Fomura yeKugumburisa Kwekukurumidza Kwekuroverana
Pengantar
Kufungidzira nepfungwa huru mufizikisi zvakakosha pakunzwisisa zviitiko zvakasiyana-siyana, kunyanya zvine chekuita nekukonana. Muchinyorwa chino, tichakurukura tsananguro, mafomula, uye misimboti ine chekuita nekukanganisa, kumhanya, uye kukonana. Tichatarisawo mienzaniso yekuverenga uye mashandisirwo anoitwa pfungwa idzi.
Tsanangudzo yeKufurirwa uye Kukurumidza
tichimhanya
Momentum (\(p\)) chiyero chehuwandu hwekufamba kwechinhu. Momentum huwandu hwevector hunoenderana nehuremu uye kumhanya kwechinhu. Pamasvomhu, momentum inotsanangurwa se:
\[ p = mv \]
Di mana:
– \( p \) isimba (kg m/s),
– \( m \) huremu hwechinhu (kg),
– \( v \) ndiyo kumhanya kwechinhu (m/s).
Kumhanya kunoratidza kuti zvakaoma sei kumisa chinhu chinofamba. Kana huremu kana kumhanya kwechinhu kuchikura, simba racho rinowedzerawo.
kupomba
Impulse (\(I\)) ishanduko yesimba rinoitwa nesimba rinoshanda pachinhu kwenguva yakati. Impulse inhamba yevector uye inotsanangurwa se:
\[ I = F \Delta t \]
Di mana:
– \( I \) ipfungwa yekufema (N s kana kg m/s),
– \( F \) isimba rinoshanda pachinhu (N),
– \( \Delta t \) inguva iyo simba rinoshanda (s).
Kufungidzira kwakaenzana nekuchinja kwesimba rechinhu:
\[ I = \Delta p = p_f – p_i \]
Di mana:
– \( \Delta p \) ndiko kuchinja kwesimba (kg m/s),
– \( p_f \) ndiyo momentum yekupedzisira (kg m/s),
– \( p_i \) ndiyo momentum yekutanga (kg m/s).
Kubonderana
Kubonderana inyaya yekudyidzana apo zvinhu zviviri kana kupfuura zvinochinjana simba. Kubonderana kunogona kupatsanurwa mumhando mbiri huru: kugongana kwe elastic uye kugongana kwe inelastic.
Kubonderana kweElastic
Mukusangana kwe elastic, simba rese re kinetic re system isati yasangana uye mushure mekusangana rinoramba rakafanana. Izvi zvinoreva kuti hapana simba re kinetic rinorasika sekupisa, ruzha, kana kushanduka kusingaperi. Mitemo yekuchengetedza simba re momentum uye kuchengetedza simba re kinetic inoshanda mukusangana kwe elastic.
Kubonderana kweInelastic
Mukurwisana kusina kusimba, rimwe simba remagetsi rinorasika serimwe simba (semuenzaniso, kupisa, ruzha, kana kushanduka kwezvinhu). Kunyangwe mutemo wekuchengetedza simba remagetsi uchiri kushanda, simba rese remagetsi harina kuchengetedzwa.
Mafomura Akakosha
Kuchengetedza Simba
Mutemo wekuchengetedza simba unotaura kuti simba rese rehurongwa risati rasangana rakaenzana ne simba rese rehurongwa mushure mekusangana, chero bedzi pasina simba rekunze rinoita basa pahurongwa:
\[ m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} \]
Di mana:
– \( m_1 \) uye \( m_2 \) ndiwo mass echinhu 1 nechinhu 2 (kg),
– \( v_{1i} \) uye \( v_{2i} \) ndiwo mamhanyiro ekutanga echinhu 1 nechinhu 2 (m/s),
– \( v_{1f} \) uye \( v_{2f} \) ndiwo mamhanyiro ekupedzisira echinhu 1 nechinhu 2 (m/s).
Kuchengetedzwa kweKinetic Energy (yeElastic Collisions)
Kana paine kuroverana kwe elastic, simba rese re kinetic re system isati yaroverana uye mushure mayo rinoramba rakafanana:
\[ \frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 = \frac{1}{2} m_1 v_{1f}^2 + \frac{1}{2} m_2 v_{2f}^2 \]
Muenzaniso weKuverenga
Ngatitarisei mimwe mienzaniso yekuverenga kuti tinzwisise kuti mafomula aya anoshanda sei mumamiriro ezvinhu chaiwo.
Muenzaniso 1: Kubonderana kweInelastic
Ngatitii mota mbiri, imwe neimwe ine huremu hwe1000 kg, dziri kufamba dzichienda kune imwe neimwe pa10 m/s uye 15 m/s, zvichiteerana. Mushure mekuroverana, mota dzese dziri kufamba pamwe chete nespeed yekupedzisira yakafanana. Tinoda kuona kumhanya kwekupedzisira ikoko.
