TALLER TALLER TUTORIA TU TORIA 1 FISICA CONCEPTUAL – PAUL HEWITT
JESSICA VA VANNESA NNESA BARRAGAN CARDONA
Cód.: 083200!2012 083200!201 2
FISICA DE ONDAS
UNIVERSIDAD DEL TOLI"A INSTITUTO DE EDUCACION A DISTANCIA #IDEAD$ IBAGUE – TOLI"A 201% TALLER TALLER TUTORIA TU TORIA 1
FISICA CONCEPTUAL – PAUL HEWITT
JESSICA VA VANNESA NNESA BARRAGAN CARDONA
Cód.: 083200!2012 083200!201 2
FISICA DE ONDAS
TUTOR ANGEL ANTONIO ANTONIO ROJAS GARCIA
PROGRA"A INGENIERIA DE SISTE"AS POR CICLOS
UNIVERSIDAD DEL TOLI"A INSTITUTO DE EDUCACION A DISTANCIA #IDEAD$ IBAGUE – TOLI"A 201%
INTRODUCCIÓN
S& '()* +, *-*'(/d,d d& */', */ &+ ,'&,+ d', d& (/ ,/ +4* ** & -,&ó &5'& ',4,6,d*7 95, */&-'(,+ d& P,(+ H&''7 4/d,d* -* &+ -*&5*7 ,+ ',4,6, &+ ,-9'(+* 7 "*)&/'* C(+,7 +*& &*d, (;*5 */ */&&-'* '*5 5 ',4 ',4,6 ,6,d ,d*5 *5 ,/'& ,/'& * *& &/' /'& & &/ +, (/) (/)& &5 5d, d,d d < &/ &+ *+& *+& * * 4,;++&,'*7 ,d&=5 d& *-&/d&+* d& (/, ,/&, =5 5&/++, ,,5 , +*5 +*5 &6& &6&-+ -+*5 *5 >(& >(& d,4, d,4,/ / ',/ ',/ d*5 d*5 , +, &,+ &,+d d,d ,d d, d,, , >(& >(& , ,+ +', ',* */ / +, ,-*-,ó/7 5& )&*/ < ;,4+,*/ d& '&,5 ** *',ó/ < &)*+(ó/7 d,/d* &6&-+*5 d& ,d, (/*7 ',4?/ 5& ','ó d& +, ,-d&@ +/&,+7 ',/&/,+ < +, ,-d&@ d& *',ó/ < ,+* (< -*',/'& >(& 5& ',4,6* (& +,5 (&@,5 >(& &5'=/ -&5&/'&5 &/ &+ *)&/'* (+,7 >(& 5*/ +, (&@, &/'9-&', < +, (&@, &/'9(,. E/ */+(5ó/ & (5'ó (;* &5'*5 ,'&,+&5 d& ',4,6* <, >(& ** d6* &+ '('*7 ,<(d, , /* */(/d5& < ,-&/d& , '&/&+& (5'* , +, ,'&,7 */ (/, ,/&, d& &-+, < 5(5'&/', &6&-+*5 =+&5 d& &/'&/d& < -,+-,4+&5 , +, &,+d,d < , +,5 &-&&/,5 & -&&/,5 ))d,5.
OBJETIVOS
R&'*, R&'*, */&-' */&-'*5 *5 d& *) *)&/' &/'* * (+, (+, ,<(d=/d ,<(d=/d*/* */*5 5 d& &6&-+ &6&-+*5 *5 < =*5. E/'& E/'&/d /d& & +, d& d&& &/ /, , &/'& &/'& *', *',ó ó/ / < &)*+ &)*+( (ó ó/7 /7 < (,/ (,/d* d* 5& ,-+ ,-+, , ,d, (/, d& &++,5. A-&/d A-&/d& & 5*4& 5*4& +*5 +*5 d5' d5'/'* /'*5 5 '-*5 '-*5 d& ,-d ,-d&@ &@ >(& >(& 5& ,-+ ,-+,/7 ,/7 ** ** +* +* &5 +, ,-d&@ +/&,+7 ',/&/,+ < ,-d&@ d& *',ó/. A/,+@ +@, +*5 ,5*5 &/ >(& 5& )& ,-+,d,5 +,5 d*5 (&@, @,5 d&+ *)&/'* (+,7 +, (&@, &/'9-&', < +, (&@, &/'9(,.
