UNIVERSIDAD UNIVERS IDAD CATÓLICA CATÓLICA DE EL SALVADOR SALVADOR FACULTAD ACULTAD DE D E INGENIERÍ INGE NIERÍA A Y ARQUITECTURA ARQUITE CTURA MATERIA: FÍSICA III ORIENTADOR: ING. SAMUEL ADOLFO DUEÑAS APARICIO
“Si consigo ver más lejos es porque me apoyé en hombros de gigantes” Isaac Newton.
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1. U!% #s,#% '#"$&i(% p#-#%) (o! !% (%+% !#"% d# q1 = -2.80 µC ) s# '%!"i#!# #! !% posi(i6! ,i% po '#dio d# sopo"#s %is&%!"#s. S# po8#("% %(i% q1 !% s#+!d% #s,#% '#"$&i(% p#-#%) (o! !% (%+% !#"% d# q2 -7.80 µC 8 !% '%s% d# 1.50 g . C%!do &%s dos #s,#%s #s"$! % 0.800 m !% d# &% o"%) q2 s# "%s&%d% %(i% q1 (o! !% %pid#/ d# 22.0 m/s H5# ,i+%. Spo!+% -# &%s dos #s,#%s s# p#d#! "%"% (o'o (%+%s p!"%&#s. No (o!sid## &% ,#/% d# +%5#d%d. % *C$& #s &% %pid#/ d# q2 (%!do &%s #s,#%s #s"$! % 0.400 m !% d# &% o"%2 0 *C$!"o #s &o '$s -# q2 s# %(#(% % q1 2 R/ a) 12.5 m/s , b) 0.323 m
3. U!% p%"4(&% p#-#% "i#!# !% (%+% d# ;.BB C 8 !% '%s% d# 3.BB J1B K+. S# "%s&%d% d#sd# #& p!"o A) do!d# #& po"#!(i%& #&7("i(o #s VA 3BB V) %& p!"o B) do!d# #& po"#!(i%& #&7("i(o #s V ?BB V. L% ,#/% #&7("i(% #s &% !i(% ,#/% -# %("% so0# &% p%"4(&%.Es"% "i#!# !% %pid#/ d# ;.BB 's #! #& p!"o A. *C$& #s s %pid#/ #! #& p!"o B2 *S# "%s&%d% (o! '$s %pid#/ o '$s &#!"%'#!"# #! B -# #! A2 EJp&i-# s #sp#s"%. R/ 7.42 m/s, es más ráp!" e# B, $a %arga #ega&'a ga#a rap!e( %a#!" se me'e a$ p"&e#%a$ ma*"r.
9. Dos (%+%s p!"%&#s q1 = +2.40 #C 8 q2 = -.50 #C #s"$! % 0.100 m !% d# &% o"%. E& p!"o A #s"$ % '#dio (%'i!o #!"# %'0%s #& p!"o B #s"$ % 0.080 m d# q1 8 % 0.00 m d# q2 H5# ,i+%. To'# #& po"#!(i%& #&7("i(o (o'o (#o #! #& i!,i!i"o. %&&# % #& po"#!(i%& #! #& p!"o A 0 #& po"#!(i%& #! #& p!"o B ( #& "%0%o #%&i/%do po #& (%'po #&7("i(o so0# !% (%+% d# 2.50 #C -# 5i%% d#& p!"o B %& p!"o A. R/ a) -738 , b) -705 , %) -8.25 10-8 .
