Chinyorwa pamusoro pemutemo waNewton wesimba rinokwevera pasi rose
Munyaya yemutemo waNewton, zvakadzidzwa kuti chinhu chega chega chinotanga kuzorora chinova kufamba, kana chero chinhu chinotanga kufamba chinova kuzorora kana paine "chimwe chinhu" chinofamba kana kumisa chinhu. Chimwe chinhu chinonzi "simba". Sei muchero uchidonha kana kufamba uchienda pamusoro penyika mushure mekunge waburitswa kubva padzinde? Mutemo waNewton unoti kana muchero uchifamba, panofanira kunge paine simba rinobata muchero. Simba rinoita kuti muchero kana chero chinhu chiwire pamusoro penyika rinonzi simba rekukwevera pasi.
Dambudziko rezvinhu zvinodonha zvine chekuita nesimba regiravhiti, rauri kudzidza parizvino, rakafungwa nezvaro uye rakadzidzwa naIsaac Newton, nyanzvi yesainzi yekuBritain. Nyaya iyi iyo Newton aifunga kuti yaivepo kubvira kuGreece Yekare. Kune nyaya mbiri huru dzakaongororwa nevaGiriki, kare kare Newton asati aberekwa. Mubvunzo unogara uchibvunzwa ndewekuti sei zvinhu zvichigara zvichidonha pamusoro penyika uye kuti mapuraneti anofamba sei, kusanganisira zuva nemwedzi. VaGiriki panguva iyoyo vaiona kunetseka kwezvinhu zvinodonha nekufamba kwemapuraneti sezvinhu zviviri zvakasiyana. Saka, zvakaramba zvakadaro kusvika panguva yaNewton. Saka, zvakagadzirwa naNewton zvakavakirwa pabasa revanhu vakamutangira. Chinosiyanisa Newton nevanhu vakamutangira ndechekuti Newton akaona kuoma kwezvinhu zvinodonha nekufamba kwemapuraneti zvichikonzerwa nechinhu chimwe chete uye anofanira kuteerera mutemo mumwe chete. Nemamwe mashoko, Newton akataura kuti simba rinoita kuti zvinhu zviwire pamusoro penyika isimba rimwe chete, rinoita kuti mwedzi ufambe-fambe pasi.
Hukama huripo pakati pesimba regiravhiti nedaro nehuremu
Pakuumba mutemo wegiravhiti, Newton akaenzanisa kukurumidza kwemichero inowira pedyo nepasi nekumhanya kwepakati pemwedzi pakutenderera nyika. Sekureva kwaNewton, kukurumidza kunoitika nemuchero unodonha uye kukurumidza kwepakati kunoitika nemwedzi uchitenderera nyika kunokonzerwa nesimba rimwe chete, simba regiravhiti repasi. Newton anoti kukurumidza kwemwedzi paunotenderera nyika kwakaenzana ne1/r2 apo r = chinhambwe chiri pakati penyika nepakati pemwedzi = 3.84 x 10 8 m. Kumhanya kwemichero inodonha kwakaenzana ne1/R 2 , apo R = chinhambwe chiri pakati penyika nepakati pemichero. Muchero uri pedyo nepamusoro penyika zvekuti R = R F , apo R E = radius yenyika = 6.37 x 10 6 m. Saka, kuenzanisa pakati pekumhanya kwemwedzi (a M ) nekumhanya kwemichero (g):
Saka, kukurumidza kwepakati pemwedzi:
a M = (2.75 x 10 -4 )(g) = (2.75 x 10 -4 )(9.8 m/s 2 ) = 2.7 x 10 -3 m/s 2
Newton akaverengawo kumhanyisa kwemwedzi pakati pemwedzi nenzira dzakasiyana. Zvinozivikanwa kuti nguva yekutenderera kwemwedzi kana kuti mwedzi wekuita kutenderera kumwe chete = mazuva 27.3 = 2.36 x 10 masekondi matanhatu . Kureba kwenzira inofambiswa nemwedzi = kutenderera kwekufamba kwemwedzi = 2 (3.14) (r) apo r = chinhambwe chiri pakati pemwedzi nepakati penyika. Kumhanya kwemwedzi pakati pemwedzi:
Kukurumidza kwemwedzi kwakawanikwa mukuverenga uku kwakafanana nemhedzisiro yekuverenga kwakapfuura. Mutemo weChipiri waNewton unoti simba rinoenderana nekumhanya (F = ma). Kuverenga kuri pamusoro apa kunoratidza kuti kukurumidza kwakaenzana ne1/r 2 kana kuti kukurumidza kwakaenzana neskweya yedaro (r 2 ). Saka, zvinogona kugumiswa kuti simba regiravhiti rakaenzana ne1/r 2 kana kuti simba regiravhiti rakaenzana neskweya yedaro. Masvomhu:
