Kugundana kwa Linear Momentum Impulse

1. Kuthamanga kwa Mzere

1.1 Tanthauzo la Linear Momentum

Mphamvu yolunjika ya chinthu imafotokozedwa ngati zotsatira za kuchulukitsa kulemera kwa chinthucho ndi liwiro la chinthucho.

p = mv

kumene:

p = mphamvu, m = kulemera (kg), v = liwiro (m/s)

Linear momentum, kapena momentum chabe, ndi kuchuluka kwa vector chifukwa kumachokera pochulukitsa vector (velocity) ndi scalar (mass). Popeza momentum ndi kuchuluka kwa vector, imakhala ndi malangizo ndi kukula. Momentum imagawana malangizo ndi liwiro kapena kuyenda kwa chinthu.

Mphamvu yake imayenderana ndi kulemera ndi liwiro chifukwa kulemera kwake kukakhala kwakukulu, mphamvu yake imakulirakulira. Mofananamo, liwiro lake likakhala lalikulu, mphamvu yake imakulirakulira. Tiyerekeze kuti pali magalimoto awiri, tinene magalimoto A ndi B. Ngati kulemera kwa galimoto A kuli kwakukulu kuposa galimoto B ndipo magalimoto onse awiri akuyenda mofulumira, galimoto A idzakhala ndi mphamvu yokulira kuposa ya galimoto B. Mofananamo, ngati magalimoto A ndi B ali ndi kulemera komweko, koma galimoto A imayenda mofulumira kuposa galimoto B, mphamvu ya galimoto A ndi yayikulu kuposa ya galimoto B.

Ngati chinthu chomwe chili ndi kulemera sichikuyenda kapena chili pampando (chili ndi liwiro losapitirira zero), mphamvu ya chinthucho ndi zero.

Chigawo cha SI cha mphamvu ndi kg m/s, chomwe chimapangidwa ndi gawo la kulemera ndi gawo la liwiro.

1.2 Lamulo Lachiwiri la Newton

M'mbuyomu, mwaphunzira Lamulo Lachiwiri la Newton lomwe lafotokozedwa mu equation ΣF = ma ndipo limafotokoza ubale pakati pa mphamvu ya neti ndi kulemera komanso kuthamanga kwa chinthu. Mphamvu ya neti imagwira ntchito pa chinthu chomwe chili ndi kulemera komwe kumapangitsa kuti chinthucho chifulumire. Nthawi ino, muyenera kudziwitsidwa za mtundu wina wa Lamulo Lachiwiri la Newton, lomwe limafotokoza ubale pakati pa mphamvu ya neti ndi kusintha kwa mphamvu ya chinthu.

Ngati mphamvu ya neti ikugwira ntchito pa chinthu chomwe poyamba chili pamalo opumulira, chinthucho chidzasuntha. Chinthucho chisanasunthe, sichikhala ndi mphamvu. Chinthucho chimakhala ndi mphamvu pambuyo poti chasunthidwa. Mwanjira ina, mphamvu ya neti yomwe ikugwira ntchito pa chinthucho imayambitsa kusintha kwa mphamvu ya chinthucho kwa nthawi inayake. Kuchuluka kwa kusintha kwa mphamvu ya chinthucho ndi kofanana ndi mphamvu ya neti yomwe ikugwira ntchito pa chinthucho.

Kugwedezeka, Kuthamanga Kwambiri, Kugundana 1 Kumene:

ΣF = mphamvu yonse (Newton), Δt = nthawi yopuma (yachiwiri), Δp = m (v _t – vo _o ) = kusintha kwa mphamvu (kg m/s).

Equation 1.1 ndi mtundu wina wa Lamulo Lachiwiri la Newton, lomwe limafotokoza ubale pakati pa mphamvu yeniyeni ndi kuchuluka kwa kusintha kwa mphamvu ya chinthu, kaya pamene kulemera kwa chinthucho kuli kosasintha kapena kusintha.

Kugwedezeka, Kuthamanga Kwambiri, Kugundana 2
Kumene:

ΣF = mphamvu yonse (Newton), m = kulemera (kg), a = kufulumira (m/s ² )

Equation 1.2 ndi equation ya Newton's Second Law yomwe imafotokoza ubale womwe ulipo pakati pa mphamvu ya neti ndi kufulumira kwa chinthu chokhala ndi kulemera kosasintha.

2. Chidwi

2.1 Tanthauzo la Impulse

Kukakamiza kumatanthauzidwa ngati zotsatira za kuchulukitsa mphamvu kapena mphamvu yeniyeni ndi nthawi.

Kumene:

I = chikoka, ΣF = mphamvu yeniyeni (Newton), Δt = nthawi yopuma (yachiwiri).

2.2 Chiphunzitso cha Impulse-Momentum

Chiphunzitso cha mphamvu ya kusinthasintha chimapezeka potengera equation kuchokera ku equation 1.1

ΣF Δt = Δp

I = Δp ……………………….. Chiyerekezo 1.3

Chiyerekezo 1.3 chikuwonetsa kuti kusinthasintha kwa mphamvu (implicity) ndikofanana ndi kusintha kwa mphamvu (momentum).

