Chinyorwa pamusoro pekufamba kweFree fall
Muhupenyu hwezuva nezuva, tinowanzoona zvinhu zvinofamba-famba nemuchero uchidonha kubva pamuti, kufamba kwezvinhu zvinodonha kana kudonha kubva pakakwirira. Sei zvinhu zvichifamba-famba nemuchero uchidonha? Kana zvikaonekwa pakareko, chinhu chinowira nekudonha sekunge chine kumhanya kwakatarwa, kana kuti nemamwe mazwi chinhu hachikurumidzi. Chokwadi chekuti zvinoitika, chinhu chega chega chinowira chinowana kukurumidza nguva dzose. Chikonzero ichi chinokonzera kufamba-famba kwemuchero uchidonha, kusanganisira muenzaniso wekufamba kusingaenzaniswi kwemutsetse. Ungaratidza sei kuti zvinhu zvinowira nekudonha zvichiwana kukurumidza nguva dzose kana kuti kumhanya kwacho kunowedzera?
Batanidza zvipikiri zviviri pasi wodonhedza dombo kubva pakukwirira kwakasiyana pachipikiri chimwe nechimwe. Uchaona kuti zvipikiri zvinoiswa pamatombo padanho repamusoro zvakanamira zvakadzika kupfuura zvimwe zvipikiri. Kana dombo rakakwirira kubva pamusoro pevhu, kumhanya kwedombo parinorova pasi kunoita kuti rinyanye kudzvanya chipikiri zvakadzika.
Kare, kufamba kwezvinhu zvichidonha pasi kwaive nyaya inonakidza zvikuru muhuzivi hwechisikigo. Aristotle, muzivi, akamboti chinhu chine huremu hwakakura chinodonha nekukurumidza kupfuura zvinhu zvakareruka. Maonero aAristotle akapesvedzera maonero evanhu vakararama Galileo asati asvika, avo vaifunga kuti zvinhu zvine huremu hwakakura zvinodonha nekukurumidza kupfuura zvinhu zvakareruka uye kuti kumhanya kwezvinhu zvinodonha kwaienderana nehuremu hwechinhu chacho. Pamwe tisati tadzidza nyaya iyi, munofungawo saizvozvo. Semuenzaniso, tinodonhedza bepa nedombo kubva pakukwirira kwakafanana. Mhedzisiro yatakaona yakaratidza kuti dombo rinotanga rabata pasi kana pamusoro pepasi kupfuura bepa. Zvino, ngatidonhedzei matombo maviri kubva pakukwirira kwakafanana, uko rimwe dombo rakakura kupfuura rimwe. Matombo maviri aya akabata pamusoro pevhu panguva imwe chete, zvichienzaniswa nedombo nebepa ratakadonhedza kare. Tinogonawo kuedza kudonhedza matombo nebepa muchimiro chezvimedu.
Chii chinopesvedzera kufamba kwematombo kana bepa rinodonha? Simba rekukweshana kwemhepo! Kudzivirirwa kwemhepo kana kukweshana kunokanganisa zvikuru kufamba kwefree-fall. Galileo akataura kuti zvinhu zvese zvichadonha nekukurumidzisa kwakafanana kana pasina mhepo kana zvimwe zvipingamupinyi. Galileo akataura kuti zvinhu zvese, zvinorema kana zvakareruka, zvinodonha nekukurumidzisa kwakafanana, zvirinani kana pasina mhepo. Galileo aitenda kuti mhepo inoshanda sechipingamupinyi kune zvinhu zvakapfava zvakanyanya zvine pamusoro wakakura. Asi mune akawanda mamiriro ezvinhu, kudzivirira uku kwemhepo kunogona kufuratirwa. Mukamuri umo mhepo yakasvetwa (vacuum), zvinhu zvakapfava zvakaita sepepa rakabatwa rakatwasuka zvichadonha nekukurumidzisa kwakafanana nezvimwe zvinhu. Mupiro waGalileo mukunzwisisa kwedu kufamba kwezvinhu zvinodonha unogona kupfupikiswa seizvi:
Panzvimbo chaiyo panyika uye isina mhepo inodzivisa, zvinhu zvese zvinowira nekumhanya kwakafanana. Tinodaidza kukurumidza uku kunokonzerwa negiravhiti uye tinokupa chiratidzo che g. Kukura kwe g kunenge 9.8 m/s 2 . Mumayuniti eSystem eChirungu, kukura kwe g kunenge 32 ft/s 2 . Kutungamira kwekumhanya kwegiravhiti kuri pakati penyika.
