Movement of jiki a karkashin mataki na nauyi: maanar dabara

Jikin motsi a karkashin nauyi ne a tsakiyar theme a tsauri kimiyyar lissafi. Wannan sashe dogara ne a kan muhimmancin da uku dokokin Newton, ya san ko da talakawa makaranta. Bari mu yi kokarin fahimtar magana sosai, da kuma wani labarin da ya bayyana a cikin daki-daki, kowane misali zai taimake mu mu yi nazarin jiki motsi a karkashin karfi na nauyi kamar yadda amfani.

A kadan tarihi

Daga a tarihi mai nisa, mutane mamaki kallon da daban-daban abubuwan dake faruwa a rayuwarmu. Mutãne na dogon lokaci ba zai iya fahimtar ka'idojin da kuma tsari da dama tsarin, duk da haka, wani dogon hanyar gano a duniya a kusa da jagoranci da kakanninmu da kimiyya da juyin juya halin. A cikin wadannan kwanaki a lokacin da fasahar da aka bunkasa tare da m gudun, mutane kusan ba tunani game da yadda za ta yi aiki da wadannan ko wasu sunadaran.

A halin yanzu, kakanninmu sun ko da yaushe aka sha'awar riddles halitta matakai da tsarin da duniya, neman amsoshin mafi wuya tambayoyi, kuma ba su gushe ba koyi, duk da haka bai sami amsoshi. Alal misali, sanannen masanin kimiyya Galileo Galilei a cikin 16th karni yin tambaya: "Don me bã jiki ko da yaushe fada saukar, abin da yake da karfi janyo hankalin su zuwa ga ƙasa?" A 1589 ya sanya jerin gwaje-gwajen, da sakamakon wanda ya tabbatar da cewa sosai muhimmanci. Ya yi karatu a daki-daki, ga dokokin na free fall na daban-daban jikinsu, amai abubuwa daga cikin shahararrun hasumiya a Pisa. The dokokin, wanda ya jagoranci, sun inganta kuma dabarbari aka bayyana a cikin mafi daki-daki, wani sanannen Birtaniya masanin kimiyya - Sir Isaakom Nyutonom. Wannan ya rike uku na dokar, wanda ta dogara ne a kan kusan dukkan zamani kimiyyar lissafi.

Gaskiyar cewa dokokin na motsi na jikinsu, ya bayyana fiye da shekaru 500 da suka wuce, suna dacewa da ba rana, shi ne cewa wannan duniya tamu shi ne batun guda dokokin. Mutumin zamani dole ne su kasance a kalla sama-sama bincika ka'idodi na tsari na duniya.

Basic Concepts na kuzarin kawo cikas da kuma goyon bayan

Domin cikakken fahimtar ka'idojin da wannan yunkuri, ya kamata ka farko familiarize kanka tare da wasu daga cikin matsalolin. Saboda haka, mafi zama dole msar tambayar sharuddan:

• Hulda - shi ne tasiri na jikuna da juna, a cikin abin da canji yakan faru ko farkon su motsi zumunta da juna. Akwai hudu iri hulda: electromagnetic, da rauni, da karfi da kuma gravitational.
• Speed - wani jiki yawa da ke nuna gudun da wanda jiki motsa. Speed ne vector, watau, yana da ba kawai da darajar amma kuma da shugabanci.
• Hanzari - da yawa wanda ya nuna mana da kudi na canji na gudu na jiki a cikin wani lokaci. Yana kuma shi ne mai vector yawa.
• A yanayin da hanya - a kwana, da kuma wani lokacin - a mike layin cewa delineates jiki a motsi. Tare da wani uniform rectilinear motsi hanya iya daidaita tare da kawar da darajar.
• Path - a hanya tsawon, wato, kamar yadda jiki da aka gudanar domin wani adadin lokaci.
• Inertial reference tsarin - yanayin da kai ne Newton ta farko doka, wato, da jiki kula da lokacinta, da proviso cewa zancen wani waje tsaro.

The sama Concepts isa ga competently zana ko sallama ga shugaban na jiki motsi kwaikwaiyo ƙarƙashin rinjayar nauyi.

Me kuke nufi ƙarfi?

