UNIVERSIDAD INDUSTRIAL DE SANTANDER SANTANDER ESCUELA DE FÍSICA
LABORATORIO DE FÍSICA I EXPERIENCIA No. L1 VELOCIDAD INSTA I NSTANTÁNEA NTÁNEA Y VELOCIDAD PROMEDIO
GRUPO: O3A SUBGRUPO: 1 KAROLL DAYANA CONTRERAS CALDERON JULIETH MARCELA MUO! HERNÁNDE! HERMES JOSE LOPE! ALBA
ELKIN ANDR"S SANTOS SUÁRE!
1# DE JUNIO DE $%1& BUCARAMANGA' I SEMESTRE DE $%1&
INTRODUCCIÓN L( )*+o,-( */ 0( 2(-40 56/-,( * ,(78,4*7 )*,4o7-(+ 90* *;7*/( *+ */;+(<(2-*4o * 0 o=>*4o ;o7 0-( * 4-*2;o. S- 0 o=>*4o ?( 7*,o77-o 0( -/4(,-( ,oo,-( * 0 +(;/o * 4-*2;o' *+ 2@0+o * /0 )*+o,-( ;7o2*-o /* ,(+,0+( -)--*o *+ */;+(<(2-*4o ;o7 *+ 4-*2;o 47(/,077-o' * ,(2=-o' +( )*+o,-( -/4(48*( ;*72-4* ,oo,*7 +( )*+o,-( * 0 2@)-+ 90* /* */;+(<( /o=7* 0( 47(*,4o7-(' ,0(o *+ +(;/o * 4-*2;o */ -5--4(2*4* ;*90*o' /-*o *4o,*/ *+ */;(,-o 7*,o77-o 4(2=- 20 ;*90*o' 7*;7*/*4(o 0 ;04o * +( 47(*,4o7-( +( )*+o,-( -/4(48*( */ /-*2;7* 4(*4* ( +( 47(*,4o7-( ;o7 2*-o * */4* -5o72* /* (78 ( ,oo,*7 +( 7*+(,-@ 90* *-/4* *47* +( )*+o,-( ;7o2*-o +( -/4(48*( /* )*78 ,o2o ( ;(74-7 * 0( /*,0*,-( * )*+o,-(*/ ;7o2*-o /* ;0** *0,-7 +( )*+o,-( -/4(48*(.
Objetivos: E;+-,(7 +( -2;o74(,-( * +( )*+o,-( -/4(48*( * +( 56/-,( ,0(o /* 47(4( * */;+(<(2-*4o/. Po7 2*-o * ,8+,0+o/ (8+-/-/ *;+-,(7 /0 -2;o74(,-( /0/ 5@720+(/. Co2;7o=(7 +( 7*+(,-@ 90* *-/4* *47* +(/ )*+o,-(*/ -/4(48*(/ +( ;7o2*-o ;(7( 0 2o)-2-*4o 0-5o72*2*4* (,*+*7(o. A;7**7 ( -*4-5-,(7 (;+-,(7 * +( )-( ,o4--(( ,(( 0o * +o/ ,o,*;4o/ ,-*284-,o/ 90* o/ 7o*(.
Teoría: VELOCIDAD PROMEDIO: S* *5-* +( )*+o,-( ;7o2*-o * 0 ,0*7;o 90* /* 20*)* entre dos puntos P 1 y P 2 ,o2o *+ ,o,-*4* *47* *+ vector desplazamiento *+ -4*7)(+o * 4-*2;o * 90* 47(/,077* *+ */;+(<(2-*4o. S0 *;7*/-@ )-** (( ;o7:
v m= ⃗
•
v m ⃗
∆r ∆ t
⃗
=
⃗r 2−r 1 ⃗
t 2 −t 1
' o*:
: V*,4o7 )*+o,-( 2*-( * *+ -4*7)(+o */40-(o
•
r ⃗ : V*,4o7 */;+(<(2-*4o * *+ -4*7)(+o */40-(o
•
t : T-*2;o *2;+*(o ;o7 *+ ,0*7;o * 7*(+-<(7 *+ 2o)-2-*4o
•
r 1⃗ ' r 2⃗
: V*,4o7*/ * ;o/-,-@ * +o/ ;04o/ --,-(+ P 1 5-(+ P 2 *+ 2o)-2-*4o
t 1, t 2: I/4(4*/ * 4-*2;o * +o/ 90* *+ ,0*7;o /* *,0*47( * +o/ ;04o/ --,-(+*/ P 1 5-(+ P 2 7*/;*,4-)(2*4*.