Tsananguro yekufamba kwemahara kwekuwa
Chinhu chinonzi chinowira pasi kana chinhu chikafamba chakatwasuka pakati penyika uye panguva yekufamba kwacho, chinhu chacho chinowira pasi nguva dzose. Kana chikawira pasi pedyo nepasi, chinhu chacho chinowira pasi nguva dzose ne9.8 m/s 2
uye gwara rekumhanya kwegiravhiti kuenda pakati penyika (rakatarisana nepamusoro penyika). Kuti zvive nyore kuverenga, g i10 m/s 2.
Kune mamiriro matatu akasiyana:
1. Zvinhu zvinofamba zvakadzika pasi zvisina kumhanya kwekutanga (hapana vo o ). Semuenzaniso, muchero unodonha kubva pamuti mushure mekusunungurwa kubva padzinde. Nzira yekufamba inogara iri pasi uye chinhu chinosangana nekukurumidzira zvekuti g inogara iri yakanaka. Mune mamwe mabhuku efizikisi anonzi kufamba kwefree-fall.
2. Chinhu chinofamba chakamira pasi nekumhanya kwekutanga (pane vo o ). Semuenzaniso, dombo rinokandwa rakadzika pasi. Nzira yekufamba inogara iri pasi uye chinhu chinosangana nekukurumidzira zvekuti g inogara iri positive. Mune mamwe mabhuku efizikisi, inonzi kufamba kwakamira pasi.
3. Chinhu chinokwira chakamira kumusoro nekumhanya kwekutanga, mushure mekusvika pakukwirira kwakanyanya, chinhu chinodzokera pasi. Ngatitii unokanda mabhora akamira kumusoro woabata zvakare kana mabhora akadzika. Paunenge uchikwira kumusoro, zvinhu zvinowana kudzikira kwedanho (negative g), kana uchidzika pasi chakamira, chinhu chinokurumidzisa (positive g). Mune mamwe mabhuku efizikisi, chinonzi kufamba kwakamira kumusoro. Zvinofanira kucherechedzwa kuti kana chinhu chikasangana nechimwe chezvinhu zvitatu zviri pamusoro apa, chinhu chinonzi chinoita kufamba kwefree-fall.
Kuenzanisa kwekufamba kwemahara kwekuwa
Kufamba kweFree-fall muenzaniso wekufamba kwemutsetse kusingaenzaniswi, saka equation yekufamba kweFree-fall yakafanana ne equation yekufamba kwemutsetse kusingaenzaniswi uye yakagadziriswa zvinoenderana nemamiriro ekufamba kweFree-Fall.
h = kureba (mita), v o = kumhanya kwekutanga (mita/sekondi), v t = kumhanya kwekupedzisira (mita/sekondi), t = nguva (yechipiri), g = kukurumidza kwegiravhiti (mita/sekondi) = 9.8 m/s 2 kana 10 m/s 2.
Kukurumidza kwegiravhiti kunogara kuri pa10 m/s 2 (g yakanaka, chinhu chinofamba pasi) zvinoreva kuti kumhanya kwechinhu kunowedzera ne10 m/s sekondi imwe neimwe. Masekondi maviri gare gare, kumhanya kwechinhu kunowedzera ne20 m/s. Masekondi matatu gare gare, kumhanya kwechinhu kunowedzera ne30 m/s. Kudzika kwegiravhiti nguva dzose kuri 10 m/s 2 (g negative, chinhu chinofamba kumusoro) zvinoreva kuti kumhanya kwechinhu kunoderera ne10 m/s sekondi imwe neimwe. Masekondi maviri gare gare, kumhanya kwechinhu kunoderera ne20 m/s. Masekondi matatu gare gare, kumhanya kwechinhu kunoderera ne30 m/s. Kumhanya kwenguva dzose kana kudzikira nguva dzose kunoitika chete pedyo nepamusoro penyika.
