Umthetho Oyisisekelo Wokulingana Kwemishini
Ukulingana kwemishini yisimo lapho into ingashintshi khona ekunyakazeni kwayo iyonke: akukho ukusheshisa kokuhumusha (ukuhamba emgqeni oqondile) futhi akukho ukusheshisa kokujikeleza (ukujikeleza). Lo mqondo uyisisekelo esibalulekile ku-physics yobunjiniyela, ikakhulukazi ku-statics, structural mechanics, mechanics, kanye nobunjiniyela bezakhiwo. Ukuze siqonde ukuthi kungani ibhuloho lingamelana ngokuqinile noma ukuthi kungani iladi lingazinza uma lincike kulo, sidinga ukuhlola imithetho eyisisekelo elawula ukulingana kwemishini. Lesi sihloko sixoxa ngezisekelo zemfundiso kanye nemithetho eyinhloko esekela ukulingana, kusukela emithethweni kaNewton kuya ezimweni zokulinganisela kwamandla nezikhathi.
1. Ukuqonda Ukulingana Kwemishini
Ngokuvamile, ukulingana kwemishini kuyisimo lapho umphumela wawo wonke amandla asebenza entweni ungo-zero kanti umphumela wazo zonke izikhathi (ama-torque) cishe kunoma yiliphi iphuzu nawo ungo-zero. Kulesi simo, into ingaba kwesinye sezimo ezimbili ezingaba khona:
1. Ukulingana okuqinile: into iphumule (ijubane eliyi-zero) futhi ihlala iphumule.
2. Ukulingana okuguquguqukayo: izinto zihamba ngesivinini esingaguquki (akukho ukusheshisa), isibonelo imoto ihamba iqonde ngesivinini esingaguquki emgwaqweni oyisicaba lapho amandla okusunduza elingana namandla okuhudula.
Kodwa-ke, ezifundweni eziyisisekelo ze-statics kanye nezakhiwo, izingxoxo zokulingana zivame ukugxila ezimweni ezi-static, ngoba yizo ezifanele kakhulu ekuklanyweni kokwakhiwa kanye nokuhlaziywa komthwalo.
2. Isisekelo Esiyinhloko Sezomthetho: Umthetho KaNewton
Isisekelo esisemthethweni sokulingana kwemishini sihlobene eduze neMithetho kaNewton, ikakhulukazi uMthetho I noMthetho II.
a. Umthetho Wokuqala KaNewton (Umthetho Wokungabi Nandaba)
UMthetho Wokuqala KaNewton uthi into izohlala iphumule noma ihambe emgqeni oqondile ngesivinini esingaguquki uma amandla asebenzayo kuyo engu-zero. Ngokwezibalo:
\[
\sum \vec{F} = 0
\]
Lokhu kuyingqikithi yokulingana kokuhumusha. Uma kungekho mandla aphelele “anqobayo” (amandla aphumelayo ayi-zero), into ngeke isheshise.
b. Umthetho Wesibili KaNewton (Ubudlelwano Phakathi Kwamandla Nokusheshisa)
UMthetho Wesibili kaNewton uthi:
\[
\sum \vec{F} = m\vec{a}
\]
Uma ukusheshisa \(\vec{a} = 0\), khona-ke ngokuzenzakalelayo \(\sum \vec{F} = 0\). Ngakho-ke, isimo sokulingana singabhekwa njengecala elikhethekile loMthetho Wesibili kaNewton lapho ukusheshisa kungu-zero.
Ngokushintshana, ukufaniswa koMthetho Wesibili kaNewton kusebenza ngendlela elandelayo:
\[
\sum \tau = I \alpha
\]
Lapho \(\tau\) kuyi-torque/umzuzu wamandla, \(I\) umzuzu we-inertia, kanye \(\alpha\) ukusheshisa kwe-angular. Ukuze kube nokulingana okujikelezayo, \(\alpha = 0\) ukuze:
\[
\isamba \isilinganiso = 0
\]
Lezi zibalo ezimbili—amandla aphumayo angu-zero kanye ne-torque ephumayo engu-zero—yizimo ezisemthethweni zokulingana kwemishini.
