Informe Caída Libre

UNIVERSIDAD MAYOR DE SAN ANDRÉS EXPERIMENTO Nº FACULTAD DE INGENIERÍA CURSO BÁSICO DOCENTE: I!": R#$%&'# P(&&( )%$(**#+ LABORATORIO DE FÍSICA BÁSICA I AUX" DOC": U,": U,": G&#%& P(*.( V,**( V,**( FIS 100-L I/2011 GRUPO: 

2. CAÍDA LIBRE ÍNDICE

2"1" OB3ETIVOS4444444 OB3ETIVOS44444444444444444 444444444444444444444 444444444444"" 4"" P5!" 2 6% 7 2"1"1" G%%&(*4444444444 G%%&(*44444444444444444444 44444444444444444""" 4444444""" P5!" 2 6% 7 2"1"2" E+8%9,#44444444 E+8%9,#4444444444444444444 444444444444444444""" 4444444""" P5!" 2 6% 7 2"2" FUNDAMENTO TE;RICO44444444444444444 TE;RICO44444444444444444444444" 444444" P5!" 2 6% 7 2"<" E=UIPO Y MATERIAL4444444444444444444444444 P5!" < 6% 7 2">" PROCEDIMIENTO44444444444 PROCEDIMIENTO444444444444444444444 444444444444444"" 44444"" P5!" < 6% 7 2"?" CÁLCULOS Y GRÁFICOS4444444 GRÁFICOS444444444444444444 4444444444444444" 44444" P5!+" >-? 6% 7 2"@" CONCLUSIONES Y RECOMENDACIONES4444 RECOMENDACIONES444444444444444 44444444444"" "" P5!" ? 6% 7 2"" CUESTIONARIO44444 CUESTIONARIO444444444444444 444444444444444444444 444444444444"" 4"" P5!+" ?-7 6% 7 2"7" BIBLIOGRAFÍA44444 BIBLIOGRAFÍA444444444444444 444444444444444444444 4444444444444" 44" P5!" 7 6% 7 2"" TABLA DE DATOS44444444444444444444444444"" P5!" 7 6% 7

Univ.: Flores Espinoza José Antonio

Página 1 de 8

UNIVERSIDAD MAYOR DE SAN ANDRÉS EXPERIMENTO Nº FACULTAD DE INGENIERÍA CURSO BÁSICO DOCENTE: I!": R#$%&'# P(&&( )%$(**#+ LABORATORIO DE FÍSICA BÁSICA I AUX" DOC": U,": G&#%& P(*.( V,**( FIS 100-L I/2011 GRUPO: 

CAÍDA LIBRE 2.1. OBJETIVOS: 2.1.1. General:  E+'6,# 6%* .#,.,%'# % (96( *,$&% 2.1.2. Específc!:  D%'%&.,(&  (*,6(& *( %(, %8%&,.%'(* 6%* .#,.,%'# % (96( *,$&%  D%'%&.,(& %* (*#& 6% *( (%*%&(, 6% *( !&(%6(6 2.2. "#NDA$ENTO TE%RICO: D%+6% H(% ( .H# ',%.8# I+(( N%J'# #.%K %* %+'6,# 6% (96( *,$&% ( % ,%&'# 69( % %* 6%+(+($( *% ( %,.( ( .(K((  %* +% 8&%!' %* 8#&  *( .(K(( (9( 6% %+( #&.( %&',(* 8%&# # +#*# *(+ .(K((+ +,# '#6# %&8#" G(*,*%# 6%.#+'& + '%#&9( 6% % '#6# %&8# % (96( *,$&% ',%% *( .,+.( (%*%&(, +, ,.8#&'(& %* '(.(# # .(+( % %+'% '%!(" A.$#+ #%8'#+ #&.(*,K(6# ( # (&,#+ %+'6,#+ +% 6%'%&., % *( (%*%&(, # *( %  %&8# +% .%% % (96( *,$&% %+ *( (%*%&(, 6% *( !&(%6(6 ! %+ ( #+%%,( 6% *( %&K( 6% ('&(, % %%&% *( ',%&&( +#$&% (*,%& #$%'# +,'(6# % + +8%&,,% 6% %+'( .(%&(: F =

