! S $stD ss$n%i%! %$ 3c!,"$s s$ &$st! $n "! i!

%$t$&in$ $" #!"o %$ S+ si "! t$nsin %$n $" c!,"$ FC $s %$ 2866() ' F

$s 185()

F6j>3k

(F)6.55 t$nsion FC88.46i>2685.56-447.59B()

F0.89j>0.45k F-30.41>182.48j()

FC2i>6j-k

FC6.4

FC0.31i>0.94j-0.26k

F6.08

F-0.16i>0.98j

106


108/139

33.-s$ ti$n$ n! c$%! ij! $n $" nto ' s$ "! A!"! con n! $! %$

100 %$s%$ $" nto F$t$&in!

!) E" #$cto X $n t&inos %$ i+j+k,)$" #$cto o'$ccin %$" #$cto X so,$ FC

c)E" Dn"o $ o&!n $" #$cto con s o'$ccin $n $" "!no 10j-2k

@-36.51>91.29j-18.26k()

XFCX*FC*FC-4i>2B

(FC) @FC4.47

@FC109.524.47

@FC(-0.89i>0.15j)XFC-21.8i>10.95B

:!n104.47

65.91

34.- i "! t$nsin $n $s %$ 39+ %$t$&in! "os #!"o$s %$ "!s t$nsion$s

$ s$ $i$$n $n C ' F !! $ "! $s"t!nt$ %$ "!s $!s !"ic!%!s

$n s$! #$tic!"

107


109/139

16i-48j>12k 0.23-0.43C0

0.31i-0.92j>0.23B 90.43C

C16i-48j-14k C21

C0.29i-0.86j-0.43k C6i-18j-9k

F-14i>18j 0.28F18.18

F-0.28i-0.96j F64.93

F-18.18i-62.33j>k()

Dinmica Rotacional

1.-

[X'&*!

2**t!n &*& @&*!

* @!c

!cQ2R

# Q2R

!Q2#Q

!Q*#

2.-

108


110/139

K-s$n&(2R)E"EX

&(2

R)&Rs$n&RX22R-2Rs$n

Ks$n&R(2R-2Rs$n)

$n2-2s$n

$n23

d41.81

3.-n c$o %$ 24B s$ A!c$ i! $& c/c"os Aoiont!"$s o &%io %$

&! c$%! co& $sistenci! ! "! t! %$ 300. C!n%o "! #$"oci%!% %$"

c$o ""$! ! 8&s s$ o&$ "! c$%!

!)Enc$nt$ $" Dn"o $ o&!n "! c$%! con "! #$tic!" $n $s$ inst!nt$

,)! "onit% %$ "! c$%!+ si $" !%io %$ "! t!'$ctoi! $s %$ 9&

&24B

t300

t8&s

Rs$nM

[X


111/139

S80$#&in8.38!%s

[Xt t

X&*Q2 2t25.0

8.9*5.0

@&Q2 t2.2s

Sr

2

S4.42!%

7.-! &!s! & i! con #$"oci%!% !n"! Q const!nt$ co&o s$ in%ic! $n "!

i! YT Q %$,$D t$n$ !! $ t132t2Z

110


112/139

:132:2

Rs$n30

R0.5&

[X'0 [X


113/139

Rcos60 [X&*!

R0.5& 2:'1.02*4000.5

&Q9.8 :816

&1.02

X&(7.250)2 [X'0*@-&103.68 S

10*@8& &

a8100.8 10&

11.- c!nt!s $#o"cion$s o s$n%o AD %$ i! !"$%$%o %$ & $j$

#$tic!"+ $" !!!to %$ "! i!+ !! $ "! c$%! o&! & Dn"o %$ 45

co& "! #$tic!"ZYc!" $s $ntonc$s "! t$nsin %$ "! c$%!Z

112


114/139

Rs$n45*

R14.4c&0.14&

:cos45&*! :2s$n45:cos45Q2*R :2.83

S8.33!%s

S1.32 R

12.-Fos ,"o$s $ ti$n$n $" $so ' "! osicin %$ "! i! %$sc!ns!n

so,$ n &!co $ i! !"$%$%o %$ n $j$ #$tic!" con #$"oci%!%

const!nt$ . $" co$ici$nt$ %$ iccin $nt$ "os ,"o$s ' $" &!co $s @0.20

F$s$ci!n%o $" $so ' "! iccin %$ "! o"$!. c!nt!s RK $&$!Dn !

%$s"i!s$ "os ,"o$s ' c!" $s "! t$nsin %$ "! c$%! $n $s$ inst!nt$Z

113


115/139

Sct$ [XG&*!