Pamusoro pekuferefeta hukama huripo pakati pemasimba ekukwevera pasi uye daro riri pakati pezvinhu, Newton akaferefetawo hukama huripo pakati pemasimba ekukwevera pasi nehuremu hwezvinhu. Mutemo wechitatu waNewton unoti kana paine simba rekuita, pane simba rekuita. Simba rekuita nesimba rekuita zvine hukuru hwakafanana uye divi rakapesana (F-action = -F reaction, chiratidzo chisina kunaka chinoratidza kuti divi resimba rakapesana). Kana simba rekubata pasi richikwevera muchero, simba rekubata pasi remuchero rinokwevera pasiwo. Simba rekubata pasi rinoshanda pamuchero, nepo simba rekubata pasi remuchero richishanda panyika. Saizvozvowo, simba rekubata pakati penyika nemwedzi. Simba rekubata pasi renyika rine simba rekubata remuchero kana simba rekubata pasi rine simba rekubata remwedzi isimba rekuita. Nekuti simba rinoenderana nehuremu (F = ma) uye nekuti simba rekuita nesimba rekuita zvine hukuru hwakafanana, simba regiravhiti riri pakati pezvinhu zviviri rinofanira kuenzana nehuremu hwezvinhu zviviri. Pamasvomhu:
Mutemo waNewton wesimba rinokwevera pasi rose
Mutemo waNewton wegravitation yepasi rose unoti chinhu chega chega chiri muchadenga chinokwezvana, uko kukwezvana pakati pezvinhu kunoenderana nehuremu hwazvo uye kunoenderana neskweya yedaro razvo. Kana zvinhu zviviri zvine huremu hwe m 1 ne m 2 zvikaparadzaniswa nedaro r saka hukuru hwesimba regravitation pakati pezvinhu zviviri ndei:
G = simba rinokwevera pasi (6.673 x 10 -11 Nm 2 / kg 2 ). G inoyerwa nekuyedza.
F12 isimba rinokwevera pasi rinoshandiswa kuna m1 pa m2 ukuwo F21 isimba rinokwevera pasi rinoshandiswa kuna m2 pa m1. F12 anoshanda pa m2 uye anodhonza m2 kuna m1, ukuwo F21 anoshanda pa m1 uye anodhonza m1 kuna m2. F21 uye F12 dzine hukuru hwakafanana uye dzakatarisana negwara rakasiyana. Saka F21 uye F12 mapeya ekuita-kuita. r idaro riri pakati penzvimbo dze m1 uye pakati pe m2Pakati pe m1 iri pakati pechinhu, sezvakaita pakati pe m2Kana r ikanyorwa mu km, zvino inotanga yashandurwa kuita mamita (international system unit).
Dambudziko remuenzaniso 1 (simba regiravhiti riri pakati pezvikamu zviviri)
Verenga simba regiravhiti pakati pevadzidzi vaviri, mumwe nemumwe aine huremu hwe30 kg ne40 kg, uye chinhambwe chemita imwe.
mhinduro
Simba regiravhiti rakakura zvekuti zvinhu zviviri izvi hazvikwezvwane.
Dambudziko remuenzaniso 2 (simba regiravhiti riri pakati pezvikamu zviviri)
Verenga simba rose regiravhiti rinoonekwa ne m2 nekuda kwesimba rinokwevera pasi rinoshandiswa pa m1 pa m2 uye simba rinokwevera pasi rinoshandiswa kuna m3 pa m2Daro riri pakati penzvimbo m1 uye m2 iri mamita maviri uye daro riri pakati penzvimbo m2 uye m3 iri 1m.
Solution:
Simba regiravhiti re m 1 pa m 2 :
Simba regiravhiti re m 3 pa m 2 :
Simba rose regiravhiti rinoonekwa ne m2 :
Fg huwandu = (6.673 – 1.668) x 10 -11 N = 5.005 x 10 -11 N. Mumufananidzo uri pazasi, museve weF 32 wakareba kupfuura museve weF 12. Saka kutungamira kwesimba rose regiravhiti kunoenda ku m 3.
Dambudziko remuenzaniso 3 (simba rose regiravhiti = zero):
Mabhora maviri A naB, rimwe nerimwe rine huremu hwe m ne 5 m. Mabhora ese ari maviri ane dhayamita yakaenzana. Kana simba regiravhiti riri pakati pebhora A nebhora B rakaenzana ne zero, saka daro renzvimbo iyoyo kubva pamusoro pebhora A ndiro …
Solution:
Dhayamita yemabhora A naB imita imwe chete, saka radius yemabhora A naB imita 0.5. Daro riri pakati pepakati pemabhora A naB imita matanhatu.
Tinoisa chinhu chekuedza chine huremu m panzvimbo iri pakati pebhora A nebhora B.