GMm R 2

D#6%: GQ C#+'('% 6% !&(,'(, ,%&+(* MQ M(+( 6% *( ',%&&( .Q M(+( 6%* #$%'# RQ R(6,# 6% *( ',%&&(

a=

2

⇒

a = g ⇒ g =

G

R%%.8*(K(6# 6('#+  #$'%%.#+

g = 9.81m / s 2

S9  %&8# +% +%*'( 6%* &%8#+# %+'5 6(6( 8#& *( %(,: Univ.: Flores Espinoza José Antonio

Página 2 de 8

UNIVERSIDAD MAYOR DE SAN ANDRÉS EXPERIMENTO Nº FACULTAD DE INGENIERÍA CURSO BÁSICO DOCENTE: I!": R#$%&'# P(&&( )%$(**#+ LABORATORIO DE FÍSICA BÁSICA I AUX" DOC": U,": G&#%& P(*.( V,**( FIS 100-L I/2011 GRUPO:  h = V 0

+ 1 gt 2 #.# V0 Q 0 %'#%+: h = 2

1 2

gt 2

A(*,K(6# *( %(, #+ 6(.#+ %'( % +% '&('( 6% ( , %8#%,(* 6% *( #&.(: H Q  '  6#6%: Q2 Q!/2 E+'( %(, 8%6% +%& '&(+#&.(6( ( ( &%!&%+, *,%(*  +% *,%(*,K( 8#& .%6,# 6% *#!(&,'.#+ ( +%( ('&(*%+ # *!(&%+ 6% *( +,!,%'% #&.(: log H = log K + n log t

# 6% *( #&.(:

ln H = ln K + n ln t

D#6% (8*,(6#  (.$,# 6% (&,($*% '%%.#+ *( %(, 6% *( #&.(:  Q A   2.&. E'#I(O ) $ATERIAL: •

E,8# 6% (96( *,$&% •

.%(,+.# 6% *,$%&(, 6% %+%&(

•

6%'%'#& 6% ,.8('#

•

C&#.%'&#

•

E+%&( .%'5*,( 6% &,+'(*

•

R%!*( 6% 1 .%'&# .

2.*. (ROCEDI$IENTO: B%# *# 8&,.%&# % H,,.#+ % (&.(& %* %,8# 6% (96( *,$&% 8#+'%&,#&.%'% '&('(.#+ 6% % ,#% ,.%6,('(.%'% 8%&# # % (+9 ( % *#+ ($*%+ 6%* %,8# 6% (96( *,$&% # %+'($( ,#(6# #&&%'(.%'% % %+% (+# %+8%&(.#+ 8(&( #.%K(& *( 8&5',(  6%+6% %* .#.%'# % ,# *# 8&,.%&# % H,,.#+ % .%6,& *( (*'&( 6% *( 8&,.%&( (96( 6%+6% (8&#,.(6(.%'% 20. .,6,%6# # *( &%!*( .%'5*,( 8#+'%&,#&.%'% H,,.#+ #'('# %'&% *( %+%&( 6% .%'(*  %* (8(&('# 6% (96( 8(&( .%6,& %* ',%.8# % '(&6($( % 6%+%6%& .%6,.#+ ? %%+ &%8%',.#+ %* 8&#%6,.,%'# 8(&( (*'&(+ (8&#,.(6(+ 6% <0. >0. @0. 70.  2.


Página  de 8


2.+. C,LC#LOS ) GR,"ICOS: ( A*'&( 6% (96( . H 20 27 >02 ?< < <

$

T,%.8#+ 6% (96( '1 01@ 02>1 02 0<> 0<1 0><

'2 01? 02>1 0272 0<>2 0<7 0><>

1 ln h = ln g + 2 ln t 2

'< 01 02>1 0271 0<<2

8#& &%!&%+, *,%(*:

'> 01 02>2 0271 0<@7 0< 0>2

y

=

'? 017 02< 0277 0<

#.1"9 + 1.9!2t

D#6% 8#& #.8(&(,: 1 ln g = #.1"9 2



%diferencia

=

g = 2 ⋅ e #.1"9

g e&p

− g teo

g teo

100% ⇒

∴

g = 9#$.20cm / s 2

% diferencia

=

9#$ .20 − 9"" .$0 9"" .$0

100 %

∴ % diferencia = 1.2#%

6 P&%$( 6% H,8'%+,+ Univ.: Flores Espinoza José Antonio

Página ! de 8

' 01 02>1 0272 0<>7 0<? 0><<


H

'

Q*H

20 27 >02 ?< < <

01@ 02>1 02 0<> 0<1 0><

Q*' <0<0 <<? <@> >07< ><< >?<<

-1@<0 -1>2< -12 -10 -0< -07>>

t c

s

=

9#$ .20 − 9"" .$0 s /

=

s y / x

∑

D#6%

x 2

t c

−

=

s y / x

n

1 n

(

∑

⇒ s = x' 2

=

P(&( %* (*#& 6% '($*(+

α

n−2

⇒ s y / x = 0.01"$"

/ 2)υ ⇒

s

∴

⇒ t c = >7"17 .

