Kufamba kwedenderedzwa - matambudziko nemhinduro

1. Chinhu chinorema 10 kg chinofamba mudenderedzwa nekumhanya kwakafanana kwe4 m/s. Kana radius yedenderedzwa iri 0.5 metres, saka:

1) Kuwanda kwemadenderedzwa i4/π Hz

2) Kukurumidza kwepakati pesimba (centripetal acceleration) kuri 32 ms ^-2

3) Simba repakati penyika i320 N

4) Nguva yacho i4π s.

Ndeapi mashoko echokwadi?

Zvinozivikanwa:

Huremu hwechinhu (m) = 10 kg

Kumhanya kwakanangana (v) = 4 m/s

Radiyo yedenderedzwa (r) = 0.5 metres

Solution:

1) Kuwanda kwedenderedzwa

v = 2 π rf

4 = 2 π (0.5) f

4 = π f

f = 4/π Hertz

2) Kukurumidza kwepakati

a _s = v ² / r = 4 ² / 0,5 = 16 / 0,5 = 32 m/s ²

3) Simba repakati

F = ma _s = (10)(32) = 320 N

4) Nguva

T = 1 : f = 1 : 4/π = 1 x π/4 = π/4

2. Chinhu chinofamba mudenderedzwa reradius remamita matanhatu. Kana chinhu chikatenderera denderedzwa gumi nematanhatu mumaminitsi maviri, chii chinonzi linear velocity yechinhu chacho?

Zvinozivikanwa:

Nharaunda (r) = 6 mamita

Kumhanya kwekona (ω) = 16 revolutions / 2 minutes = 8 revolutions / minutes = 8 revolutions / 60 seconds = 0.13 revolutions/second.

Zvinodiwa: Mwero wekufamba (v) uri pamutsetse?

Solution:

v = r ω = (6 metres)(0.13 revolutions/second) = 0.8 metres/second

Muma radians:

1 revolution = 2π radians = 2(3.14) = 6.28 radians

Kumhanya kwekona = 8 (6.28) radians / 60 seconds = 50.24 radians / 60 seconds = 0.84 radians/second

v = r ω = (6 metres)(0.84 radians/second) = 5.04 radians/second.

3. Chinhu chine radius ye 20/π cm chinotenderera ka4 musekondi imwe. Chii chinonzi linear velocity yemucheto wechinhu?

Zvinozivikanwa:

Nharaunda (r) = 20/π cm = 20 / 3.14 cm = 6.4 cm = 0.064 mamita

Kumhanya kwekona (ω) = 4 revolutions / 1 second = 4 revolutions / second.

1 revolution = (2)(3.14) radians = 6.28 radians

Kumhanya kwekona (ω) = (4)(6.28) radians/second = 25.12 radians/second

Zvinodiwa: Kumhanya kwakanangana kwemucheto wechinhu (v)

Solution:

v = r ω = (0.064 metres)(25.12 radians/sekondi) = 1.6 metres/sekondi

4. Chinhu chichifamba mudenderedzwa nekumhanya kwakafanana, kumhanya kwemutsara kwechinhu kunoenderana…

onawo Kuongorora mativi - matambudziko nemhinduro

Solution:

Kuenzanisa kwekukurumidza kwekufamba kwedenderedzwa:

v = kumhanya kwakanangana

d = 2πr = denderedzwa

T = nguva = nguva inodiwa kuti pave nekutenderera kamwe chete kwakakwana.

5. Chinhu chinofamba mudenderedzwa reradius yemamita makumi mashanu. Kana kumhanya kwekona kwechinhu kuri 120 rpm, chii chinonzi nguva uye kumhanya kwemutsara kwechinhu chacho?

Zvinozivikanwa:

Nharaunda (r) = 50 cm = 0.5 mamita

Kumhanya kwekona (ω) = 120 rpm = 120 revolutions / 1 miniti = 120 revolutions / 60 maminitsi = 2 revolutions / 1 sekondi

1 revolution = 2π radian

Kumhanya kwekona (ω) = 2 (2π radians) / 1 sekondi = 4π radians/sekondi

Zvinodiwa: Nguva (T) uye kumhanya kwakarongeka (v)

Solution:

Nguva (T):

Nguva inodiwa kuti pave nechinjo imwe chete yakakwana.

Chinhu chinotenderera mapoinzi maviri musekondi imwe = 1 revolution pamasekondi 0.5. Nguva = masekondi 0.5.

Kumhanya kwakanangana (v):

v = r ω = (0.5 metres)(4π radians/second) = 2π metres/second.