F A = simba rinokwevera pasi rinoshandiswa nebhora A kune chinhu chekuedza (gwara rinokwevera pasi kuenda kubhora A).
F B = simba regiravhiti rinoshandiswa nebhora B kune chinhu chekuedza (gwara regiravhiti rinoenda kubhora B).
Saka kuti simba rinokwevera pasi rinowanikwa nechikamu chebvunzo rive zero, ipapo F A = F B (F A naF B vane mativi akasiyana).
Shandisa fomura yequadratic kuti uone kukosha kwe x
Saka x = 4.88 mamita
4.88 m – 0.5 m = 4.38 m. Simba regiravhiti harisi zero, 4.38 metres kubva pamusoro pebhora A. Ndeipi daro kubva pamusoro pebhora B?
Kuyerwa kwesimba regiravhiti rinogara riripo (G)
Kuti uzive huremu hwemuviri wako, unongoda kumira pachikero wobva waverenga chiyero chehuremu hwemuviri wako. Zviri nyore kuyera huremu hwemuviri wako. Zvakanaka, ungayera sei huremu hwenyika? Hakuna makiro makuru anoshandiswa kuyera huremu hwenyika. Kana pasina chiyero, hatigone kuyera huremu hwenyika tichishandisa makiro aya nekuti nyika inogara ichifamba nguva dzese. Huremu hwenyika hunozivikanwa kuburikidza nekuverenga mushure mekunge giravhiti repasi rose (G) rayerwa nekuyedza.
uremu
Huremu hwechinhu isimba rose rinokwevera zvinhu pasi rinoita basa pachinhu nekuda kwesimba rinokwevera zvinhu pasi rose rinoshandiswa nezvinhu zvese zviri muchadenga pachinhu ichocho. Kana chinhu chacho chiri pamusoro penyika kana pamusoro penyika, saka hatina hanya nesimba rinokwevera zvinhu pasi rinotakurwa nezvimwe zvinhu muchadenga. Funga nezvehuremu hwechinhu sesimba rinokwevera zvinhu pasi rinoita basa pachinhu chacho.
w = huremu hwechinhu, m E = huremu hwenyika, m = huremu hwechinhu, R E = nharaunda yenyika.
Kana chinhu chiri pamusoro penyika (zvinhu zviri pamusoro pehurefu hwakati sa plane, semuenzaniso) kana zvinhu zvakakamurwa r pamusoro penyika apo r = R E + h,
ipapo simba rinokwevera zvinhu pasi rinoshanda pachinhu kana huremu hwechinhu chacho nderinotevera:
Iyi equation inoratidza kuti huremu hwechinhu hunoderera kusvika pa square yedaro kubva pakati penyika. Saka kure nepamusoro penyika, huremu hwezvinhu hunoderera.
Kukurumidza kwegiravhiti
Zvichibva pamutemo wechipiri waNewton, tinoziva kuti huremu hwechinhu isimba rinoita kuti chinhu chiwedzere kudonha (gravitational acceleration):
w = mg
Sanganisa ma equation ese ari maviri w = F g uye w = mg :
Iyi equation inotsanangura kukurumidza kwegiravhiti kunoitika kune chinhu chiri pakakwirira pamusoro penyika. Kuburikidza ne equation iyi, zvinozivikanwa kuti kukurumidza kwegiravhiti kunoderera nekuwedzera kwekukwirira uye hazvitsamiri pahuwandu hwezvinhu zvinodonha zvakasununguka.
Kukurumidza kwesimba rinokwevera zvinhu zviri pamusoro penyika kana pamusoro penyika:
Huremu hwenyika hunogona kuverengwa nekushandura equation iri pamusoro apa kuita:
Verenga huremu hwenyika uchishandisa equation iyi!
Matambudziko uye Kugadziriswa
1. Zvinhu zviviri m 1 uye m 2 chimwe nechimwe chine huremu hwe6 kg uye 9 kg zvakaparadzaniswa nedaro re5 cm. Chinhu m 3 = 1 kg chinoiswa pakati pezviviri. Kana simba rekukwevera rakawanikwa na m 3 = 0 saka daro m 3 kubva m 1 ndiro …
Simba regiravhiti = 0 kana F 13 = F 23.
a = -1, b = -20, c = 50
Shandisa fomura yequadratic:
Mhedzisiro yacho haifanirwe kuva negative. Saka x = r 13 = daro m 3 uye m 1 = 2.25 cm.
2. Zvinhu zviviri A naB zvakaparadzana ne60 cm. Huremu A hunosvika 24 kg uye huremu B hunosvika 10 kg. Nzvimbo yenzvimbo ine simba guru regiravhiti yakaenzana ne zero iri kupi?
Munda wegiravhiti = 0 kana g A = g B.
kuti = 7
b = -1440
c = 43200
Shandisa fomura yequadratic:
x = r A = 169.25 cm kana
x = r A = 36.46 cm
