Qhov nruab nrab ntawm lub ntiajteb txawj nqus (CG) yog qhov nruab nrab ntawm qhov hnyav faib ntawm ib yam khoom thaum qhov chaw ntawm lub ntiajteb txawj nqus tuaj yeem suav tias yog lub zog. Qhov no yog lub ntsiab lus uas cov khoom nyob hauv qhov zoo sib xws, tsis hais yuav ua li cas cov khoom tau tig los yog ntxeev ntawm lub ntsiab lus ntawd. Yog tias koj xav nrhiav tus nqi ntawm qhov nruab nrab ntawm qhov nqus ntawm ib yam khoom, koj yuav tsum xub paub tus nqi ntawm qhov hnyav ntawm qhov khoom, thiab cov khoom ntawm nws, qhov chaw nyob ntawm datum, thiab ntsaws qhov tseem ceeb rau hauv sib npaug los xam qhov nruab nrab ntawm lub ntiajteb txawj nqus. Nyeem kab lus no kom paub ntau ntxiv txog nws
Kauj ruam
Txoj Kev 1 ntawm 4: Txheeb Xyuas Qhov hnyav ntawm Lub Hom Phiaj
Kauj Ruam 1. Xam qhov hnyav ntawm ib yam khoom
Thaum koj xam qhov nruab nrab ntawm lub ntiajteb txawj nqus, thawj qhov koj yuav tsum tau ua yog nrhiav qhov hnyav ntawm qhov khoom. Hais tias koj suav qhov hnyav ntawm lub saw nrog qhov hnyav ntawm 30 kg. Txij li cov khoom no yog qhov sib npaug thiab tsis muaj ib tus neeg nce ntawm nws, qhov khoom nruab nrab ntawm lub ntiajteb txawj nqus yuav nyob hauv nruab nrab. Txawm li cas los xij, yog tias cov saw saw tau nce los ntawm tib neeg ntawm ob qho kawg, qhov teeb meem yuav dhau los nyuab dua.
Kauj Ruam 2. Xam qhov hnyav ntxiv
Txhawm rau nrhiav qhov nruab nrab ntawm lub ntiajteb txawj nqus uas pom ob tug menyuam caij, koj xav tau qhov hnyav ntawm txhua tus menyuam. Piv txwv li, thawj tus menyuam hnyav 40 kg thiab tus menyuam thib ob hnyav 60 kg.
Txoj Kev 2 ntawm 4: Txheeb Xyuas Datum
Kauj Ruam 1. Xaiv cov ntaub ntawv
Cov ntaub ntawv yog qhov kev xav pib qhov pib muab tso rau ntawm ib kawg ntawm qhov pom. Wb hais tias lub saw saw ntev 16 meters. Muab cov ntaub ntawv tso rau sab laug ntawm qhov pom, ze rau thawj tus menyuam.
Kauj Ruam 2. Ntsuas qhov ntsuas qhov deb ntawm qhov chaw nruab nrab ntawm lub hom phiaj tseem ceeb thiab los ntawm ob qhov hnyav ntxiv
Qhia rau txhua tus menyuam zaum 1 meter ntawm qhov taub ntawm qhov pom. Qhov nruab nrab ntawm lub ntiajteb txawj nqus yog nyob nruab nrab ntawm qhov pom, uas yog 8 meters vim tias 16 meters faib los ntawm 2 yog 8. Nov yog qhov kev ncua deb ntawm lub hom phiaj tseem ceeb thiab ob yam khoom ntxiv uas ua rau cov ntaub ntawv:
- Qhov nruab nrab ntawm qhov pom = 8 metres los ntawm cov ntaub ntawv.
- Menyuam 1 = 1 meter deb ntawm datum.
- Menyuam 2 = 15 meters deb ntawm datum
Txoj Kev 3 ntawm 4: Nrhiav Qhov Chaw Ntawm Lub Ntiajteb
Kauj Ruam 1. Muab txhua yam khoom nrug deb ntawm cov ntaub ntawv los ntawm nws qhov hnyav kom pom tus nqi tam sim no
Yog li, koj tau txais lub sijhawm ntawm txhua qhov khoom. Nov yog yuav ua li cas muab cov khoom hnyav los ntawm txhua qhov khoom nrug ntawm nws cov ntaub ntawv:
- Seesaw: 30 kg x 8 meters = 240 kg x m.
- Menyuam 1 = 40 kg x 1 meter = 40 kg x m
- Menyuam 2 = 60 kg x 15 m = 900 kg x m
Kauj Ruam 2. Ntxiv peb lub sijhawm
Tsuas yog xam 240 kg x m + 40 kg x m + 900 kg x m = 1,180 kg x m. Tag nrho lub sijhawm yog 1,180 kg x m.
