Practica 4. Movimientos Rectilineos

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

Vrèitdih #0. Jlvdjdoetls roitdcêeols

8. -

Lbkotdvls Jo`dheto oc usl `o sdjuch`lr hiocorhidùe osirdbdr chs ihrhitorêsihs `o cls jlvdjdoetls

sdgudoetos sdgud oetos (roicêeol (roicêeol uedalrjo uedalrjo (J.R._.), (J.R._.), roicêeol uedalrjo uedalrjo hiocorh`l hiocorh`l (J.R (J.R._.H ._.H.) .) y roicêeol roicêeol uedalrjo rothr`h`l (J.R._.R.).

-

Ile oc jl`ocl h`oiuh`l, osirdbdr chs oiuhidleos jhtojèihs quo oxproshe ch rochidùe

oetro plsdidùe-ojpl y voclid`h`-ojpl phrh cls jlvdjdoetls roicêeols joeidleh`ls oe oc lbkovl hetordlr.

2.

Jhtordhcos y oqudpls @OYIRDVIDÙE 

ROAOROEIDH  

_eh iljputh`lrh ile oc sdjuch`lr hiocorhidùe   mps;//www.whctoraoe`t.`o/mtjc?/pmos/hiiocorhle\os.mtj

Oc prlgrhjh Clggorprl  

_e iocuchr ile ch hpcdihidùe Qoredor

Grhpmdihc Hehcysds

9. Jhril toùrdil eoioshrdl Ch phrto `o ch joièedih quo ostu`dh oc jlvdjdoetl y cl `osirdbo h phrr `o ch trhyoitlrdh os ch ideojèih. Iuhe`l ueh phriuch so `ospchzh ile trhyoitlrdh roith, so osthbcoio ue jlvdjdoetl roicêeol.

92

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

Ch trhyoitlrdh roicêeoh os ue ilekuetl deedtl `o tl`hs chs plsdidleos `o ch phriuch. Yd so socoiidleh ueh juostrh roprosoethvh `oc ilekuetl `o plsdidleos, os plsdbco `osirdbdr oc jlvdjdoetl. _e jlvdjdoetl so `osirdbo h rosple`or chs sdgudoetos progueths; ¼@ùe`o ostè ch phriuch oe iuhcqudor destheto< ¼Iuèc os su voclid`h`< T ¼Iuèc os su hiocorhidùe< Oxdstoe `ls oiuhidleos djplrthetos. _eh oxprosh ch rochidùe oetro ch `dstheidh oe ih`h plsdidùe y oc ojpl y ch ltrh oetro ch voclid`h` desthetèeoh y oc ojpl. Osths sle () : 6 + 6 + os ch plsdidùe oe iuhcqudor destheto ,

8 2

2  y () : 6 + > `le`o () 

() :  (, , ), 6 os ch plsdidùe oe  : 6, 6 : 

(6, 6, 6), 6 os ch voclid`h` oe  : 6, 6 : (6, 6, 6). Oe osto oxpordjoetl so ilesd`orh quo ch phriuch so juovo oe ueh slch `djoesdùe, quo os ch `djoesdùe `oc oko mlrdzlethc

> plr thetl, () : 6 + 6 + 82 2  y () : 6 + .  Oe oc sdstojh detorehidlehc ch plsdidùe so jd`o oe jotrls (j), oc ojpl oe sogue`ls sog ue`ls (s), ch voclid`h` oe (j/s) y ch hiocorhidùe oe (j/s2).

Chs ile`didleos dedidhcos bhkl chs iuhcos so prl`uidrèe cls jlvdjdoetls y cls rosucth`ls ihrhitorêsils sle iljl so de`dihe oe oc sdgudoeto roiuh`rl.  

99

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

Ile`didleos dedidhcos `o ch phriuch

Rosucth`ls ihrhitorêsils

8)

Eljbro `oc jlvdjdoetl

Ch grèih  : () os ueh roith

deicdeh`h mhidh oc lrdgoe (l, l)> ostl os

Roicêeol uedalrjo J.R._.

 : .   : 6 

2)

Ch poe`doeto `o ch grèih

 : () roprosoeth ch voclid`h`.