TABLA DE CONTENIDO
• • • • • • •
P*',d, C*/',-*',d, I/'*d(ó/ O46&')*5 ",-, C*/&-'(,+ E/5,<*: "*)&/'* C(+, T,++& P&(/',5 d& R&-,5* P&/5, < &-+, P&/5, < &5(&+)&
MAPA CONCEPTUAL
ENSAYO EL MOVIMIENTO CIRCULAR
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R,-d&@ ,/(+, /. *',*/&5 '&-* ' &-* R,-d&@ +/&,+ ) F(&@, &/'9-&', F ) 2 2
TALLER PREGUNTAS DE REPASO 1. Explica Explica la dif!"cia dif!"cia "#! "#! l$% l$% #&!'i"$% #&!'i"$% d !$#aci(" !$#aci(" ) !*$l+ci !*$l+ci(". (". L, d&&/, &/'& +, *',ó/ < +, &)*+(ó/ &57 >(& +, *',ó/ &5 &+ *46&'* >(& , ,+&d&d* d& (/ &6& /'&/*7 d&/'* d&+ (&-* d&+ *46&'*7 &/',5 >(& +, &)*+(ó/ ',4?/ &5 (/ *46&'* >(& , ,+&d&d* d& (/ &6&7 -&* &'&/*.
,. -+& -+& #ip$ d '$*i '$*i'i 'i"# "#$ $ d%c d%c!i !i/ / +" "i0$ "i0$ " +" ca!!+ ca!!+% %l l +"a !*$l+ci(" $ +"a !$#aci("2 E+ *)&/'* >(& 5& d&54& &/ (/ ,(5&+7 &5 (/, *',ó/7 <, >(& , , ,+& ,+&d& d&d* d* d& (/ &6& &6& * &/' &/'* * d&+ d&+ ,( ,(5& 5&+7 +7 >(& >(& &5'= &5'= d&/' d&/'* * d&+ d&+ ,(5&+.
3. Explica Explica la dif!"cia dif!"cia "#! "#! !apid4 !apid4 li"al li"al ) la !apid4 !apid4 d !$#aci( !$#aci(". ".
L, ,-d&@ +/&,+ &5 +, d5',/, &*d, &/ (/ '&-* d&'&/,d*7 &/',5 >(& ,-d&@ d& +, *',ó/7 &5 &+ /&* d& *',*/&5 &/ (/ '&-* d&'&/,d*.
5. -C('$ % % l lla'a a la la !apid4 !apid4 li"al li"al d +" $/6#$ $/6#$ 7+ 7+ % '+* '+* " +" c8!c+l$2 L, ,-d&@ +/&,+ &/ (/ *)&/'* (+,7 '*, &+ /*4& d& R,-d&@ T,/&/,+7 ,/&/,+7 >(& &5 (,/d* &+ *46&'* '&/& (/, ',<&'*, >(& 5&-& &5 (+,.
9. A +"a +"a di%#a"cia di%#a"cia %pcific %pcifica a !%pc#$ !%pc#$ al 6: 6: -C('$ ca'/ia ca'/ia la !apid4 !apid4 li"al ;$ #a"<"cial= a 'dida d 7+ % '$difica la !apid4 d !$#aci("2 L, ,-d&@ *',*/,+ /* 5& *d,7 5&-& &5 */5',/'&7 < -&,/&& */5', */5',/'& /'& &/ '*d* *&/'* *&/'*77 +, /, >(& ,(&/' ,(&/', , 5( ,-d&@ ,-d&@ &5 +, ',/&/,+ , &dd, >(& 5& ,+&6, d&+ &6&.