Kauj Ruam 3. Ntxiv qhov hnyav ntawm txhua yam khoom
Nrhiav qhov hnyav tag nrho ntawm qhov pom, tus menyuam thawj, thiab tus menyuam thib ob. Yog li: 30 kg + 40 kg + 60 kg = 130 kg.
Kauj Ruam 4. Sib faib tag nrho lub sijhawm los ntawm qhov hnyav tag nrho
Yog li, koj tau txais qhov kev ncua deb ntawm cov ntaub ntawv mus rau lub hom phiaj qhov chaw ntawm lub ntiajteb txawj nqus. Txhawm rau ua qhov no, faib 1,180 kg x m los 130 kg.
- 1,180 kg x m 130 kg = 9.08 m
- Qhov pom qhov nruab nrab ntawm lub ntiajteb txawj nqus yog 9.08 los ntawm qhov chaw nyob, piv txwv li los ntawm sab laug kawg ntawm qhov pom.
Txoj Kev 4 ntawm 4: Txheeb Cov Lus Teb
Kauj Ruam 1. Nrhiav qhov nruab nrab ntawm lub ntiajteb txawj nqus hauv daim duab
Yog tias qhov nruab nrab ntawm lub ntiajteb txawj nqus pom nyob sab nraum cov khoom siv, koj cov lus teb yuav tsis yog lawm. Tej zaum koj tau ntsuas qhov deb mus rau ntau dua ib lub ntsiab lus. Sim dua nrog ib qho datum.
- Piv txwv li, rau ib tus neeg ntawm lub saw pom, qhov nruab nrab ntawm lub ntiajteb txawj nqus yuav tsum nyob rau ntawm qhov pom, tsis yog nyob rau sab laug lossis sab xis ntawm qhov pom. Nws tsis tas yuav yog qhov tseeb ntawm ib tus neeg.
- Qhov no siv rau teeb meem ob sab. Kos ib lub xwmfab loj txaus los tuav tag nrho cov khoom hauv qhov teeb meem. Qhov nruab nrab ntawm lub ntiajteb txawj nqus yuav tsum sab hauv lub xwmfab no.
Kauj Ruam 2. Txheeb xyuas koj cov kev suav yog tias cov lus teb muaj tsawg heev
Yog tias koj xaiv ib qho kawg ntawm qhov system raws li cov ntaub ntawv, cov lus teb me me tso qhov chaw nruab nrab ntawm lub ntiajteb txawj nqus raws qhov kawg. Cov lus teb no yuav raug, tab sis feem ntau yog kos npe ntawm cov lus teb tsis raug. Thaum xam lub sijhawm, koj puas "sib npaug" qhov hnyav thiab nrug? Qhov no yog txoj hauv kev kom pom tus nqi tam sim no. Yog tias koj "ntxiv lawv" hloov, cov lus teb feem ntau me dua.
Kauj Ruam 3. Kho qhov teeb meem yog tias koj muaj ntau dua ib lub hauv paus ntawm lub ntiajteb txawj nqus
Txhua qhov system tsuas muaj ib lub hauv paus ntawm lub ntiajteb txawj nqus. Yog tias koj tau txais ntau dua ib qho lus teb, yuav muaj feem koj tsis tau ua cov kauj ruam los ntxiv rau txhua lub sijhawm hauv qhov khoom. Qhov nruab nrab ntawm lub ntiajteb txawj nqus yog lub sijhawm "tag nrho" faib los ntawm "tag nrho" qhov hnyav. Koj tsis tas yuav faib "txhua" lub sijhawm los ntawm "txhua" qhov hnyav, uas yooj yim qhia txoj haujlwm ntawm txhua yam khoom.
Kauj Ruam 4. Txheeb xyuas cov ntaub ntawv yog tias koj cov lus teb tsis muaj ob peb tus lej
Hais qhov lus teb raug yog 9.08 metres, thiab cov lus teb koj tau yog 1.08 metres, 7.08 meters, lossis tus lej xaus rau ", 08". Qhov no feem ntau tshwm sim vim tias peb xaiv sab laug raws li cov ntaub ntawv, thaum koj xaiv sab xis ntawm lub sawaw. Koj cov lus teb yog "raug", tsis muaj teeb meem dab tsi koj xaiv! Koj tsuas yog yuav tsum nco ntsoov datum ib txwm nyob ntawm x = 0. Nov yog qhov piv txwv:
- Raws li txoj hauv kev hauv kab lus no, cov ntaub ntawv yog nyob rau sab laug ntawm qhov pom. Peb cov lus teb yog 9.08 meters yog li qhov nruab nrab ntawm lub ntiajteb txawj nqus yog 9.08 los ntawm cov ntaub ntawv nyob rau sab laug ntawm qhov pom.