. U! %!i&&o d#&+%do (o! (%+% !i,o'# "i#!# ! %dio d# 1;.B (' 8 !% (%+% "o"%& d# 3 !C. S# (o&o(% ! #&#("6! so0# #& ## d#& %!i&&o) % !% dis"%!(i% d# 9B.B (' d# s (#!"o) o0&i+$!do&o % p#'%!#(# #! #poso so0# #& ## d#& %!i&&o. D#sp7s s# d#% &i0# #& #&#("6!. %&&# &% %pid#/ d#& #&#("6! (%!do 7s"# %&(%!/% #& (#!"o d#& %!i&&o. R/ 1.7107 m/s
;. U!% #s,#% p#-#% (o! !% '%s% d# 1.;B + (#&+% d# ! (od#& #!"# dos p&%(%s 5#"i(%&#s p%%&#&%s s#p%%d%s po !% dis"%!(i% d# ;.BB ('. L%s p&%(%s so! %is&%do%s 8 "i#!#! d#!sid%d#s d# (%+% sp#,i(i%&#s !i,o'#s 8 . L% (%+% d# &% #s,#% #s q = 8.010- C. *Q7 di,##!(i% d# po"#!(i%& #!"# &%s p&%(%s %$ -# #& (od#& %dop"# ! $!+&o d# 9B.Bo (o! #sp#("o % &% 5#"i(%&2 R/ 47.8
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1B. U! (%p%(i"o "i#!# !% (%p%(i"%!(i% d# >.3? F. *Q7 (%!"id%d d# (%+% s# d#0# (o&o(% #! (%d% !% d# ss p&%(%s p%% -# &% di,##!(i% d# po"#!(i%& #!"# #&&%s s#% i+%& % 3;.B V2 R/ 1.8210-4 C
11. L%s p&%(%s d# ! (%p%(i"o d# p&%(%s p%#&#&%s #s"$! s#p%%d%s 9.3? '' 8 #& $#% d# (%d% !% #s d# 13.3 ('3 . C%d% p&%(% "i#!# !% (%+% (8% '%+!i"d #s d# .9; J1B? C . L%s p&%(%s #s"$! #! ! 5%(4o. % *C$& #s &% (%p%(i"%!(i%2 0*C$& #s &% di,##!(i% d# po"#!(i%& #!"# &%s p&%(%s2 ( *C$& #s &% '%+!i"d d#& (%'po #&7("i(o #!"# &%s p&%(%s2 R/ a) 3.2 p:, b) 13.2 , %) 4.0210 /m
13. S# (o!#("% ! (%p%(i"o d# p&%(%s p%%&#&%s d# 1B.B F % !% 0%"#4% d# 13.B V. U!% 5#/ -# #& (%p%(i"o #s"$ "o"%&'#!"# (%+%do) s# d#s(o!#("% &% 0%"#4% si! -# s# pi#d% !%d% d# &% (%+% d# &%s p&%(%s. % S# (o!#("% ! 5o&"i'#"o #!"# &%s dos p&%(%s si! d#s(%+%&%s. *C$& #s s &#("%2 0 * C$& s#4% &% &#("% d#& 5o&"i'#"o si i s# dp&i(% &% s#p%%(i6! d# p&%(%s ii s# dp&i(% #& %dio d# (%d% p&%(% si! -# (%'0i# s s#p%%(i6!2 R/ a) 12.0 , b) ) 24.0 , 3.00
19. E!(o!"% &% (%p%(i"%!(i% #-i5%&#!"# d#& (i(i"o 'os"%do R/ 1.83 C
1. C%"o (%p%(i"o#s #s"$! (o!#("%dos (o'o s# '#s"% #! &% ,i+%. % E!(o!"% &% (%p%(i"%!(i% #-i5%&#!"# #!"# &os p!"os a 8 b. 0 C%&(&# &% (%+% #! (%d% (%p%(i"o si ab = 15.0 . R/ a) 5. µ:, b) 20 = 8.5 µC, = 3.2 µC, 3 * 15 = 2.3 µC
1;. E!(#!"# &% (%p%(i"%!(i% #-i5%&#!"# #!"# &os p!"os a 8 b d#& +po d# (%p%(i"o#s (o!#("%dos (o'o s# '#s"% #! &% ,i+% si C1 ;.BB F) C3 1B.B F) 8 C9 3.BB F. R/ .04 µ:
1<. P%% #& sis"#'% d# (%p%(i"o#s 'os"%dos) #!(o!"% % L% (%p%(i"%!(i% #-i5%&#!"# d#& sis"#'%) 0 E& po"#!(i%& #! (%d% (%p%(i"o) ( &% (%+% #! (%d% (%p%(i"o 8 d &% #!#+4% "o"%& %&'%(#!%d% po #& +po. R/ a) 3.33 µ:, b) 3 * = 180 µC , 2 * 4 = 120 µC, %) 3 = 0.0 , = 30.0 , 2 = 0.0 * 4 = 30.0 , !) 13.4 m.