>. A +"a !apid4 !apid4 d !$#aci( !$#aci(" " d#!' d#!'i"a i"ada: da: -C('$ -C('$ ca'/ia ca'/ia la !apid !apid44 li"al ;$ #a"<"cial= a 'dida 7+ % '$difica la di%#a"cia !%pc#$ al 62 A &dd, >(& 5& ,+&6, d&+ &/'* * &6&7 &5'& ), ,(&/',/d* 5( ,-d&@ ',/ ',/&/ &/ ,+ ,+ < (,/ (,/'* '* =5 =5 5& ,+&6 ,+&6& & d&+ d&+ &6&7 &6&7 &5', &5', ,- ,-d& d&@ @ ',/ ',/&/ &/ ,+ ,+ ,(& ,(&/' /', ,, , =57 =57 <, >(& >(& (,/ (,/d* d* 5& / /, , &+ *) *) &/ &/'* '* < &5'& &5'& 5& &/(&/', &/ &+ &6&7 +, ,-d&@ ',/&/,+ &5 0.
?. C+a"d$ C+a"d$ @ac'$ @ac'$%% !$da! !$da! +" cil cili"d i"d!$ !$ %$/! %$/! +"a %+p!f %+p!fici ici %i<+ %i<+ la #!a)c#$!ia " l8"a !c#a. U" *a%$ c("ic$ 7+ !+da %$/! la 'i%'a %+p!fici 7+ % '+* " c8!c+l$% -P$!7+2
E5'* 5(&d& -*>(&7 &+ ),5* ó/* '&/& (/ &'&* =5 ,/;* #'&/& (/ ,d* ,<*$ >(& &+ *'* &'&*7 < ** 4&/ 5,4&*57 +, ,-d&@ +/&,+ d&-&/d& d&+ ,d* ), , '&/& (/, ,<* ,-d&@ +/&,+ &+ &'&* >(& '&/& (/ ,d* ,<*.
. C+a"d$ @ac'$%
L, d&ó/ >(& '&/& +, (&@, >(& &5'= &6&?/d*5& &6&?/d*5& 5*4& +, +,', &57 ;,, &+ &/'*7 &5 d& 5& &5'= ,-+,/d* (/, (&@, &/'9-&',.
. -" 7+& 7+& %"#id$ %"#id$ !%pc#$ !%pc#$ al c"#!$ c"#!$ d la la pla#af$!'a pla#af$!'a ac#a ac#a la f+!4a f+!4a 7+ %$%#i" a l$% $c+pa"#% dl 6+<$ 'c"ic$ d la fi<+!a .12
L, (&@, >(& 5& ,-+, 5*4& +*5 *(-,/'&5 d&+ 6(&* &=/* d&+ 6(&*7 &5 ;,, ,(&,7 &5 d& +,5 ,+&6, d&+ &/'* * &6& d&+ 6(&*7 +* >(& 5/, >(& 5& ,-+, +, (&@, &/'9(,.
1. E" 7+& %"#id$ % 6!c la f+!4a 7+ ac#a %$/! la% p!"da% d+!a"# l cicl$ d c"#!if+
L, (& (&@ @, >(& 5& ,-+ ,-+, , 5*4& 4& +,5 +,5 -&/ &/d,5 d,5 d(,/ (,/'& '& &+ +* +* d& &/'(,d* &5 +, &/'9-&',7 >(& +, &6&&/ +, -,&d /'&* d& +, '/,7 -,, >(& +, *-, 5& (&), &/ *, (+,.
11.. C+a"d$ +" a+#$ *i!a: -%+'i"i%#!a" l$% ci"#+!$"% d %<+!idad 11 %<+!idad +"a f+!4a c"#!8p#a $ c"#!if+(& &)', >(& (,/d* ;,<, (/ *)&/'* * &/* 4(5*7 &+ (&-* 5& ),<, ;,, ,+ ',4+&* d& ,/d*.