1. Kufambira mberi kwekutanga kwehurongwa:
\[ p_{total\_initial} = m_1 v_{1i} + m_2 v_{2i} \]
\[ p_{total\_initial} = 1000 \kawa 10 + 1000 \kawa (-15) \]
\[ p_{total\_initial} = 10000 – 15000 \]
\[ p_{total\_initial} = -5000 \, \text{kg m/s} \]
2. Mushure mekuroverana, mota mbiri idzi dzinofamba pamwe chete zvekuti huwandu hwese hwese huve \(m_1 + m_2\), uye kumhanya kwekupedzisira kuri \(v_f\):
\[ p_{total\_final} = (m_1 + m_2) v_f \]
\[ -5000 = (1000 + 1000) v_f \]
\[ -5000 = 2000 v_f \]
\[ v_f = \frac{-5000}{2000} \]
\[ v_f = -2.5 \, \text{m/s} \]
Kumhanya kwekupedzisira kwemotokari dzese mbiri mushure mekuroverana i -2.5 m/s, zvichireva kuti dzinofamba pamwe chete munzira imwe chete nekumhanya kwe2.5 m/s munzira yekutanga yemotokari yechipiri.
Muenzaniso 2: Kubonderana kweElastic
Ngatitii bhora rine huremu hwe2 kg richifamba kurudyi nekumhanya kwe4 m/s rinoroverana nerimwe bhora rine huremu hwe3 kg richifamba kuruboshwe nekumhanya kwe2 m/s. Tinoda kuona kumhanya kwekupedzisira kwemabhora ese ari maviri mushure mekuroverana.
1. Kufambira mberi kwekutanga kwehurongwa:
\[ p_{total\_initial} = m_1 v_{1i} + m_2 v_{2i} \]
\[ p_{total\_initial} = 2 \kawa 4 + 3 \kawa (-2) \]
\[ p_{total\_initial} = 8 – 6 \]
\[ p_{total\_initial} = 2 \, \text{kg m/s} \]
2. Simba rese remagetsi rehurongwa risati rasangana:
\[ KE_{total\_initial} = \frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 \]
\[ KE_{total\_initial} = \frac{1}{2} \times 2 \times 4^2 + \frac{1}{2} \times 3 \times 2^2 \]
\[ KE_{zvakazara\_kutanga} = 16 + 6 \]
\[ KE_{zvose\_kutanga} = 22 \, \zvinyorwa{J} \]
3. Mushure mekusangana, tinofanira kugadzirisa maequation ekuchengetedza emomentum uye kinetic energy panguva imwe chete kuti tiwane velocities yekupedzisira \(v_{1f}\) uye \(v_{2f}\).
\[
\kutanga{zviitiko}
m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} \\
\frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 = \frac{1}{2} m_1 v_{1f}^2 + \frac{1}{2} m_2 v_{2f}^2
\kupera{cases}
\]
Nekutsiva uye kuverenga, tinogona kuwana kumhanya kwekupedzisira kwemabhora ese ari maviri. Mhedzisiro yekupedzisira ndeiyi:
\[ v_{1f} \inenge -2.2 \, \text{m/s} \]
\[ v_{2f} \inenge 3.2 \, \text{m/s} \]
Saka, mushure mekubonderana kwe elastic, bhora rekutanga rinofamba kuruboshwe pa 2.2 m/s, uye bhora rechipiri rinofamba kurudyi pa 3.2 m/s.
Maitiro Anoshanda
1. Mota uye Kuchengetedzeka
Pfungwa dzekukurumidza uye simba rekufamba kwemotokari dzakakosha pakugadzira masisitimu ekuchengetedza mota. Mabhegi emhepo nenzvimbo dzakapwanyika dzakagadzirirwa kuwedzera nguva yekurovera, kuderedza simba rinoshanda pavanhu vari mumotokari, uye kuderedza kukuvara.
2. Mitambo
Mumitambo yakaita senhabvu, bhokisi, uye hockey, kunzwisisa kurudziro uye simba revatambi kunobatsira vatambi kuvandudza mashandiro avo. Semuenzaniso, mubhokisi, kurova kunoshanda kunosanganisira kuwedzera simba rekufambisa nekukurumidza munguva pfupi.
3. Uinjiniya hweZvivakwa uye Dhizaini
Mainjiniya anoshandisa misimboti yekukurumidza uye simba kugadzira zvivakwa zvinogona kutsungirira mitoro inochinja-chinja, senge mabhiriji nezvivakwa zvakakura, uye kuona kuti zvivakwa zvinogara zvakanaka panguva yekurovera kana kuvhunduka.
