FACULTAD DE INGENIERÍA INDUSTRIAL ESCUELA ACADÉMICO PROFESIONAL DE INGENIERÍA TEXTIL CONFECCIONES LABORATORIO DE FÍSICA I PRÁCTICA Nº 7
Dinámica y a! "y"! #" N"$%&n
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Ín#ic"
I.
Introducción
3
II.
Objetivos
4
III.
Materiales
4
IV.
Fundamento teórico
5
V.
Procedimiento
6
VI.
Cuestionario
1
VII.
Conclusiones
1!
INTRODUCCIÓN En " ("!"n%" %(a@a& 2" m&!%(am&! a c&n%in2aci?n /"m&! ("ai>a#& 2n @("4" anái!i! #" "!%2#i& #" a #inámica y !2 ("aci?n c&n a! "y"! #" N"$%&n3 %"ni"n#& c&m& 2n& #" &! &@"%i4&! #"a( "n ca(& " c&nc"%& y mani<"!%aci?n #" in"(cia c&m& (&i"#a# #" &! c2"(&! 3 "n ca%2 ca%2&! &! an%"(i an%"(i&( &("! "! n2"!%( n2"!%(& & anái! anái!i! i! !" c"n%( c"n%(? ? "n " "2ii "2ii@(i @(i& & 2
m"cánic& #" &! c2"(&! y !2 in2"ncia #" a! <2"(>a! a(a man%"n"( #ic/a !i%2aci?n m"cánica 3"n "!%a &&(%2ni#a# n2"!%(& (&?!i%& !"(á ":amina( !i%2aci&n"! <!ica! c&n%(a(ia! a a #" "2ii@(i& m"cánic& #" 2n c2"(& & !i!%"ma 2"! a/&(a "n #inámica "!%2#ia("m&! "!%2#ia("m&! !i%2aci&n"! "n a! c2a"! " "2ii@(i& "! a%"(a#& E anái!i! #" "!%a ":"(i"ncia n& n&! "! a"n& a n2"!%(a 4i#a c&%i#iana 2"! "n m2c/&! #" n2"!%(&! ca!&! #i(a 2" "!%am&! ac&!%2m@(a#&! a 2" a 4"&ci#a# #" 2n c2"(& !&& 2"#" 4a(ia( c2an#& &%(& c2"(& ac% ac %a a !& !&@( @(" " P&( ""m ""m &3 &3 2n i@( i@(& & 2" 2" "! "!%%á "n n2"! n2"!%( %(a a m" m"!a !a c&mi"n c&mi"n>a >a a m&4"(! m&4"(!" " Hcam@ Hcam@ia ia a 4"&ci 4"&ci#a# #a# c2an#& c2an#& & "m2a "m2am& m&!3 !3 aam&! & an>am&! an>am&! Si a 4"&ci#a# cam@ia3 %an%& !2 m?#2& c&m& !2 #i("cci?n 2"#"n 4a(ia( P"(&3 J&( 2 cam@ia a #i("cci?n #" a 4"&ci#a#K Cam@ia &(2" " c2"(& in%"(ac%a c&n &%(& c2"(& E!%& & c&m(&@am&! an>an#& 2n @a?n c&n%(a a a("#3 &@!"(4am&! 2" 2"0& #" imac%&3 "!%" cam@ia a #i("cci?n #" !2 m&4imi"n%& O%(& ""m& a ci%a( "! c2an#& 2n "!%2#ian%" 2" a c&((i"n#& c&n 0(an (ai#"> &( a 4"("#a #"!"a #&@a( "n a "!2ina3 a(a "& a! an2(a! #" !2! >aa%ia! in%"(ac%an c&n a! a!"(">a! #" a 4"("#a a(a #a( a 42"%a L&! ca ca!& !&!! 2" 2" ci%a ci%a#& #& an%" an%"(i (i&( &(m" m"n% n%" " /a! /a! !i#& !i#& c& c&n n a in%" in%"nc nci? i?n n #" ":amina( y "n%"n#"( 2na (&i"#a# #" &! c2"(&! "n a na%2(a">a #"n&mina#a in"(cia y !2 ("aci?n c&n a aicaci?n #" a! "y"! #" N"$%&n
3
I.-OBJETIVO:
="(ica( a! "y"! #" n"$%&n
E:"(im"n%a( c&n #i<"("n%"! im"m"n%&! #" a@&(a%&(i&
D"!c(i@i( a! in%"(acci&n"! "n%(" c2"(&! ma%"(ia"!