1,.Si 1,. Si % !$'p l c$!dl 7+ 'a"#i" a +"a la#a " #!a)c#$!ia ci!c+la! -C+l % la ca+%a d 7+ la la#a %i
L, +,', 5(& 5( ',<&'*, &/ +9/&, &',7 -*>(& <, /* ;,< //(/, (&@, >(& 5& &6&@, 5*4& &5'&7 <, >(& +, (&@, &/'9-&', &, +, >(& +, ;,9, ,/'&/& 5( ',<&'*, (+,7 -* &5', ,@ó/ (,/d* 5& *-& &+ *d&+7 +, +,', 5(& 5( ',<&'*, +/&,+7 4,5,d, &/ +, +&< d& /&, d& N&'*/.
13.Id"#ifica la% f+!4a% d acci(" ) d !acci(" " la i"#!acci(" "#! la 'a!i7+i#a ) la la#a
L, (&@, d& ,ó/ >(& 5& ,-+, &/'& +, ,>(', < +, +,', ,'*,7 &5 +, (&@, &/'9(,7 >(& &5 +, >(& ,/'&/& ,+ /5&'* &/ &+ */d* d& +, +,',7 < +, (&@, d& &,ó/ &5 +, (&@, &/'9-&', -*>(& &5 +, >(& ,',& , +, ,>(', , +, -,&d d& +, +,',.
15.U"a .U"a 'a!i7+i#a 7+ %# " l f$"d$ d +"a la#a 7+
N* 5& ,-+, (&@, d& &,ó/7 <, >(& ** -(d*5 ,/,+@, +, (&@, &/'9(, >(& 5& ,-+, &5 5*+,&/'& (/, (&@, ',7 >(& 5&/'& +, ,>(', >(& &5'= &/ &+ */d* d& +, +,',.
19.-P$! 7+& % c$"%id!a c$'$ +"a H+!4a fic#icia la f+!4a 7+ la 'a!i7+i#a p!ci/ " l 'a!c$ d !f!"cia !$#a#$!i$2 S& */5d&,/ (&@, ', <, >(& &5',*5 ',',/d* d& +, ,)&d,d7 >(& 5/, ,',ó/ d& (/, ,5, , +, '&,7 >(& &/ &5'& ,5* /* ,-+, <, >(& 5&9, +, ,',ó/ d& (/, ,5, , *', ,5,7 -&* &/ &5'& ,5* &5', &5 (/ &&'* d& +, *',ó/7 /* &5 -,'& d& +, /'&,ó/ d& d*5 ,5,57 < /* 5& '*, ** (/, (&@, )&d,d&,7 -* &5, ,@ó/ 5& +& d&/*/, ** (/, (&@, ',.
1>.E" +" @/i#a# %pacial !$#a#$!i$ d +" #a'a0$ d#!'i"ad$: -C+l % la !laci(" "#! la 'a<"i#+d d la (& ;,< &/'& +, ,/'(d d& +, (&@, &/'9(, #,)&d,d 5(+,d,$ < +, ,-d&@ d& +, *',ó/ &57 +, ,&+&,ó/ &/'9-&', * &/'(, d&4d* , +, *',ó/ >(& '&/& &+ ;=4','.
1?.Pa!a d$% @/i#a#% %pacial% 7+ (& ;,< &/'& +, ,)&d,d 5(+,d, < &+ ,d* d&+ ;,4',d7 &5 >(& ,+ ,(&/', +, d5',/, ,d,+7 ,(&/',, +, ,&+&,ó/ &/'9-&', * &/'(, < +, ,-d&@ +/&,+.
1.. -P$! 1 -P$! 7+& 7+& la la%% % %#a #aci ci$" $"% % % %pa paci cial al% % " (!/i (!/i#a #a 7+ 7+ %i'+ %i'+la la" " la (& -*>(& 5 5*/ d& &/* d=&'*7 '&/d9,/ >(& , */ ,/ ,-d&@ -,, -*-**/, (/, ,&+&,ó/ ,)',*/,+ 5(+,d, d& 1 7 < -,, 5(+, +, ,)&d,d /*,+ d& +, '&, , 1RP" 5& &>(&& >(& 5&, (/, &5'('(, ,/d& d& ,5 2 d& d=&'*.
