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7/25/2019 Solucionario de Fisica(1)
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Solucionario de Fsica Bsica
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INDICE
Vectores.2
Cinemtica.37
Dinmica89
Trabajo, otencia y Ener!a121
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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#$=%1"SE#90!12=102+102 &='RCSE#(RSE#90"!1)=45!1=14.14*g %1=(14.14*g135)
'=53,+0j-=(-1.76,-18.91j)
-= 484
|-|=22/
'=E E'E='+E 'E"E=EC"E='C" 'E=2E 'C=2E=C EC=E+C
E=2E
R=++++e
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'=++eR=++R=2+
R=2+j-2(2)$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
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|'+2|= 22 4Ba +
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EJERCICIO 5
COS30=!>"> =7.32#=23.8 !R=(7.3210)#
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>=-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)#
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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
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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
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!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/
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'>=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
$=51.32
| G1|= 410 +| G2|=2 Hp=(5,+2j+0*)| G3|= 41104 =+
| G4|=2
| G
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CA='B"' '>= 22 AzAxz
C11.7='B"13.5 '>= 22 )99.4(09.12 +
'B=-4.99 '>=11.01
'?=e26.4113.5'>B=12.09
R=(11.01+6j-4.99*)Se58=>"9.43 R'-=R-R>=7.99
g58=7.99"B R'-=11.01,+6j-4.99*B=4.99 7.99,+5.98j-4.99*?="51.96 e30=H?"60H>=44.99 H?=30
C60=H"51.96 H>B=51.96HB=28.98
10.59,-25.08j+10.59*44.99,+30j-25.48*55.8,+30j-15.39*
Se45=>"14.99 e60=?"30S>=10.59 ?=25.98SB=10.59
g60=25.98"S>B
S=(10.59,-25.98j+10.59*)
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C?=20e60 CB=C>B30C?=17.32 CB=1030C>B=2060 CB=8.66C>=C>e30 =(517.328.66)C>=10e30 +C=(-2+5,)+(17.32)j+(8.66-3):DC>=5 +C===3,+17.32j+5.66*
>B= m41.666.53 22 =+||=18.47
C$=>">B$=27.99
) C=(5,+17.32j+2.66*) KC=(5,+17.32j+2.66*)"20
|C|= 222
66.232.175 ++ KC=(0.25,+0.87j+0.43*)|C|=20
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)V1=200/ #40O eLe.60 V1B=V1>B40
V2=160/ SE eLe.45 V1B=76.6/V1?=200e60 V1=(-64.28,+173.21j-76.6*)V1?173.21/
V2?=160e45V1>B=20060 V2?=113.14/V1>B=100/
V2>B=16045V1>=V1>Be40 V2>B=113.14/V1>=64.28/
V2>=V2>=V2>Be45 V2=(80,+113.14j+80*)V2>=80/ Vr=(80-64.28),+(173.21+113.14)j+(80-76.6)*D
Vr=(15.72,+286.35j+3.4*)
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C=>" =5,+5j+7.07* ?=1"2(-2)>=1060 C=(C%-C,)=(2-0)+(2-4)+(1-5)D ?=-1>=5 C=2,-2j-4*||2=>2+?2+B2
B=7.07 '>+>-1"2C>+>=0 B=1"2(-4)-7.07-3
>=-14 B=-6.07=(-14,-j-6.07*)
|'|=100K 60 eLe45 30=>"50
||=50/ 30A75 >=43.3/
'?=|'|e45 75=B"50'?=70.71 B=12.94/
'>B=|'|45 502=43.32+12.92+?2
'>B=70.71/ ?=21.4/'>=70.71e60'>=-61.24/ '>+>+C>=0'=70.7160 C>=->-'>'B=-35.4/ C>=61.24-43.3'=(-61.24,+70.71j-35.4*) C>=17.94/ CB=-B+CB
C?-?-'? CB=35.4-12.94C?=-70.71-21 C=(17.94,-
92.11j+22.46*)C?=-92.11/C=(17.94,-92.11+22j.46*)
|'|=100/ ='>"' '2='>2+'?2+'B2
C=0.7 '>=70 'B2='2-'>2-'?2
C&=0.2 '?=1000.2 'B= 222 2070100
'?=20 'B=68.56'=(70,+20j+68.56*)
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2'=10,-4j-3=-12,-15j R=-5,-16jC=-3,+3j
R='- e$=0.46|R|2=102+162-21016105 $=27.53+135|R|2=356+82.82 $=162.53R=20.9R"e105='"e$ R>=R162.53Se$=10e105"20.9 R>=-19.9
R?=Re162.5R?=6.27
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'?='e50 '>=3.21'?=7.6 'B='>B30
'>B='50 'B='>B30
'>B=6.43 'B=-5.57'>='>=e30
'(3.21,+7.6j-5.57*)
'=4,-2j+6* 2'=-8,+4j-12* R1prLeL R1-2=2,-8j+2* 3=-3,+12j-3* R=24.54(0.42,+0.7j+0.57*)R1=6,-10j+8* R2=-11,+16j-15*
KR1=(6,-10j+8*) |R2|= 222 151611 ++
222 8106 + |R2|=24.54/
KR1=0.42,-0.7j+0.57*
'C=(2+5+7),+(1-1+2)j+(2+4+1)*D e$=2"15.8