1>. P%% (%d% (o!,i+%(i6!) d#"#'i!# #& 5o&"%# #! (%d% (%p%(i"o 8 &% (%+% #! (%d% (%p%(i"o
1?. E! #& (i(i"o H5# ,i+% C1 9.BB F) C3 ;.BB F 8 C9 <.BB F. E& po"#!(i%& %p&i(%do #s V%0 3.B V. C%&(&# % &% (%+% d# (%d% (%p%(i"o 0 &% di,##!(i% d# po"#!(i%& #!"# &os 0o!#s d# (%d% (%p%(i"o ( &% di,##!(i% d# po"#!(i%& #!"# &os p!"os a 8 ! . R/ a) 1 = 3.08 10-5 C, 2 = 5.13 10-5 C * 3 = 8.2110-5 C, b) 2 = 1 = 10.3 . 3 = 13.7 . %) a! = 10.3 .
1@. E! &% si+i#!"# ,i+%) (%d% (%p%(i"o "i#!# C = 4.00 µ; 8 ab = +28.0 . C%&(&# % &% (%+% d# (%d% (%p%(i"o 0 &% di,##!(i% d# po"#!(i%& #!"# &os 0o!#s d# (%d% (%p%(i"o ( &% di,##!(i% d# po"#!(i%& #!"# &os p!"os a 8 ! R/ a) 1 = 2 = 2.2410-5 C, 3 = 4.4810-5 C, 4 = .7210-5 C. b) 1 = 2 = 5.0 , 3 = 11.2 , 4 = 1.8 . %) a! = 11.2 .
3B. E! &% ,i+%) C 1 = C 5 = 8.4 µ: 8 C 2 = C 3 = C 4 = 4.2 µ: . E& po"#!(i%& %p&i(%do #s ab = 220 . % *C$& #s &% (%p%(i"%!(i% #-i5%&#!"# d# &% #d #!"# &os p!"os a 8 b2 0 C%&(&# &% (%+% d# (%d% (%p%(i"o 8 &% di,##!(i% d# po"#!(i%& #!"# &os 0o!#s d# (%d% !o. R/ a) 2.52 µ:, b) 1 = 5 = 5.5410-4 C 1 = 5 = 2 = 3.7010-4 C, 2 = 88 3 = 4 = 1.8510-4 C. , 3 = 4 = 44 .
31. Los (%p%(i"o#s d# &% ,i+% #s"$! i!i(i%&'#!"# si! (%+% 8 (o!#("%dos) (o'o s# i!di(% #! #& di%+%'%) (o! #& i!"#p"o < %0i#"o. L% di,##!(i% d# po"#!(i%& %p&i(%d% #s ab = +210 . % *C$& #s &% di,##!(i% d# po"#!(i%& %! 2 0 *C$& #s &% di,##!(i% d# po"#!(i%& #!"# &os 0o!#s d# (%d% (%p%(i"o d#sp7s d# (#% #& i!"#p"o < 2 ( *C$!"% (%+% ,&86 % "%57s d#& i!"#p"o (%!do 7s"# s# (#62 R/ a) 70 , b) 105 . %) 315 µC
33. E! &% si+i#!"# ,i+%) (%d% (%p%(i"%!(i% C 1 #s d# <.@ F) 8 (%d% (%p%(i"%!(i% C 2) d# .< F. % C%&(&# &% (%p%(i"%!(i% #-i5%&#!"# d# &% #d #!"# &os p!"os a 8 b. 0 C%&(&# &% (%+% d# (%d% !o d# &os "#s (%p%(i"o#s '$s p6Ji'os % a 8 b (%!do ab = 420 . ( Co! 420 #!"# a 8 b) (%&(&# %! R/ a) 2.3 µ:, b) %1 = .7 10-4 C * C2 = .4410-4 C, %) 4.7
