Lub ntsiab lus ntawm kev nrawm, tangential thiab acceleration ib txwm. Cov qauv

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2023-12-17 05:28

Yuav kom daws tau ntau yam teeb meem ntawm kev txav ntawm lub cev hauv physics, koj yuav tsum paub cov ntsiab lus ntawm lub cev kom muaj nuj nqis, nrog rau cov qauv uas lawv muaj feem xyuam. Kab lus no yuav hais txog cov lus nug ntawm dab tsi yog tangential tshaj tawm, dab tsi yog qhov nrawm nrawm thiab cov khoom siv dab tsi ua rau nws.

Lub tswvyim ntawm kev nrawm

Ob qhov tseem ceeb ntawm kinematics ntawm lub cev txav hauv qhov chaw yog qhov nrawm thiab nrawm. Speed piav qhia qhov nrawm ntawm kev txav mus los, yog li cov lej lej rau nws yog raws li hauv qab no:

v¯=dl¯/dt.

Ntawm no l¯ - yog qhov hloov pauv vector. Hauv lwm lo lus, ceev yog lub sij hawm derivative ntawm qhov kev ncua deb mus.

Raws li koj paub, txhua lub cev txav mus raws txoj kab kev xav, uas yog hu ua trajectory. Lub vector nrawm yog ib txwm qhia tangentially rau txoj kev no, txawm tias lub cev txav mus los nyob qhov twg.

Muaj ntau lub npe rau kom muaj nuj nqis v¯, yog tias peb txiav txim siab ua ke nrog txoj hauv kev. Yog, txij li nws tau qhiayog tangential, nws yog hu ua tangential velocity. Nws kuj tseem tuaj yeem hais tau raws li lub cev muaj nuj nqis raws li qhov tsis sib xws rau qhov nrawm nrawm.

Qhov ceev yog xam hauv meters ib ob hauv SI, tab sis hauv kev xyaum kilometers ib teev feem ntau siv.

Lub tswvyim ntawm acceleration

Tsis zoo li qhov nrawm, uas qhia qhov nrawm ntawm lub cev hla txoj hauv kev, acceleration yog qhov ntau uas piav txog qhov kev hloov ntawm qhov nrawm, uas yog lej sau raws li hauv qab no:

a¯=dv¯/dt.

Zoo li nrawm, acceleration yog vector yam ntxwv. Txawm li cas los xij, nws cov kev taw qhia tsis cuam tshuam nrog kev tshaj tawm vector. Nws yog txiav txim los ntawm kev hloov pauv hauv kev coj ua v¯. Yog hais tias thaum lub sij hawm cov lus tsa suab qhov ceev tsis hloov nws vector, ces a¯ acceleration yuav raug coj mus rau tib txoj kab raws li qhov ceev. Xws li acceleration yog hu ua tangential. Yog hais tias qhov ceev hloov cov kev taw qhia, thaum tswj tus nqi kiag li, ces lub acceleration yuav raug coj mus rau qhov chaw ntawm curvature ntawm lub trajectory. Nws hu ua normal.

ntsuas acceleration hauv m/s². Piv txwv li, qhov zoo-paub lub caij nplooj zeeg acceleration yog tangential thaum ib yam khoom nce los yog ntog vertically. Nws tus nqi nyob ze ntawm qhov chaw ntawm peb ntiaj chaw yog 9.81 m / s², uas yog, rau txhua thib ob ntawm kev poob, qhov ceev ntawm lub cev nce los ntawm 9.81 m / s.

Yog vim li cas qhov tsos ntawm acceleration tsis yog ceev, tab sis quab yuam. Yog lub zog F exertskev txiav txim ntawm lub cev ntawm m, ces nws yuav inevitably tsim ib tug acceleration, uas yuav xam tau raws li nram no:

a=F/m.

Cov qauv no yog qhov tshwm sim ncaj qha ntawm Newton txoj cai thib ob.

puv, ib txwm thiab tangential accelerations

Kev nrawm thiab nrawm raws li lub cev muaj nuj nqis tau tham hauv kab lus dhau los. Tam sim no peb yuav saib ze dua ntawm cov khoom siv ua kom tag nrho a¯.

Xav tias lub cev txav nrawm v¯ raws txoj kev nkhaus. Ces qhov sib npaug yuav muaj tseeb:

v¯=vu¯.

Vector u¯ muaj qhov ntev thiab raug coj raws txoj kab tangent mus rau txoj kev taug. Siv qhov kev sawv cev ntawm qhov ceev v¯, peb tau txais kev sib npaug rau tag nrho acceleration:

a¯=dv¯/dt=d(vu¯)/dt=dv/dtu¯ + vdu¯/dt.

Thawj lo lus tau txais nyob rau hauv txoj cai sib npaug yog hu ua tangential acceleration. Kev nrawm yog cuam tshuam nrog nws los ntawm qhov tseeb tias nws ntsuas qhov kev hloov pauv ntawm tus nqi tiag ntawm v¯, tsis hais nws cov kev taw qhia.

Lub sijhawm thib ob yog qhov nrawm nrawm. Nws quantitatively piav qhia txog qhov kev hloov pauv ntawm qhov nrawm vector, yam tsis xav txog qhov kev hloov pauv hauv nws cov qauv.

Yog tias peb txhais tau tias yog a_tand a cov tangential thiab ib txwm cov khoom ntawm tag nrho acceleration a, ces qhov modulus ntawm tom kawg tuaj yeem yog xam los ntawm tus qauv:

a=√(a_t²+a²).

Kev sib raug zoo ntawm tangential acceleration thiab ceev

Qhov sib txuas sib txuas tau piav qhia los ntawm cov kab lus kinematic. Piv txwv li, nyob rau hauv cov ntaub ntawv ntawm kev txav mus rau hauv txoj kab ncaj nraim nrog qhov nrawm nrawm, uas yog tangential (qhov ib txwm muaj yog xoom), cov kab lus siv tau:

v=a_tt;

v=v₀ ±a_tt.

Thaum cov lus tsa suab hauv lub voj voog nrog kev nrawm nrawm, cov qauv no kuj siv tau.

Yog li, txawm li cas los xij ntawm lub cev, qhov tangential acceleration los ntawm tangential tshaj tawm yog xam raws li lub sij hawm derivative ntawm nws modulus, uas yog:

a_t=dv/dt.

Piv txwv li, yog tias qhov nrawm hloov raws li txoj cai v=3t³+ 4t, ces a_t yuav muab sib npaug rau:

a_t=dv/dt=9t²+ 4.

Kev nrawm thiab nrawm nrawm

Cia peb sau meej meej cov qauv rau cov khoom ib txwm a, peb muaj:

a¯=vdu¯/dt=vdu¯/dldl/dt=v²/r r_e¯

R_e¯ is a vector of unit length directed to the center of curvature of the trajectory. Qhov kev qhia no tsim kev sib raug zoo ntawm tangential tshaj tawm thiab ib txwm acceleration. Peb pom tias tom kawg yog nyob ntawm lub modulus v ntawm ib lub sijhawm thiab ntawm lub vojvoog ntawm curvature r.

Ib txwm acceleration tshwm sim thaum twg lub nrawm vector hloov, txawm li cas los nws yog xoom yog tiasno vector khaws cov kev taw qhia. Hais txog tus nqi a¯ ua rau kev nkag siab tsuas yog thaum qhov curvature ntawm txoj kev yog tus nqi kawg.

Peb tau sau tseg saum toj no tias thaum tsiv hauv txoj kab ncaj nraim, tsis muaj kev nrawm li qub. Txawm li cas los xij, nyob rau hauv qhov xwm txheej muaj ib hom kev sib tw, thaum tsiv raws qhov a muaj tus nqi kawg, thiab a_t=0 rau |v¯|=const. Txoj kev no yog ib lub voj voog. Piv txwv li, kev sib hloov nrog qhov zaus ntawm cov hlau ncej, carousel lossis lub ntiaj teb nyob ib puag ncig nws tus kheej axis tshwm sim nrog kev nrawm nrawm a thiab xoom tangential acceleration a_t.