I = ΣF Δt

Δp = mv _t – mv _o = m (v _t – v _o )

Chitsanzo cha funso 1:

Mpira wolemera makilogalamu 1 umaponyedwa mopingasa pa liwiro la 2 m/s. Kenako, mpirawo umamenyedwa mbali imodzi ndi mbali yoyambirira. Mpirawo umatenga 1 ms kuti ugwirizane ndi womenya, ndipo liwiro la mpirawo akachoka pa womenya ndi 4 m/s. Kodi mphamvu yomwe womenyayo amagwiritsa ntchito pa mpirawo ndi yotani?

Zodziwika:

kulemera (m) = 1 kg, Liwiro loyambirira (v _o ) = 2 m/s, nthawi yopuma (Δt) = 1 x 10 ^-3 seconds, liwiro lomaliza (v _t ) = 4 m/s

Kayendedwe ka mpira sikasintha, kotero liwiro loyamba ndi liwiro lomaliza zimakhala ndi chizindikiro chomwecho.

Akufuna: mphamvu (F)

Yankho:

Kugwedezeka, Kuthamanga Kwambiri, Kugundana 4

Chitsanzo cha funso 2:

Mpira wolemera makilogalamu 1 umaponyedwa mopingasa kumanja pa liwiro la 10 m/s. Ukagundidwa, mpirawo umapita kumanzere pa liwiro la 20 m/s. Dziwani kuti mphamvu ikugwira ntchito pa mpirawo.

Zodziwika:

kulemera (m) = 1 kg

Liwiro loyambirira (v _o ) = 10 m/s,

Liwiro lomaliza (v _t ) = -20 m/s

Mayendedwe a mpira (mayendedwe a liwiro) ndi osiyana, kotero liwiro loyamba ndi liwiro lomaliza zimakhala ndi zizindikiro zosiyana.

Akufuna: Kusakhazikika (I)

Yankho:

I = m (v _t – vo _o ) = 1 kg (-20 m/s – 10 m/s) = 1 kg (-30 m/s) = – 30 kg m/s

Chizindikiro choyipa chimasonyeza kuti komwe kumayambira ndi komwe kuli liwiro lomaliza la mpira (kumanzere)

Chitsanzo cha funso 3

Wophunzira wagunda volleyball yolemera makilogalamu 0.1 yomwe poyamba imakhala itapumula. Dzanja la wophunzirayo lagunda volleyball kwa masekondi 0.01. Volleyball ikagundidwa, imayenda pa liwiro la 2 m/s.

(a) Kodi mphamvu zomwe wophunzira amagwiritsa ntchito pa mpira wa volleyball ndi zingati?

(b) Lamulo Lachitatu la Newton limati ngati wophunzira agwiritsa ntchito mphamvu pa volleyball, volleyball imagwiritsanso ntchito mphamvu pa wophunzirayo. Kodi mphamvu yomwe volleyball imagwiritsira ntchito m'manja mwa wophunzirayo ndi yaikulu bwanji?

(c) Ngati dzanja la wophunzira likhudza mpira wa volleyball kwa masekondi 0.001, kodi mphamvu ya mpira wa volleyball yomwe imagwiritsa ntchito pa dzanja la wophunzirayo ndi yaikulu bwanji?

Zodziwika:

kulemera (m) = 0.1 kg,

Nthawi yopuma 1 (Δt ₁ ) = 0.01 s = 1 x 10 ^-2 s

Liwiro loyambirira (v _o ) = 0

Liwiro lomaliza (v _t ) = 2 m/s

Nthawi yopuma 2 (Δt ₂ ) = 0.001 s = 1 x 10 ^-3 s

Akufuna: mphamvu (F)

Yankho:

(a) Mphamvu yomwe dzanja la wophunzira limagwiritsa ntchito pa volleyball kwa nthawi yokhudza ya masekondi 0.01 ndi

(b) Mphamvu yomwe volebo imaperekedwa m'manja mwa wophunzira kwa nthawi yokhudza ya masekondi 0.01 ndi

Lamulo Lachitatu la Newton: F action = – F reaction

Kukula kwa mphamvu yomwe mpira umapatsa m'manja mwa wophunzira ndi 200 N

Kutengera ndi zotsatira zomwe zapezeka, zitha kutsimikizika kuti mphamvu yomwe mpira umagwiritsa ntchito pa dzanja la wophunzira imakhala yayikulu pamene nthawi yolumikizirana ndi yochepa. Mphamvu yayikulu imayambitsa ululu waukulu pa dzanja la wophunzira. Mutha kutsimikizira izi mukamasewera volleyball. Nthawi yolumikizirana yomwe mungatenge mukamenya volleyball yolimba ndi yochepa kuposa mukamenya yofewa. Kusiyana kwa nthawi yolumikizirana kumapangitsa dzanja lanu kumva ululu waukulu mukamenya mpira wolimba.

