Kusunga mphamvu zamakanika - mavuto ndi mayankho
1. Chipika cha m-kg chimatulutsidwa kuchokera pamwamba pa malo osalala opendekeka , monga momwe chithunzi chili pansipa chikusonyezera. Kuyerekeza pakati pa mphamvu yokoka ndi mphamvu ya kinetic ya chipikacho pamalo a M ndi…
Anakonza
Mphamvu yokoka yomwe imapezeka pa mfundo M:
PE M = mg (1/3 ola) = 1/3 mgh
Mphamvu ya kinetic pa mfundo M:
KE M = EP = mg (2/3 h) = 2/3 mgh
EP M : EK M
1/3 mg: 2/3 mg
1/3: 2/3
1: 2
2. Wokwera pa ayezi akutsetsereka kuchokera kutalika kwa A, monga momwe chithunzi chili pansipa chikusonyezera. Ngati liwiro loyambirira = 0 ndi kufulumira chifukwa cha mphamvu yokoka ndi 10 ms -2 , ndiye kuti liwiro la wokwera pa B ndi lotani.
Zodziwika:
Liwiro loyambirira (v o ) = 0
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kusintha kwa kutalika = mamita 50 - mamita 10 = mamita 40
Kufunidwa: Liwiro la wokwera ski pamalo B
Yankho:
Mfundo yosungira mphamvu ya makina imati mphamvu yoyamba ya makina = mphamvu yomaliza ya makina.
Mphamvu yoyambirira ya makina = mphamvu yomwe ingatheke pamalo B (kutalika = mamita 40)
Mphamvu yomaliza yamakina = mphamvu ya kinetic pa mfundo B
Mphamvu yomaliza yamakina = Mphamvu yoyambirira yamakina
½ mv t 2 = mgh
½ v t 2 = gh
½ v t 2 = (10)(50-10)
½ v t 2 = (10)(40)
½ v t 2 = 400
v t 2 = (2)(400) = 800
v t = √800 = √(2)(400) = 20√2 m/s
3. Chinthu chimayamba kutsetsereka kuchokera pa mfundo ya A popanda liwiro loyambirira. Ngati palibe mphamvu yokangana, kodi liwiro la chinthucho pamalo otsika kwambiri ndi liti?
Zodziwika:
Unyinji wa chinthu = m
Liwiro loyambirira (v o ) = 0
Kutalika (h) = mamita 20
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kufunidwa: Liwiro lomaliza (v t )
Yankho:
Mphamvu yoyambirira yamakina (ME 1 ) = Mphamvu yokoka yomwe ingathe kukoka pamalo A (PE A ) = mgh = (m)(10)(20) = 200 m
Mphamvu yomaliza yamakina (ME 2 ) = mphamvu ya kinetic (KE) = ½ mv t 2
Liwiro la chinthucho pamalo otsika kwambiri (v t )?
Gwiritsani ntchito mfundo yosungira mphamvu ya makina imati mphamvu yoyamba ya makina = mphamvu yomaliza ya makina.
EM1 = EM2
200 m = ½ mv t 2
200 = ½ v t 2
400 = v t 2
v t = 20 m/s
4. Mpira wolemera makilogalamu awiri umagwa kuchokera pa mfundo A, monga momwe zasonyezedwera pachithunzi pansipa (g = 10 ms -2 ). Ukafika pa mfundo B, mphamvu ya kinetic = kuwirikiza kawiri mphamvu yomwe ingatheke. Kodi kutalika kwa mfundo B pamwamba pa dziko lapansi ndi kotani?
Zodziwika:
Kulemera kwa mpira (m) = 2 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms -2
Kutalika kwa mfundo A (h A ) = mamita 90
Kufunidwa: Kutalika kwa mfundo B (h B )
Yankho:
Mukafika pa mfundo B, mphamvu ya kinetic ya mpira pa mfundo B = mphamvu yokoka yamphamvu yokwana kawiri pa mfundo B.
EK = 2 EP
½ mv 2 = 2 mph B
½ v 2 = 2 gh B
v 2 = 2(2)(10) h B
v 2 = 40 maola B
Liwiro (v) la mpira likafika pa point B pambuyo pa free fall kuchokera pa point A:
v 2 = 2 gh = 2(10)(90–h B ) = 20(90–h B )
M'malo mwa v 2 pa equation yomwe ili pamwambapa ndi v 2 pa equation iyi.
v 2 = 40 maola B
20(90–maola B ) = 40 maola B
1800–20 maola B = 40 maola B
1800 = 40 maola B + 20 maola B
1800 = 60 maola B
h B = 1800 / 60
h B = mamita 30
5. Mpira wolemera makilogalamu 1 umatulutsidwa ndikutsika kuchokera pa mfundo A kupita pa mfundo C, monga momwe chithunzi chili pansipa. Ngati kuthamanga chifukwa cha mphamvu yokoka = 10 ms -2 , kodi mphamvu ya kinetic ya mpirawo ikafika pa mfundo C ndi yotani?