VELOCIDAD INSTANTANEA: S* *5-* ,o2o *+ +62-4* * +( )*+o,-( 2*-( ,0(o *+ -4*7)(+o * 4-*2;o ,o/-*7(o 4-** ( %. T(2=-' ,o2o +( *7-)(( *+ )*,4o7 * ;o/-,-@ 7*/;*,4o (+ 4-*2;o. S0 *;7*/-@ )-** (( ;o7: ∆r
dr
lim lim v⃗ ¿ ∆t → 0 v m=∆ t → 0 ∆ t = ∆ t ⃗
•
v⃗ : V*,4o7 )*+o,-( -/4(48*( 2 /s.
•
v⃗ m: V*,4o7 )*+o,-( 2*-( m/s.
•
•
⃗
⃗
, o*:
r ⃗ : V*,4o7 */;+(<(2-*4o 2. t : I4*7)(+o * 4-*2;o 90* 4-** ( %' */ *,-7 0 -4*7)(+o -5--4(2*4* ;*90*o s.
Descripción del montaje experimental / ista del e!"ipo "sado # $rocedimiento desarrollado en la pr%ctica: C0(o *,o47(2o/ +o/ -2;+*2*4o/ * +(=o7(4o7-o +o ;7-2*7o 90* ?-,-2o/ 50* 47(4(7 * *,o47(7 +( 2*-( ,o77*,4( * (+407( *+ 40=o * (-7* * (,0*7o (+ */;(,-o 7*,o77-o. D*/;0/ * */o ;0-2o/ ,o+o,(7 +(/ 5o4o ,*+(/ * 2(*7( 90* ( ;(74-7 * ,-*74( (+407(' /* ;0-*7( 7*-/47(7 +o/ (4o/ * *+ 4*2;o7-<(o7 .P(7( ;o*7 ( 50,-o(7 *+ 4*2;o7-<(o7 +o *,**2o/ +* (2o/ *+ =o4@ PULSE ;(7( 90* o/ *2;-*,* ( ,o4(7 *+ 4-*2;o. P7o,*-2o/ ( ,o+o,(7 *+ 7-*+ * 2(*7( 90* */4* 7*,o77-*7( ,-*74o -4*7)(+o * 4-*2;o 2*-o * *+ 4*2;o7-<(o7. R*(+-<(2o/ )(7-o/ -4*4o/ * ;70*=(. U=-,(2o/ *+ 7-*+ * 0 ;04o X% * 2(*7( 90* * */4* /* 4o2* 0( -/4(,-( ;(/(o ;o7 +(/ o/ 5o4o ,*+(/. To2(2o/ /*-/ 2*-(/ * */4* ,(/o' */;0/ * ,(( 2*-( +* -2o/ RESET (+ 4*2;o7-<(o7 ;7o,**2o/ ( ,o77*7 +(/ -/4(,-(/ * ( $% ,2 7*/;*,4o ( X%. T(2=- ,o+o,(2o/ +(/ (+*4(/ /o=7* *+ (,?o 90* ;o/** * +( ;(74* /0;*7-o7 *+ 7-*+ 90* 4-** ( /0 )*< +( 2-/2( -/4(,-( ?(,-( +o/ +(o/. To2(2o/ 2*-(/ ,o +(/ (+*4(/ * .' .%' .% 1. (/6 ,o2;+*4(2o/ +( 4(=+( 1. P(7( ,o2;+*4(7 +( 4(=+( $ ( o *,*/-4(2o/ *+ ;04o 5->o X% /-o 90* 2(/ =-* o/ 0-(2o/ ;o7 +( -/4(,-( 4o4(+ (+ 5-(+ X5 0=-,(2o/ +( o/ 5o4o ,*+(/ ( +( 2-/2( -/4(,-( * +( 2-4(' )(2o/ (,*7,(o (2=(/ 5o4o ,*+(/' ?(,-( *+ ,*47o *+ 40=o o ;04o ,*47(+ *+ 40=o' 4o2(2o/ ;7-2*7o /-*4* 2*-(/ (,*7,(o +o/ 7-*+*/ ( ,(( 0( * *++(/ 4o2(o ,o2o 2*-( * +( 4(=+( +( -/4(,-( 4o4(+ *47* +(/ $. To2(2o/ /-*4* 2*-(/ * 2(*7( 90* /* (>0/4* ( +( 0=-,(,-@ * +( 5o4o ,*+( */ *,-7 90* o ,o-,-( ,o +(/ ;(4(/ *+ 40=o. EUIPO:
R-*+. Bo2=(. D*/+-<(o7. R*-/47(o7 * 4-*2;o. Do/ 5o4o,*+(/. A+*4(/ * .' .%' .%' 1. ,2.
• • • • • •
C%lc"lo& res"ltados # an%lisis de datos' 1. E,0*47* *+ )(+o7 4*@7-,o * +( )*+o,-( -/4(48*( v-/4 * */4* ;04o 4o2* g ,o2o .#12 / #' 1 ,2/ v inst
vi
2
( √ 2 gsenθ ∆ x
x i
v o +2 a ¿ x 0 2
x i=100 cm
x o
¿ 1&,2
∆ x =85 cm
θ=¿ 1'%#
√ 2 gsenθL
v inst
v inst
√(
cm 2 s
&'$
cm S
v inst
2 978,1
)∗
sen ( 1,098 )∗(85 cm )
$. E,0*47* *+ *77o7 (=/o+04o 7*+(4-)o * *+ )(+o7 4*@7-,o * +( )*+o,-(. V inst
= √ 2 gsenθ ∆ x
|| || ||
δv =
δv δv δv δx + δy + δh δx δy δh
S en θ =
O h
|√
δv =
1 2∗g∗ y
h
( ∗∆ x
| |√
g∗ y ) δx + h
1 2∗g∗ y
h
( g∗ ∆ ∗∆ x
| |√
x ∗ y ) δy + h
1 2∗ g∗ y
h
( g∗∆
x∗ y∗−1
∗∆ x
δx =0,1 cmδy =0,1 cmδh =0,1 cm cm y =1,15 cm h=60 cm g= 978,1 2 ∆ x = 85 cm s
Error absoluto: Ea=δv = 2,9029
Error relativo: Er =
Ea 2,9029 = 56,4472 = 0,0514 v´
3. P(7( ,(( )(+o7 * D * +( 4(=+( 1' ,o2;+*4* +( /-0-*4* 4(=+(: I/4702*4o * 2*-,-@ 1: Cinta métrica S*/-=-+-(: 0,1 [cm] I/4702*4o * 2*-,-@ $: Foto Celda S*/-=-+-(: 0,0001 [s] I/4702*4o * 2*-,-@ 3: !scuadra S*/-=-+-(: 0,1 [cm] x 1=100
Q,2
Á0+o * -,+-(,-@' 1'%#
Tabla )' Tabla *' D +cm, 1% 1$% #% % % $% ' '% '% 1'
tprom 1'&# 1'1#3 1'3 1'%$ %' %'33 %'1$#$ %'%#3 %'%# %'%31&
D2cm3 -.tprom )56 vprom %'%%%1)46 #'%$ %'%%%176 1%1'1& %'%%%186 &'#3 %'%%%156 &#'&&& %'%%%146 %'1& %'%%%1): D&'%& leta ( 9& %'%%%14: D1'3#& leta ( 8&6 %'%%%1*: D1'%1 leta ( 5&6 %'%%%15: D&'##%$ leta 6 )& %'%%%1 %'3#1