3. Izimo Zokulingana: Amandla Aphumelayo kanye Nesikhathi Esiphumelayo
Ekusebenzeni kwe-statics, ukulingana kuhlaziywa ngamaqembu amabili ezibalo:
a. Ukulingana Kokuhumusha
Kuhlelo lwamandla endizeni enezinhlangothi ezimbili (2D), izimo yilezi:
\[
\isamba F_x = 0,\ikota \isamba F_y = 0
\]
Ngezilinganiso ezintathu (3D):
\[
\isamba F_x = 0,\ikota \isamba F_y = 0,\ikota \isamba F_z = 0
\]
Lokhu kusho ukuthi izingxenye zamandla ku-axis ngayinye kumele zihlukane.
b. Ibhalansi Yokujikeleza
Nge-2D (izikhathi mayelana ne-axis eqondile endizeni):
\[
\isamba M = 0
\]
Nge-3D:
\[
\isamba M_x = 0,\ikota \isamba M_y = 0,\ikota \isamba M_z = 0
\]
Lesi simo siqinisekisa ukuthi izinto azivamile ukuzungeza.
4. Umqondo Wesikhathi Samandla (I-Torque) Njengesisekelo Sokulinganisela
Umzuzu wamandla “yikhono” lamandla lokujikeleza into endaweni ezungezayo. Ngamagama alula:
\[
\tau = F \cdot r \cdot \sin\theta
\]
ngebanga elisuka endaweni ejikelezayo kuya emgqeni wesenzo samandla (ingalo yesikhashana), kanye ne-(\theta\) i-engeli ephakathi kwesiqondiso samandla nengalo yesikhashana. Ukulingana kokujikeleza kudinga ukuthi izikhathi ezihambisana newashi kanye neziphambene newashi zilinganiselane.
Ekwakhiweni, lo mqondo ungokoqobo kakhulu: umthwalo ekugcineni komshayo uzodala umzuzu okumele ulwisane nokusabela kokusekelwa noma ezinye izakhi zesakhiwo.
5. Umthetho Wesenzo–Ukusabela kanye Namandla Angaphakathi
UMthetho Wesithathu kaNewton uthi:
> Isenzo ngasinye sibangela ukusabela okulinganayo nokuphambene.
Uma kuqhathaniswa nokulinganisela, lo mthetho usiza ukuqonda amandla okuxhumana kanye namandla angaphakathi. Isibonelo, lapho ibhloko licindezela phansi ekusekeleni kwalo, ukwesekwa kunamandla okusabela aphezulu alinganayo. La mandla okusabela abalulekile ngoba ngokuvamile ayiguquguquki okumele ibhekwe ekuhlaziyeni okungaguquki.
Ngaphezu kwalokho, ezakhiweni ezakhiwe ngezinto eziningi, amandla angaphakathi (ukucindezela ukucindezeleka, ukugunda, izikhathi zokugoba) avela njengemibhangqwana yokusabela kwesenzo ngaphakathi kwezinto. Nakuba amandla angaphakathi engabonakali ngaphandle, anquma ukuthi isakhiwo siphephile noma sehluleka.
6. Umdwebo Womzimba Wamahhala Njengendlela Yokuhlaziya
Ngokomthetho, ukulingana kuvezwa ngokwezibalo zamandla nezikhathi. Kodwa-ke, ngokwendlela yokusebenza, ukuhlaziywa kokulingana cishe njalo kuqala ngomdwebo womzimba okhululekile (i-FBD): umdwebo wento ecatshangelwayo kanye nawo wonke amandla angaphandle asebenza kuyo.
I-DBB icacisa:
– amandla adonsela phansi (mg),
– amandla avamile,
- amandla okungqubuzana,
- amandla okucindezela intambo,
- ukusekela amandla okusabela,
– imithwalo esatshalalisiwe kanye nemithwalo egxilile,
– umzuzu wangaphandle (umbhangqwana).
Uma i-DBB isidaliwe, izilinganiso \(\sum F=0\) kanye \(\sum M=0\) zisetshenziswa ngokuhlelekile. Ngamanye amazwi, i-DBB "iyibhuloho" phakathi kwesimo somzimba kanye nezibalo zezibalo.
