Txoj kev quab yuam ntawm lub axis thiab ntawm lub dav hlau. Physics

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

Power yog ib lub ntsiab lus tseem ceeb tshaj plaws hauv physics. Nws ua rau muaj kev hloov pauv hauv lub xeev ntawm txhua yam khoom. Hauv kab lus no, peb yuav txiav txim siab seb tus nqi no yog dab tsi, lub zog twg muaj, thiab tseem qhia seb yuav ua li cas thiaj nrhiav tau qhov projection ntawm lub zog ntawm lub axis thiab ntawm lub dav hlau.

Power thiab nws lub ntsiab lus ntawm lub cev

Nyob rau hauv physics, quab yuam yog ib tug vector kom muaj nuj nqis uas qhia tau hais tias qhov kev hloov nyob rau hauv lub zog ntawm lub cev ib chav tsev ntawm lub sij hawm. Qhov kev txhais no suav hais tias kev quab yuam yog ib qho dynamic yam ntxwv. Los ntawm qhov pom ntawm statics, quab yuam hauv physics yog qhov ntsuas ntawm elastic lossis yas deformation ntawm lub cev.

Lub thoob ntiaj teb SI system qhia txog quab yuam hauv Newtons (N). Dab tsi yog 1 newton, qhov yooj yim tshaj plaws kom nkag siab qhov piv txwv ntawm txoj cai thib ob ntawm kev siv tshuab classical. Nws cov lej lej yog raws li hauv qab no:

F¯=ma¯

Ntawm F¯ yog qee qhov kev quab yuam sab nraud ua rau lub cev ntawm m thiab ua rau kom nrawm a¯. Lub ntsiab txhais ntawm ib tug newton raws li nram no los ntawm cov mis: 1 N yog xws li ib tug quab yuam uas ua rau ib tug hloov nyob rau hauv lub ceev ntawm lub cev nrog ib tug loj ntawm 1 kg los ntawm 1 m / s rau txhua ob.

Piv txwv ntawm dynamicmanifestations of force yog acceleration of a car or a freely falling body in the earth gravitational field.

Qhov tshwm sim zoo li qub ntawm lub zog, raws li tau sau tseg, cuam tshuam nrog deformation tshwm sim. Cov qauv hauv qab no yuav tsum tau muab rau ntawm no:

F=PS

F=-kx

Thawj qhov kev qhia hais txog lub zog F rau lub siab P uas nws tawm ntawm qee thaj tsam S. Los ntawm cov qauv no, 1 N tuaj yeem txhais tau tias yog lub siab ntawm 1 pascal siv rau thaj tsam ntawm 1 m 2^{. Piv txwv li, ib kem ntawm atmospheric huab cua nyob rau hauv hiav txwv theem presses ntawm ib qhov chaw ntawm 1 m} 2^{nrog ib tug quab yuam ntawm 10} 5^N!

Qhov thib ob qhia yog daim ntawv classical ntawm Hooke txoj cai. Piv txwv li, ncab los yog compressing lub caij nplooj ntoos hlav los ntawm tus nqi linear x ua rau qhov tshwm sim ntawm kev tawm tsam F (hauv kev qhia k yog qhov proportionality).

Yuav ua li cas muaj zog

Nws twb tau qhia saum toj no tias lub zog tuaj yeem ua tau zoo li qub thiab muaj zog. Ntawm no peb hais tias ntxiv rau qhov tshwj xeeb no, lawv tuaj yeem tiv tauj lossis ntev-ntev rog. Piv txwv li, kev sib txhuam quab yuam, kev txhawb nqa kev sib cuag yog kev sib tiv tauj. Qhov laj thawj rau lawv qhov tsos yog qhov siv tau ntawm Pauli txoj cai. Cov tom kawg hais tias ob lub electrons tsis tuaj yeem nyob hauv tib lub xeev. Yog vim li cas qhov kov ntawm ob lub atom ua rau lawv repulsion.

