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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( La" &ondi&ione" de euili/!io "on la" le.e" ue !i3en la e")9)i&a( La e")9)i&a e" la &ien&ia ue e")udia la" ,ue!-a" ue "e a+li&an a un &ue!+o +a!a de"&!i/i! un "i")ema en euili/!io( Di!emo" ue un "i")ema e")9 en euili/!io &uando lo" &ue!+o" ue lo ,o!man e")9n en !e+o"o% e" de&i!% "in moimien)o( La" ,ue!-a" ue "e a+li&an "o/!e un &ue!+o +ueden "e! de )!e" ,o!ma":
F3-)9&/ &34&)-/: Do" ,ue!-a" "e di&e ue "on an3ula!e"% &uando a&)$an "o/!e un mi"mo +un)o ,o!mando un 9n3ulo( 9n3u lo(
F3-)9&/ (4+-&4-/: Do" ,ue!-a" "on &olineale" &uando la !e&)a de a&&i4n e" la mi"ma% aunue la" ,ue!-a" +ueden e")a! en la mi"ma di!e&&i4n o en di!e&&ione" o+ue")a"(
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,(
A nue")!o al!ededo! +odemo" en&on)!a! nume!o"o" &ue!+o" ue "e en&uen)!an en euili/!io( La e<+li&a&i4n ,="i&a +a!a ue e")o o&u!!a "e de/e a la" &ondi&ione" de euili/!io:
P)+-)& (,++; ,- -3+4+')+(: Di!emo" ue un &ue!+o "e en&uen)!a en -3+4+')+( ,- *)&/4&+; &uando la ,ue!-a !e"ul)an)e de )oda" la" ∑ F < 0= De"de el +un)o de i")a ,ue!-a" ue a&)$an "o/!e 'l e" nula: ma)em9)i&o% en el &a"o de ,ue!-a" &o+lana!ia"% "e )iene ue &um+li! ue la "uma a!i)m')i&a de la" ,ue!-a" o de "u" &om+onen)e" ue e")9n en la di!e&&i4n +o"i)ia del eje > "ea i3ual a la" &om+onen)e" de la" ue e")9n en la di!e&&i4n ne3a)ia( De ,o!ma an9lo3a% la "uma a!i)m')i&a de la" &om+onen)e" ue e")9n en la di!e&&i4n +o"i)ia del eje Y )iene ue "e! i3ual a la" &om+onen)e" ue "e en&uen)!an en la di!e&&i4n ne3a)ia:
#o! o)!o lado% de"de el +un)o de i")a 3eom')!i&o% "e )iene ue &um+li! ue la" ,ue!-a" ue a&)$an "o/!e un &ue!+o en euili/!io )ienen un 3!9&o &on ,o!ma de +ol=3ono &e!!ado? .a ue en el 3!9&o de la" ,ue!-a"% el o!i3en de &ada ,ue!-a "e !e+!e"en)a a +a!)i! del e<)!emo de la ,ue!-a an)e!io!% )al . &omo +odemo" o/"e!a! en la "i3uien)e ima3en(
El @e&@o de ue "u 3!9&o &o!!e"+onda a un +ol=3ono &e!!ado e!i&a ue la ,ue!-a !e"ul)an)e "ea nula% .a ue el o!i3en de la +!ime!a ,ue!-a 517 &oin&ide &on el e<)!emo de la $l)ima 5B7(
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,(