Bari mu matsa zuwa na asali ra'ayi na mu na theme. Saboda haka, da ikon - shi ne darajar, da ma'anar wanda yake shi ne tasiri ko tasiri na jiki daya a kan wani quantitatively. A nauyi - ne da karfi da cewa abubuwa a kan cikakken kowane jiki located a kan ko kusa da surface na duniya tamu. A tambaya shi ne: inda ya aikata wannan ikon? Amsar ta'allaka a cikin dokokin duniya gravitation.

Mene ne nauyi?

A wani jiki ne shafa da gravitational karfi a duniya, wanda ya ba shi wani hanzari. Nauyi ne ko da yaushe a tsaye shugabanci saukar zuwa tsakiyar duniya. A wasu kalmomin, da karfi na nauyi na jan abubuwa zuwa ga Duniya, ke me ya sa abubuwa ko da yaushe fada saukar. Sai dai itace cewa da karfi na nauyi - wannan shi ne na musamman hali na gravitational karfi. Newton ya kawo daya daga cikin manyan dabarbari domin gano an janye karfi tsakanin biyu jikinsu. Ga alama kamar haka: F = G * (m ₁ x m ₂₎ / R ^2.

Mene ne cikin hanzari saboda nauyi?

The jiki, wadda aka saki daga wani tsawo, ko da yaushe tashi saukar karkashin karfi nauyi. Movement of jiki a ƙarƙashin rinjayar nauyi tsaye sama da kasa za a iya bayyana ta lissafai inda asali m zai zama tamanin da hanzari "g". Wannan darajar aka ƙaddara na musamman da karfi na nauyi, da kuma muhimmancinsa ne kamar daidai 9.8 m / s ^2. Sai dai itace cewa jiki yana jefa daga tsawo daga sifili na farko gudu, za ta motsa saukar da darajar da hanzari "g".

Movement of jiki a karkashin mataki na nauyi: da dabara domin warware

Ainihin dabara nauyi binciken ne kamar haka: F _nauyi = m x g, inda m - shi ne taro na jiki a kan abin da karfi ayyukan, da kuma "g" - free fall hanzari (ya rage wuya da ayyuka shi an dauke su, sunã daidaita da 10 m / s ²⁾ .

Akwai da dama dabarbari amfani ga gano wani musamman ba a sani ba tare da free motsi na jiki. Alal misali, domin yin lissafi da hanyar traversed ta jiki, shi wajibi ne don musanya da aka sani da dabi'u a cikin wannan dabara: S = V ₀ x t + wani x t ^2/2 (hanya daidai da Naira Miliyan Xari da kayayyakin na farko gudu ta tara da lokacin da kuma cikin hanzari a lokacin Squared, raba ta 2).

A lissafai for kwatanta tsaye motsi na jiki

Movement of jiki a ƙarƙashin rinjayar nauyi tsaye zuwa lissafi, wanda shi ne kamar haka: x = x ₀ + v ₀ x t + wani x t ^2/2 Amfani da wannan magana, shi ne zai yiwu a sami da lura na jiki a lõkaci sananne. Wajibi ne kawai zuwa musanya wata san matsalar dabi'u: fara wuri, da farko rate (idan jiki ba kawai saki, da kuma tura da wasu da karfi) da hanzari, a cikin wannan harka shi ne daidai da hanzari g.

A wannan hanyar za a iya samu da kuma gudu daga jiki wanda motsa karkashin mataki na nauyi. The magana domin gano da ba a sani ba yawa a kowane lokaci: v = v ₀ + g x t (da farko darajar gudun iya zama daidai a sifili, sa'an nan gudun zai zama daidai da samfurin na gravitational hanzari da darajar lokaci ga wanda jiki ke sa wani motsi).

The motsi na jikinsu karkashin mataki na nauyi: kalubale da kuma mafita

A warware matsaloli da yawa a hade da nauyi, mun bayar da shawarar da wadannan shirin:

1. Ƙayyade wa kansu wani m inertial firam na reference mafi yawa ana yi a zabi Duniya domin shi ya gana da yawa daga cikin bukatun na ISO.
2. Zana a kananan zane ko hoto, wanda ya siffanta da babban sojojin aiki a jiki. Movement of jiki a ƙarƙashin rinjayar nauyi kwakwalwa mai zane ko zane dake nuna shugabanci a da jiki motsa, idan shi abubuwa hanzari daidai g.
3. Sa'an nan zabi shugabanci to Project sojojin da accelerations samu.
4. Record unknown yawa da kuma sanin su shugabanci.
5. A karshe, ta amfani da sama dabara don warware matsaloli, to lissafi duk unknowns yaron da data cikin lissafi domin gano da hanzari da kuma nesa tafiya.