39. C%d% (o'0i!%(i6! d# (%p%(i"o#s #!"# &os p!"os a 8 b d# &% ,i+% s# (o!#("% pi'#o #!"# &os 0o!#s d# !% 0%"#4% d# 13B V p%% (%+% &% (o'0i!%(i6! % 13B V. Es"%s (o'0i!%(io!#s s# (o!#("%! d#sp7s p%% ,o'% &os (i(i"os -# s# '#s"%!. C%!do s# %((io!% #& i!"#p"o S) ,&8# !% o&#%d% d# (%+% d# &os (%p%(i"o#s -# s# d#s(%+%!) &% (%& %("i5% #& disposi"i5o d# s#%&. *C$!"% (%+% ,&8# % "%57s d#& disposi"i5o d# s#%&2 R/ a) 7200 µC , b) 54 µC
3. %&&% &% (%p%(id%d #-i5%&#!"# #!"# A 8 ) si s# s%0# -# "odos &os (o!d#!s%do#s 'os"%dos "i#!#! !% (%p%(id%d d# 9 , ( R/. . µ;
3;. U! (%p%(i"o d# %i# #!"# &%s p&%(%s p%%&#&%s "i#!# !% (%p%(i"%!(i% d# @3B pF. L% (%+% d# (%d% p&%(% #s d# 3.;; C. % *C$& #s &% di,##!(i% d# po"#!(i%& #!"# &%s p&%(%s2 0 Si &% (%+% p#'%!#(# (o!s"%!"#) *C$& s#$ &% di,##!(i% d# po"#!(i%& #!"# &%s p&%(%s si s# dp&i(% &% s#p%%(i6!2 ( *C$!"o "%0%o s# !#(#si"% p%% dp&i(% &% s#p%%(i6!2 R/ a) 2772 , b) 5544 , %) 3.5310-3 .
3<. *C$!"os #&#("o!#s #! #J(#so s# d#0#! %+#+% % !% p&%(% 8 -i"% % &% o"% p%% popo(io!% % ! (%p%(i"o d# p&%(%s p%%&#&%s d# ;.BB !F 3;.B d# #!#+4% %&'%(#!%d%2 R/ 3.121015 e$e%&r"#es
3>. U! (%p%(i"o (i&4!di(o d# %i# d# 1;.B ' d# &%+o %&'%(#!% 9.3B J1B@ d# #!#+4% (%!do &% di,##!(i% d# po"#!(i%& #!"# &os dos (o!d("o#s #s d# .BB V. % C%&(&# &% '%+!i"d d# &% (%+% d# (%d% (o!d("o. 0 C%&(&# &% popo(i6! d# &os %dios d# &os (o!d("o#s i!"#io 8
#J"#io. R/ a) 1.0 10- C, b) ra/ rb = 8.05
3?. U! (%p%(i"o #s,7i(o (o!s"% d# dos (o%/%s (o!d("o%s (o!(#!"i(%s s#p%%d%s po ! 5%(4o. L% #s,#% i!"#io "i#!# ! %dio d# 1B.B (' 8 &% s#p%%(i6! #!"# &%s #s,#%s #s d# 1.;B ('. L% '%+!i"d d# &% (%+% d# (%d% #s,#% #s d# 9.9B !C. % *C$& #s &% di,##!(i% d# po"#!(i%& #!"# &%s dos #s,#%s2 0 *C$& #s &% #!#+4% d# (%'po #&7("i(o %&'%(#!%d% #! #& (%p%(i"o2 R/ a) 38.7 , b) .3810-8 .
3@. Dos p&%(%s p%%&#&%s "i#!#! (%+%s i+%&#s 8 op#s"%s. C%!do s# #5%(% #& #sp%(io #!"# &%s p&%(%s) #& (%'po #&7("i(o #s E 9.3B J1B; V'. C%!do #& 'is'o #sp%(io s# &&#!% (o! di#&7("i(o) #& (%'po #&7("i(o #s E 3.;B J1B; V'. % *C$& #s &% d#!sid%d d# (%+% #! (%d% sp#,i(i# d#& di#&7("i(o2 0 *C$& #s &% (o!s"%!"# di#&7("i(%2 R/ a) .20 10-7 C/m2 , b) 1.28