# t

2

0.1"$" 1 9.0#8 − ( −".191' 2 #

9#$ .20 − 9"" .$0 0.#2$1 /

∑e

WQ %QW- %2 <01< -001 00002> <>1? 0020 0000>20 <@ 000? 000002@ >0< 0010 0000107 >?> 000 00000?? 00012
t T

=

2.!!" #.# t c

t

=

0.#2$1

∴ c =

0.!81

< t T +% *# (%8'( (* (*#&

2.-. CONCL#SIONES ) RECO$ENDACIONES: P#6%.#+ #*,& % *( !&(%6(6 6% L( P(K %+ 6,%&%'% ( *( 6%* ,%* 6%* .(& %+# +% 6%$% ( *( (*'&(  *(','6 % *( % #+ %#'&(.#+ 6% ,!(* #&.( (8&%6,.#+ (*!(+ 6% *(+ .H(+ (8*,(,#%+ 6% (+'% 6% &(+  8&%$( 6% H,8'%+,+ '(.$, (*% &%(*(& % 8(&( %+'( 8&(',( +% 6%$% .%6,& %('(.%'% *( (*'&( 6%* %&8# % (96( *,$&% ( % (+# #'&(&,# *( 6,%&%,( H$,%+% +,6# ( .(#& 2.. C#ESTIONARIO: 1" D% *#+ (*#&%+ 6% ! (**(6#+ Z(* *% 8(&%% %* .5+ #,($*%[ R"- E* (*#& 6% !&(%6(6 % *#!&(.#+ H(**(& ',%% ( 6,%&%,( 6%* 1"2@\ (+9 % +, $,% # %+ %* %('# 6% "? 8#& *# .%#+ %+ (8&#,.(6#  (%8'($*% 2" S, % %* %8%&,.%'# +% %.8*%(&( 6#+ %+%&(+ A  B 6% 6,+','#+ '(.(#+ Z%* (*#& 6% ! #$'%,6# # *( %+%&( A +%&5 6,%&%'% 6% *( %+%&( B[


Página $ de 8


R"- N# ( % % (96( *,$&% # +% '#.( % %'( *( .(+( 6%* #$%'# 8#& .5+ !&(6% # 8%%( % +%( (%&5 # *( .,+.( (%*%&(, *(&# % % *( &%(*,6(6 +% 6%$% '#.(& % %'( *( &%+,+'%,( 6%* (,&% <" S% 6%( (%& 6%+6% *( .,+.( (*'&(  (* .,+.# ',%.8# < #$%'#+ A 6% 10 ! B 6% 100 !  C 6% 1 ! 6% .(+( #+,6%&(6# (96( *,$&% ZC5* #$%'# **%!( 8&,.%&# (* 8,+#[ R"- C#.# +% %8*, ('%&,#&.%'% # ,.8#&'( *( .(+( 6%* #$%'# ( % % %+'% (+# +, *#+ '&%+ #$%'#+ +% 6%( (%& (* .,+.# ',%.8# *#+ < **%!(&5 (* 8,+# % %* .,+.# ',%.8# >" E #.8(&(, # *( !&(%6(6 6% *( ',%&&( #.# +# *(+ 6% *( *(  %* +#* R"- E #.8(&(, # *( *( *( (%*%&(, 6% %+'&# +('*,'% %+ 6% 1"@2

m / s 2 

%+

6%,& % %+ .%#& % *( !&(%6(6 6% *( ',%&&(  #.8(&(6# # %* +#* % ',%% ( !&(%6(6 % + +8%&,,% 6% 2>

m / s 2 %+

.(#& ( *( (%*%&(, 6% !&(%6(6 6% *(

',%&&( ?" C#+,6%&(6#  8*(%'( 6% *( .,+.( .(+( 6% *( ',%&&( 8%&# +, ('.+%&( #.# +%&5 *( !&(%6(6 % %+'% 8*(%'( R"-S%&5 .%#& ( % *( ('.+%&( ',%%  %%'# +#$&% *( !&(%6(6 % *( ',%&&(  *# (.%'( ( % # *# 6%( (* (9# @" S,  #$%'( +% *(K( H(,( (&&,$( # ( V 0 (* +%&5 + (%*%&(, % + 8'# 6% (*'&( .5,.# R"- S (%*%&(, +%&5 %* (*#& 6% *( (%*%&(, 6% *( !&(%6(6 % %+ 6% "?