8) Ch grèih  : () 

os ueh ueh phrèblch `oroimh iljl osth

Roicêeol uedalrjo hiocorh`l (J.R._.H.)

 :    5 6  Osirdb rdbh h hqu hquêê ch oiuhidùe oiuhidùe `o  : 2) Osi

 () 

90

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

2)

Ch grèih  : ()  os ueh roith

iljl osth.

 

9)

ch poe`doeto `o ch grèih

 : () os ch hiocorhidùe 8)

Ch grèih  : () os ueh

phrèblch devor`h iljl osth

 :   Roicêeol uedalrjo rothr`h`l (J.R._.R.)

 3 6 

2)

Ch grèih `o  : () os ueh

roith iljl osth

 

9)

Ch poe`doeto `o ch grèih

: () os ch hiocorhidùe.

9?



 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

0. Vrlio`djdoet Vrlio`djdoetls, ls, heècdsds y rosucth`ls Vrlio`djdoetl #8; Jlvdjdoetl roicêeol uedalrjo (J.R._.) 8.8 Yocoiidleh oe ch iljputh`lrh oc sdjuch`lr hiocorhidùe. Oe oc ihjpl `o voclid`h` osirdbo 86 j/s y oe oc `o hiocorhidùe hio corhidùe iorl. Dedidh oc jlvdjdoetl y helth cl lbsorvh`l. El `okos `o ththr oc osquojh `o cls grèils quo so juostrhe oe `diml sdjuch`lr. Ostl os;

] (j)

h (j/s2)

Q (j/s)

t(s)

8.2

t(s)

t (s)

Iljpcoth ch thbch #8 ile ch hyu`h `o tu prlaoslr

Phbch #8 Pdojpl

t(s)

6

8.669

2.=04

0.68?

?.647

?.408

1.=19

Vlsdidùe

x(j)

6

86.69

2=.04

06.8?

?6.47

?4.08

1=.19

Qoclid`h`

v(j/s)

86

86

86

86

86

86

86

Hiocorhidùe

h(j/s2)

6

6

6

6

6

6

6

  8.9 _she`l oc prlgrhjh `o ch iljputh`lrh Clggorprl, ilestruyo ch grèih `o ]:a(t). ¼Xuä rosucth< ueh cêeoh deicdeh`h mhidh oc lrdgoe 8.0 Hkusth ch iurvh hc jl`ocl quo jès so ilrrosple`h y iletosth i letosth chs sdgudoetos progueths. 8.0.8 ¼Iuèc os ch poe`doeto `o ch grèih< j:86 ¼Xuä ued`h`os oeo y iuèc os su sdgedih`l< Vlsdidùe/ojpl dguhc h 86 voclid`h` 8.0.2 Osirdbo ch oiuhidùe jhtojèih oetro chs vhrdhbcos  y . ]:86t

91

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

@otorjdeh oc `ospchzhjdoetl tlthc ∁x :   −  : 1=.19j 8.? Ilestruyo ch grèih `o  : () ¼Xuä rosucth< ueh cêeoh roith mlrdzlethc ¼Ch voclid`h` os vhrdhbco l ilestheto< sdojpro ilestheto  8.1 Ihciuch oc èroh bhkl ch grèih

 : () y iljphrh `diml rosucth`l ile oc jèxdjl

`ospchzhjdoetl oxpordjoeth`l plr ch phriuch. ¼Xuä rosucth< cls vhclros sle dguhcos 8.7

Osirdbo bhsèe`lto oe cls rosucth`ls, chs ihrhitorêsihs `oc J.R._.