Ndeupi musiyano uripo pakati pekumhanya kwetangential nekumhanya kwekona mukufamba kwedenderedzwa?
Mhinduro : Kumhanya kweTangential ndiko kumhanya kwemutsara kwepoindi pachinhu chinotenderera uye kunoratidza kuti poindi iri kufamba nekukurumidza sei munzira yayo yakatenderera. Kumhanya kweAngular, kune rumwe rutivi, kunoreva kukurumidza kwekona inoshanduka sei sezvo chinhu chinotenderera. Kumhanya kweTangential kunowanzo kuyerwa mumamita pasekondi (m/s) nepo kumhanya kweAngular kuchiyerwa mumaradians pasekondi (rad/s).
Chii chinonzi centripetal acceleration uye chinobatanidzwa sei nekufamba kwedenderedzwa?
Mhinduro : Kukurumidza kwepakati (centripetal acceleration) ndiko kukurumidza kunoitika kana chinhu chichifamba munzira yakatenderera. Nguva dzose kunongedzera pakati pedenderedzwa uye ndiko kunoita kuti chinhu chirambe chiri munzira yacho yakatenderera. Fomura yekumhanyisa kwepakati (centripetal acceleration) i $_{c} = v 2 ^{/ r}$ apo $v$ iri kumhanya kwetangential uye $r$ iri radius yedenderedzwa.
Sei chinhu chakafanana nedenderedzwa chichifamba chichimhanya kunyangwe kumhanya kwacho kuri kwakafanana?
Mhinduro : Kunyange zvazvo hukuru (kana saizi) hwekumhanya huchiramba hwakafanana mukufamba kwakatenderera, divi rekumhanya rinochinja. Sezvo kukurumidza kuchitsanangurwa sekuchinja kwekukurumidza, uye kumhanya kuri huwandu hwevector hune hukuru negwara, chero shanduko mugwara inoumba kukurumidza. Muchiitiko ichi, kukurumidza kwepakati.
Simba rinodiwa kuti rirambe rakatenderera rinoenderana sei nehuremu hwechinhu uye nharaunda yedenderedzwa?
Mhinduro : Simba rinodiwa kuti rirambe rakatenderera rinopihwa nefomura yesimba repakati: $F_{c} = m \times a_{c} = m \times v ^{2 /r}$
Sei uchinzwa uchisundidzirwa kunze kana mota ikatendeuka zvakanyanya (semuenzaniso, mu roundabout)?
Mhinduro : Izvi zvinokonzerwa nesimba re "centrifugal" re "ngano", iro simba rinoonekwa rinobuda kunze kwemuviri uchifamba munzira yakatenderera. Harisi simba chairo mupfungwa yekusunda kana kudhonza, asi mhedzisiro yekusaita chinhu. Muviri wako unoda kufamba wakatwasuka (mutemo wekutanga waNewton), asi madziro emotokari kana bhandi rechigaro zvinoshandisa simba rekukuchengetedza uchifamba wakatenderera. Izvi zvinogadzira kunzwa kwekusundidzirwa kunze.
Kukweshana kunoita basa rei mukufamba kwedenderedzwa, kunyanya kana mota ichitenderera mumugwagwa?
Mhinduro : Kukweshana pakati pematayi nemugwagwa kunoita kuti mota ikwanise kutenderera zvakanaka. Kana pasina kukweshana kwakakwana, mota inotsvedza kana kutsvedza, ichitadza kutevera nzira yayo yakatenderera.
Simba repakati rinoshanduka sei kana radius yenzira yakatenderera ikaderedzwa nehafu asi kumhanya kwacho kukaramba kwakafanana?
Mhinduro : Kana radius ikadzikiswa nehafu uye kumhanya kukaramba kwakafanana, simba repakati rinopetwa kaviri, sezvo simba repakati rinoenderana neradius.
Sei tisingagoni kuva nesimba repakati nepakati tisina simba repakati nepakati mukufamba kwedenderedzwa?
Mhinduro : Simba repakati (centrifugal force) isimba rinoita serinoshanduka kana kuti "rinonyepedzera" rinoonekwa richitenderera. Rinoita serinosundira zvinhu kunze kubva pakati pekutenderera. Zvisinei, kuti chinhu chifambe munzira yakatenderera, panofanira kunge paine simba chairo rinoshanda richienda pakati, iro riri simba repakati. Pasina simba repakati, paisazova nekufamba kwakatenderera pakutanga, uye nekudaro, hapana maonero esimba repakati.
Simba rinokwevera pasi riri pakati peNyika neMwedzi ndiro rinoita sei kuti Mwedzi utenderere uchitenderera?
Mhinduro : Simba rinokwevera pasi riri pakati peNyika neMwedzi rinoshanda sesimba repakati rinochengetedza Mwedzi uri mudenderedzwa rawo uchitenderera Nyika. Pasina kukwevera uku, Mwedzi waizofamba wakatwasuka panzvimbo pedenderedzwa rawo (kana kuti rakatenderera).
Kana tambo yakasungirirwa pabhora ikapfupikiswa nehafu uku uchitenderedza bhora mudenderedzwa nekumhanya kwakafanana, kusimba kwetambo kwaizochinja sei?

Mhinduro : Kana kureba kwetambo (kunoenderana neradius yenzira yakatenderera) kukaderedzwa nehafu ukuwo kumhanya kuchiramba kuripo, simba repakati rinodiwa (uye nokudaro kumanikidzwa kuri mutambo) kuchapetwa kaviri. Izvi zvinodaro nekuti simba repakati (uye nenzira dzakasiyana, kumanikidzwa kwechiitiko ichi) kunoenderana neradius.