II.-MATERIALES:
Ca((& #" ma#"(a
P("n!a!
2"0& #" "!a! "!a!
P("n!a &(%a &"a!
P&"a!
R"0a
P("n!a! #" #&! 0anc/&!
S&&(%"! 2ni4"(!a"!
C(&n&m"%(&
=a(ia
Cam!
Li!%?n #" ma#"(a
Dinam?m"%(&
C&(#"i%&!
III.-FUNDAMENTO TEORICO: 4
P(incii&! F2n#am"n%a"! F2n#am"n%a"! #" a #inámica & "y"! #" N"$%&n) La! i#"a! @á!ica! #" a a Dinámica <2"(&n "!%a@"ci#a! &( Gai"& #&n#" "0? a a! !i02i"n%"! c&nc2!i&n"!)
E! n"c"!a(ia 2na in2"ncia ":%"(na a(a &n"( 2n c2"(& "n m&4imi"n%&3 "(& n& !" n"c"!i%a 2na in2"ncia ":%"(na a(a c&n!"(4a( " m&4imi"n%& #" 2n c2"(&
L&! "!%a#&! na%2(a"! #" 2n c2"(& !&n) " ("&!& y " m&4imi"n%& ("c%in"& y 2ni<&(m"
T&#& T&#& c2"(& &( na%2(a">a %i"n#" a c&n!"(4a( #ic/&! "!%a#&! mi"n%(a! n& /aya 2na ca2!a ":%"(i&( 2" &! m&#i2"
E!%a %"n#"ncia #" &! c2"(&! a c&n!"(4a( !2 "!%a#& na%2(a !" ama in"(cia
La ca2!a caa> #" 4"nc"( a in"(cia #" 2n c2"(& "! a in%"(acci?n c&n &%(&! c2"(&!
E m&4imi"n%& #" 2n c2"(& "! " ("!2%a#& #" a! in%"(acci&n"! 2" ":i!%"n "n%(" y &! c2"(&! 2" " (&#"an
La in%"(acci?n "n%(" #&! c2"(&! ("ci@" " n&m@(" #" <2"(>a
La! &@!"(4aci&n"! #" Gai"& <2"(&n ("c&0i#a! &( N"$%&n "n %("! "y"!) Principio de Inercia - . 1ª LEY DE NEWTON: T&#& T&#& c2"(& %i"n#" a c&n!"(4a( !2 "!%a#& #" ("&!& & #" m&4imi"n%& ("c%in"& y 2ni<&(m" mi"n%(a! n& !" ""(>a !&@(" 2na <2"(>a fuerza "! %&#a ca2!a caa> #" 4"nc"( a in"(cia #" &! c2"(&! La fuerza "!
P(incii& #" (&&(ci&nai#a# + LE DE NEQTON T&#a T&#a <2"(>a aica#a !&@(" 2n c2"(&3 2" n& "!% "2ii@(a#a3 (c" 2na ac""(aci?n 2" "! (&&(ci&na a #ic/a <2"(>a ier!e "! a ":("!i?n La masa ier!e "! ":("!i?n c2an%i%a%i4a #" in"(cia) c2an%& may&( !"a a ma!a may&( ("!i!%"ncia &<("c" " c2"(& a cam@ia( !2 "!%a#& #" m&4imi"n%&3 "! a ("aci?n 2" ":i!%" "n%(" a <2"(>a aica#a a 2n c2"(& y a ac""(aci?n a#2i(i#a &( !%"
5
La masa "ra#i!a!$ria "! a ("aci?n 2" ":i!%" "n%(" " "!& #" 2n c2"(& y a ac""(aci?n #" a 0(a4"#a# La ma!a "! 2na ma0ni%2# in%(n!"ca #" 2n c2"(& y !2 4a&( "! c&n!%an%" E "!& "! 2na ma0ni%2# ":%(n!"ca y !2 4a&( #""n#" #" 20a( y #" a! c&n#ici&n"! "n 2" !" mi#a
Ne%!$) Ne%!$) "! a <2"(>a 2" aica#a a 2n c2"(& #" * i& #" ma!a " c&m2nica
2na ac""(aci?n #" * m! + &i'$($)i$) &i'$($)i$) "! a <2"(>a 2" aica#a a 2n c2"(& #" 2na 2ni#a# %cnica #" ma!a " c&m2nica 2na ac""(aci?n #" * m! +