Dambudziko remuenzaniso 1:
Mango inoburitswa yowira pasi. Kana nzvimbo yekutanga iri mamita gumi kubva pamusoro pevhu uye huremu hwemango huri magiramu mashanu, sarudza:
(a) kumhanya kwemango kana yasvika pasi
(b) nguva iyo mango inosvika pasi.
g = 9.8 m/s 2
Solution:
Inozivikanwa: h = 10 m, g = 9.8 m/s 2
a) Kumhanya kwemanga kana yasvika pasi
Huremu hunoverengerwa muequation yekufamba kwe free-fall
b) Nguva iri mumhepo
Dambudziko remuenzaniso 2:
Chinhu chinodonhedzwa kubva pakakwirira. Sarudza:
(a) hukuru hwekukurumidzira kwechinhu
(b) daro rakafambwa nechinhu ichi kwemasekondi maviri ekutanga
(c) kumhanya kwechinhu mushure mekudonha kwemamita makumi mashanu
(d) inguva yakareba sei inodiwa kuti chinhu chisvike kumhanya kwe20 m/s,
(e) inguva yakareba sei inodiwa kuti chinhu chiwire kusvika pamamita zana
Solution:
Inozivikanwa: g = 9.8 m/s 2
a) Kukura kwekumhanya kwechinhu chacho
Kukurumidza kwechinhu = kukurumidza kwegiravhiti = g = 9.8 m/s 2
b) Nhambwe yakafambwa nechinhu ichi kwemasekondi maviri ekutanga
Inozivikanwa: g = 9.8 m/s 2 , t = 2 s
Aida: h
h = 1⁄2 gt 2 = 1⁄2 (9.8)(2) 2 = (4.9)(4) = 19.6 mamita
c) Kumhanya kwechinhu mushure mekudonha kusvika pamamita makumi mashanu
Inozivikanwa: h = 50 m, g = 9,8 m/s 2
Zvaidiwa: v t
d) Inguva yakareba sei inodiwa kuti zvinhu zvisvike kumhanya kwe20 m/s
Inozivikanwa: v t = 20 m/s, g = 9,8 m/s 2
Zvaidiwa: t
e) Nguva inodiwa kuti zvinhu zviwire kusvika pamamita zana
Zvinodiwa: h = 100 m, g = 9,8 m/s 2
Mhinduro: t
Dambudziko remuenzaniso 3:
Dombo rinokandwa mutsime nekumhanya kwekutanga kwe5 m/s. Kana dombo rikawira mumvura mushure memasekonzi mana, sarudza:
(a) kumhanya kwedombo kana rapinda mumvura
(b) kudzika kwetsime
Solution:
a) Kumhanya kwedombo kana rapinda mumvura
Anozivikanwa:
v o = 5 m/s, t = 4 s, g = 9.8 m/s 2
Zvaidiwa: v t
v t = vo o + g t
v t = 5 m/s + (9.8 m/s 2 )(4 s) = 5 m/s + 39.2 m/s
v t = 44.2 m/s
b) Kudzika kwetsime
Anozivikanwa:
v o = 5 m/s, t = 4 s, g = 9.8 m/s 2
Aida: h
h = vot + ½ gt 2
h = (5)(4) + ½ (9.8)(4) 2
h = 20 + (4.9)(16)
h = 20 + 78.4
h = mamita mashanu
Dambudziko remuenzaniso 4:
Kubva pamusoro pechivako kusvika pamamita makumi mashanu, pasuru inokandwa yakatwasuka ichidzika pasi nekumhanya kwe10 m/s. Sarudza:
(a) Nguva iri mudenga
(b) Kumhanya kwepakeji painorova pasi
Solution:
a) Nguva iri mumhepo
Anozivikanwa:
h = 50 m, g = 9.8 m/s 2 , v o = 10 m/s
Zvaidiwa: t
h = vot + ½ gt 2
50 = 10 t + ½ (9.8) t 2
50 = 10 t + 4.9 t 2
4.9 t 2 + 10 t – 50 = 0
Shandisa fomura yequadratic:
Nguva iri mumhepo = masekondi 2.3
b) Kumhanya kwepakeji painorova pasi
Anozivikanwa:
h = 50 m, g = 9.8 m/s 2 , v o = 10 m/s
Zvaidiwa: v t
Dambudziko remuenzaniso 5:
Bhora rinokandwa rakamira kumusoro nekumhanya kwekutanga kwe20 m/s. Sarudza kukwirira kwakanyanya kunosvikwa nebhora.