7. Izinhlobo Zokulinganisela: Okuzinzile, Okungazinzile, Nokungachemi
Ngaphezu kwezidingo zamandla nomzuzu ongu-zero, ezimweni eziningi (isb. isikhungo sobunzima nezakhiwo), ukulingana nakho kuhlukaniswa ngokwempendulo yomzimba ekuphazamisekeni okuncane:
1. Ukulingana okuzinzile: uma kuphazamiseka kancane, into ivame ukubuyela endaweni yayo yokuqala. Isibonelo: ibhola phansi kwesitsha.
2. Ukulingana okungazinzile: ukuphazamiseka okuncane kubangela into ukuba isuke kude nendawo yayo yokuqala. Isibonelo: ibhola phezu kwegquma.
3. Ukulingana okungathathi hlangothi: ngemva kokuphazamiseka, into ima endaweni yayo entsha ngaphandle kokuthambekela kokubuya noma ukuhamba. Isibonelo: ibhola endaweni eyisicaba.
Lokhu kuhlukaniswa kuhlobene eduze namandla angaba khona kanye nendawo yesikhungo sobunzima. Kubunjiniyela, ukwakheka okuphephile kuvame ukulandela ukulingana okuzinzile.
8. Indima Yesikhungo SeMisa kanye Nomugqa Wesenzo
Isisindo sento sisebenza phakathi nendawo yesisindo. Entweni elele phezu kobuso, indawo yomugqa wesenzo sesisindo maqondana nobuso obusekelayo inquma ukuthambekela kwento ekuweni noma ekuhlaleni izinzile.
Isimiso esisebenzayo: uma nje ukuvela okuqondile kwesikhungo sobunzima kuwela endaweni yokusekela, into cishe ayinakuwiswa. Uma iwiswa, into izokhiqiza umzuzu obangela ukuba iwele. Ngakho-ke, lesi sici sibaluleke kakhulu ekuzinzeni kwezimoto, ekwakhiweni kwemilenze yetafula, ama-crane, kanye nemishini esindayo.
9. Ukulingana Kwezinhlelo Zezinhlayiya Nezinto Eziqinile
Ibhalansi yemishini isebenza ku:
– Izinhlelo zezinhlayiya: zigxila emandleni aphumayo. Ukujikeleza kuvame ukunganakwa uma izinhlayiya zibhekwa njengezici.
– Umzimba oqinile: kumele uhlangabezane nezidingo zokuhumusha nokujikeleza. Yilapho isikhathi samandla siba khona esibalulekile.
Ku-structural statics, into ehlaziywayo ngokuvamile ithathwa njengomzimba oqinile ukuze izilinganiso zokulingana zisetshenziswe ngokucacile ngaphambi kokucabangela ukuguquguquka kwezinto.
Isiphetho
Isisekelo esisemthethweni sokulingana kwemishini sisekelwe emithethweni kaNewton kanye nemibono yamandla aphumelayo kanye nezikhathi eziphumelayo. Ngokomthetho, into iba sekulinganani uma ihlangabezana:
– \(\sum \vec{F} = 0\) (ukulingana kokuhumusha),
– \(\sum \tau = 0\) (ukulingana kokujikeleza).
Ukusetshenziswa kwalesi simiso kwezobunjiniyela kubanzi, kusukela ekubaleni ukusabela kokusekela emisebeni, ekunqumeni ukuzinza kwezinto ngokumelene nokuwa, kuya ekuhlaziyeni amandla angaphakathi ezakhiweni. Ngosizo lwemidwebo yomzimba okhululekile, izimo zokulingana zingasetshenziswa ngokuhlelekile futhi zisebenze njengesisekelo esibalulekile somklamo ophephile, ophumelelayo, nothembekile.
Uma uthanda, ngingangeza isibonelo esilula sokubala (isibonelo, ibhlogo elisekelwe amaphuzu amabili noma iladi elincike odongeni) ukuze umqondo womthetho wokulingana kwemishini uzwakale usebenza kakhulu.