Tiempo 2s3 Toma ) Toma 4 -.vprom 1'&& 1'&&% %'%$3 '% 1'1#3 1'1# %'131 #'3 1'3& 1'3#%# %'%3%# 1%'&& 1'%$& 1'%$ %'%1& 11'#3$$ %'3 %' %'%3$ 1$'1 %'33# %'33& %'$%3 13'1 %'1$ %'1$# %'1#1 13'#%% %'%#& %'%#% %'13#% 13'$# %'% %'%& 1' 1'%%%% %'%31 %'%311 %'&&3 1'%#
Toma * 1'&% 0 1#'31 1'1#& 1'###& 1'3## 1'33$ 1'%$&1 1'1$& %'&& 1&'1 %'33% 1'#3$ %'1$#$ 1'1# %'%#& 1'3&$ %'%# 1'$#$ %'%31 1'$%$
1 $'1#&1 $'#3$# $'# $'& $#'11% $#'$## $#'$## $#'$#11 $#'$#$ $#'$#%
h
2
|
) δh
. T7(,* 0( ,07)( /0()* * )*+o,-( ;7o2*-o v ;7o2 ,o47( -/4(,-( D' ,o D * *+ *>* "#' * 0 ;(;*+ 2-+-2*47(o -=0>* * +( 2-/2( ?o>( 0( (/64o4( * v ;7o2 v-/4. &. H(( 0( 785-,( * )*+o,-( ;7o2*-o v ;7o2 ,o47( $ 0/(o *+ 24oo * +o/ 26-2o/ ,0(7(o/. I4*7;7*4* ((+-,* +( 785-,(. . E)(+* * *+ *>* * +(/ )*+o,-(*/ *+ ;04o o* D %' */ *,-7 ,0(o Y =2 √ 2 x 1 4o2* */4* ,o2o *+ )(+o7 *;*7-2*4(+ * +( velocidad -/4(48*( ,o2;(7* */4* *+ )(+o7 4*@7-,o. Y =2 √ 2 x 1 Y =2 √ 2 ( 100 ) Y =2 √ 2 x 1 Y =28,2843
error =
VT −VE ∗100 VT
error =
56,4472 −28,2843 ∗100 =50 56,4472
. D*20*/47* 90* +( )*+o,-( 2*-( * 50,-@ * +( -/4(,-( D /* ;0** */,7-=-7 ,o2o:
¿ √ [ √ 2 x 1 − D + √ 2 x 1+ D ] ' o* a */ +( (,*+*7(,-@ * */4* ,(/o )(+* a g /* 2 a
v
g */ *+ )(+o7 * +( (,*+*7(,-@ * +( 7()*(. W0 ;(/( ,0(o D 4-** ( ,*7o 1 2
2
x = x 0+ v 0 + a t
v =v 0 + at
t 2 =
1 2
x 2= a t 2
v2
t 1 =
a
1 2
2
x 1= a t 1
v 12
1
2
2
x = a t 2
a
v =a t
x 2− x 1
∆x v´ = = t 2−t 1 ∆ t
v´ =
v2 1 a ( ) a 2
2
2
1 v − a ( 1 ) a 2
v2
v1
a
a
−
2
1 ( v 2−v 1 ) = 2 v +v
v´ =
v 2+ v 1 2
x B− x A = D
x B= x A + D v
v´ =
v´ =
2
B
D 2
D D x B = x 1− x1− x A = 2
2
=2 a x B v2 A =2 a x A
√ 2 a x B + √ 2 a x A
√ a 2
x A= x 1−
2
v´ =
√
2 a ( x 1−
D 2
)+ 2
√ (
2 a x 1+
D 2
)
√ 2 a ( x1 − D)+ √ 2 a ( x 1+ D )
Si D tiende a cero, el cambio del tiempo tiende a cero, por tanto, la velocidad
√ a promedio es igual a la velocidad instantnea! v´ = 2 2 √ 2 a x 1 v´ =√ a √ 2 a x 1
v´ =√ 2 a x 1