Cara*!er+s!i*as: * Si 2n c2"( c2"(& & %i"n %i"n" " m&4i m&4imi mi"n "n%& %& ("c%i "c%i n" n"& & y 2ni< 2ni<&( &(m" m" a ("!2 ("!2% %an an%" %" #" a! a! <2"(>a! 2" ac%an !&@(" "! n2a + Una <2"(>a <2"(>a in!%an%án"a in!%an%án"a (c" (c" 2n m&4imi"n%& ("c%in"& y 2ni<&(m" 2ni<&(m" 8 Una <2"(>a <2"(>a c&n!%a c&n!%an%" n%" ( (c" c" 2n m&4im m&4imi"n i"n%& %& ("c%i ("c%in n"& "& y 2ni<& 2ni<&(m (m"m "m"n% "n%" " ac""(a#& . Una <2"(>a <2"(>a c&n!%an% c&n!%an%" " "n m?#2& y !"n%i#&3 !"n%i#&3 "(& 2" cam@ia cam@ia c&n%in2a c&n%in2am"n% m"n%" " #" #i("cci?n3 (c" 2n m&4imi"n%& ci(c2a( 2ni<&(m"
P(incii& #" acci?n acci?n y ("acci?n 8 LE LE DE NEQTON C2an#& 2n c2"(& ""(c" 2na <2"(>a !&@(" &%(&3 !%" ""(c" &%(a <2"(>a i02a y #" !"n%i#& c&n%(a(i& !&@(" " (im"(& La acci?n y a ("acci?n amá! !" 2"#"n an2a( m2%2am"n%" m2%2am"n%" &(2" ac%an !&@(" c2"(&! #i!%in%&!
IV.- ,ROCEDIMIENTO:
De la relación FUERZ ! "ELER"I#N * U!" a @aan>a @aan>a #" #" 8 @(a>&! @(a>&! a(a ma!a! ma!a! may&("! may&("! #" ;*, 0 C&&2 C&&2" " a "!a #" +53, 0 "n " ":%("m& ":%("m& #" &! @(a>&!3 @(a>&!3 & c2a " "(mi%i(á "(mi%i(á m"#i( /a!%a * ;*, 0 Mi#a a ma!a #" ca((& + C& C&& &2 2" " a ("n! ("n!a a &(%a &(%a& &"a "a "n " @&(#" @&(#" anc/& anc/& #" a m"! m"!a a y a2! a2!%" %" 4"(%icam"n%" " i!%?n #" ma#"(a "n " @&(#" c&n a! #&! ("n!a!3 " c2a !" c&m&(%a c&m& a(ac/&2"! a(a ca((& ca((& 8 C& C&& &2 2" " a cin%a in%a !&@( &@(" a m"! "!a a y ma ma((2" 2" 2na 2na #i!%a i!%anc ncia ia #" ,6, ,6, m L&n0i%2# "n%(" " 2n%& #" a(%i#a y " " a(ac/&2"! 6
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De 'a re'a*i/ FUER@A EN LA ACCION REACCION 1. r$e el $on%a&e $on%a&e N' ( )e*+n )e*+n la ,*ra. ,*ra. "on%e)%e "on%e)%e la pre*n%a pre*n%a /0 /0 )i*ni,ca el alor 2e indica el dina$ó$e%ro3
E #inam?m"%(& in#ica " 4a&( #" a %"n!i?n #" a c2"(#a a 2" a %"n!i?n 4"n#(a /ac"( i02a a "!& #" @&2" 2" !&!%i"n" a c2"(#a "! &( "& 2" n& in#ica c"(& c&m& !" /aca !2&n"( !2&n"( En " !i02i"n%" 0(ac& !" ":("!a(a ":("!a(a m"&(3 a "c%2(a #" #inam?m"%(&
8
D" 0(ác&) T = Mg
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De n %iró %irón n nor nor$a $al4 l4 con con n na a $a) $a)a a de de $5) $5) o $eno $eno) ) 167 167 8*4 8*4 9aci 9acia a aa& aa&o. o. En En 2 20 0 p pn% n%o o de la) la) cer cerda da) ) )e ro$pe3 E;pli2e lo) )cedido