Zodziwika:
Kulemera kwa mpira (m) = 1 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kusintha kwa kutalika (h) = 0.75 m
Mphamvu yoyambira (PE o ) = mgh = (1)(10)(0.75) = 7.5 Joules
Mphamvu yoyambira ya kinetic (KE o ) = ½ mv o 2 = ½ m (0) 2 = 0
Mphamvu yomaliza yokoka (PE t ) = mgh = mg (0) = 0
Kufunidwa: Mphamvu ya kinetic ya mpira pa mfundo C
Yankho:
Mphamvu yoyambirira yamakina (ME o ) = Mphamvu yomaliza yamakina (ME t )
Mphamvu yoyambira yokoka (PE o ) + mphamvu yoyambira yokoka (KE o ) = Mphamvu yomaliza yokoka (PE t ) + mphamvu yomaliza yokoka (KE t )
Ma Joules 7.5 + 0 = 0 + KE t
Ma Joules 7.5 = KE t
Mphamvu ya kinetic ya mpira pa mfundo C = 7.5 Joules.
6. Mpira wolemera makilogalamu awiri umatulutsidwa kuchokera pa mfundo A, monga momwe chithunzi chili pansipa chikusonyezera. Mzere wokhotakhota ndi wosalala. Ngati kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms -2 , kodi mphamvu ya kinetic ya mpira pa mfundo B ndi yotani?
Zodziwika:
Kulemera kwa mpira (m) = 2 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kusintha kwa kutalika (h) = 120 cm = 1.2 mamita
Mphamvu yoyambira yokoka (PE o ) = mgh = (2)(10)(1.2) = 24 Joules
Mphamvu yoyambirira ya kinetic (KE o ) = ½ mv o 2 = ½ m (0) 2 = 0
Mphamvu yomaliza yokoka (PE t ) = mgh = mg (0) = 0
Kufunidwa: Mphamvu ya kinetic ya mpira pa mfundo B
Yankho:
Mphamvu yamakina pamalo A (mphamvu yoyamba yamakina) = mphamvu yamakina pamalo B (mphamvu yomaliza yamakina)
Mphamvu yoyambirira yamakina (ME o ) = mphamvu yomaliza yamakina (ME t )
Mphamvu yoyambira yokoka (PE o ) + mphamvu yoyambira yokoka (KE o ) = mphamvu yomaliza yokoka (PE t ) + mphamvu yomaliza yokoka (KE t )
Ma Joules 24 + 0 = 0 + KE t
Ma Joules 24 = KE t
Mphamvu ya kinetic (KE) ya mpira pa mfundo C = 24 Joules.
7. Chinthu chili ndi mphamvu yokhazikika ya makina, mphamvu yayikulu ya kayendedwe kake, komanso mphamvu yochepa yokoka. Chinthucho ndi…
A. Pa nthawi yopuma
B. pita mmwamba
C. pita pansi
D. Kuthamanga mmwamba
Yankho:
Mphamvu ya kinetic ikukulirakulira kutanthauza kuti liwiro la chinthucho likukulirakulirakulira ndipo mphamvu yokoka ikucheperachepera kutanthauza kuti kutalika kwa chinthucho kuchokera pamwamba pa nthaka ndi kochepa. Izi zimachitika pamene chinthucho chikusuntha kuchokera kutalika kwina kupita pansi.
Ubale pakati pa liwiro ndi mphamvu ya kinetic umawonetsedwa ndi fomula ya mphamvu ya kinetic:
KE = ½ mv 2
Kufotokozera kwa fomula: KE = mphamvu ya kinetic, m = kulemera, v = liwiro
Ubale pakati pa kutalika ndi mphamvu yokoka umaimiridwa ndi fomula ya mphamvu yokoka:
PE = mgh
Kufotokozera kwa fomula: PE = mphamvu yokoka, m = kulemera, g = kufulumira kwa mphamvu yokoka, h = kutalika
Yankho lolondola ndi C.
- Kodi mphamvu ya makina ndi chiyani?
- Yankho: Mphamvu ya makina ndi kuchuluka kwa mphamvu ya kayendedwe ka chinthu ndi mphamvu yomwe ingatheke. Mphamvu ya kayendedwe ka chinthu imakhudzana ndi kayendedwe ka chinthu, pomwe mphamvu yomwe ingatheke imakhudzana ndi malo ake kapena kapangidwe kake.
- Kodi mfundo yosungira mphamvu zamakanika imatanthauza chiyani?
- Yankho: Mfundoyi imati mu dongosolo lokhalokha lomwe limagwira ntchito ndi mphamvu zodziletsa zokha, mphamvu yonse ya makina imakhalabe yofanana. Izi zikutanthauza kuti kuchuluka kwa mphamvu ya kinetic ndi potential sikusintha pakapita nthawi.
- Kodi mphamvu zosungira zinthu zakale komanso zosasunga zinthu zakale zimakhudza bwanji kusunga mphamvu zamakanika?
