Muenzaniso wemubvunzo wekukurukurirana pamusoro pekuwedzera kumhanya
Kumhanya-mhanya ipfungwa huru mufizikisi, kunyanya mu kinematics, bazi refizikisi rinoongorora kufamba kwezvinhu pasina kufunga nezvechikonzero chekufamba ikoko. Pfungwa iyi inokosha kwete chete muzvidzidzo asiwo mumashandisirwo ezuva nezuva akadai seinjiniya, mitambo, uye kutakura. Chinyorwa chino chichakurukura mienzaniso yakati wandei yezvinetso zvine chekuita nekumhanya-mhanya, yakazara netsananguro nhanho nhanho dzekubatsira kunzwisisa.
Pfungwa Yekutanga Yekuwedzera Kukurumidza
Tisati tapinda mumibvunzo yemuenzaniso, zvingava zvakanaka kuti tirangarire pfungwa huru maererano nekumhanya uye kumhanyisa.
1. Kumhanya (v) kunotsanangurwa sekuchinja kwenzvimbo panguva imwe neimwe.
2. Kukurumidza (a) huwandu hunoratidza shanduko yekumhanya pachikamu chimwe nechimwe chenguva.
Nzira huru yekukurumidzira ndeye:
\[ a = \frac{\Delta v}{\Delta t} \]
Dimana:
– \( a \) ndiko kukurumidza,
– \( \Delta v \) ndiko kuchinja kwespeed,
– \( \Delta t \) ndiyo nguva inotsamira.
Muenzaniso Mubvunzo 1
Mubvunzo:
Mota inotanga kufamba nekumhanya kwe10 m/s. Mushure memasekonzi mashanu, kumhanya kwemota kunosvika 20 m/s. Avhareji yekumhanya kwemota ndeyei?
Kukurukurirana:
Zvinozivikanwa:
– Kumhanya kwekutanga (\( v_0 \)) = 10 m/s,
– Kumhanya kwekupedzisira (\( v_f \)) = 20 m/s,
– Nguva (\( \Delta t \)) = masekondi mashanu.
Tinogona kushandisa fomura yekukurumidzira:
\[ a = \frac{v_f – v_0}{\Delta t} \]
Tsiva tsika dzinozivikanwa:
\[ a = \frac{20 – 10}{5} \]
\[ a = \frac{10}{5} \]
\[ a = 2 \, \text{m/s}^2 \]
Saka, avhareji yekumhanyisa mota ndeye 2 m/s².
Muenzaniso Mubvunzo 2
Mubvunzo:
Chitima chinotanga kubva pakuzorora uye chinosvika kumhanya kwe30 m/s mumasekonzi gumi. Verenga avhareji yekumhanya kwacho uye daro rakafambwa panguva iyoyo.
Kukurukurirana:
Kukurumidzisa:
Zvinozivikanwa:
– Kumhanya kwekutanga (\( v_0 \)) = 0 m/s (nekuti kunotangira kubva pamamiriro asina kumira),
– Kumhanya kwekupedzisira (\( v_f \)) = 30 m/s,
– Nguva (\( \Delta t \)) = masekondi mashanu.
Kushandisa fomura yekukurumidzira:
\[ a = \frac{v_f – v_0}{\Delta t} = \frac{30 – 0}{10} = 3 \, \text{m/s}^2 \]
Kufamba kure:
Kuti tiverenge daro (\( s \)) rakafambwa, tinogona kushandisa imwe ye kinematic equations:
\[ s = v_0 t + \frac{1}{2} pa^2 \]
Tsiva tsika dzinozivikanwa:
\[ s = 0 \cdot 10 + \frac{1}{2} \cdot 3 \cdot (10)^2 \]
\[ s = \frac{1}{2} \cdot 3 \cdot 100 \]
\[ s = 150 \, \text{m} \]
Saka, daro rinofambwa nechitima i150 metres.
Muenzaniso Mubvunzo 3
Mubvunzo:
Mudhudhudhu wakamira panzvimbo imwe wotanga kufamba nekumhanya-mhanya kwe4 m/s². Mushure mekufamba kwemasekonzi masere, kumhanya kwekupedzisira uye daro rinofambwa nemudhudhudhu chii?