Solution:
Huwandu hwevector ine divi riri kumusoro hunoratidza kuti iri nani, huwandu hwevector ine divi riri pasi hunoratidza kuti iri pasi. Nzvimbo yekutanga yebhora inosarudzwa senzvimbo yekutarisa.
Anozivikanwa:
v o = 20 m/s (kwakananga kumhanya kwekutanga kuri mudenga, bhora rinokandwa mudenga, saka v o iri positive)
v t = 0 m/s (kumhanya kwebhora pakukwirira kwakanyanya i0 m/s)
g = – 9.8 m/s 2 (gwara rekumhanya kwegiravhiti riri pasi, saka g ari negative)
Aida: h
Dambudziko remuenzaniso 6:
Marble inokandwa yakatwasuka ichibva pamusoro pechivako chiri pamamita zana kubva pasi nekumhanya kwekutanga kwe20 m/s. Sarudza:
(a) Nguva iri mumhepo
(b) kumhanya kwedombo remabhuru parinorova pasi
Solution:
Nzvimbo pakakandwa dombo remabhura senzvimbo yekunongedzera; pamusoro pechivako ndipo panongedzera. Kukura kwevekita ine divi rekukwira kumusoro kwakanaka, kukura kwevekita ine divi rekudzika pasi hakuna kunaka.
a) Nguva iri mumhepo
Anozivikanwa:
h = – 100 m (h haina kunaka nekuti pasi riri pasi penzvimbo yekutanga kana nzvimbo yekunongedzera)
v o = 20 m/s (gwara rekumhanya kwekutanga riri kumusoro, saka v o rakanaka)
g = – 9.8 m/s 2 (gwara rekumhanya kwegiravhiti riri pasi, saka g ari negative)
Zvaidiwa: t
Shandisa fomura yequadratic:
Nguva yaidiwa kuti usvike pasi kubvira
bhora rakakandwa = masekondi manomwe.
b) Kumhanya kwedombo remabhuru kana richirova pamusoro pevhu
Anozivikanwa:
h = -100 m (negative nekuti pasi riri pasi penzvimbo yekunongedzera kana nzvimbo yekutanga)
v o = 20 m/s (kwakananga kumhanya kwekutanga kuri kumusoro, saka v o iri positive)
g = -9.8 m/s 2 (gwara rekumhanya kwegiravhiti riri pasi, saka g ari negative).
Zvaidiwa: v t
Mibvunzo nemhinduro pamusoro pekufamba kwemahara kwemwaka wechando
- Chii chinonzi kufamba kwemahara kwekuwa?
Kufamba kwemahara kwemvura (free fall motion) ndiko kufamba kwechinhu chiri pasi pesimba regiravhiti chete, pasina mamwe masimba anoshanda pachiri, akadai sekudzivirira mhepo.
- Chii chinonzi kukurumidza kunokonzerwa negiravhiti?
Kumhanya kunokonzerwa negiravhiti ndiko kumhanya kunoitika chinhu pachinodonha zvakasununguka pedyo nepasi. Kazhinji chinonzi 'g' uye chine kukosha kunosvika 9.8 m/s².
- Ndeipi nzira yekuchinja kufamba kwe free fall, tichifunga nezvespeed yekutanga nenguva?
Fomura yacho inoti h = ut + ½gt², apo h iri displacement (kukwirira), u iri initial velocity, g iri acceleration nekuda kwegravity, uye t iri time.
- Kumhanya kwechinhu kunochinja sei panguva yekufamba kwemahara?
Munguva yekudonha kwakasununguka, kumhanya kwechinhu kunowedzera zvakananga nekufamba kwenguva nekuda kwekumhanya kwesimba rinokwevera pasi nguva dzose.
- Ndeipi fomura yekumhanya kwekupedzisira mukufamba kwefree fall, tichifunga nezvekukurumidza kwekutanga nenguva?