Ntev-ntev rog tshwm sim los ntawm kev cuam tshuam ntawm lub cev los ntawm qee qhov chaw nqa khoom. Piv txwv li, xws li yog lub zog ntawm lub ntiajteb txawj nqus los yog electromagnetic cuam tshuam. Ob lub hwj chim muaj ntau yam tsis kawg,Txawm li cas los xij, lawv qhov kev siv zog poob qis raws li qhov square ntawm qhov deb (Coulomb txoj cai thiab lub ntiajteb txawj nqus).

Power is a vector quantity

Tom qab tau hais txog lub ntsiab lus ntawm qhov xav tau ntawm lub cev, peb tuaj yeem mus rau txoj kev kawm txog qhov teeb meem ntawm kev quab yuam ntawm lub axis. Ua ntej tshaj plaws, peb nco ntsoov tias qhov ntau npaum li cas yog vector, uas yog, nws yog tus yam ntxwv los ntawm ib qho module thiab kev taw qhia. Peb yuav qhia yuav ua li cas xam lub zog modulus thiab nws cov kev taw qhia.

Nws paub tias txhua tus vector tuaj yeem txhais tau tshwj xeeb hauv qhov muab kev sib koom ua ke yog tias qhov tseem ceeb ntawm kev tswj hwm ntawm nws qhov pib thiab qhov kawg paub. Xav tias muaj qee ntu qhia MN¯. Tom qab ntawd nws cov kev taw qhia thiab cov qauv tuaj yeem txiav txim siab siv cov kab lus hauv qab no:

MN¯=(x₂-x₁; y₂-y ₁; z₂-z₁);

|MN¯|=√((x₂-x₁)²+ (y_{2 -y}1₎2^{+ (z}2_-z1 ₎2^).

Ntawm no, kev tswj xyuas nrog qhov ntsuas 2 sib raug rau taw tes N, cov uas muaj qhov ntsuas 1 sib raug rau taw tes M. Tus vector MN¯ yog qhia los ntawm M rau N.

Rau qhov dav dav, peb tau qhia yuav ua li cas nrhiav cov qauv thiab kev tswj hwm (kev taw qhia) ntawm vector hauv qhov chaw peb sab. Cov qauv zoo sib xws uas tsis muaj kev sib koom tes thib peb yog siv tau rau rooj plaub ntawm lub dav hlau.

Yog li, qhov kev hloov pauv ntawm qhov quab yuam yog nws tus nqi tiag, qhia hauv newtons. Los ntawm qhov pom ntawm geometry, lub modulus yog qhov ntev ntawm ntu qhia.

Qhov projection ntawm quab yuam yog dab tsiaxis?

Nws yog qhov yooj yim tshaj plaws los tham txog qhov kev kwv yees ntawm cov ntu qhia mus rau kev sib koom tes axes thiab dav hlau yog tias koj xub tso cov vector sib thooj ntawm lub hauv paus, uas yog, ntawm qhov taw tes (0; 0; 0). Piv txwv tias peb muaj qee qhov quab yuam vector F¯. Cia peb tso nws qhov pib ntawm qhov taw tes (0; 0; 0), ces cov kev tswj hwm ntawm vector tuaj yeem sau tau raws li hauv qab no:

F¯=((x₁- 0); (y₁- 0); (z₁ - 0))=(x₁; y₁; z₁).

Vector F¯ qhia cov kev taw qhia ntawm lub zog hauv qhov chaw hauv qhov muab kev sib koom tes. Tam sim no cia peb kos cov ntu ntawm qhov kawg ntawm F¯ mus rau txhua qhov ntawm cov axes. Qhov kev ncua deb ntawm qhov chaw ntawm kev sib tshuam ntawm lub perpendicular nrog cov axis coj mus rau lub hauv paus chiv keeb yog hu ua projection ntawm lub zog ntawm lub axis. Nws tsis yog qhov nyuaj rau kwv yees tias thaum lub zog F¯, nws qhov kev kwv yees ntawm x, y thiab z axes yuav yog x₁, y_{1and z 1}, ntsig. Nco ntsoov tias cov kev sib koom ua ke no qhia cov qauv ntawm cov phiaj xwm quab yuam (qhov ntev ntawm ntu).