Turnkey bayani sauki aiki

Idan ya zo ga irin wannan sabon abu kamar yadda jiki motsi a karkashin mataki na nauyi, domin sanin yadda za m hanyar warware aiki zai iya zama da wuya. Duk da haka, akwai da dama da dabaru yin amfani da abin da ka iya warware ko da mafi wuya aiki. Saboda haka, za mu bayyana wa rayayyu misalai na yadda za a warware wannan ko da matsala. Bari mu fara da wani sauki gane matsalar.

A jikin saki daga tsawo na 20 m ba tare da wani na farko gudu. Ƙayyade ga yadda da yawa lokaci ya kai gare shi da surface na duniya.

The bayani: mu san hanyar traversed ta jiki, an san cewa na farko gudu ne daidai da 0. Mun kuma iya sanin ko cewa jiki ne kawai da karfi na nauyi Ayyukan Manzanni, shi dai itace cewa wannan yunkuri na jiki a karkashin mataki na nauyi, kuma haka ya kamata ka yi amfani da wannan dabara: S = V ₀ x t + wani x t ^2/2. Tun a cikin yanayin mai = g, sa'an nan bayan da wasu canje da muke samu da wadannan lissafi: S = g x t ² / 2. Yana yanzu ya rage kawai kar lokaci ta hanyar wannan dabara, mun sami cewa t ² = 2s / g. Musanya da aka sani da darajar (a cikin wannan harka ɗauka cewa g = 10 m / s ²⁾ t ² = 2 x 20/10 = 4. Saboda haka, t = 2 s.

Saboda haka mu Amsa: jiki hasarar 2 seconds.

Trick don magance matsalar da sauri, shi ne wadannan: shi za a iya gani cewa jiki motsi da aka bayyana a cikin wadannan matsalar na faruwa a daya shugabanci (vertically downward). Yana da matukar kama da gaba ɗaya kara motsi, tun jiki babu karfi fiye da sauran da karfi na nauyi (na karfi na iska juriya da aka saka manta). Saboda wannan za mu iya amfani da dabara domin gano wani sauki hanya a gaba ɗaya kara motsi, wucewa hotunan zane tsari aiki a jiki sojojin.

An misali na mafi wuya ayyuka

Yanzu bari mu ga yadda mafi kyau ga warware matsalar a jiki motsi da nauyi, idan jiki ba ya motsa tsaye, amma yana da wani hadadden motsi.

Alal misali, na gaba aiki. Wasu abu motsi taro m tare da wani ba a sani ba hanzari saukar da karkata jirgin sama, da coefficient na gogayya ne daidai k. Ƙayyade darajar hanzari, wanda shi ne samuwa a lokacin tashin na jiki a lokacin da karkata kwana α da aka sani.

Magani: Wajibi ne a yi amfani da shirin, wanda aka bayyana a sama. A farko Draw jawo wani karkata jirgin sama tare da jiki image da kuma dukan sojojin aiki a kan ta. Sai dai itace cewa yana da uku aka gyara: da karfi na nauyi, gogayya da bene dauki karfi. Ga alama janar lissafi kamar yadda resultant sojojin: F _gogayya + N + MG = ma.

Babban haskaka daga cikin matsala ne da yanayin karkata kwana α. Lokacin da doguwar sojojin a kan sa axis da Oy axis, wannan yanayin dole ne a ɗauke shi zuwa lissafi, sa'an nan muka samu da wadannan magana: MG x zunubi α - F _gogayya = ma (axis sa) da kuma N - MG x cos α = F _gogayya (ga Oy axis) .

F _gogayya ne sauƙi lasafta ta gano da dabara frictional karfi, shi ne daidai k x MG (coefficient na gogayya yawaita da samfurin na da nauyin da gravitational hanzari). Bayan duk computations kasance kawai musanya da samu dabi'u a cikin dabara, mun samu wani Saukake lissafi ga kirga cikin hanzari zuwa da jiki motsa tare da karkata jirgin sama.