Kodi mphamvu yolunjika ndi chiyani, ndipo imasiyana bwanji ndi mphamvu?
- yankho: Mphamvu yolunjika ( $p$ ) cha chinthu ndi chipatso cha kulemera kwake ( $m$ ) ndi liwiro lake ( $v$ ), ie, $p = m v$ Ngakhale kuti mphamvu imakhudzana ndi kusintha kwa mphamvu ya chinthu ndi nthawi, mphamvu yokha ndi muyeso wa kayendedwe ka chinthu ndi komwe chikupita.
Kodi kusinthasintha kwa mphamvu ya chinthu kumakhudzana bwanji ndi kusintha kwa mphamvu ya chinthu?
- yankho: Impulse ndi zotsatira za mphamvu yapakati yomwe imagwiritsidwa ntchito pa chinthu ndi nthawi yomwe imagwiritsidwa ntchito. Ndi yofanana ndi kusintha kwa mphamvu ya chinthucho. Mwa masamu: I $m p u l se = Δ p = F_{a v er a g e} \times Δ t$ .
Kodi kusunga mphamvu kumatanthauza chiyani pa kugundana?
- yankho: Kusunga mphamvu kumati mphamvu yonse ya dongosolo lotsekedwa isanachitike kugundana ndi yofanana ndi mphamvu yonse ya dongosolo pambuyo pa kugundana, bola ngati palibe mphamvu zakunja zomwe zimachita pa dongosololi.
Kusiyanitsa pakati pa kugundana kwa elastic ndi inelastic.
- yankho: Mu kugundana kosalala, mphamvu ya mphamvu ya mphamvu ndi mphamvu ya ...
Kodi zingatheke bwanji kuti mphamvu yaying'ono yomwe ikugwira ntchito kwa nthawi yayitali ipange kusintha komweko kwa mphamvu yayikulu yomwe ikugwira ntchito kwa nthawi yochepa?
- yankho: Popeza mphamvu ndi zotsatira za mphamvu ndi nthawi, mphamvu yaying'ono yomwe imagwira ntchito kwa nthawi yayitali imatha kupanga mphamvu yomweyo (ndipo motero kusintha komweko kwa mphamvu) monga mphamvu yayikulu yomwe imagwira ntchito kwa nthawi yochepa.
Ngati galimoto yagunda khoma n’kuima, kodi mphamvu yake imasungidwa?
- yankho: Kwa galimoto yokha, mphamvu siisungidwa chifukwa imaima. Komabe, mu dongosolo lonse (kuphatikizapo Dziko Lapansi ndi khoma), mphamvu imasungidwa. Mphamvu yomwe imaperekedwa ku galimoto imaperekedwa mofanana komanso mosiyana ndi Dziko Lapansi ndi khoma, koma chifukwa cha kusiyana kwakukulu kwa kulemera, kusintha kwa liwiro la Dziko Lapansi ndi kochepa kwambiri.
N’chifukwa chiyani ma airbag m’magalimoto amathandiza kuchepetsa kuvulala panthawi ya ngozi?
- yankhoMa airbags amawonjezera nthawi yomwe mphamvu ya munthu imasinthasintha akaima, zomwe zimachepetsa mphamvu yapakati panthawi ya ngozi. Kuchepa kwa mphamvu kumeneku kumathandiza kuchepetsa kuvulala.
Ngati zinthu ziwiri zokhala ndi kulemera komweko zili ndi liwiro losiyana la kukula kofanana ndipo zimagundana maso ndi maso, kodi liwiro lawo lonse lidzakhala lotani pambuyo pa kugundanako?
- yankho: Ngati kugundana kosalala komanso popanda mphamvu zakunja, zinthuzo zidzabwerera m'mbuyo ndi liwiro lomwelo koma mosiyana. Ngati kugundanako kuli kosalimba, zidzagwirizana ndipo zidzaima chifukwa nthawi yawo idzasokonezana.
N’chifukwa chiyani mipira yodumphadumpha imasiya ngakhale itakhala mu vacuum (yopanda kukana mpweya)?
- yankhoNgakhale kuti vacuum imachotsa kukana kwa mpweya, siiletsa mpirawo kugundana ndi nthaka. Nthawi iliyonse mpirawo ukagunda, mphamvu zina za kinetic zimasinthidwa kukhala mitundu ina (monga mphamvu ya phokoso kapena kusintha), zomwe zimapangitsa mpirawo kudumphadumpha pang'onopang'ono ndi kudumpha kotsatizana mpaka utasiya.
Kodi mphamvu ya zinthu ingathe bwanji “kubisika” m’machitidwe, monga zinthu zozungulira?

yankho: Ngakhale kuti mphamvu yolunjika imasunga kayendedwe ka zinthu molunjika, zinthu zozungulira zimakhala ndi mphamvu yozungulira. Chinthu chingakhale ndi mphamvu yolunjika koma mphamvu yozungulira yofunika ngati chikuzungulira. Mwachitsanzo, pamwamba pozungulira patebulo sipakhala mphamvu yozungulira koma imakhala ndi mphamvu yozungulira chifukwa cha kuzungulira kwake.