Lub kaum sab xis ntawm lub zog thiab nws qhov kev kwv yees ntawm kev sib koom tes

Xaiv cov kaum no tsis yooj yim. Txhua yam uas yuav tsum tau daws nws yog kev paub txog cov khoom ntawm trigonometric functions thiab lub peev xwm los siv Pythagorean theorem.

Piv txwv li, cia peb txhais lub kaum sab xis ntawm qhov kev taw qhia quab yuam thiab nws qhov projection ntawm x-axis. Cov duab peb sab sib raug zoo yuav raug tsim los ntawm hypotenuse (vector F¯) thiab ceg (ntu x₁). Ob txhais ceg yog qhov deb ntawm qhov kawg ntawm vector F¯ mus rau x-axis. Lub kaum sab xis ntawm F¯ thiab x-axis yog xam los ntawm tus qauv:

α=arccos(|x₁|/|F¯|)=arccos(x₁/√(x ₁²+y₁²+z₁ ²)).

Raws li koj tuaj yeem pom, txhawm rau txiav txim siab lub kaum sab xis ntawm lub axis thiab vector, nws yog qhov tsim nyog thiab txaus kom paub qhov kev sib koom ua ke ntawm qhov kawg ntawm ntu qhia.

Rau cov ces kaum nrog lwm axes (y thiab z), koj tuaj yeem sau cov kab lus zoo sib xws:

β=arccos(|y₁|/|F¯|)=arccos(y₁/√(x ₁²+y₁²+z ₁²));

γ=arccos(|z₁|/|F¯|)=arccos(z₁/√(x 12^+y12^+z 12^)).

Nco ntsoov tias hauv txhua tus qauv muaj cov qauv hauv cov lej, uas tshem tawm qhov pom ntawm obtuse fab. Nruab nrab ntawm lub zog thiab nws qhov kev kwv yees axial, cov ces kaum ib txwm tsawg dua lossis sib npaug rau 90^o.

Force thiab nws qhov kev kwv yees ntawm lub dav hlau ua haujlwm

Lub ntsiab lus ntawm lub zog qhov projection rau lub dav hlau yog tib yam li rau lub axis, tsuas yog nyob rau hauv cov ntaub ntawv no lub perpendicular yuav tsum tau qis qis mus rau lub axis, tab sis mus rau lub dav hlau.

Raws li cov txheej txheem ntawm qhov sib koom ua ke, peb muaj peb lub dav hlau sib koom ua ke xy (kab rov tav), yz (pem hauv ntej ntsug), xz (sab nraub qaum). Cov ntsiab lus ntawm kev sib tshuam ntawm cov perpendiculars poob los ntawm qhov kawg ntawm vector mus rau lub npe dav hlau yog:

(x₁; y₁; 0) rau xy;

(x₁; 0; z₁) rau xz;

(0; y₁; z₁) rau zy.

Yog tias txhua qhov cim cim txuas nrog lub hauv paus, ces peb tau txais qhov kev kwv yees ntawm lub zog F¯ mus rau lub dav hlau sib txuas. Dab tsi yog qhov modulus ntawm quab yuam, peb paub. Yuav kom nrhiav tau qhov modulus ntawm txhua qhov projection, koj yuav tsum siv Pythagorean theorem. Cia peb qhia txog qhov kev kwv yees ntawm lub dav hlau li F_xy, F_xz thiab F_zy. Ces qhov sib npaug yuav siv tau rau lawv cov modules:

F_xy=√(x₁²+y₁ ²);

F_xz=√(x₁²+ z₁ ²);

F_zy=√(y₁²+ z₁ ²).

Lub kaum sab xis ntawm qhov projection mus rau lub dav hlau thiab quab yuam vector

Nyob rau hauv nqe lus saum toj no, cov qauv tau muab rau cov qauv ntawm kev kwv yees mus rau lub dav hlau ntawm qhov kev txiav txim siab vector F¯. Cov kev kwv yees no, ua ke nrog ntu F¯ thiab qhov kev ncua deb ntawm nws qhov kawg mus rau lub dav hlau, tsim cov duab peb sab sab xis. Yog li ntawd, raws li nyob rau hauv cov ntaub ntawv ntawm projections ntawm lub axis, koj muaj peev xwm siv lub ntsiab txhais ntawm trigonometric functions los xam cov ces kaum nyob rau hauv nqe lus nug. Koj tuaj yeem sau qhov sib npaug hauv qab no:

α=arccos(F_xy/|F¯|)=arccos(√(x₁^{2 +y}12^{) /√(x}12 +y¹₂+z¹₂));

β=arccos(F_xz/|F¯|)=arccos(√(x₁^{2 +z}12^)/√(x12 +y¹₂+z¹₂));

γ=arccos(F_zy/|F¯|)=arccos(√(y₁²+z₁²)/√(x₁²+y₁² +z₁²)).