'C=14,+2j+7* $=7.27
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|'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
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'?='e30 '>='>Be45 = 222 5.27155.30 ++
'?=20 '>=24.5 =43.7
'>B='30 'B='>B45
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!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:
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>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:
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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+*)
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'+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
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'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
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'=(-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=
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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
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=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
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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*
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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*
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'=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*
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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
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'=([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
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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*
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'+=11,-j+5* |'|=9.11'-=-5,+11j+9* )'(')='(')"$2'=6,+10j+14* $045.52'=3,+5j+7*
'('+)=5111
753
kji
=25,-3*+7j-55*+7,+15j
'+=11,-j+5*-'+=5,-11j-9* '('+)=32,+62j-58*2=16,-12j-4*=8,-6j-2*
Se40='?"15 =7.5,-125.5j+25*'?=9.64 252=7.52+11.52+252
2=0.66C40='>B"15 =0.81'>B=11.5
C=7.5,-12.5j+20.25*Se60='"11.5 3'-5C=(28.98-37.5),+(28.92+62.5)j+(-17.25-101.25)*'>=9.96 =-8.52,+91.42j-118.5*
C60='B"11.5 7+5=(28+35),+(14+75)j+(-21-150)*'B=-5.75 =63,+89j-171*
'=9.66,+9.64j-5.75*
Q=1718963
5.11842.9152.8
kji
Q=-5096.58,-8922.42j-6475.14*
33
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)R=R-=(,-j) '=1"2
112
121
123
=1"2(-2)
HR= 22 )21()31( ++ '=1
HR=2.24)H=H-=(2,-4j)
C18='?"' '=006.5754.18
045.449.22
kji
'?=-57.06 '=2130.77:
Se18='>"' '"'=$'>=-18.54 $=134.74
'=-18.54,-57.06j
'=05.499.22
006.5754.18
kji
=-824.1:-1306.67:'=-2130.77:
C='"' '2='>2+'?2+'B2 60=>B"'=1050 '?2=100-(6.43)2-(1.71) >B=2060'=6.43 '?=7.46 >B=10
CA='B"' '=(6.43,+7.46j-1.74*) e50=">B'B=10100 e60=?" >=7.66'B=-1.74 ?=20e60 50=B">B
?=-17.32 B=6.43
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=(7.66,-17.32j+6.43*)
K'='"10
K'=0.64,+0.75j-0.17* '=
43.632.1766.7
74.146.743.6
kji
K="20 |'>|=178.05K=0.38,-0.87j+0.52*
) '='$ 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
$=60.5
=(-1.74,+7.66j+6.19*)
C=>" =425
19.666.774.1
kji
35
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>=10100>=-1.74
C&=?"?=1040
?=7.66
102=1.742+7.66,2+B2 |'|=67.08B2=100-61.7 K'=0.64,+0.57j-0.52*B=6.19 K'=-0.64,-0.57j+0.52*
V=|"2|=K''=(43.12,+37.97j-34.82*) V=(-5.3,-4.7j+4.3*)2'=10,-4j+8*-=1.74,-7.66j-6.19*C=11.74,-11.66j+1.89*
"2=5.87,-5.83j+0.97*|"2|=8.32
CINEMATICA
EJERCICIO 9
1.-Encont! "! #$"oci%!% &$%i! ' "! osicin in!"+ s!,i$n%o $ n!
!t/c"! !t$ %$" nto (201)& ' s$ %$&o! 5s !! ""$! ! $ $st!
!" E %$ . $ s!,$ $ $" &%"o %$" %$s"!!&i$nto $s 20&
36
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o(201) &%t
:5s &205
%200& &4&s
;20&E ;-oCos4520 s$n45 t) * t%10(8>2) 10(2> t)12.5* t
%100& t812.5&s
37
)37( jiV =
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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&!