En "!%a a(%" #" a ":"(i"ncia a c2"(#a !" (&m" "n a a(%" !2"(i&(3 #"@i#& a 2" a <2"(>a !" #i!%(i@2y? a %&#& " !i!%"ma3 c2min#&!" a! "y"! #" n"$%&n En " !i!%"ma3 !i!%"ma3 "n a a(%" !2"(i&( !2"(i&( !&& /a@a a <2"(>a #" %"n!i?n3 %"n!i?n3 y "n a a(%" in<"(i&( /a@a <2"(>a c&n a 2" !" aa@a3 má! a <2"(>a #" @&2"3 & 2" /i>& 2" !" (&ma a c2"(#a "n a a(%" !2"(i&( !2"(i&( En " !i0 !i02i"n 2i"n%" %" 0(a 0(ac& c& !" ":i :ica ca " #ia0 #ia0(a (ama ma #" <2"( <2"(>a >a!! 2" 2" ac%2a(&n !&@(" " @&2"
9
D" a 0(áca) Mg + F > T
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De n %irón )eco con na $a)a de $5) o $eno) = 8* 9acia aa&o.
>acia aa&o. En 20 pn%o de la cerda )e ro$pe3 E;pli2e lo )cedido. Para esta parte de la experiencia la cuerda se rompe en la parte inferior. inferior. Esto es por la rapidez de la fuerza que se aplicó en la cuerda, dejando de cumplirse las leyes de newton. La fuerza fue tan rápida que, no se distribuyó en todo el sistema, y como la acción fue tan rápida la masa quería seuir en reposo lo que !nero que la cuerda se rompa en la parte inferior.
8E:"(im"n%" a" #" ":%("m& #" a c2"(#a a((a!%(an#& a "!a #" 0anc/&! #" ,5W0 2" !" "nc2"n%(a !&@(" a m"!a #" #&! m&#&!)
10
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?ale del del e;% e;%re$o de la c cerda con con na na @e @erAa 2e 2e )ea )ea ),cie ),cien% n%e e co$o co$o para para arra arra)% )%ra rarr o de)l de)liA iAar ar la pe)a )ore la l a $e)a. "ó$o e;plica e)%e e@ec%o3 )e c$ple la) le!e) de neB%on3 La fuerza que se aplicó a esta masa fue e lo su"ciente como para mo#er el bloque, #enciendo la fuerza de fricción, de este modo se cumplen las leyes de newton.
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pli2e el %iró irón en )eco al e;%re$o de la c cerda. E;pli2e lo ocrrido ! co$p5relo con el ca)o an%erior. En este caso la fuerza que aplicamos fue tan rápida que se rompía la cuerda, por la primera ley de newton este este bloq bloque ue quie quiere re seu seuir ir en repos eposo, o, ent entonce onces s jala jalar r rápidam rápidament ente e la cuerda cuerda en forma forma $orizo $orizontal ntal no causaría causaría nin%n efecto sobre el bloque, porque este quiere seuir en reposo.