S4R :&*!

&* :0.3(25.12)2R

& :17.37

&0.03&

14.-n c$o %$ 30k i! con &o#i&i$nto cic"! nio&$ so,$ n!

&$s! Aoiont!" co&"$t!&$nt$ "is!+ sj$t! ! n! c$%! %$ 60c& %$

"onit%$s. Oto c$o %$ 10B %$ &!s! %$sc!ns! so,$ $" c$o !nt$io.

C!"c"!

!)E" co$ici$nt$ %$ o!&i$nto &/ni&o $nt$ "!s s$ici$s %$ "os

c$os !! $ con n! #$"oci%!% !n"! %$ 2!%s $" c$o %$ 10B no

s$ %$s"ic$.

,)! t$nsin %$ "! c$%!

:&*Q2*R

:40*4*0.6

:96

15.-s$ A!c$ i! n c$o %$ &!s! 5B. En n! cicn$$nci! Aoiont!"

co&o s$ in%ic! $n "! i!+ sj$t! ! n! c$%! %$ "onit% %$ 2& '

co&nn! #$"oci%!% o const!nt$. i "! c$%! o&! n Dn"o %$ 45 con

"! #$tic!"!)! t$nsin $n "! c$%!

114


116/139

,)E" #!"o %$ "! #$"oci%!% %$" c$o o

[X:s$n330&*

C2.11& :(s$n60>s$n30)44.5

RC*cos60 :3060

54.44

sensen +R2.11cos60 :32.61

R1.055& 44.544.32

210.35

3.21&s

17.-n! $$`! $s$! %$ 10 %$ $so s$ sosti$n$ &$%i!nt$ %os c$%!s

' C co&o s$ &$st! $n "! i!. En "! osicin &ost!%! s$ "$

%$sci,! n! t!'$ctoi! cic"! #$tic!". F$t$&in! "! t$nsin $n "!sc$%!s $n $" nto &Ds ,!jo %$ "! t!'$ctoi!

115


117/139

R(1-0.752) [X'0

R0.66& 2:'&*2R

2:s$n41.4618.43

CosM0.75 :468.5

M41.4

18.-E" sist$&! %$ "! i! i! !"$%$%o %$ n $j$ #$tic!" con #$"oci%!%

const!nt$. Conoci$n%o $ $" co$ici$nt$ %$ o!&i$nto $nt$ $" $$`o

,"o$ ' "! !$% ci"/n%ic! $s 0+2 %$t$&in$ "! #$"oci%!% !! $ $"

,"o$ $&!n$c! $n cont!cto con "! !$%.

@0.2

R0.2& &R

v2

X-&0R

vm

mg 2=

@&*

& @ #2.0

2.0*8.9

3.13&s

116


118/139

19.-n $$`o c$o %$ &!s! 1B. F$sc!ns! n "!no inc"in!%o $ i!

!"$%$%o %$ n $j$ #$tic!" con n! #$"oci%!% !n"! const!nt$ %$ 20

RK. i $" c$o $stD ni%o !" $j$ %$ ot!cin o &$%io %$ n! c$%!+co&o s$ &$st! $n "! i!+ ' s$ consi%$! %$s$ci!,"$ $" o!&i$nto

$nt$ $" c$o ' $" "!no. C!"c"$ "! t$nsin $n "! c$%!

S20RK2.09 !%s [X


119/139

S5B(9.8)49 [X0.49& ts$n60-s$n30&2R

!) 0.13&s -0.5>0.86:2.05

[X'0 [X:cos60-Q0 :CO60S

0.86>0.5:R2 :49cos60

:98

[X'&2R

:s$n60&2R

28.48

2.91

RcosM*! :i::'

[X'0 :i&*Q2*!>20&s

:s$nM :i&(Q2*>10)

:s$nM&*10!2

:s$nM20&

:'20&

118


120/139

Cos MRfR [XG&*!

RfRcosM cosMQ2RcosM

s$nMQ Q2 rseng

sen

gm *Q

cosR

g

119


121/139

T#$B$%", "TENCI$ & ENE#'I$

EJERCICIO 18

X200

S Z SX*%

F200& SXcos30*200

M30 S69282.03j

X4000

5&s !)S4000*5&s*300s

:5&in300s S6*106J

%t ,) S4000*2.5&s*300s

%*t S3*106JSX*%

SX**t

120


122/139

:12B*


123/139

gX'0 gX12!t2 gX'&*!c

A12(2)*2s X$-SK*!

A25& &*>&*!

