Tangential lossis tangential acceleration

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2024-01-02 17:48

Txhua lub cev uas nyob ib puag ncig peb yog nyob rau hauv qhov kev txav mus tas li. Lub zog ntawm lub cev nyob rau hauv qhov chaw yog pom nyob rau hauv tag nrho cov scale theem, pib nrog lub zog ntawm lub hauv paus ntsiab lus nyob rau hauv lub atoms ntawm teeb meem thiab xaus nrog ceev ceev ntawm galaxies nyob rau hauv lub ntug. Nyob rau hauv txhua rooj plaub, tus txheej txheem ntawm kev txav tshwm sim nrog acceleration. Nyob rau hauv tsab xov xwm no, peb yuav txiav txim siab nyob rau hauv kom meej lub tswvyim ntawm tangential acceleration thiab muab ib tug formula uas nws yuav muab xam.

Kinematic ntau

Ua ntej tham txog tangential acceleration, cia peb xav txog qhov ntau npaum li cas nws yog kev cai los ua tus yam ntxwv ntawm cov neeg kho tshuab txav ntawm lub cev hauv qhov chaw.

Ua ntej tshaj plaws, qhov no yog txoj kev L. Nws qhia qhov kev ncua deb hauv metres, centimeters, mais, thiab lwm yam, lub cev tau mus rau ib lub sijhawm.

Tus yam ntxwv tseem ceeb thib ob hauv kinematics yog qhov ceev ntawm lub cev. Tsis zoo li txoj kev, nws yog vector kom muaj nuj nqis thiab raug coj raws li txoj kevlub cev txav. Kev nrawm txiav txim siab tus nqi ntawm kev hloov pauv ntawm spatial coordinates hauv lub sijhawm. Cov mis rau xam nws yog:

v¯=dL/dt

Kev nrawm yog lub sij hawm derivative ntawm txoj kev.

Thaum kawg, tus yam ntxwv tseem ceeb thib peb ntawm kev txav ntawm lub cev yog acceleration. Raws li cov lus txhais hauv physics, acceleration yog ib qhov ntau uas txiav txim siab qhov kev hloov ntawm qhov nrawm nrog lub sijhawm. Cov mis rau nws tuaj yeem sau ua:

a¯=dv¯/dt

Acceleration, zoo li ceev, kuj yog ib tug vector kom muaj nuj nqis, tab sis tsis zoo li nws, nws yog qhia nyob rau hauv cov kev taw qhia ntawm ceev hloov. Cov kev taw qhia ntawm acceleration kuj coincides nrog lub vector ntawm lub resulting quab yuam ua rau lub cev.

Kev sib tw thiab kev nrawm

Ntau yam teeb meem hauv physics raug txiav txim siab nyob rau hauv lub moj khaum ntawm rectilinear motion. Nyob rau hauv cov ntaub ntawv no, raws li ib tug txoj cai, lawv tsis tham txog lub tangential acceleration ntawm lub point, tab sis ua hauj lwm nrog linear acceleration. Txawm li cas los xij, yog tias qhov kev txav ntawm lub cev tsis yog linear, ces nws qhov kev nrawm nrawm tuaj yeem decomposed ua ob yam:

• tangent;
• normal.

Nyob rau hauv cov ntaub ntawv ntawm cov lus tsa suab, cov khoom ib txwm yog xoom, yog li peb tsis tham txog vector expansion ntawm acceleration.

Yog li, txoj hauv kev ntawm kev txav mus los txiav txim siab qhov xwm txheej thiab cov khoom ntawm kev nrawm nrawm. Lub trajectory ntawm kev txav yog to taub raws li txoj kab kev xav hauv qhov chaw uas lub cev txav mus. Ib qhoib qho curvilinear trajectory ua rau cov tsos ntawm cov tsis-zero acceleration Cheebtsam sau tseg saum toj no.

Kev txiav txim siab ntawm tangential acceleration

Tangential los yog, raws li nws tseem hu ua, tangential acceleration yog ib feem ntawm tag nrho acceleration, uas yog qhia tangentially rau txoj kev khiav. Txij li thaum lub nrawm kuj tau qhia raws li txoj hauv kev, tangential acceleration vector coincides nrog lub nrawm vector.

Lub tswvyim ntawm acceleration raws li ib qho kev ntsuas ntawm kev hloov nyob rau hauv ceev tau muab rau saum toj no. Txij li qhov ceev yog vector, nws tuaj yeem hloov pauv yog modulo lossis directionally. Lub tangential acceleration tsuas txiav txim qhov kev hloov ntawm qhov ceev modulus.

Nco ntsoov tias nyob rau hauv cov ntaub ntawv ntawm rectilinear motion, lub nrawm vector tsis hloov nws cov kev taw qhia, yog li ntawd, raws li cov ntsiab lus saum toj no, tangential acceleration thiab linear acceleration yog tib yam nqi.

Tau qhov tangential acceleration equation

Xav tias lub cev txav mus raws qee qhov kev nkhaus. Tom qab ntawd nws ceev v¯ ntawm qhov chaw xaiv tuaj yeem sawv cev raws li hauv qab no:

v¯=vu_t¯

Ntawm v yog qhov modulus ntawm vector v¯, u_{t¯ is the unit velocity vector directed tangentially to the trajectory.}

Siv tus lej txhais ntawm kev nrawm, peb tau txais:

a¯=dv¯/dt=d(vu_t¯)/dt=dv/dtu_t ¯ + vd(u_t¯)/dt

Thaum pom cov txiaj ntsig, cov cuab yeej ntawm cov khoom ntawm ob txoj haujlwm tau siv ntawm no. Peb pom tias tag nrho a¯ a¯ ntawm qhov kev txiav txim siab sib raug rau cov lej ntawm ob nqe lus. Lawv yog cov tangent thiab ib txwm acceleration ntawm lub point, feem.

Cia peb hais ob peb lo lus hais txog kev nrawm nrawm. Nws yog lub luag haujlwm rau kev hloov pauv qhov nrawm vector, uas yog, hloov cov kev taw qhia ntawm kev txav ntawm lub cev raws qhov nkhaus. Yog hais tias peb qhia meej xam tus nqi ntawm lub sij hawm thib ob, peb tau txais cov qauv rau ib txwm acceleration:

a=vd(u_t¯)/dt=v^{2/ r}

Ib txwm acceleration yog qhia raws li ib txwm rov qab mus rau qhov muab ntawm qhov nkhaus. Nyob rau hauv cov ntaub ntawv ntawm lub voj voog, ib txwm acceleration yog centripetal.

Tangential acceleration equation a_{t¯ is:}

a_t¯=dv/dtu_t¯

Qhov kev qhia no hais tias tangential acceleration tsis yog hloov pauv, tab sis mus rau kev hloov pauv ntawm qhov nrawm modulus v¯ dhau ib pliag. Txij li thaum lub tangential acceleration yog qhia tangentially mus rau lub ntsiab lus ntawm lub trajectory, nws yog ib txwm perpendicular mus rau ib txwm tivthaiv.

Tangential acceleration thiab tag nrho acceleration modulus

Tag nrho cov ntaub ntawv saum toj no tau nthuav tawm uas tso cai rau koj los laij tag nrho cov acceleration los ntawm tangent thiab ib txwm. Qhov tseeb, txij li ob qho tib si yog qhov sib koom ua ke, lawv cov vectors tsim ob txhais ceg ntawm daim duab peb sab,nws hypotenuse yog tag nrho acceleration vector. Qhov tseeb no tso cai rau peb sau cov qauv rau tag nrho cov acceleration module hauv daim ntawv hauv qab no:

a=√(a² + a_t²⁾

Lub kaum sab xis θ ntawm kev nrawm nrawm thiab tangential acceleration tuaj yeem txhais raws li hauv qab no:

θ=arccos(a_t/a)

Qhov ntau dua qhov tangential acceleration, qhov ze dua cov lus qhia ntawm tangential thiab tag nrho acceleration.

Kev sib raug zoo ntawm tangential thiab angular acceleration

Ib txoj hauv kev curvilinear raws li lub cev txav mus rau hauv kev siv tshuab thiab qhov xwm txheej yog lub voj voog. Tseeb tiag, kev txav ntawm lub zog, cov hniav thiab cov ntiaj chaw nyob ib puag ncig lawv tus kheej axis lossis nyob ib puag ncig lawv cov luminaries tshwm sim hauv lub voj voog. Qhov kev txav mus los ntawm txoj kev no yog hu ua kev sib hloov.

Kinematics ntawm kev sib hloov yog tus cwj pwm los ntawm cov txiaj ntsig zoo ib yam li kinematics ntawm cov lus tsa suab raws txoj kab ncaj nraim, txawm li cas los xij, lawv muaj lub cim angular. Yog li, los piav txog qhov kev sib hloov, lub hauv paus lub kaum sab xis ntawm kev sib hloov θ, lub kaum sab xis ω thiab acceleration α yog siv. Cov qauv hauv qab no siv tau rau cov khoom no:

ω=dθ/dt;

α=dω/dt

Xav tias lub cev tau ua ib lub kiv puag ncig ntawm lub axis ntawm kev sib hloov nyob rau hauv lub sij hawm t, ces rau lub angular tshaj tawm peb sau tau:

ω=2pi/t

Kab nrawm hauv qhov no yuav muab sib npaug rau:

v=2pir/t

Qhov twg r yog lub vojvoog ntawm txoj kev taug. Ob nqe lus kawg tso cai rau peb sautus qauv rau kev sib txuas ntawm ob lub nrawm:

v=ωr

Tam sim no peb suav lub sij hawm derivative ntawm sab laug thiab sab xis ntawm kab zauv, peb tau txais:

dv/dt=rdω/dt

Sab xis ntawm qhov sib npaug yog cov khoom ntawm angular acceleration thiab lub vojvoog ntawm lub voj voog. Sab laug ntawm qhov sib npaug yog qhov hloov ntawm qhov nrawm nrawm, uas yog, tangential acceleration.

Yog li, tangential acceleration thiab tus nqi zoo sib xws yog cuam tshuam los ntawm kev sib npaug:

a_t=αr

Yog tias peb xav tias lub disk tig, ces qhov tangential acceleration ntawm ib qho chaw ntawm tus nqi tas li ntawm α yuav nce linearly nrog nce kev ncua deb ntawm qhov taw tes rau qhov kev sib hloov axis r.

Tom ntej no, peb yuav daws ob qho teeb meem uas siv cov qauv saum toj no.

Kev txiav txim siab ntawm tangential acceleration los ntawm kev paub nrawm ua haujlwm

Nws paub tias qhov nrawm ntawm lub cev uas txav mus raws qee qhov kev nkhaus tau piav qhia los ntawm cov haujlwm hauv qab no:

v=2t2+ 3t + 5

Nws yog ib qho tsim nyog los txiav txim siab cov qauv rau tangential acceleration thiab nrhiav nws tus nqi ntawm lub sij hawm t=5 vib nas this.

Ua ntej, cia peb sau cov qauv rau lub tangential acceleration module:

a_t=dv/dt

Ntawd yog, txhawm rau xam qhov ua haujlwm a_{t (t), koj yuav tsum txiav txim siab qhov sib piv ntawm qhov nrawm nrog rau lub sijhawm. Peb muaj:}

a_t=d(2t^{2+ 3t + 5)/dt=4t + 3}

Substituting time t=5 seconds rau hauv cov lus qhia, peb tuaj txog ntawm cov lus teb: a_t=23 m/s^2.

Nco ntsoov tias daim duab ntawm qhov nrawm piv rau lub sijhawm ntawm qhov teeb meem no yog parabola, thaum daim duab ntawm tangential acceleration yog ib txoj kab ncaj nraim.

Tangential acceleration task

Nws paub tias cov khoom siv tau pib sib npaug nrawm nrawm los ntawm lub sijhawm xoom lub sijhawm. 10 vib nas this tom qab pib kev sib hloov, nws centripetal acceleration tau sib npaug rau 20 m/s 2. Nws yog ib qho tsim nyog los txiav txim siab tangential acceleration ntawm ib qho taw tes tom qab 10 vib nas this, yog tias nws paub tias lub vojvoog ntawm kev sib hloov yog 1 meter.

Ua ntej, sau cov qauv rau centripetal lossis ib txwm acceleration a_c:

a_c=v^2/r

Siv cov qauv rau kev sib raug zoo ntawm kab thiab angular ceev, peb tau txais:

a_c=ω^2r

Nyob rau hauv uniformly nrawm zog, ceev thiab angular acceleration muaj feem xyuam los ntawm cov mis:

ω=αt

Hloov ω rau hauv kab zauv rau a_{c, peb tau txais:}

a_c=α²t^2r

Linear acceleration los ntawm tangential acceleration yog qhia raws li nram no:

α=a_t/r

Hloov qhov sib npaug kawg rau hauv qhov kawg, peb tau txais:

a_c=a_t²/r² t²r=a_t²/rt^2=>

a_t=√(a_cr)/t

Cov qauv kawg, suav nrog cov ntaub ntawv los ntawm cov xwm txheej ntawm qhov teeb meem, ua rau cov lus teb: a_t=0, 447m/s^2.