- Yog tias koj xaiv cov ntaub ntawv ntawm 1 meter los ntawm sab laug ntawm qhov pom, cov lus teb tau yog 8.08 meters. Qhov nruab nrab ntawm lub ntiajteb txawj nqus yog 8.08 metres los ntawm cov ntaub ntawv tshiab, uas yog 1 meter ntawm sab laug ntawm qhov pom. Qhov nruab nrab ntawm lub ntiajteb txawj nqus yog 8.08 + 1 = 9.08 meters los ntawm sab laug deb, thiab yog tib cov lus teb los ntawm ua ntej.
- (Faj seeb: Thaum ntsuas nrug deb, tsis txhob hnov qab tias qhov nrug ze ntawm sab laug ' datum yog qhov tsis zoo, thiab qhov deb ntawm ib sab txoj cai datum yog qhov zoo.)
Kauj Ruam 5. Ua kom ntseeg tau tias tag nrho koj cov ntaub ntawv sizing yog nyob hauv kab ncaj
Hais tias koj tau pom lwm tus piv txwv ntawm "tus menyuam ua si ntawm lub saw pom", tab sis ib tus ntawm cov menyuam siab dua lwm tus, lossis tau dai nyob hauv qab lub qhov rooj tsis txhob zaum ntawm nws. Tsis quav ntsej qhov sib txawv no thiab nqa tag nrho cov ntaub ntawv sizing raws txoj kab ncaj ntawm lub saw saw. Kev ntsuas nrug siv cov ces kaum yuav ua rau cov lus teb uas yuav luag yog tab sis tawm me ntsis.
Txog qhov teeb meem pom, txhua yam koj yuav tsum tau ua tib zoo saib yog qhov nruab nrab ntawm lub ntiajteb txawj nqus nyob rau sab laug lossis sab xis ntawm qhov pom. Tom qab ntawd, koj yuav kawm paub ntau txoj hauv kev los xam qhov nruab nrab ntawm qhov nqus hauv ob qhov ntev
Lub tswv yim
- Txhawm rau nrhiav qhov nrug nws yuav siv tus neeg txav mus rau qhov sib npaug ntawm qhov pom ntawm qhov pom, siv cov qauv: (qhov hnyav hloov) / (tag nrho qhov hnyav) = (nrug mus rau qhov nruab nrab ntawm lub ntiajteb txawj nqus) / (nrug mus rau qhov hnyav hloov mus). Cov mis no tuaj yeem rov sau dua kom pom qhov deb qhov hnyav (tib neeg) tau txav mus los yog sib npaug ntawm qhov nruab nrab ntawm qhov nruab nrab ntawm lub ntiajteb txawj nqus thiab lub sijhawm ua puv puv qhov hnyav ntawm tus neeg faib los ntawm qhov hnyav tag nrho. Yog li, thawj tus menyuam yuav tsum tau tsiv -1.08 meters * 40 kg / 130 kg = -0.33 meters (mus rau ntawm ntug ntawm qhov pom). Lossis, tus menyuam thib ob yuav tsum txav mus -0.08 meters * 130 kg / 60 kg = -2.33 meters (mus rau nruab nrab ntawm qhov pom).
- Txhawm rau nrhiav qhov nruab nrab ntawm lub ntiajteb txawj nqus ntawm ob yam khoom siv, siv cov mis Xcg = xW/∑W txhawm rau nrhiav qhov nruab nrab ntawm lub ntiajteb txawj nqus raws X axis, thiab Ycg = yW/∑W txhawm rau nrhiav qhov nruab nrab ntawm lub ntiajteb txawj nqus raws Y axis yam khoom.
- Lub ntsiab lus ntawm qhov nruab nrab ntawm lub ntiajteb txawj nqus ntawm qhov kev faib loj yog (∫ r dW/∫ dW) qhov twg dW yog qhov hnyav sib txawv, r yog txoj haujlwm vector thiab qhov tseem ceeb hu ua Stieltjes ib feem ntawm lub cev. Txawm li cas los xij, koj tuaj yeem nthuav tawm nws raws li ib txwm muaj ntau dua Riemann lossis Lebesgue ntim ib feem rau kev faib khoom uas lees paub qhov ua haujlwm ntom ntom. Pib los ntawm qhov kev txhais no, txhua yam khoom ntawm qhov nruab nrab ntawm lub ntiajteb txawj nqus, suav nrog cov uas siv hauv kab lus no, tuaj yeem muab tau los ntawm Stieltjes cov khoom tseem ceeb.