-Oc jlvdjdoetl sdojpro trhesiurro h cl chrgl `o ueh cêeoh roith -_e jùvdc ile JR_ roilrro `dstheidhs l osphidls dguhcos oe ojpls dguhcos. -Ch voclid`h` porjheoio dehctorhbco thetl oe jhgedtu` iljl oe `droiidùe y soe`l. -Oc JR_ ihroio `o hiocorhidùe (el mhy ihjbdls oe ch voclid`h`). -Vuostl quo ch voclid`h` so jheoeo ilestheto oe oc ojpl, ch grèih `o su jhgedtu` oe aueidùe `oc ojpl os ueh cêeoh roith. 8.= ¼Cls rosucth`ls lbtoed`ls sle ilesdstoetos ile i le chs tolrêhs< Oxpcdquo

cls rosucth`ls sle ilesdstoetos ile chs tolrêhs sle iljl ueh pruobh `o vordihidùe ih`h ihsl oe ch oxpordoeidh oe jlvdjdoetl roicêeol, mhy roidprlid`h` oe cls rosucth`ls.

97

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

Vrlio`djdoetl #2; Jlvdjdoetl roicêeol uedalrjojoeto hiocorh`l.  hiocorh`l.   2.8 Ile oc sdjuch`lr ush`l oe oc prlio`djdoetl #8, oe oc ihjpl `o voclid`h` osirdbo iorl y oe oc `o hiocorhidùe 8.? j/s2. Dedidh oc jlvdjdoetl y helth cl lbsorvh`l. e iuorpl rohcdzh ue jlvdjdoetl roicêeol uedalrjojoeto hiocorh`l iuhe`l su trhyoitlrdh os ueh cêeoh roith y su hiocorhidùe os ilestheto. Ostl djpcdih quo ch voclid`h` hujoeth l `dsjdeuyo su jù`ucl `o jheorh uedalrjo

2.2 Iljpcoth ch thbch #2 ile ch hyu`h `oc prlaoslr. Phbch #2 Pdojpl t(s)

6

 9.  9.608

0.660

0.711

?.004

1.6?8

1.?72

7.80?

8.?21 Vlsdidùe x(j)

6

8.7?

1.40

82.62

87.60

22.27

27.01

92.94

9=.24

Qoclid`h` v(j/s)

6

2.24

0.?1

1.68

7.8?

=.87

4.6=

4.=1

86.72

Hiocorhidùe h(j/s2)

8.?

8.?

8.?

8.?

8.?

8.?

8.?

8.?

8.?

  2.9 _she`l oc prlgrhjh `o ch iljputh`lrh Clggorprl ilestruyo ch grèih `o

 : (). ¼Xuä rosucth< ueh phrèblch mhidh hrrdbh 2.0 hkusth ch iurvh hc jl`ocl jès h`oiuh`l y iletosth chs sdgudoetos progueths. 2.0.8. ¼Iuèc os ch oiuhidùe `o ]:a(x) phrh ch iurvh hkusth`h< x:6.7?t2   2.0.2.

Osirdbo oc sdgedih`l sdgedih`l `o cls iloidoetos `o osth oiuhidùe

Os ch jdth` `o hiocorhidùe, os `oidr h/2 :6,7? 2.0.9. Ile cls vhclros `o ch plsdidùe dedidhc 6: 6 j, ch voclid`h` dedidhc 6: 6 j/s y ch hiocorhidùe

: 8.? j/s2 y oc jl`ocl jhtojèil () : 6 + 6 + 82 2  osirdbo 2

 : () 6.7?t 9=

ch oiuhidùe

`o

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

2.0.0. Iljphrh cls rosucth`ls `o osth oiuhidùe ile ch `o ch iurvh hkusth`h. Oxpcdquo.

Cls rosucth`ls sle dguhcos, oe oc jlvdjdoetl roicêeol _edalrjo, oc iloidoeto dguhc h oiuhidùe iurvh hkusth`h. 2.?.

Ilestruyo ch grèih `o  : () ¼Xuä rosucth< ueh roith deicdeh`h mhidh oc lrdgoe

2.?.8. Ihciuch oc èroh bhkl ch grèih  :() y iljphrh ile oc jèxdjl `ospchzhjdoetl `o ch 2

phriuch. ¼Xuä rosucth< 9=.24j

2.?.2. Osirdbo ch oiuhidùe quo rochidleh chs vhrdhbcos voclid`h` y ojpl (): 8.?t 2.?.9. Hkusth ch grèih  : () y iljphrh ch oiuhidùe hkusth`h oe ch oiuhidùe hetordlr. 2.1. Osirdbo bhsèe`lto oe cls rosucth`ls, chs ihrhitorêsihs `oc J.R._.H.

Ch trhyoitlrdh os ueh cêeoh roith y, plr thetl, ch hiocorhidùe elrjhc iorl Ch voclid`h` desthetèeoh ihjbdh su jù`ucl `o jheorh uedalrjo; hujoeth l `dsjdeuyo oe ch jdsjh ihe`h` plr ih`h ued`h` `o ojpl. Ostl djpcdih oc sdgudoeto puetl Ch hiocorhidùe thegoeidhc ilestheto. Vlr occl ch hiocorhidùe jo`dh ildeid`o ile ch hiocorhidùe desthetèeoh phrh iuhcqudor pordl`l ostu`dh`l (h:hj) 2.7.

¼Ilrrlblrhe `dimls rosucth`ls ile ch tolrêh<

Oxpcdquo.

Cls rosucth`ls sle ilrrlblrh`ls ile chs tolrêhs, sle iljl ueh pruobh `o vordihidùe `o ih`h ihsl oe ch oxpordoeidh oe jlvdjdoetl roicêeol, mhy roidprlid`h` oe cls rosucth`ls.

Vrlio`djdoetl #9; Jlvdjdoetl roicêeol uedalrjojoeto rothr`h`l (J.R._.R.)  (J.R._.R.)   9.8. Ileeûh ushe`l oc sdjuch`lr, hmlrh oe oc ihjpl voclid`h`, osirdbo 4.?6 j/s y oe oc hiocorhidùe -8.96 j/s2. Dedidh oc jlvdjdoetl y helth cl lbsorvh`l.

Grèih plsdidùe-ojpl. Ch poe`doeto `oc grèil `o x(t) oe ih`h destheto os oc vhclr `o ch voclid`h` oe oso destheto. Ch iurvh quo roprosoeth x(t) os ih`h voz joels deicdeh`h, plr cl quo oc vhclr `o ch voclid`h` `oiroiorè ile oc ojpl. Yd x(t) os ueh mdpärblch, oetleios, v(t) sorè ueh roith `osioe`oeto.

94

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

9.2. Iljpcoth ch thbch #9, ushe`l oc prlio`djdoetl rohcdzh`l plr tu prlaoslr oe cls prlio`djdoetls hetordlros.

Phbch #9 Pdojpl t(s)

6

6.91?

6.498

8.?99

2.990

9.0?1

0.14=

Vlsdidùe x(ij)

6

9.9=

=.2=

89.60

8=.19

2?.67

96.2=

Qoclid`h` v(ij/s)

4.?

4.69

=.24

7.?8

1.07

?.68

9.94

Hiocorhidùe h(ij/s2)

-8.96

-8.96

-8.96

-8.96

-8.96

-8.96

-8.96

  9.9. _she`l oc prlgrhjh `o ch iljputh`lrh Clggorprl l ch hpcdihidùe `oc iocuchr Qoredor Grhpmdihc Hehcysds, ilestruyo ch grèih `o  : () ¼Xuä rosucth< os ueh phrèblch devorsh   9.9.8. Mhcch oc `ospchzhjdoetl tlthc, tlthc, ∁ :   −

: 20.?0 j 

9.0. Hkusth ch iurvh hc jl`ocl jès h`oiuh`l (plr okojpcl, oc jl`ocl iuh`rèil) y rosple`o cl sdgudoeto; 9.0.8. 9.0.2.

¼Iuèc os ch oiuhidùe `o  : () phrh ch iurvh hkusth`h < -6.1?t2+4.?t+6... Osirdbo

oc

sdgedih`l

`o

cls

iloidoetos

`o

osth

oiuhidùe.

i:h/2, os `oidr i:-8.9/2 os dguhc h -6,1? 9.0.9. Ile cls vhclros `o 6,

6 y h osirdbo ch oiuhidùe ilrrosple`doeto phrh

 :  ) : 6+6+ º (-8.9) t2: -6.1?t2 9.0.0. Iljphrh hjbhs oiuhidleos. Oxpcdquo.

chs 2 oiuhidleos sle dguhcos, ilrrosple`o ile oc jdsjl eûjorl. 9.?.

Ilestruyo

ch

grèih

`o

_eh cêeoh roith `oiroidoeto

06

 : ().

¼Xuä

rosucth<

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

9.?.8. Ihciuch oc èroh bhkl ch grèih

 : () y iljphrh osth jo`d`h ile oc `ospchzhjdoetl

jèxdjl hcihezh`l plr ch phriuch, ¼Xuä rosucth< 7.41j2 9.?.2. Osirdbo ch oiuhidùe quo rochidleh chs vhrdhbcos voclid`h` y ojpl, 

): 4.?-8.9t 

9.1. Osirdbo chs ihrhitorêsihs `oc J.R._.R. y oxpcdih sd ilrrlblrhe ile chs tolrêhs.

Oe osto jlvdjdoetl oc lbkotl sdojpro so `ospchzh ile ueh iljpleoeto mlrdzlethc `o hiocorhidùe oe (hx) ilestheto> plr cl thetl, sus ihrhitorêsihs prdeidphcos sle; Ch hiocorhidùe sdojpro os ilestheto oe. Ch voclid`h` so deirojoeth oe ch jdsjh prlplridùe plr ih`h detorvhcl `o ojpl. Ch rhpd`oz y ch voclid`h` jo`dh sle dguhcos. Oc osphidl roilrrd`l oe ue detorvhcl `o ojpl sdojpro os jhylr quo oe oc detorvhcl hetordlr.

?. Ileicusdùe Pljhe`l oe iuoeth chs ihrhitorêsihs oe ih`h jlvdjdoetl, osirdbo chs ileicusdleos `oc oxpordjoetl.

Ovhcuhidùe `o ch prèitdih  

Eljbro y hpoccd`ls; jheuoch iruz Qhc`oz  Jhtrêiuch(s); 2684-8690

D.

Pêtucl `o ch prèitdih

@daoroetos tdpls `o jlvdjdoetls roitdcêeols

DD.

Lbkotdvls

@otorjdehr ch voclid`h`, tdojpl y ch `dstheidh quo hcihezh oc lbkotl `o ostu`dl. Hproe`or h roslcvor ue prlbcojh `o jlvdjdoetl roitdcêeol uedalrjo y uedalrjojoeto hiocorh`l. Iljprlbhr quo ch voclid`h` os ilestheto. Ihciuchr ch hiocorhidùe `o ue iuorpl oe ihê`h cdbro. Hproe`or h roilelior chs grèadihs `dstheidh-tdojpl y voclid`h`-tdojpl `o ue jlvdjdoetl uedalrjojoeto hiocorh`l.

08

 

Jheuhc `o Vrèitdih `o Chblrhtlrdl `o Aêsdih Bèsdih

DDD.

Phbchs `o `htls, ièciucls prdeidphcos y grèadihs djproshs y/l jheuhc.

_she`l cls `ls jätl`ls phrh hpcdihr chs oxpordoeidhs `o jlvdjdoetl roitdcêeol DQ.

Ileicusdleos

_eh `o chs ihrhitorêsihs `oc jlvdjdoetl roicêeol uedalrjojoeto rothr`h`l (JR_R)os quo ch hiocorhidùe vh oe iletrh `oc soe`l `oc jlvdjdoetl, plr cl quo oc o c iuorpl vh `dsjdeuyoe`l su voclid`h` h jo`d`h quo trhesiurro oc ojpl, mhsth quo ehcjoeto so `ooeo. Oc JR_R so rdgo plr chs sdgudoetos oiuhidleos, jdoetrhs quo _e jlvdjdoetl os roicêeol iuhe`l ue lbkotl `osirdbo ueh trhyoitlrdh roith h voclid`h` ilestheto, `h`l quo su hiocorhidùe os euch. J.R._.H.os hquoc oe oc quo ue jùvdc so `ospchzh slbro ueh roith ile hiocorhidùe ilestheto. Ostl djpcdih quo, oe iuhcqudor detorvhcl `o ojpl, ch hiocorhidùe jo`dh `o ue jùvdc toe`rè sdojpro oc jdsjl vhclr.  

02