iii
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Si !" #"!i>a 2n #i!c& #" /&c"y !&@(" a !2"(ci" #" 2na ca"3 " #i!c& !" #"%i #"%i"n "n" " m2y m2y (&n (&n%& %& Si !" #"! #"!i> i>a a !& !&@( @(" " " /i"& /i"&33 " #i!c #i!c& & ("! "!@a @aa a 2na 2na #i!%ancia may&( La (a>?n #" "& "! 2" a <2"(>a #" <(icci?n "! m2y "2"9a Si !" #"!i>a "n 2na m"!a #" ai(" #&n#" (ác%icam"n%" n& /ay <(icci?n3 " #i!c& !" #"!a>a !in 2na (#i#a aa("n%" #" (ai#"> ="m&!3 2"! 2"!33 2" 2" "n a2!" a2!"nc ncia ia #" <2"( <2"(>a >a!! 2n &@" &@"%& %& "n m&4i m&4imi mi"n "n%& %& %i"n %i"n#" #" a #"!a>a(!" "n n"a ("c%a #" <&(ma in#"ni#a La "y #" a in"(cia n&! /ac" 4"( 2" a na%2(a">a n& "! "(">&!a ya 2" &! &@"%&! c&n%inan m&4in#&!" &( ! !&&! S" n"c"!i%an <2"(>a! a(a 4"nc"( a <(icci?n y a(a &n"( &! &@"%&! "n m&4imi"n%& "n " in!%an%" inicia Una 4"> 2" " &@"%& !" #"!a>a "n 2n "n%&(n& i@(" #" <2"(>a!3 !" m&4"(á "n n"a ("c%a &( %i"m& in#"ni#&
2. Dea Dea *$m$ re'a*i/ re'a*i/ )e masas )e '$s )$s *uer($s *uer($s a' re*+(r$* re*+(r$*$ $ )e sus a*e'era*i$es (r$)u*i)as s$re es!$s *uer($s ($r 'a misma fuerza. De ua i!er(re!a*i/ Cu' )e '$s m/#i'es !iee ma0$r ier*ia 0 *u' es su #a'$r La in"(cia "! a &&!ici?n 2" ("!"n%an &! c2"(&! a cam@ia( !2 "!%a#& #" ("&!& & #" m&4imi"n%& m&4imi"n%& S" 2"#" &@!"(4a( 2" a in"(cia !" mi#" a a(%i( #" a can%i#a# #" ma%"(ia & ma!a 2" %i"n" 2n c2"(&3 "! &( "& 2" a may&( ma!a may&( !"(á a in"(cia
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7 Aa' Aa'i* i*e e '$s '$s err$ err$re res s ($r* ($r*e e!u !ua' a'es es 0 'as 'as *aus *ausas as *$rr *$rres es($ ($) )ie ie! !es es..
Eu*ie sus *$*'usi$es. C$ '$s )a!$s $!ei)$s eG(erime!a'me!e se *um('e 'as 'e0es )e 'a )imi*a DE LA RELACION FUER@A ACELERACIÓN: "a)a): A anai>a( &! ("!2%a#&! &@%"ni#&! "n " (&c"#imi"n%& ":"(im"n%a3 !" &@!"(4a 2" ":i!%" 2na 4a(iaci?n mnima3 a c2a !" 2!%ica "n a! !i02i"n%"! n"a!) * La @aan>a @aan>a n& "!%24& "!%24& @i"n cai@(a#a3 & c2a 0"n"(? 0"n"(? 2n ma(0"n #" "((&( "((&( mnim& "n #ic/a "!a#a + En a &@%"nci?n &@%"nci?n #" &! #a%&! #" #" %i"m& "nc&n%(am&! "nc&n%(am&! ci"(%&! "((&("!3 "((&("!3 "!%& !" !" #"@" a %i"m& #" ("acci?n 2" !" %24& a m&m"n%& #" %&ma( #ic/& %i"m& c&n " c(&n?m"%(& 8 12" 12" a m" m"#i #i(( a #i!% #i!%an anci cia a "n%( "n%(" " " 2n% 2n%& & #" a(%i# a(%i#a a y " a(a a(ac/ c/& &2" 2"!! n& <2" <2" ":ac%am"n%" ,;, m . 12" 12" a !&%a !&%a(( " ca((i%& ca((i%& n& !" #"!a #"!a>? >? "n n"a n"a ("c%a3 ("c%a3 &( a c2a !" &@%24& &@%24& 2na 2na "2"9a 4a(iaci?n "n " %i"m& "oncl)ione): L2"0& #" %"(mina( a (im"(a ":"(i"ncia "0am&! a a! !i02i"n%"! c&nc2!i&n"!) * 12" a(a &#"( &#"( /aa( /aa( a ac""(aci?n ac""(aci?n ":"(im ":"(im"n%a "n%a3 3 !" #"@" %"n"( %"n"( c&m& #a%&! #a%&! " %i"m& y a #i!