Kukurukurirana:
Kumhanya kwekupedzisira:
Zvinozivikanwa:
– Kumhanya kwekutanga (\( v_0 \)) = 0 m/s (nekuti kunotangira kubva pamamiriro asina kumira),
– Kukurumidza (\( a \)) = 4 m/s²,
– Nguva (\( t \)) = 8 s.
Kushandisa fomura yekumhanya:
\[ v_f = v_0 + pa \]
Tsiva tsika dzinozivikanwa:
\[ v_f = 0 + 4 \cdot 8 \]
\[ v_f = 32 \, \text{m/s} \]
Kufamba kure:
Uchishandisa fomura yekureba:
\[ s = v_0 t + \frac{1}{2} pa^2 \]
Tsiva tsika dzinozivikanwa:
\[ s = 0 \cdot 8 + \frac{1}{2} \cdot 4 \cdot (8)^2 \]
\[ s = \frac{1}{2} \cdot 4 \cdot 64 \]
\[ s = 128 \, \text{m} \]
Saka, mushure mekufamba kwemasekonzi masere, kumhanya kwekupedzisira kwemudhudhudhu i32 m/s uye daro rawafamba i128 metres.
Muenzaniso Mubvunzo 4
Mubvunzo:
Bhora rinokandwa rakamira kumusoro nekumhanya kwekutanga kwe20 m/s. Kana rasvika panzvimbo yaro yepamusoro, bhora rinodzokera pasi nekumhanya nekuda kwesimba rinokwevera pasi \( g = 9.8 \, \text{m/s}^2 \). Zvinotora nguva yakareba sei kuti bhora risvike pasi zvakare?
Kukurukurirana:
Nguva inotorwa kuti munhu akwire nekudzika yakafanana. Saka tinongoda kuverenga nguva inotorwa kuti munhu akwire, tobva tawedzera kaviri kuti tiwane nguva yese.
Zvinozivikanwa:
– Kumhanya kwekutanga (\( v_0 \)) = 20 m/s,
– Kumhanya pakakwirira (\( v_f \)) = 0 m/s (nekuti inomira kwechinguva),
– Kukurumidza kukwira nekuda kwegiravhiti (\(g \)) = 9.8 m/s².
Kushandisa fomura yekumhanya:
\[ v_f = v_0 + (-g) t \]
Tsiva tsika dzinozivikanwa:
\[0 = 20 – 9.8 t \]
\[ 9.8 t = 20 \]
\[t = \frac{20}{9.8} \]
\[ t \inenge 2.04 \, \text{s} \]
Ino ndiyo nguva yekuti bhora risvike pakakwirira. Saka, nguva yese yekukwira nekudonha ndeiyi:
\[ 2 \cdot 2.04 \inenge 4.08 \, \text{s} \]
Saka, nguva yose inotorwa kuti bhora risvike pasi zvakare imasekondi angangoita 4.08.
Mhedziso
Mumatambudziko ese ataurwa pamusoro apa, danho guru nderekunzwisisa pfungwa huru dzekumhanya nekukurumidzisa uye kuti dzinoshandiswa sei mumafomula chaiwo. Kunyangwe matambudziko acho akasiyana, nzira yacho inotevedzera misimboti yefizikisi. Zvinotarisirwa kuti nekudzidzira matambudziko aya, vadzidzi vachawana kunzwisisa kwakadzama kwekuti kumhanya nekukurumidzisa zvinobatana sei mukufamba kwezvinhu.
Ehe, mukushandiswa kwezuva nezuva, kunzwisisa pfungwa iyi kunogona kubatsira zvikuru, kwete chete muzvidzidzo asiwo mumabasa akasiyana-siyana ehunyanzvi akadai seinjiniya, kutakura, nedzimwewo. Gara uchiyeuka kutanga wanzwisisa dambudziko, usati waedza kurigadzirisa, kuitira kuti nzira yekunzwisisa nekugadzirisa dambudziko ive nyore uye inobudirira.