PIENSA Y EPLICA 1. Si # %+l#a %+l#a% % d +" ca!!+% ca!!+%ll 7+
S & 5(&+ 5(&+'* '* d& (/ ,( ,(5& 5&+7 +7 >(& >(& , , */ */ ,- ,-d& d&@7 @7 )*< )*< , ,& ,& 5/ 5/ ',<&'*,7 &/ +9/&, &',7 -*>(& <, /* ;,< //(/, (&@, >(& 5& &6&@, 5*4& (&-* ;,, &+ &6&7 &5'* 4,5,/d* 5*4& +, +&< d& +, /&, #-&, +&< d& /&'*/$.
,. U"a 'a!i7 'a!i7+i# +i#a a %#a p$%ad p$%adaa a la 'i#ad 'i#ad dl ca'i" ca'i"$ $ "#! "#! l 6 ) l /$!d d +"a #$!"a'%a 7+ (& &5', ,-d&@ &5 d&',&/'& -*-**/,+ , +, d5',/, ,d,+ < , +, ,-d&@ d& *',ó/.
/. La 'a!i7 'a!i7+i# +i#a a % p$%a p$%a " l /$!d /$!d2 2 V, , ,(&/', d&4d* , >(& , &dd, >(& &+ *46&'* 5& ,+&6& d&+ &6&7 ,(&/',, =5 5( ,-d&@ +/&,+ #T,/&/,+$.
c. Oc Oc+! +!! ! #a"# #a"#$ $ a c(' c('$ $ /2 A4*5 ,'*&5 /+(<&/7 ',/'* ** &+ ,(&/'* d& +, ,-d&@ d& *',ó/7 ** +, d5',/, d&+ *46&'* */ &5-&'* ,+ &6&7 /+(<&/ &/ &+ ,(&/'* d& +, ,-d&@ ',/&/,+.
3. -C+l -C+l % l %#ad$ %#ad$ d E%#ad$% E%#ad$% U"id$% U"id$% c$" 'a)$! 'a)$! !apid4 !apid4 #a"<"ci #a"<"cial al " *i!#+d d la !$#aci(" d la #i!!a al!dd$! d %+ 62 E/ &5', &5',d* d*5 5 (/d (/d*5 *577 &+ &5', &5',d* d* >(& >(& -(&d -(&d& & -&5 -&5&/ &/', ', ,<* ,<* ,- ,-d& d&@ @ ',/&/,+ &/ )'(d d& +, *',ó/ d& +, '&, ,+&d&d* d& 5( &6&7 &5 F+*d,7
5. El *l l$c $c8' 8'# #!$ !$ d +" a+#$ a+#$ % '+* '+* p$! 'di$ di$ d +" ca/l a/l c$"c#ad$ al 6 7+ @ac (&K,57 -&>(&K,57 &+ )&+*9&'* *5',, (/, +&'(, &/* d&4d* , +, *d,ó/ d& +, d5',/, ,d,+ &5',5 d&4&=/ ,(&/', 5( ,-d&@ *',*/,+ -,, +*, '&/& (/, ,-d&@ &,+ (,+ , +,5 (&d,5 =5 ,/d&57 <, >(& ,+ ,4,+,5 *d,*5 +, d5',/, ,d,+ d& +, (&d,. (&d,.
9. T" p!% p!%"# "# l c$"cp c$"cp#$ #$ d la p!<+"# p!<+"#aa a"#!i a"#!i$! $! pa!a !%$l* !%$l*! ! l$ %i<+i %i<+i"# "#.. El c$"d+c c$"d+c#$! #$! d +" #axi #axi i"#"# i"#"#aa a+'"# a+'"#a! a! (& ,(&/'& &+ ,d* d& +, (/&&/,7 < d& &5, ,/&, ,(&/'& +, ,-d&@ ',/&/,+ d&+ ',.