En e")e &a"o% de"de el +un)o de i")a ma)em9)i&o% . en el &a"o an)e!io! en el ue la" ,ue!-a" "on &o+lana!ia"? "e )iene ue &um+li! ue la "uma de lo" momen)o" o ,ue!-a" a"o&iado" a la" !o)a&ione" an)i@o!a!ia" 5en el "en)ido &on)!a!io de la" a3uja" del !eloj7% )iene ue "e! i3ual a la "uma a!i)m')i&a de lo" momen)o" o ,ue!-a" ue e")9n a"o&iado" a la" !o)a&ione" @o!a!ia" 5en el "en)ido de la" a3uja" del !eloj7( Un &ue!+o "e en&uen)!a en euili/!io )!a"la&ional . !o)a&ional &uando "e e!iuen de ,o!ma "imul)9nea la" do" &ondi&ione" de euili/!io( E")a" &ondi&ione" de euili/!io "e &onie!)en% 3!a&ia" al 9l3e/!a e&)o!ial% en un "i")ema de e&ua&ione" &u.a "olu&i4n "e!9 la "olu&i4n de la &ondi&i4n del euili/!io(
PROCEDIMIENTO: 1( A!me el "i")ema de la i3( 6(( Su"+enda en lo" e<)!emo" e<)!emo" de la &ue!da +e"o" di,e!en)e" 1% 2 . en el &en)!o un +e"o E;( Deje ue el "i")ema "e e")a/ili&e( Re&ue!de ue de/e &um+li!"e la le. de la de"i3ualdad de lo" lado" lado" del )!i9n3u )!i9n3ulo lo un lado lado e" meno! ue la "uma "uma de lo" o)!o" o)!o" do" . ma.o! ue "u di,e!en&ia(
2( Coloue el )a/le!o 5&on un +a+el7 en la +a!)e +o")e!io! de la &ue!da . ma!ue la" di!e&&ione" de la" &ue!da" en el +a+el(
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( ( Re+i)a lo" +a"o" 1% 2% ; . B( a( Coloue 1% 2 . E i3uale" en m4dulo . mida lo" 9n3ulo" F% G . H ue "e ,o!man al !ededo! del +un)o( /( Coloue 1: 2 . E ue e")'n en la !ela&i4n de ;: B: . mida lo" 9n3ulo" ue ,o!ma en)!e ello"( &( Coloue 1: 2 : E ue e")'n en la !ela&i4n 12: : 1;(
6( Su"+enda la !e3la &on lo" dinam4me)!o"% u)ili&e lo" a3uje!o" de 10&m . J0 &m +a!a la" ,ue!-a" 1 . 2 &omo mue")!a la 3u!a ( Ano)e la" le&)u!a" en &ada dinam4me)!o
J( Coloue en el a3uje!o del &en)!o de 3!aedad de la !e3la un &ue!+o de ma"a a"a KKKK KKKKK3 K3 ue ue e" la ue ue e" la ;( Ano)e no)e la" le&)u! &)u!a" a" de &ada &ada dinam4me)!o( 8( De"+la&e el &ue!+o de ; al a3uje!o a ;0&m del +!ime! dinam4me)!o( Ano)e la" le&)u!a" de &ada una de ella"( ( Adi&ione un &ue!+o de ma"a KKKKKK3 a 10 &m del o)!o dinam4me)!o( Ano)e la" le&)u!a" de &ada uno de ello"
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( 1*
1003
1003
1003
11*
120*
121*
603
803
1003
126*
1BB*
10*
1203
03
1;03
1*
11B*
8J*
Ca"o 2* Ca"o ;* Ca"o
P)+-)& &)*- ,-4 --)+-*(:
S-3,& &)*- ,-4 --)+-*(: 6 Su"+enda la !e3la &on lo" dinam4me)!o"% u)ili&e lo" a3uje!o" de !110 &m( . !2J0 &m( Y !/0&m +a!a la ,ue!-a"
´1 F
´ . F 2
i3( 6(6( Ano)e la" le&)u!a" de &ada dinam4me)!o( din am4me)!o(
&omo "e mue")!a en la
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( 7 !110 &m( % !2J0 &m( Y !/0&m Coloue !; 0&m de la !e3la un &ue!+o de ma"a de 0(103 ue e" la ue e"
´3 F ( Ano)e la" le&)u!a" de &ada
dinam4me)!o( Lectura de los dinamómetros:
D1
10(JN
D2
21(8N ;1N
´ ´ 8 De"+la&e el &ue!+o de F 3 5m F 0(1037 0(1037 al a3uje!o de B0&m( Ano)e 3
la" le&)u!a" de &ada una de ella"( Lectura de los dinamómetros:
D1
10(N
D2
21(6N ;1N
$ adi&ione un &ue!+o de ma"a 1J03! a 60 &m(( Ano)e la" le&)u!a" de &ada uno de ello"( Lectura de los dinamómetros:
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( CUESTIONARIO: 1= C( C(3-) 3-),& ,& -4 &4() &4() &44&,( &44&,( () -4 *(,( *(,( )H( )H( ( 4& 3-)9& E Q3 ,+-)-+&/ &K -*)- 4& 3-)9& )-/34*&*K 3-)9& -3+4+')&*- RE R
2 1
E
F3-)9& )-/34*&*Si "o/!e un &ue!+o a&)$an a!ia" ,ue!-a" "e +ueden "uma! la" mi"ma" de ,o!ma e&)o!ial ial 5&omo "uma de e&)o!e"7 o/)eniendo u na ,ue!-a !e"ul) !e"ul)an) an)e% e% e" de&i! de&i! euia euialen) len)e e a )oda" )oda" la" dem9"( Si la !e"ul)an)e de ,ue!-a" e" i3ual a &e!o% el e,e&)o e" el mi"mo ue "i no @u/ie!a ,ue!-a" a+li&a da": el &ue!+o "e man)iene en !e+o"o o &on moimien)o !e&)i e&)il= l=ne neo o uni, uni,o! o!me me%% e" de& de&i! ue ue no modi&a "u elo&idad(
F3-)9& -3+4+')&*-
Se llama ,ue!-a euili/!an)e a una ,ue!-a &on mi"mo m4dulo . di!e&&i4n ue la !e"ul)an)e 5en &a"o de ue "ea di")in)a de &e!o7 +e!o de "en)ido &on)!a!io( E" la ,ue!-a ue euili/!a el "i")ema( Sumando e&)o!ialmen)e
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( --)+-*&4-/ ()-*3&4-/ ( )-/-*( & 4& -3+4+')&*(4(&,&=
´ F ´ 2 F
34(/ ´ E´ F ∡
γ
F
G
∡ 1
R-4&+; ,- 4&/ 3-)9&/
2
´ F ´ 1 E
∡
A
´ 1 : F ´ 2 : E ´ F
1:1:1
120*
11*
121*
B
´ 1 : F ´ 2 : E´ F
#:!:5
0*
1BB*
126*
C
´ 1 : F ´ 2 : E ´ F
12:5:1#
8J*
11B*
1*
De/emo" )ene! en &uen)a ue La 3!aedad en Lima e":
Cuad!o &on la" e<+e!imen)almen)e:
9,78
´ = F ´ 3 R= E m s
2
,ue!-a"
´1 F
´2 F
´ E
C&/( 1
0 =$ 7 8
0 = $7 8
0= $ 7 8
C&/( 2
0 =5 8 7
0 = 78 2
0= $ 7 8
C&/( #
1 =1 7 !