Fomura yacho ndeiyi: v = u + gt, apo v iri velocity yekupedzisira, u iri velocity yekutanga, uye g iri acceleration nekuda kwegravity.
- Chii chinoitika kumhanya kwechinhu chiri padanho repamusoro penzira yacho mukufamba kwakasununguka?
Pakukwira kwayo, kumhanya kwechinhu kunova zero kwechinguvana.
- Chiratidzo chisina kunaka chinomiririrei kana tichitarisa kufamba kwemahara kwekufamba?
Chiratidzo chekuramba chinowanzo ratidza gwara rakapesana negwara rakanaka rakasarudzwa. Zvichienderana nemamiriro ezvinhu, chinogona kuratidza kudonha pasi (kana kumusoro kuri kwakanaka) kana kudonhedzwa pasi (kana kumusoro kuri kure).
- Chii chinoitika pakumhanya kwechinhu panguva yekudonha kwakasununguka kana chasvika pakukwirira kwacho kwepamusoro?
Kumhanya kwechinhu pahurefu hwacho hwakanyanya mukudonha kwakasununguka kunoramba kwakaenzana ne g (inenge -9.8 m/s² pedyo nepamusoro peNyika), kuchinongedzera pasi.
- Kudzivirirwa kwemhepo kunokanganisa sei kufamba kwemahara kwekudonha?
Muchokwadi, kuramba mhepo kunogona kunonotsa kudzika kwechinhu, zvichiita kuti kufamba kwacho kusave kudonha kwakasununguka. Zvisinei, mumatambudziko mazhinji efizikisi, kuramba mhepo hakutariswi kuti zvive nyore.
- Ndeipi nguva yekubhururuka mukufamba kwemahara kwekudonha?
Nguva yekubhururuka inguva yese inopedzwa nechinhu chiri mudenga. Kana chinhu chakaburitswa nekumhara pakakwirira zvakafanana, nguva yekubhururuka inogona kuwanikwa nefomura t = 2u/g.
Matambudziko nemhinduro pamusoro pekufamba kwemahara kwemwaka wekudonha
- Problem: Dombo rinodonhedzwa kubva padombo rakareba mamita 78.4. Zvinotora nguva yakareba sei kuti dombo risvike pasi? Solution: Tinoshandisa equation h = ½gt². Kugadzirisa nguva, t = √(2h/g) = √(2×78.4/9.8) = 4 s.
- Problem: Bhora rinokandwa mudenga nekumhanya kwekutanga kwe19.6 m/s. Bhora rinokwira zvakadii? Solution: Uchishandisa equation h = v₀t – ½gt² pakukwirira kwakanyanya (apo kumhanya kwekupedzisira kuri 0), kukwirira h = v₀² / (2g) = (19.6)² / (2×9.8) = 20 m.
- Problem: Dombo rinokandwa mudenga nekumhanya kwekutanga kwe10 m/s. Kumhanya kwaro kuchava kwakadii mushure memasekonzi maviri? Solution: Equation iyi v = v₀ – gt inopa velocity v = 10 – 9.8×2 = -9.6 m/s.
- Problem: Mari yesimbi inodonhedzwa mutsime yobva yawira mumvura mushure memasekonzi matatu. Tsime racho rakadzika zvakadii? Solution: Uchishandisa h = ½gt², hudzamu h = ½x9.8×3² = 44.1 m.
- Problem: Bhuku rakadonha patafura robva rawira pasi mushure memasekonzi 0.5. Tafura yakanga yakareba sei? Solution: Uchishandisa h = ½gt², kukwirira h = ½x9.8x(0.5)² = 1.225 m.
- Problem: Bhora rinokandwa mudenga nekumhanya kwekutanga kwe20 m/s. Richasvika rini pakukwirira kwaro kwakanyanya? Solution: Pakukwirira kwakanyanya, v = 0. Kugadzirisa t = (v – v₀) / -g, nguva t = (0 – 20) / -9.8 = 2.04 s.
- Problem: Chinhu chinowira kwemasekonzi matanhatu. Chii chinonzi kumhanya kwacho kwekupedzisira? Solution: Uchishandisa v = v₀ + gt nekutanga kwekukurumidza v₀ = 0, kumhanya kwekupedzisira v = 0 + 9.8×6 = 58.8 m/s.