>. C$"% C$"%id id! !aa l pa! d *a%$% *a%$% +"id$% +"id$% c$" ci"# ci"#aa ad@ ad@%i* %i*aa c$'$ c$'$ % '+%#!a " la fi<+!a. -S!a capa4 %# di%0$ d a+#$! !
S &,+ &,+@ @, ,*5 *5 &5'& &5'& d5& d5&K* K* -*d& -*d&*5 *5 /*', /*', >(&7 >(&7 5 +*5 +*5 ),5* ),5*5 5 &5'= &5'=/ / &/',d*57 5*/ d& (,+ ,d* < +, 5, -,'& d&+ ),5* &5'= '*,/d* &+ &+ * &+,7 ,+ *)&5& ),/ , ,/'&/& (/ *)&/'* &/ +9/&, &', < ,4*5 +,d*5 ),/ , '&/& +, 5, ,-d&@ +/&,+7 5 -* (,+>(& ,@ó/ 5& (&d, d& ,/&, '*d, +*5 ),5*57 &++*5 5*5 5& *&/ <, >(& &5'& *)&/'* < *, d& +*5 ),5*5 +*5 (4, &/ (/ -(/'* &d* &/'& +*5 &+&5.
?. U" '$#$cic '$#$cicli% li%#a #a p+d p+d '$*!% '$*!% a l$ la!<$ d la pa!d pa!d *!#ical *!#ical d +"a pi%#a " f$!'a d c+"c$: c$'$ % '+%#!a " la fi<+!a.
-Ac# -Ac#aa +"a +"a f+! f+!4a 4a c c"# "#!8 !8p p#a #a $ +"a +"a f+! f+!4a 4a c c"# "#!8 !8f+< f+
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. C+a"d$ C+a"d$ +" <+ila <+ila Efc# Efc#a a +" *i!a6 *i!a6 d+!a"# d+!a"# l *+l$: *+l$: -C+l % la f+"# d la f+!4a c"#!8p#a 7+ ac#a %$/! lla2 L, /, (&/'& d& +, (&@, &/'9-&', >(& ,', 5*4& &+ =(+,7 &5 &+ ,&7 +, *&/'& d& ,&.
. S$/! S$/! " +" a+#$ a+#$ " !p$%$ !p$%$ " +" ca'i"$ ca'i"$ @$!i4$ @$!i4$"#al "#al % 6!c 6!c" " d$% f+!4a% %+ p%$ ;@acia a/a6$= ) la f+!4a "$!'al ;@acia a!!i/a=. Rc+!da ;capi#+l$ 5= 7+ la f+!4a "$!'al % la f+!4a d %$p$!#: la c+al % %i'p! % p!p"dic+la! a la %+p!fici d ap$)$. Si l a+#$ fc#a +" *i!a6 %$/! +" ca'i"$ @$!i4$"#al: la f+!4a "$!'al c$"%!*a %+ di!cci(" @acia a!!i/a. La f!icci(" "#! la% !+da% ) l ca'i"$ % la "ica f+!4a c"#!8p#a 7+ p!'i# l '$*i'i"#$ c+!*il8"$. S+p(" 7+ l ca'i"$ +" p!al#: d '$d$ 7+ la f+!4a "$!' "$!'al al #i" #i" +"a +"a c$'p c$'p$" $"" "# # 7+ 7+ p!$p p!$p$! $!ci ci$" $"aa +"a +"a f+! f+!4a 4a c"#!8p#a c$'$ % '+%#!a " l di/+6$. -c$"%id!a% 7+ % p$d!8a da! al ca'i"$ +" p!al# #al 7+ pa!a +"a !apid4 ) +" !adi$ d c+!*a c+!*a#+! #+!aa d#!' d#!'i"a i"ad$ d$%% +" *@8c+ *@8c+l$ l$ p$d!8 p$d!8aa *i!a! *i!a! %i" f!icci f!icci("2 ("2 Explica #+ !%p+%#a.