%ancia ":"(im"n%a + La ac""(aci?n ac""(aci?n ":"(im"n%a ":"(im"n%a !" /aa /aa a %(a4! #" a !i02i"n%" <&(m2a a+#%^% 8 Pa(a &#"( &#"( &@%"n &@%"n"( "( @2"n @2"n&! &! ("!2 ("!2%a# %a#&! &! !" n"c"!i n"c"!i%?3 %?3 &@%"n"( &@%"n"( %("! %("! #a%&! #a%&!33 #" &! c2a"! !" 2%ii>? " (&m"#i& a(a &! các2&! c&(("!&n#i"n%" LA RELACION MASA ACELERACION "a)a): A anai>a( &! ("!2%a#&! &@%"ni#&! "n " (&c"#imi"n%& ":"(im"n%a3 !" &@!"(4a 2" ":i!%" 2na 4a(iaci?n mnima3 a c2a !" 2!%ica "n a! !i02i"n%"! n"a! * L&! "((&( "((&("! "! !" #"@"n #"@"n a 2" " c&n%(&a# c&n%(&a#&( &( #" %i"m& %i"m& !" #"? "4a( "4a( &( " !&ni#& !&ni#& #" c/&2" & c2a 0"n"(& ci"(%& ma(0"n #" "((&( + La c2"(#a c2"(#a n& "!%a@a "!%a@a ":ac%am"n% ":ac%am"n%" " a(a"a a(a"a a a m"!a & c2a 0"n"(& 0"n"(& #i!%&(!i? #i!%&(!i?n n "n &! #a%&! 18
"oncl)ione): L2"0& #" %"(mina( a (im"(a ":"(i"ncia "0am&! a a! !i02i"n%"! c&nc2!i&n"!) * 12" a(a &#"( &#"( /aa( /aa( a ac""(aci?n ac""(aci?n ":"(im ":"(im"n%a "n%a3 3 !" #"@" %"n"( %"n"( c&m& #a%&! #a%&! " %i"m& y a #i!%ancia ":"(im"n%a + La ac""(aci?n ac""(aci?n ":"(im"n%a ":"(im"n%a !" /aa /aa a %(a4! #" a !i02i"n%" <&(m2a a+#%^% 8 Pa(a &#"( &#"( &@%"n &@%"n"( "( @2"n @2"n&! &! ("!2 ("!2%a# %a#&! &! !" n"c"!i n"c"!i%?3 %?3 &@%"n"( &@%"n"( %("! %("! #a%&! #a%&!33 #" &! c2a"! !" 2%ii>? " (&m"#i& a(a &! các2&! c&(("!&n#i"n%" . En "!%a ":"(i ":"(i"nci "ncia a a a2n2" a2n2" a(">ca a(">ca ca!i i02a i02a a a an%"(i&(3 an%"(i&(3 !" &@!"(4a &@!"(4a 2" a ma!a #" !i!%"ma !i 4a(ia &( & 2" &! ("!2%a#&! !"(án #i<"("n%"!
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R"!"c%& a &! ("!2%a#&! /"m&! &#i#& n&%a( 2" &! má(0"n"! #" "((&( "n 2" 2n ":"(im"n%a#&( 2"#" inc2((i( H!i "! 2" n& !" ("ai>an a#"c2a#am"n%" a! m"#i#a! m"#i#a! ":"(im"n ":"(im"n%a" %a"! ! P&( P&( & %an%& "!%a (ác%ica (ác%ica n&! /a "(mi%i#& "(mi%i#& aan>a( aan>a( n2"!%(&! c&n&cimi"n%&! ac"(ca #" a T"&(a #" a M"#ici?n
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L&! c2"(&! "n m&4imi"n%&3 c2an#& !" "! ""(c" a02na <2"(>a "!%&! !" ac""(an3 0(acia! a "!a "y 2#" 4"( &( ""m&3 a0& 2" "nc&n%(am&! (c%& #" a in4"!%i0aci?n3 &( 2 c2an#& a! a%ina#&(a! #" /i"& !a%an3 a ca"(3 %&man má! 4"&ci#a#3 y "! &(2" a ("!i?n ""(ci#a !&@(" &! a%in"! "! m2y 0(an#" y "!%& (&m" a <(icci?n y /ac" 2" " c2"(&3 "n "!%" ca!&3 a a%ina#&(a3 !" #"!ic" c&n má! (ai#"> 2" an%"!
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Tam@in Tam@in 2" &! c2"(&! !i"m(" %i"n#"n a c&n!"(4a( !2 "!%a#& #" m&4imi"n%&3 ya !"a "!%aci&na(i& & "n m&4imi"n%&3 y 2" a "!%" <"n?m"n& !" " #"n&mina in"(cia
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