G13c& G210c&

SX*% SX*%

S(75)(9.8)(0.03&) S(75)(9.8)(0.13&)

S122.05J S95.55J

124


126/139

o !"&!c$n! t!,!jo

@c0.20

SX*%

g'0 g


127/139

X**cos50

X50cos*5

50Cv

X**cosM

(Xcos6.84)

6764.1S!::

&1B S&**A St

A10& S1*10*10 10010

t10s S100J 10Q!tt10&s

EJERCICIO20

Ec>$0

12>&**A0

!)gX'&*! gX'&*!

-S&* #2 &2*&*

& #

2

>&* &(

2

-)&(#2>)

126


128/139

c)!! $ $)

2

*9.8

2.

gX'0

:cosVS

2ScosVS

cos12

V60

K2B o9.8&s $&**A $c>$0

S19.6B X0.82 $-19.5*5 -980

X0 o0 20 $-98 9.89&s

gX'0 gX


129/139

19.68 !77.84&s2

&5B S1-S2E1-E2

'110& S1-S2(&**'2*&**'1)

'5& S1-S2(5B*9.8*5)(5*9.8*10)

'31& S1-S2245J

:22

B1500& EQ1(S1-S2)>( S2-S3)

0 EQt245>196

EQt441JS2-S3(&**'3*&**'2)

S2-S3(5*9.8*1)>(5*9.8*5)

S2-S3196J

:12B


130/139

!):10J $c$c1-$c2:X;$c>$)( $c2>$c2>$2>>X)

S'112&o2>10@&Rcos30($c>$>$c1) ($c2>$2>$c2) Xc@c

&**;&** ;< :cc&*30

(A) ;< ;8.666

o6.53&s

gX'&*!c

>&&oc2

oc3.16&s

129


131/139

g'0 Kt&1>&2 (12& 2-12&o2)>(&*A- &*A)0

:-&0 &t0.3>15 -35.03>153A-153Ao0

:-15.3(10)0 &t15.3 A-Ao 0.23&

:153 ;A 0.23&

:;$ X(&*9.58*100) ,2220

:588& ,&*>&22010

,23&,

&(2- o2)2588& E&!E&,

22*588 ($c>$>$)($c2>$2>$)

34.29 (10)(100)12 ,2>10*-10

,46.9gX'K!'

,-&K,2

130


132/139

S$c>$$>$

X%12&2>12B122

2*5k*k2*25-400>2002

10-50-400>202

1.51

%)2& Ec12(2)(31.69)2

:12&c2-12& Ec1009

c21250 :1250J

c35.41&s !):X*%

:50*20&:;$c :1000J

100,2-4 ,):*%

,31.69 :(50)(10&)

:500J

:12c2

c35.35&s

131


133/139

2>2Ao2 E&!&*!c E&*!c

107.8>9.8#2 EEc -&cos60K*,2

c2117.5 ,2107.8 &**cos60>107.8

112.7

!)Ec!12&!2 ,)E!&*A* c)E!E

Ec!12*40*36 E!40*9.8*120 E!>Ec!Ec,Ec!720J E!48000J &**A>12&!212&,2

,2436

,49.35&s

132


134/139

$n30 xh

+ 5.041

E&!E&c

12k12&*2

A1(s$n30)(3.5>0.512(1)(4.43)

A11.75>0.5< 30004.99.8

3000


135/139

E&E&2

K**AD-&**A>12&2

22A-*A

2o2>2!%

F2RA

0.5,29.89&s :-Ec>E

a&(cos30)EC>E,>E$,>E!0.2*1*9.8*cos30*4&12B,2>B(9.8)2

6.78764.89-0.5Go*4000

Go0.451

134


136/139

)gX


137/139

EcE

K**A&*(0.4R)>X10&R-10(0.4&R)S

10&-4&SX

6&S

!)E&!E&, )E&E&c

Ec!>E! Ec,>E, Ec,Ecc>Ec

12!2>&**A0 12&,212&*,2>&**A

0.5*2,298 0.5*2*9.80.5*2c2>2*9.8*2.5c7&s

,9.8&s Ecc>EcEco>Eo

0.5*4.9>9.8*1.250.52>9.8*7.5

o5&s

E&E&

(E$>E>Ec)(E$>E>Ec)

EcEc

12&2&**A A22

E&E&,

136


138/139

(E$>E>Ec)(E$>E>Ec)

&L!12&,2>12B


139/139

CosM0.5

M60

gX'0 gXEcEc

&**A>12&212& 2

# 2*2

61.113.2*8.9*2 2+

6.68&s

Solucionario de Fisica(1)

Documents

Transcript of Solucionario de Fisica(1)