Nws yog ib qho tseem ceeb kom nkag siab tias lub kaum sab xis ntawm qhov kev taw qhia ntawm lub zog F¯ thiab nws cov kev sib raug zoo rau lub dav hlau yog sib npaug rau lub kaum sab xis ntawm F¯ thiab lub dav hlau no. Yog tias peb xav txog qhov teeb meem no los ntawm qhov pom ntawm geometry, ces peb tuaj yeem hais tias ntu F¯ yog inclined nrog kev hwm rau lub dav hlau xy, xz thiab zy.

Kev siv dag zog siv nyob qhov twg?

Cov qauv saum toj no rau kev kwv yees ntawm kev sib koom tes axes thiab ntawm lub dav hlau tsis yog qhov kev xav tau xwb. Lawv feem ntau siv los daws teeb meem ntawm lub cev. Cov txheej txheem ntawm kev nrhiav kev kwv yees yog hu ua decomposition ntawm lub zog rau hauv nws cov khoom. Cov tom kawg yog vectors, cov sum ntawm uas yuav tsum muab tus thawj quab yuam vector. Nyob rau hauv cov ntaub ntawv dav dav, nws muaj peev xwm decompose lub quab yuam mus rau hauv arbitrary Cheebtsam, txawm li cas los, rau kev daws teeb meem, nws yog ib qho yooj yim mus use projections rau perpendicular axes thiab dav hlau.

Teeb meem qhov twg lub tswv yim ntawm kev siv dag zog yuav sib txawv heev. Piv txwv li, tib txoj cai Newton thib ob xav tias lub zog sab nraud F¯ ua haujlwm ntawm lub cev yuav tsum tau coj mus rau tib txoj kev raws li qhov nrawm vector v¯. Yog tias lawv cov lus qhia txawv ntawm qee lub kaum sab xis, ces, txhawm rau kom muaj kev sib txig sib luag kom nyob twj ywm, ib tus yuav tsum hloov mus rau hauv nws tsis yog lub zog F¯ nws tus kheej, tab sis nws qhov projection mus rau qhov kev taw qhia v¯.

Tom ntej no, peb yuav muab ob peb yam piv txwv, qhov twg peb yuav qhia yuav ua li cas siv cov kawcov formulas.

Txoj haujlwm ntawm kev txiav txim siab lub zog ntawm lub dav hlau thiab ntawm kev sib koom tes

Xav tias muaj qee qhov quab yuam F¯, uas yog sawv cev los ntawm vector muaj qhov kawg hauv qab no thiab pib ua haujlwm:

(2; 0; 1);

(-1; 4; -1).

Nws yog qhov tsim nyog los txiav txim siab qhov kev hloov pauv ntawm lub zog, nrog rau tag nrho nws qhov kev kwv yees ntawm kev sib koom tes axes thiab dav hlau, thiab lub kaum sab xis ntawm F¯ thiab txhua qhov kev kwv yees.

Cia peb pib daws qhov teeb meem los ntawm kev suav cov kev tswj hwm ntawm vector F¯. Peb muaj:

F¯=(-1; 4; -1) - (2; 0; 1)=(-3; 4; -2).

Tom qab ntawd tus qauv ntawm lub zog yuav yog:

|F¯|=√(9+16+4)=√29 ≈ 5,385 N.

Kev kwv yees mus rau qhov kev sib koom ua ke yog sib npaug rau qhov sib koom ua ke ntawm vector F¯. Cia peb xam cov ces kaum ntawm lawv thiab F¯ kev taw qhia. Peb muaj:

α=arccos(|-3 |/5, 385) ≈ 56, 14^o;

β=arccos(|4|/5, 385) ≈ 42, 03^o;

γ=arccos(|-2|/5, 385) ≈ 68, 20^o.