- Yankho: Mphamvu zosungira, monga mphamvu yokoka, sizisintha mphamvu yonse ya makina a dongosolo. Zingasinthe mphamvu yomwe ingakhalepo kukhala mphamvu ya kinetic kapena mosemphanitsa, koma kuchuluka kwake kumakhalabe kosasintha. Mphamvu zosasunga, monga kukangana, zimatha kufalitsa mphamvu ya makina, nthawi zambiri kuzisintha kukhala mphamvu yotentha.
- N’chifukwa chiyani mphamvu ya makina siisungidwa m’zochitika zenizeni zokhudzana ndi kukangana?
- Yankho: Kukangana ndi mphamvu yosasintha zinthu. Pamene zinthu zikusunthana, kukangana kumasintha mphamvu zina za makina a dongosolo kukhala mphamvu yotentha, zomwe zimapangitsa kuti mphamvu yonse ya makina a dongosolo ichepe.
- Kodi kusunga mphamvu ya makina kumawonetsedwa bwanji mu pendulum yozungulira?
- Yankho: Ngati palibe mphamvu yolimbana ndi mpweya (mphamvu yosasintha), pamene pendulum ikukwera mmwamba, mphamvu yake ya kinetic imasinthidwa kukhala mphamvu yokoka. Pamwamba kwambiri pa kugwedezeka kwake, imakhala ndi mphamvu yayikulu komanso mphamvu yochepa ya kinetic. Pamene ikubwerera pansi, mphamvu iyi imasinthidwanso kukhala mphamvu ya kinetic. Mphamvu yonse yamakina imakhalabe yokhazikika, ngakhale mitundu ya mphamvu ikusinthana.
- N’chifukwa chiyani mpira wodumpha umatha kukhazikika ngakhale palibe mphamvu zakunja?
- Yankho: Mpira ukagunda, mphamvu zake zonse sizimasinthidwa kukhala mphamvu zomwe zingatheke. Mphamvu zina zimatayika, nthawi zambiri ngati phokoso kapena kusintha kwa mpira, makamaka chifukwa cha kukangana kwamkati mkati mwa zinthu zomwe zili mu mpirawo. Izi ndi mitundu ya mphamvu zosasintha zomwe zimasewera, zomwe zimachepetsa mphamvu ya makina a mpirawo nthawi iliyonse ikagunda mpaka itapuma.
- Mu roller coaster, kodi mphamvu yamakina yapamwamba kwambiri komanso yotsika kwambiri ili kuti?
- Yankho: Mphamvu yonse ya makina a roller coaster imakhalabe yofanana ngati tinyalanyaza kukana kwa mpweya ndi kukangana. Komabe, pamalo okwera kwambiri, mphamvu yamagetsi imakhala pamlingo wake wapamwamba pomwe mphamvu yamagetsi imakhala pamlingo wocheperako. Pamene ikutsika, mphamvu yamagetsi imasanduka mphamvu yamagetsi, kotero pamalo otsika kwambiri, mphamvu yamagetsi imakhala pamlingo wake wapamwamba ndipo mphamvu yamagetsi imakhala pamlingo wocheperako.
- Kodi kusunga mphamvu zamakanika kumathandiza bwanji kumvetsetsa mayendedwe a mapulaneti?
- Yankho: Mapulaneti ozungulira nyenyezi ngati Dzuwa ali ndi mphamvu ya kinetic (chifukwa cha kuyenda kwawo) komanso mphamvu yokoka (chifukwa cha malo awo poyerekeza ndi Dzuwa). Pamene pulaneti ikuyandikira Dzuwa, imathamanga kwambiri, kuwonjezera mphamvu yake ya kinetic pomwe mphamvu yake yokoka imachepa, komanso mosemphanitsa. Mphamvu yonse ya makina a pulaneti imakhalabe yokhazikika pakapita nthawi, poganiza kuti mphamvu zina (monga za mapulaneti ena) sizingafanane.
- N’chifukwa chiyani satelayiti yomwe ili mumlengalenga wokhazikika siigwera mu Dziko Lapansi?
- Yankho: Ngakhale kuti satelayiti ikukokedwadi ku Dziko Lapansi chifukwa cha mphamvu yokoka, mphamvu yake yakutsogolo ya kinetic imaisunga ikuyenda mu mkombero wake. Kulinganiza kwa mphamvu ya kinetic iyi ndi mphamvu yokoka kumapangitsa satelayiti kukhala mu mkombero wokhazikika ndi mphamvu yosalekeza yamakina.
- Ngati wokwera ski ayamba kuchokera pamalo opumula pamwamba pa phiri lopanda kukangana kenako n’kutsika, kodi liwiro lake pansi lidzakhala bwanji poyerekeza ndi ngati atayamba pang’ono kutsika phiri?
- Yankho: Pa phiri lopanda kukangana, mphamvu zonse za makina za wokwera phirilo zimasungidwa. Ngati ayambira kuchokera pamwamba, adzakhala ndi mphamvu zambiri zoyambira nazo kuposa ngati ayambira pang'ono pansi. Mphamvu izi zidzasanduka mphamvu ya kinetic ikatsika. Chifukwa chake, adzakhala wachangu pansi ngati ayambira pamwamba kuposa ngati ayambira pang'ono pansi.