S (/ ,* /'&/', , (,/d* 5& &/(&/', ,',)&5,/d* (/ -&,+'&7 5& -(&d& d,7 -&* 5& d(+',, d&4d* , +, ó/ -*d(d, -* +, /+/,ó/ d& +, ,&'&, < , +, /+/,ó/ d& +, (&@, /*,+ */ &5-&'* ,+ -&5*7 +* >(& ;,= >(& &+ ,* 5&-& '&/d, , &/ d&ó/ , +, -,'& */ &/*5 /+/,ó/ d& +, ,&'&,7 ,+ -(/'* &6& d&+ * >(& &+ ,* &5'= d,/d*7 &5 ,>(9 d*/d& 5& -&5&/', +, (&@, &/'9-&',.
1.-Rali4a #!a/a6$ la f+!4a c"#!8p#a %$/! +" $/6#$ " !$#aci("2 ;S+<!"cia C$"%id!a la di!cci(" d la f+!4a c"#!8p#a ) la di!cci(" dl '$*i'i"#$=. L, (&@, &/'9-&', 5*4& 5*4& (/ *46&'* &/ *',ó/7 ,59 5( *)&/'* 5&, ;*@*/',+7 )&',+7 ;,, +, d&&;, * @>(&d,7 5 &,+@, (/ ',4,6* ,+ ,-+ ,-+, , 5( (& (&@, @, ;, ;,, , &+ &/' &/'* * d&+ d&+ &6& &6& d& +, *', *', ó/ ó/ d&+ d&+ *46& *46&'* '*77 -&' -&'&/ &/d* d* >(& >(& +*5 *46&'* *46&'*5 5 >(& >(& &5'?/ &5'?/ &,+@ &,+@,/d ,/d* * +, *', *',ó/ ó/77 /* 5& 5,+,/ d& +, ',<&'*, (+, >(& '&/&. ' &/&.
11.. Explica p$! 7+& c+a"#$ '% !pid$ (& /(&5'*5 (&-*5 5&,/ ,',9d*5 , +, '&,7 &/'& +, '&, ,(&/'& 5( *',ó/7 ,(&/',,
+, (&@, &/'9(, < d5/(<& +, (&@, &/'9-&',7 +* >(& d5/(<& +, (&@, >(& /*5 ,',& , +, '&,7 -* ',/'* /*5 ;,& 5&/' =5 +),/*57 &/',5 >(& &/ +, &5',ó/ &5-,,+7 '&/& ,<* (&@, &/'9(, -* ',+ ,@ó/ 5& 5&/'& =5 +),/*7 &/'& =5 &7 5& d5/(<& +, (&@, &/'9(, < ,(&/', +, (&@, &/'9-&', >(& ;,& +*5 (&-*5 =5 -&5,d*5.
1,.L$% $c+pa"#% d +" #!a"%/$!dad$! %pacial " (!/i#a xp!i'"#a +"a %"%aci(" d i"(& 5& &/(&/',/ &/ &+ ',/54*d,d* d&4&= d& *& &+ ,4+& < &-&@, , ,7 '*,/d* ** &6& &+ *'* *46&'* d& ,/ ,5,7 '&/&/d* (/ ,(&/'* &/ +, *',ó/7 d& &5', ,/&, ,(&/', +, (&@, &/' &/'9 9-& -&', ',77 ,(& ,(&/' /',/ ,/d* d* +, ,) ,)&d &d,d ,d77 5/' 5/'& &/d /d* * (/ -** -** =5 =5 d& **dd,d */ +, ,-*,ó/ , +, ,)&d,d /*,+ d& +, '&,.