Vim tias qhov kev tswj hwm ntawm vector F¯ paub, nws tuaj yeem suav cov qauv ntawm cov phiaj xwm quab yuam ntawm lub dav hlau ua haujlwm. Siv cov qauv saum toj no, peb tau txais:

F_xy=√(9 +16)=5 N;

F_xz=√(9 + 4)=3, 606 N;

F_zy=√(16 + 4)=4, 472 N.

Thaum kawg, nws tseem yuav suav cov kaum sab xis ntawm qhov pom pom ntawm lub dav hlau thiab lub zog vector. Peb muaj:

α=arccos(F_xy/|F¯|)=arccos(5/5, 385) ≈ 21, 8^o;

β=arccos(F_xz/|F¯|)=arccos(3, 606/5, 385) ≈ 48, 0^o;

γ=arccos(F_zy/|F¯|)=arccos(4, 472/5, 385) ≈ 33, 9^o.

Yog li, lub vector F¯ ze tshaj plaws rau lub dav hlau xyiv fab.

Teeb meem nrog zawv zawg bar ntawm lub dav hlau inclined

Tam sim no cia peb daws qhov teeb meem ntawm lub cev uas nws yuav tsim nyog los siv lub tswv yim ntawm kev quab yuam. Cia ib tug ntoo inclined dav hlau muab. Lub kaum sab xis ntawm nws inclination mus rau lub qab ntug yog 45^o. Nyob rau hauv lub dav hlau yog ib tug ntoo thaiv muaj ib tug loj ntawm 3 kg. Nws yog ib qho tsim nyog los txiav txim siab seb qhov kev nrawm no yuav txav mus rau hauv lub dav hlau yog tias nws paub tias tus coefficient ntawm zawv zawg kev sib txhuam yog 0.7.

Ua ntej, cia peb ua qhov sib npaug ntawm kev txav ntawm lub cev. Txij li thaum tsuas yog ob lub zog yuav ua rau nws (qhov kev kwv yees ntawm lub ntiajteb txawj nqus mus rau lub dav hlau thiab kev sib txhuam quab yuam), qhov sib npaug yuav siv daim ntawv:

F_g- F_f=ma=>

a=(F_g- F_f)/m.

Ntawm no F_g, F_f yog qhov kev kwv yees ntawm lub ntiajteb txawj nqus thiab kev sib txhuam, feem. Ntawd yog, txoj haujlwm raug txo kom suav lawv cov txiaj ntsig.

Txij thaum lub kaum sab xis ntawm lub dav hlau inclined mus rau lub qab ntug yog 45^o, nws yooj yim qhia tias qhov projection ntawm lub ntiajteb txawj nqus F_graws ntawm lub dav hlau yuav muab sib npaug rau:

F_g=mgsin(45^o)=39, 81/√2 ≈ 20, 81 N.

Qhov kev ua kom yuam kev no nrhiav kev daws teeb meemntoo thaiv thiab muab nws acceleration.

Raws li lub ntsiab txhais, lub zog ntawm zawv zawg kev sib txhuam yog:

F_f=ΜN

Where Μ=0, 7 (saib qhov teeb meem). Cov tshuaj tiv thaiv quab yuam ntawm kev txhawb nqa N yog sib npaug rau qhov kev kwv yees ntawm lub zog ntawm lub ntiajteb txawj nqus ntawm lub axis perpendicular mus rau lub dav hlau inclined, uas yog:

N=mgcos(45^o)

Tom qab ntawd lub zog sib txhuam yog:

F_f=Μmgcos(45^o)=0, 739, 81/√2 ≈ 14, 57 N.

Hloov cov pom rog rau hauv qhov sib npaug ntawm cov lus tsa suab, peb tau txais:

a=(F_g- F_f)/m=(20.81 - 14.57)/3=2.08 m/ c².

Yog li, qhov thaiv yuav nqes mus rau hauv lub dav hlau inclined, nce nws ceev los ntawm 2.08 m / s txhua ob.