Matsalolin da aka Magance a fannin Fizik na Asali

9 Ma'aunin zafin jiki mai canzawa (ma'aunin Celsius ma'aunin Fahrenheit ma'aunin Kelvin)

1. 50 ^o C = ….. ^o F ?

Magani

A matsi na yanayi na yau da kullun , wurin daskarewar ruwa shine 0 ^oC akan ma'aunin Celsius da 32 ^oF akan ma'aunin Fahrenheit. A matsi na yanayi na yau da kullun, wurin tafasar ruwa shine 100 ^oC akan ma'aunin Celsius da 212 ^oF akan ma'aunin Fahrenheit.

0 ^o C = 32 ^o F da 1 00 ^o C = 212 ^o F. Canjin 5 C ⁼ canjin 9 ^F.

Ga ma'aunin Celsius, an raba tazara tsakanin 0 ^o C da 100 ^o C zuwa tazara 100 daidai. Ga ma'aunin Fahrenheit, an raba tazara tsakanin 0 ^o C da 100 ^o C zuwa tazara 180 daidai.

To ^o F = (180/100) To ^o C + 32

To ^o F = (9/5) To ^o C + 32

To ^o F = (9/5) 50 + 32

To ^o F = (9) 10 + 32

T ^o F = 90 + 32

To ^o F = 122

50 ^o C = 122 ^o F

[irp]

2. 86 ^o F = ….. ^o C ?

Magani

To ^o C = (100/180)(Zuwa ^F – 32)

To ^o C = (5/9)(Zuwa ^F – 32)

To ^o C = (5/9)(86 – 32)

To ^o C = (5/9)(54)

To ^o C = (5)(6)

To ^o C = 30

86 ^o F = 30 ^o C

3. 50 ^o C = ….. K?

Magani

T = T ^o C + 273

T = 50 + 273

T = 323

50 ^o C = 323 K

[irp]

4. 212 ^o F = ….. K?

Magani

To ^o C = (100/180)(Zuwa ^F – 32)

To ^o C = (5/9)(Zuwa ^F – 32)

To ^o C = (5/9)(212 – 32)

To ^o C = (5/9)(180)

To ^o C = (5)(20)

To ^o C = 100

212 ^o F = 100 ^o C + 273

212 ^o F = 373 K

 

5. x ^o C = x ^o F

x = ……?

Magani

1: Canza ma'aunin Celsius zuwa ma'aunin Fahrenheit

2: Canza ma'aunin Fahrenheit zuwa ma'aunin Celsius

[irp]

6. 122°F = ….. Celsius

Magani

Za a iya rubuta canjin da ke tsakanin ma'aunin zafin jiki guda biyu:

T _C = 5/9 (T _F – 32)

T _C = Zafin jiki a Celsius, T _F = Zafin jiki a Fahrenheit

Zafin Celsius:

T _C = 5/9 (122 – 32) = T _C = 5/9 (90) = 5 (10)

T _C = 50 ^o C

7. Hoton da ke ƙasa yana nuna ma'aunin zafin ruwa tare da ma'aunin zafi na sikelin Fahrenheit! Idan an auna zafin ruwan ta amfani da ma'aunin zafi na sikelin Celsius, to menene zafin ruwan e.

An sani:

Sikelin Fahrenheit (T _F ) = 95 ^o F

Ana so: sikelin Celsius

Magani:

A matsin lamba na atm 1, wurin daskarewar ruwa shine 0 °C yayin da sikelin Fahrenheit shine 32 ^o F. Akasin haka, wurin tafasar ruwa don sikelin Celsius shine 100 ^o C yayin da sikelin Fahrenheit shine 212 ^o F.

A ma'aunin Celsius, tsakanin 0 °C da 100 °C akwai 100 ° yayin da a ma'aunin Fahrenheit tsakanin 32 °F zuwa 212 °F akwai 180 °.

T _C = 100/180 (T _F – 32)

T _C = 5/9 (T _F – 32)

T _C = 5/9 ( 95 – 32)

T _C = 5/9 ( 63 )

T _C = 315/9

T _C = 35 ^o C

8. Dangane da hoton da ke ƙasa, ƙayyade zafin jiki na P akan ma'aunin zafi na Celsius.

Magani

T_C = 100/180 (T)_F - 32)

T _C = 5/9 (T _F – 32)

T _C = 5/9 (104 – 32)

T _C = 5/9 (72)

T _C = 360/9

T _C = 40 ^oC

9. Idan zafin ma'aunin Celsius ya nuna a cikin hoton da ke ƙasa, a ƙayyade zafin ma'aunin Fahrenheit kamar yadda aka nuna a cikin hoton da ke ƙasa.

Magani:

T^oF = (180/100) T^oC + 32

To ^o F = (9/5) To ^o C + 32

To ^o F = (9/5) 60 + 32

To ^o F = (9) 12 + 32

T ^o F = 108 + 32

To ^o F = 140

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

1. An nuna jadawalin ƙarfi (F) idan aka kwatanta da tsawo (x ) a cikin hoton da ke ƙasa. Nemo madaidaicin bazara!

Magani

Tsarin dokar Hooke :

ku = F / x

F = ƙarfi (Newton)

k = madaidaitan bazara (Newton/mita)

x = canjin tsayi (mita)

Madaidaicin bazara:

k = 10 / 0.02 = 20 / 0.04

k = 500 N/m

[irp]

2. Ƙayyade ma'aunin bazara.