0 = !8 $
1= 2 7 1
Por la ley de senos o de Lamy:
o/)enido
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,(
´1 ´2 ´ F F E E 0.587 N 0.782 N = = = = E=1 N ⟹ ⟹ Senα Senβ Senγ Sen 144 ° Sen 126 ° Sen 90 °
P&)& C<&/( #: ´1 ´ ´ F F E E 1.174 N 0.489 N ⟹ ⟹ = 2 = = = E= 1.3 N Senα Senβ Senγ Sen 114 ° Sen 159 ° Sen 87 °
Por la ley de cosenos: Por la Ley de Cosenos hallamos la fuerza resultante que será igual en módulo y dirección que la fuerza equilibrante pero de sentido contrario 2
2
2
R = F 1+ F 2 + 2 F 1 F 2 cos γ
P&)& A: E =0.978 + 0.978 + 2 ( 0.978 ) ( 0.978 ) cos120 ° =2.869 ⟹ E= 0.978 N 2
2
2
P&)& B: E
2
=0.587 + 0.782 + 2 ( 0.587 ) ( 0.782 ) cos90 ° = 0.956 E =0.978 N 2
P&)& C:
2
⟹
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( 36 36
(¿ ° )+ ( 0.782 N ) sin ( 54 ° ) E =0.978 N (¿ ° )+ F sin ( 54 ° )=( 0.587 N ) ) sin ¿ E = F sin ¿ ⟹
2
1
P&)& C: 69 69
(¿ ° )+ ( 0.489 N ) ) sin ( 24 ° ) E =1.295 N (¿ ° )+ F sin (24 ° )= (1.174 N ) ) sin ¿ E= F sin ¿ ⟹
2
1
C&/(/ D&*(/ | E´ |experimental
CA SO 1 CAS O 2 C ASO # 0( J8N
0( J8N
1 ( 2 N
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( e=
0.978 −0.978 0.978
x 100 = 0
Ca"o 2: e=
0.978 −0.978 0.978
x 100 = 0
Ca"o ;: e=
1.271
−1.295
1.271
x 100 =− =−1.9
#= M+,& M+,& 4(/ 34( 34(/ / - 4(/ &/(/ &/(/ 5=& C(3C(3-),& ),& ( -4 &4() &4() *-;)+( ,- 120° Se3$n el &uad!o @e&@o en &la"e de ,o!ma e<+e!imen)al% "e o/"e!a ue lo" 9n3ulo 9n3ulo" " medido medido" " no "on i3uale" i3uale" a lo" )e4!i&o"( )e4!i&o"( E")o "e de/e al e!!o! in")!umen)al% de")!e-a del o+e!ado!% e)&(
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,( 5= S( +3&4-/ +3&4-/ 4&/ 4-*3)&/ 4-*3)&/ - 4(/ ,+&;-*)( ,+&;-*)(/ / - 4(/ &/(/ 6 K 7 () 3 E 3 &/( 4(/ ,+&;-*)(/ &)&) +3& +3&4 4 && && 3 )H )H( ( 3 3- -) -)-/ -/- +/3 +/3&4 &4-* *- 4( 3 3-4+3- - /3 )-/3-/*& La" le&)u!a" de lo" dinam4me)!o" no "on i3uale" en am/o" &a"o" .a ue en el +a"o J a3!e3amo" un &ue!+o de ma"a de 0%10 3% donde e")a ma"a e")9 m9" &e!&a a uno de lo" dinam4me)!o" . un +o&o lejo" del o)!o(
´1 F
P&/( 6 P&/( 7
´2 F
´3 F
&/&
&,++(&, &
0(BN 1(0N 0(JN 1(8N 1(0N Lo" dinam4me)!o" ma!&a!9n i3ual en am/o" &a"o" "i . "olo "= el &en)!o de ma"a del "i")ema "e u/i&a"e a i3ual di")an&ia de lo" dinam4me)!o"(
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,(
6= C&4 C&434 34- *-;) *-;)+ +& &- -**- 4&/ 4&/ )-& )-&+ +( (-/ -/ - 4(/ 4(/ 3 3* *(/ (/ ,/3/-/+; &)& 4(/ &/(/ 8 K $ K (&)- ( 4&/ 4-*3)&/ - 4(/ ,+&;-*)(/= 87 1
Q
#a!a el &a"o 87
2
Q !e3la
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,(
Ca"o7 (Siendo F 1 el origen)
7= Q3 ('/-)& ,- 4&/ 3-)9& -)9&/ / 3- &*& *& /(')- 4& )-4& &&&4&,&
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#!a&)i&a N*6
L&'()&*()+( ,- F./+& I E3+4+')+( ,- 3 3-)( ).+,(
en un +un)o +o!
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