m / s 2

E L( P(K " S,  #$%'# 6%+6% %* &%8#+# 6%.#&(  ',%.8# ' 1 % (%& ( (*'&( H % ',%.8# ' 2 6%.#&(&5 % (%& ( (*'&( 6% >H R"- h = v0 t +

1 2

gt 2

⇒h=

1 2

gt 2 //>


!h

=

2 gt 2 T(&6(&5

2' 8(&( (%& 6% *( (*'&( >H Página # de 8


7" E %* %(6# I**,.(, 6% (*'&( 6% @>00 ."+""." Z5* +%&5 + !&(%6(6 % %* 8,# 6% %+'%[ R"-D% *( %(,: g = g =

GM T R 2

6#6% R +(.#+ %* &(6,# 6% *( ',%&&( .5+ *( (*'&( ,6,(6(

#.#" ⋅ 10 −11 ( Nm 2 / kg 2 ' ⋅ $.98 ⋅ 10 2! ( Kg ' (#."8 ⋅ 10

#

+ #!00'm

g Ill .

∴

2

=

2

9."89(m / s '

" U #$%'# *(K(6# %&',(*.%'% H(,( (&&,$( # ( V 0 (*(K( ( (*'&( ]" +, %* #$%'# +% *(K( # %* 6#$*% 6% %*#,6(6 (* +%&5 + (*'&( R"- v

2

=

v0

2

−

2 gh ⇒ v 0

2

=

2 gh //2

2v 0

2

= ! gh +%&5 ( >H

10" D%+6% %* '%H# 6%  %6,,,# +% +%*'( ( %+%&( A '&(+&&,6#+ 2 +%!6#+ +% +%*'( #'&( %+%&( B Z*( 6,%&%,( 6% (*'&(+ +% .('%6&5 #+'('%[ R"-#.# *( %*#,6(6 ( +$,%6# 6% *( .,+.( #&.( % 6%* %&8# % ( $((6# %+ 6%,& 8#& *( !&(%6(6 *( 6,%&%,( 6% (*'&(+ # +% .('%6&5 #+'('%+ ,&5 +%8(&56#+% (6( %K .5+ 11" D%+6% %* '%H# 6%  %6,,,# +% *(K( H(,( (&&,$(  #$%'# A # V 0" E %* .,+.# ,+'('% +% *(K( H(,( ($(#  #$%'# B # *( .,+.( %*#,6(6 (* 6% %**#+ **%!( (* +%*# # .(#& %*#,6(6 R"- L#+ 6#+ **%!( (* +%*# # *( .,+.( %*#,6(6

12" P(&( 6%'%&.,(& *( (*,6%K 6% *( %(,

h =

1 2

gt 2 

+% +%*'(  #$%'# ( 8(&',& 6%*

&%8#+# 6% 10 6,%&%'%+ (*'&(+ *#+ 6('#+ .%,#(6#+ '&(+#&.(6#+ ( *#!(&,'.#+ +% (+'( 8#& .9,.#+ (6&(6#+  +% #$',%%: y*

=

0.#"9 + 1.89t (

8(&',& 6% %+'(

%(, (**% *( (%*%&(, %8%&,.%'(*


Página " de 8


R"- solución

 1 g    2 

0.#"9 = log

y* = log h

1.89t = 2 log t

D#6% 8#& #.8(&(,:

 m   1 g   D%+8%(6# ! g = 2 ⋅ 10 0.#"9 ⇒∴ g = 9.$$1 2   2   s 

0.#"9 = log

2./. BIBLIOGRA"ÍA: •

•

M%6,6(+  %&&#&%+ I!": Á*(&%K I!": ]('(2007 <0 >-7@ F9+,( M%5,( 2º %6,, I!": Á*(&%K I!": ]('( 1 127-1<0


Página 8 de 8

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