Haɓaka ƙwanƙwasa na tsakiya - matsaloli da mafita

1. Ana juya ƙwallon, wanda aka haɗa a ƙarshen igiya mai kwance, a cikin da'irar radius 20 cm. Ƙwallon yana kusa da 360 ^o kowace daƙiƙa. Ka ƙayyade girman hanzarin centripetal!

An sani:

Gudun kusurwa (ω ) = 360 ^o /daƙi = juyin juya hali 1/daƙi = 6.28 radians/daƙi

Radius (r) = 20 cm = 0.2 m

Ana so: Hanzarin tsakiya (a _r )

Magani:

a _r = v ² / r —> v = r ω

a _r = (r ω) ² / r = r ² ω ² / r

a _r = r ω ²

a _s = hanzarin centripetal, v = saurin layi, r = radius, ω = saurin kusurwa

Girman hanzarin centripetal :

a _r = r ω ² a _r = (0,2 m) ( 6.28 rad/s)

a _r = 1.256 m/s ²

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2. Tayar da ke da santimita 30 a radius tana juyawa a gudun 180 rpm. Kayyade hanzarin centripetal na wani wuri a gefen tayar!

An sani:

Radius (r) = 30 cm = 0.3 m

Gudun kusurwa ( ω ) = juyin juya hali 180 / daƙiƙa 60 = juyin juya hali 3 / daƙiƙa = (3)(radian 6.28) / daƙiƙa = radian 18.84/daƙiƙa

Ana so: hanzarin tsakiya ( a _r ) na r = 0.3 m

Magani:

Girman hanzarin centripetal:

a _r = r ω ²

a _r = (0.3 m)(18.84 rad/s)

a _r = 5.65 m/s ²

3. Motar tsere tana tafiya a kan hanyar zagaye ta radius mita 50. Idan gudun motar ya kai kilomita 72/h, a tantance girman saurin centripetal!

An sani:

Radius (r) = mita 50

Gudun (v) = 72 km/h = (72)(mita 1000) / daƙiƙa 3600 = mita 20/daƙiƙa

Ana so : girman hanzarin centripetal (a _r )

Magani:

a _r = v ² / r = 20 ² / 50 = 400 / 50 = 8 m/s ²

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4. Mota tana da matsakaicin saurin centripetal na 10 m/s ² , don haka motar za ta iya juyawa ba tare da ta zame daga kan hanya mai lanƙwasa ba. Idan motar tana tafiya a daidai gudun 108 km/h, menene radius na lanƙwasa mara bango?

An sani:

Hanzarin tsakiya (a _r ) = 10 m/s ²

Gudun mota (v) = 108 km/ h = (108)(1000) / 3600 = mita 30 a /sec c akan d

Ana so: radius (r)

Magani:

r = v ² / a _r

r = 30 ^2/10 = 900 / 10 = mita 90 a s

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1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita