Dab tsi yog acceleration hauv physics. Lub tswv yim ntawm tag nrho acceleration thiab nws cov Cheebtsam. Uniformly accelerated rectilinear motion

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

Mechanical txav puag ncig peb txij thaum yug los. Txhua txhua hnub peb pom tias lub tsheb txav mus raws li txoj kev, cov nkoj tab tom txav mus rau hauv hiav txwv thiab dej hiav txwv, dav hlau ya, txawm tias peb lub ntiaj teb tab tom tsiv, hla qhov chaw sab nraud. Ib tug yam ntxwv tseem ceeb rau txhua hom kev txav uas tsis muaj kev zam yog acceleration. Qhov no yog lub cev kom muaj nuj nqis, hom thiab cov yam ntxwv tseem ceeb uas yuav tau tham hauv kab lus no.

Lub cev lub tswv yim ntawm acceleration

Ntau lub sij hawm "acceleration" yog intuitively paub. Nyob rau hauv physics, acceleration yog ib tug kom muaj nuj nqis uas characterizes tej kev hloov nyob rau hauv ceev lub sij hawm. Cov qauv lej sib raug yog:

a¯=dv¯/ dt

Txoj kab saum lub cim hauv cov qauv txhais tau tias tus nqi no yog vector. Yog li, a¯ acceleration yog vector thiab nws kuj piav qhia txog kev hloov pauv hauv vector kom muaj nuj nqis - qhov ceev v¯. Qhov no yogacceleration yog hu ua tag nrho, nws yog ntsuas nyob rau hauv meters ib square thib ob. Piv txwv li, yog hais tias lub cev nce ceev los ntawm 1 m / s rau txhua thib ob ntawm nws lub zog, ces qhov sib txuas acceleration yog 1 m / s ².

kev nrawm los ntawm qhov twg thiab nws mus qhov twg?

Peb xam pom lub ntsiab txhais ntawm dab tsi yog acceleration. Nws kuj tau pom tias peb tab tom tham txog qhov loj ntawm vector. Qhov no vector taw tes nyob qhov twg?

Txhawm rau muab cov lus teb raug rau cov lus nug saum toj no, ib tus yuav tsum nco ntsoov Newton txoj cai thib ob. Hauv daim ntawv no, nws tau sau raws li hauv qab no:

F¯=ma¯

Hauv cov lus, qhov kev sib npaug no tuaj yeem nyeem tau raws li hauv qab no: lub zog F¯ ntawm txhua qhov xwm txheej ua rau lub cev ntawm pawg m ua rau kom nrawm a¯ ntawm lub cev no. Txij li thaum huab hwm coj yog ib qho scalar kom muaj nuj nqis, nws hloov tawm hais tias lub zog thiab acceleration vectors yuav raug coj raws tib txoj kab ncaj nraim. Nyob rau hauv lwm yam lus, acceleration yog ib txwm qhia nyob rau hauv cov kev taw qhia ntawm lub quab yuam thiab yog kiag li ywj siab ntawm lub ceev vector v¯. Lub tom kawg yog qhia raws tangent mus rau txoj kev txav.

Curvilinear motion thiab tag nrho acceleration Cheebtsam

Nyob rau hauv qhov xwm txheej, peb feem ntau ntsib nrog kev txav ntawm lub cev raws curvilinear trajectories. Xav txog seb peb tuaj yeem piav qhia qhov nrawm li cas hauv qhov no. Rau qhov no, peb xav tias qhov nrawm ntawm cov khoom taw tes hauv qhov kev txiav txim siab ntawm txoj kev tuaj yeem sau tau li:

v¯=vu_t¯

Tus ceev v¯ yog cov khoom ntawm nws tus nqi kiag v los ntawmunit vector u_t¯ directed raws tangent mus rau trajectory (tangential tivthaiv).

Raws li lub ntsiab txhais, acceleration yog qhov derivative ntawm ceev nrog rau lub sij hawm. Peb muaj:

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

thawj lo lus nyob rau sab xis ntawm qhov sau sib npaug yog hu ua tangential acceleration. Ib yam li qhov tshaj tawm, nws yog qhia raws li tangent thiab characterizes qhov kev hloov ntawm tus nqi kiag li v¯. Lub sij hawm thib ob yog qhov ib txwm acceleration (centripetal), nws yog qhia perpendicular mus rau tangent thiab characterizes qhov kev hloov nyob rau hauv lub magnitude vector v¯.

Yog li, yog lub vojvoog ntawm curvature ntawm txoj kev sib npaug sib npaug rau infinity (txoj kab ncaj nraim), ces lub nrawm vector tsis hloov nws txoj kev coj mus rau hauv tus txheej txheem ntawm kev txav lub cev. Qhov kawg txhais tau hais tias qhov ib txwm muaj ntawm tag nrho acceleration yog xoom.

Thaum cov khoom taw tes txav mus raws ib lub voj voog sib npaug, qhov ntsuas qhov nrawm tseem nyob tas li, uas yog, qhov sib npaug ntawm tag nrho cov acceleration yog sib npaug rau xoom. Cov khoom siv ib txwm raug coj mus rau qhov chaw ntawm lub voj voog thiab suav los ntawm cov qauv:

a=v²/r

Ntawm no yog lub vojvoog. Yog vim li cas rau qhov tshwm sim ntawm centripetal acceleration yog qhov kev txiav txim ntawm lub cev ntawm qee qhov kev quab yuam sab hauv, uas yog coj mus rau qhov chaw ntawm lub voj voog. Piv txwv li, rau lub zog ntawm cov ntiaj chaw nyob ib ncig ntawm lub hnub, lub zog no yog gravitational attraction.

Cov mis uas txuas rau tag nrho acceleration modules thiab nwsCheebtsam a_t(tangent), a (ib txwm), zoo li:

a=√(a_t² + a2)

Usformly nrawm txav hauv txoj kab ncaj nraim

Kev txav mus rau hauv txoj kab ncaj nraim nrog kev nrawm nrawm yog feem ntau pom hauv lub neej txhua hnub, piv txwv li, qhov no yog kev txav ntawm lub tsheb raws txoj kev. Cov lus tsa suab no tau piav qhia los ntawm qhov sib npaug nrawm hauv qab no:

v=v₀+ at

Ntawm no v₀- qee qhov nrawm uas lub cev tau ua ntej nws nrawm a.

Yog tias peb npaj cov haujlwm v(t), peb yuav tau txais txoj kab ncaj nraim uas hla y-axis ntawm qhov taw tes nrog kev tswj hwm (0; v₀), thiab lub tangent ntawm txoj kab nqes mus rau x-axis yog sib npaug rau acceleration modulus a.

Kev ua kom muaj nuj nqis v(t), peb tau txais cov qauv rau txoj kev L:

L=v₀t + at²/2

Daim duab ntawm txoj haujlwm L(t) yog ceg ntawm parabola, uas pib ntawm qhov taw tes (0; 0).

Cov qauv saum toj no yog cov qauv sib npaug ntawm cov kinematics ntawm kev nrawm nrawm raws txoj kab ncaj nraim.

Yog lub cev, muaj qhov pib nrawm v₀, pib qeeb nws txoj kev txav nrog kev nrawm nrawm, ces peb hais txog kev txav mus los tsis sib xws. Cov qauv hauv qab no siv tau rau nws:

v=v₀- at;

L=v₀t - at²/2

daws qhov teeb meem ntawm kev suav acceleration

Nyob zoomob, lub tsheb pib tsiv. Nyob rau tib lub sijhawm, thawj 20 vib nas this, nws taug kev deb ntawm 200 meters. Lub acceleration ntawm lub tsheb yog dab tsi?

Ua ntej, cia peb sau cov kab zauv dav dav rau txoj kev L:

L=v₀t + at²/2

Vim peb rooj plaub lub tsheb tau so, nws ceev v₀ yog sib npaug rau xoom. Peb tau txais cov qauv rau acceleration:

L=at²/2=>

a=2L/t²

Hloov tus nqi ntawm qhov kev ncua deb L=200 m rau lub sijhawm luv t=20 s thiab sau cov lus teb rau cov lus nug: a=1 m/s ².