#. E,0*47* *+ )(+o7 4*@7-,o * +( (,*+*7(,-@ a * */4* 2o)-2-*4o 4o2* g ,o2o .#12/$ at
at
at
=g senθ
=(
978,1
cm s
" sen ( 1,098 )
2
cm
= 1#,$429
s
2
. E,0*47* *+ *77o7 (=/o+04o 7*+(4-)o * *+ )(+o7 4*@7-,o * +( (,*+*7(,-@. y =1,15 cm h=60 cm g= 978,1
| || |
δa =
δa δy
+
cm 2
s
a =18,7429
cm s
2
|| | |
δv g −gy δ h → δ a = δy + 2 δ h δy h h
sin θ=
y h
;rror absol"to: )&88)5 ;rror relativo: 6&6778
1%. Co +o/ 7*/0+4(o/ * +( 4(=+( $' ,o2;+*4* +( /-0-*4* 4(=+(: T(=+( $. xf (cm)
110 100 90 #0 $0 %0 50 xf (cm)
tprom
±δtpr om
110
1,2%0 1
%'%%%1
Tiempo (s) Toma 1 Toma 2 Toma 3 1,25$4 1,2%25 1,2%0& 1,1040 1,1105 1,1152 1,95$1 1,9%1# 1,9%&# 1,#090 1,#1&5 1,#0$4 1,%444 1,%&$9 1,%&#% 1,4$19 1,4$&4 1,4$&# 1,2919 1,294& 1,2#99 vpro m #$,29 $0
±δvpr om
Error Absoluto
Error Relativo[%
0,12&2
0,12&2
0,1411
100 90 #0 $0 %0 50
1,109 9 1,9%0 9 1,#10 0 1,%40 & 1,4$& 0 1,292 0
%'%%%1 %'%%%1 %'%%%1 %'%%%1 %'%%%1 %'%%%1
90,09 #2 45,#9 $& 44,19 9$ 42,%$ 51 40,$& 2& &#,%9 #$
0,&195
0,&195
0,&54%
0,059&
0,059&
0,1292
0,05$5
0,05$5
0,1&01
0,0$11
0,0$11
0,1%%5
0,0209
0,0209
0,051&
0,045&
0,045&
0,11%9
11.
O0<;R=CION;<' D*=*2o/ 4**7 * ,0*4( +o/ 5(,4o7*/ 90* -5+0* * *+ 2o)-2-*4o * *+ 2o2*4o * ((+-<(7 ;(7( 90* 0*/47o/ ,8+,0+o/ /*( 28/ ;7*,-/o/. D*=*2o/ ,o/-*7(7 90* *-/4* ,o,*;4o/ 90* * ,-*284-,( /* 7*+(,-o( ;*7o 90* o /o /*2*>(4*/ ,o2o 7(;-*< )*+o,-( o )*+o,-( ;7o2*-o )*+o,-( -/4(48*(.
CONCU
•
A+ *4*72-(7 +( 7*+(,-@ *47* )*+o,-( ;7o2*-o )*+o,-( -/4(48*( o/ (2o/ ,0*4( 90* +( )*+o,-( -/4(48*( ;0** /*7 ,(+,0+(( o=4*-*o *;*7-2*4(+2*4* +( )*+o,-( ;7o2*-o. Lo7(7 *;+-,(7 ;o7 2*-o * (8+-/-/ ,8+,0+o/ +( )*+o,-( ;7o2*-o )*+o,-( -/4(48*( * 5o72( ,+(7(.
0iblio>ra?ía: • •
?44;/:ZZZ.5-/-,(+(=.,o2(;(74(o)*+o,-(-/4(4(*( ?44;/:ZZZ.5-/-,(+(=.,o2(;(74(o)*+o,-(2*-([,o4*-o/
•
nexos: @oja de Aarol