- Problem: Apuro rinodonha kubva pamuti uye rinotora masekondi 1.5 kuti rirove pasi. Muti wacho wakareba sei? Solution: Uchishandisa h = ½gt², kukwirira h = ½x9.8x(1.5)² = 11 m.
- Problem: Bhora renhabvu rinokandwa rakamira mudenga nekumhanya kwekutanga kwe25 m/s. Rinotora nguva yakareba sei kuti rirove pasi? Solution: Nguva yekusvika pakureba kwakanyanya t = v₀ / g = 25 / 9.8 = 2.55 s. Nguva yese yekurova pasi yakapetwa kaviri izvi, saka t = 2×2.55 = 5.1 s.
- Problem: Dombo rinodonhedzwa kubva pabhiriji robva rarova mvura mushure memasekonzi mana. Bhiriji racho rakareba sei? Solution: Uchishandisa h = ½gt², kukwirira h = ½x9.8×4² = 78.4 m.
- Problem: Roketi rinoburitswa rakananga mudenga pa50 m/s. Rinokwira zvakadii? Solution: Uchishandisa h = v₀² / (2g), kukwirira h = (50)² / (2×9.8) = 127.55 m.
- Problem: Bhora rinokandwa pasi nekumhanya kwekutanga kwe10 m/s. Kumhanya kwaro kwakadii mushure memasekonzi maviri? Solution: Uchishandisa v = v₀ + gt, kumhanya v = 10 + 9.8×2 = 29.6 m/s.
- Problem: Bhora rinokandwa rakamira kumusoro rodzokera pasi mumasekonzi matanhatu. Kumhanya kwaro kwekutanga kwaive kwakadii? Solution: Uchishandisa v₀ = gt / 2 (sezvo nguva yose iri kaviri nguva yekusvika pakukwirira kwakanyanya), kumhanya kwekutanga v₀ = 9.8×6 / 2 = 29.4 m/s.
- Problem: Chinhu chinowira kwemasekonzi gumi. Chinowira kure zvakadii? Solution: Uchishandisa h = ½gt², daro h = ½x9.8×10² = 490 m.
- Problem: Matombo anodonhedzwa kubva pashongwe uye zvinotora masekonzi mashanu kuti arove pasi. Shongwe yacho yakareba sei? Solution: Uchishandisa h = ½gt², kukwirira h = ½x9.8×5² = 122.5 m.
- Problem: Baseball inokandwa yakatwasuka mudenga nekumhanya kwekutanga kwe15 m/s. Ichasvika rini pakukwirira kwayo kwakanyanya? Solution: Pakukwirira kwakanyanya, v = 0. Kugadzirisa t = (v – v₀) / -g, nguva t = (0 – 15) / -9.8 = 1.53 s.
- Problem: Chinhu chinodonhedzwa chodonha kwemasekonzi manomwe. Chii chiri kumhanya kwacho kwekupedzisira? Solution: Uchishandisa v = v₀ + gt nekutanga kwekukurumidza v₀ = 0, kumhanya kwekupedzisira v = 0 + 9.8×7 = 68.6 m/s.
- Problem: Dombo rinokandwa mudenga nekumhanya kwekutanga kwe30 m/s. Kumhanya kwaro kuchava kwakadii mushure memasekonzi matatu? Solution: Uchishandisa v = v₀ – gt, kumhanya v = 30 – 9.8×3 = 0.6 m/s.
- Problem: Dombo rinodonhedzwa kubva padombo robva rawira pasi mushure memasekonzi masere. Dombo racho rakareba zvakadii? Solution: Uchishandisa h = ½gt², kukwirira h = ½x9.8×8² = 313.6 m.
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Dambudziko: Museve unopfurwa wakananga mudenga pa 60 m/s. Unosvika riini kusvika warova pasi? Mhinduro: Nguva yekusvika pakureba kwakanyanya t = v₀ / g = 60 / 9.8 = 6.12 s. Nguva yese yekurova pasi yakapetwa kaviri izvi, saka t = 2×6.12 = 12.24 s.