PIENSA Y RESUELVE 1. Ma!# Ma!# % %#a #a ap!$ ap!$xi xi'a 'ada da' '"# "# d$% d$% *c c% % '% '% l6$ l6$%% dl dl %$l %$l 7+ 7+ *"+%. E" +" a0$ 'a!cia"$: 7+ % l #i'p$ 7+ #a!da 'a!# " da! +"a *+l#a al!dd$! dl %$l: % +"a% #!% *c% '% la!<$ 7+ l a0$ *"+%i"$. a. -C+l -C+l d %#$% %#$% d$% pla"# pla"#a% a% #i" #i" +"a !apid !apid44 d !$#aci(" !$#aci(" 'a)$! 'a)$! " %+ (!/i#a2 E+ -+,/&', >(& '&/& ,<* ,-d&@ d& *',ó/ &/ 5( ó4', &5 ,'& <, >(& '&/& (/, ó4', =5 ,/d& >(& )&/(57 < ,'& d(, =5 '&-* &/ *-+&', (/ ,K*7 =5 &5-&9,&/'& 3 ,K*5 )&/(5,/*5.
/. -C+l -C+l d ll$% ll$% #i" #i" +"a +"a !apid4 !apid4 li"al li"al 'a)$! 'a)$!2 2 E+ -+,/&', >(& '&/& ,<* ,-d&@ +/&,+ * ',/&/,+7 &5 ,'& <, >(& 5( -*d,d ,+ 5*+ &5 &/*5 , +, d& )&/(57 -,, &*& 5( ó4', '&/& >(& &*& ,<* d5',/,.
,. E" l$ al#$ d +"a +"a '$"#a0a '$"#a0a % "c+ "c+"#! "#!a a +"a #$!"a' #$!"a'%a %a 7+
l%! 7+ 'i# +" /!illa"# @a4 d l+4: c$"f$!' la #$!"a'%a ) l l%!
/. -+& -+& #a" ap!i%a ap!i%a /a!! /a!! la 'a"c@a 'a"c@a d l+4 l%! l%! +"a% +"a% "+/% "+/% 7+ %#" a , ' d di%#a"cia2 ) S&/d* ) )&+*d,d +/&,+ * ',/&/,+ #5$ ,d* #'5$ )&+*d,d ,/(+, &/ ,d5
V 20 10 - V2000 '5 2.83 ,d5 V 12%0 '55
c. -A 7+& 7+& di%# di%#a" a"ci ciaa /a!! /a!!! !aa l @a4 d l+4 l+4 l% l%!! l cil$ cil$ c$" la !apid4 d la l+4 ;3 '%=2 S&/d* ) )&+*d,d +/&,+ * ',/&/,+ #5$ ,d* #'5$ )&+*d,d ,/(+, &/ ,d5 ) 300000 10 -5 300000 2.83 ,d5 300000000 '55 2.83 ,d5 M!!M!8711 '5
3. C$"%id!a C$"%id!a +"a +"a %#aci(" %#aci(" %pacial %pacial d'a%iad d'a%iada a p7+0a p7+0a 7+ c$"%i%# c$"%i%# " +"a %f!a
d pi +" @$'/! d , ' d %#a#+!a c+)$% pi% xp!i'"#a" +"a acl! ac l!ac aci(" i(" d 1 <. -+& -+& ac acl! l!aci aci(" (" xp!i xp!i'" '"#a #a %+ ca/4a ca/4a2 2 Explic Explicaa p$! 7+& % "c%a "c%a!i$ !i$ 7+ %a
=
2g 4
=
1g 2
=
0.5 g
E/ (/, &5',ó/ &5-,,+ >(& d, M '5 d& ,d*7 5 (/ ;*4& d& 2 '5 d& &5','(,7 &/ 5(5 -&5 &-&&/', (/, ,&+&,ó/ d& 1 .7 ,+ d(-+,5& &+ -(/'* -(/'* * +, d5',/,7 d5',/,7 +, ,)&d,d d5/(<&7 d5/(<&7 &5 d& >(& >(& &/ +, ,4&@, +, ,)&d,d 5&= 0.% .
5. C+a" C+a"d$ d$ %#a% %#a% d pi " l i"# i"#!i !i$ $! d +"a +"a %#a %#aci(" ci(" %pac %pacia iall
=
0.99 g −→
1 100
g
C** -*d&*5 *45&),7 &/'& &/'& 1 < 0.7 ;,< 1100