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;'-44.1&
H44&
L
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o 22 VoyVox +
o 2530.16 2 +
o17.11&s
'o-t'16.36-9.8*3
'-13.03&s
LtM
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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
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!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
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8.43j)(0.5i>0.86j) 7.25 '692.82&s
!t9.7&s2
@#0.5i>0.86j
200&
68
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:sos$nM tsos$n
:s0.05o ts0.08o
ot!0.05 o(ts)0.08
0.08:s0.05:s :!:,
:sP:s
o
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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
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H22.65& o
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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
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#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
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S80& MQ*t 29.7j)&s2
S4!%sR0.25&
74
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1&s
c2R
c4&s2
EJERCICIO 15
;Mts1s30 30 !%s
Q*R4!%s 0.5&2&s2
75
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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
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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
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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
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A!st! t3s----n4.5#$"t!s
GM*R ;MS,*t>12t2 SSo>!t
M 4!%*10& 24 S2*2
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;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
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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
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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
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!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
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;MSot>t22 ;*t
7 420t>100 t22 ;t
200 t2>80t-20 100.01
t0.0425 100&s
SSo>t M tWoWf
*2
+
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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
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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
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%R*M M1.56!%89.38 2R!c
%2*2 !tR 2*1
% & 1!%s -1.41j
SoR SSo-t
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S*R!c M tWoWf
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+
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!c0.5&s
!t
1!%s n ;M282 1.27#$"t!s
n ;M2182 2.86#$"t!s
oSo ;MSot>12t
86
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So4!%s ;M12(1)(36)
o>!t nt1.27>2.86
04>(-1)t nt4.13#$"t!s
:4s
87
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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 @@!
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+
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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
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6+721 !t2 A11+64&
3+27&s ;'2
1(3+27)*12
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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
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inst&$ntos s$ s$"t!n YCD" $s #$"oci%!% %$ "os inst&$ntos $n $"
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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 $!
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sii$nt$s sit!cion$s %$t$&in$ "! $! $ $" iso $j$c$ so,$ "! $son!
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@k0+30 !! "! &!s! ' @s0+50 ' @k0+40. Inici!"&$nt$ !&,os
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C$o1
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&1&22 B
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c$oC c$o
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S200&20.41B
S
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K!30B %ot>12!t2
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&!&!>&C!C
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24.- F$t$&in! "! !c$"$!cin con "! c!" s$ &$#$ "os c$os $n "! i!
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26.-H!""! "! !c$"$!cin ' "! $! X A!D $ $" ,"o$ %$ $so S+ $st$4 !
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:18873!22.78
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4i>j-7k
()9
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$! $n -00i>200j-350B()
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i!. F$t$&in! $" #!"o %$ Q+ si "! t$nsin $n $" c!,"$ F $s %$ 975
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31.- !,i$n%o $ "! t$nsin $n $" c!,"$ 450. C!"c"! "!s
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F-0.16i>0.98j
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100 %$s%$ $" nto F$t$&in!
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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
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1.-
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108
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R)&Rs$n&RX22R-2Rs$n
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:132:2
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Sct$ [XG&*!
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& :17.37
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114
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,)E" #!"o %$ "! #$"oci%!% %$" c$o o
[X:s$n330&*
C2.11& :(s$n60>s$n30)44.5
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54.44
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210.35
3.21&s
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115
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R(1-0.752) [X'0
R0.66& 2:'&*2R
2:s$n41.4618.43
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M41.4
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const!nt$. Conoci$n%o $ $" co$ici$nt$ %$ o!&i$nto $nt$ $" $$`o
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116
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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
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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
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[X'&2R
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28.48
2.91
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118
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Cos MRfR [XG&*!
RfRcosM cosMQ2RcosM
s$nMQ Q2 rseng
sen
gm *Q
cosR
g
119
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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
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:12B*
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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
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o !"&!c$n! t!,!jo
@c0.20
SX*%
g'0 g
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X**cos50
X50cos*5
50Cv
X**cosM
(Xcos6.84)
6764.1S!::
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A10& S1*10*10 10010
t10s S100J 10Q!tt10&s
EJERCICIO20
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& #
2
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2
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126
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c)!! $ $)
2
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2.
gX'0
:cosVS
2ScosVS
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K2B o9.8&s $&**A $c>$0
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X0 o0 20 $-98 9.89&s
gX'0 gX
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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
7/25/2019 Solucionario de Fisica(1)
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!):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
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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&
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:588& ,&*>&22010
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22*588 ($c>$>$)($c2>$2>$)
34.29 (10)(100)12 ,2>10*-10
,46.9gX'K!'
,-&K,2
130
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S$c>$$>$
X%12&2>12B122
2*5k*k2*25-400>2002
10-50-400>202
1.51
%)2& Ec12(2)(31.69)2
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100,2-4 ,):*%
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131
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2>2Ao2 E&!&*!c E&*!c
107.8>9.8#2 EEc -&cos60K*,2
c2117.5 ,2107.8 &**cos60>107.8
112.7
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,2436
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132
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$n30 xh
+ 5.041
E&!E&c
12k12&*2
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A11.75>0.5< 30004.99.8
3000
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E&E&2
K**AD-&**A>12&2
22A-*A
2o2>2!%
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0.5,29.89&s :-Ec>E
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6.78764.89-0.5Go*4000
Go0.451
134
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)gX
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EcE
K**A&*(0.4R)>X10&R-10(0.4&R)S
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E&E&,
136
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(E$>E>Ec)(E$>E>Ec)
&L!12&,2>12B
7/25/2019 Solucionario de Fisica(1)
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CosM0.5
M60
gX'0 gXEcEc
&**A>12&212& 2
# 2*2
61.113.2*8.9*2 2+
6.68&s