Magani

Madaidaicin bazara:

ku = F / x

k = 5 / 0.01 = 10 / 0.02 = 15 / 0.03 = 20 / 0.04

k = 500 N/m

[irp]

3. Bazara ta A tana da tsayin asali na 60 cm, kuma bazara ta B tana da tsayin asali na 90 cm. Bazara ta A tana da tsayin 100 N/m, bazara ta B kuma tana da tsayin 200 N/m. Rabon canjin tsawon bazara A zuwa canjin tsawon bazara B shine…

An sani:

Daidaiton bazara A (kA ₎ = 100 N/m

Daidaiton bazara B (kB ₎ = 200 N/m

Ƙarfin da ke kan bazara A (F _A ) = F

Ƙarfin da ke kan bazara B (F _B ) = F

Ana so: Δl _A : Δl _B

Magani:

Tsarin dokar Hooke:

Δl = F / k

Δl = canjin tsayi, F = ƙarfi, k = m

Canjin tsawon bazara A:

Δl _A = F _A / k _A = F / 100

Canjin tsawon bazara B:

Δl _B = F _B / k _B = F / 200

Rabon canjin tsawon bazara A zuwa canjin tsawon bazara B:

Δl _A : Δl _B

F/100: F/200

1 / 100: 1 / 200

1 / 1: 1 / 2

2: 1

[irp]

4. Zaren nailan mai tsayin asali na santimita 20, ana jan shi da ƙarfin N10. Canjin tsawon zaren shine santimita 2. A ƙayyade girman ƙarfin idan canjin tsawon shine santimita 6.

An sani:

Ƙarfi (F) = 10 N

Canjin tsayi ( Δl ) = 2 cm = 0.02 m

Ana so: girman ƙarfin (F) idan Δl = 0.06 m.

Magani:

Kullum:

k = F / Δl

k = 10 / 0.02 = 500 N/m

Girman ƙarfin (F) idan Δl = 0.06 m:

F = kx

F = (500)(0.06)

F = 30N

[irp]

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1. Dokar Hooke
2. Damuwa, damuwa, tsarin Young

Karin bayani

Tsarin Matsalar Damuwa ta Matasa - Matsaloli da Magani

1. Zaren nailan yana da diamita na 2 mm, wanda ƙarfin N100 ke ja. Ka ƙayyade damuwa!

An sani:

Ƙarfi (F) = 100 N

Diamita (d) = 2 mm = 0.002 m

Radius (r) = 1 mm = 0.001 m

Ana so: Damuwa

Magani:

Yanki:

A = π r ²

A = (3.14)(0.001 m) ² = 0.00000314 m ²

A = 3.14 x 10 ^-6 m ²

Damuwa:

[irp]

2. Igiya tana da tsawon asali na santimita 100, ƙarfin da ke jan ta. Canjin tsawon igiyar shine milimita 2. Ka ƙayyade irin ƙarfin!

An sani:

Tsawon asali (l ₀ ) = 100 cm = 1 m

Canjin tsayi (Δl) = 2 mm = 0.002 m

Ana so: Nau'in

Magani:

Jirgin ƙasa :

[irp]

3. Zaren da diamitansa ya kai mm 4 yana da tsayin asali na mita 2. Ana jan zaren da ƙarfin N 200. Idan tsawon bazara na ƙarshe ya kai mita 2.02, a tantance: (a) damuwa (b) nau'in (c) Tsarin Young

An sani:

Diamita (d) = 4 mm = 0.004 m

Radius (r) = 2 mm = 0.002 m

Yanki (A) = π r ² = (3.14) (0.002 m) ²

Yanki (A) = 0.00001256 m ² = 12.56 x 10 ^-6 m ²

Ƙarfi (F) = 200 N

Tsawon asali na bazara (l ₀ ) = 2 m

Canjin tsayi (Δl) = 2.02 – 2 = 0.02 m

Ana so: (a) Damuwa (b) Nau'in c) Tsarin Young

Magani:

(a) Damuwa

(b) Matsalar

(c) Tsarin Young

[irp]

4. Zaren yana da diamita na 1 cm kuma tsawon asali na 2 m. Ana jan zaren da ƙarfin 200 N. Kayyade canjin tsawon zaren! Matakan Young na zaren = 5 x 10 ⁹ N/m ²

An sani:

Matakan Young (E) = 5 x 10 ⁹ N/m ²

Tsawon asali (l ₀ ) = 2 m

Ƙarfi (F) = 200 N

Diamita (d) = 1 cm = 0.01 m

Radius (r) = 0.5 cm = 0.005 m = 5 x 10 ^-3 m

Yanki ( A) = π r ² = (3.14)(5 x 10 ^-3 m) ² = (3.14)(25 x 10 ^-6 m2 ⁾

Yanki (A) = 78.5 x 10 ^-6 m ² = 7.85 x 10 ^-5 m ²

Ana so : Canjin tsayi (Δl)

Magani:

Tsarin tsarin Young:

Canjin tsayi :

[irp]

5. Siminti yana da tsayin mita 5 kuma yana da yanki na yanki na 3 m3 ^wanda ke tallafawa nauyin kilogiram 30,000. Ƙayyade (a) Damuwa (b) Matsala (c) Canjin tsayi! Saurin nauyi saboda nauyi (g) = 10 m/s ^2. Matakan siminti na Young = 20 x 10 ⁹ N/m ²

An sani:

Tsarin siminti na Young = 20 x 10 ⁹ N/m ²

Tsawon farko (l ₀ ) = mita 5

Yankin sashe (A) = 3 m ²

Nauyi (w) = mg = (30,000)(10) = 300,000 N

Ana so: (a) Damuwa (b) Damuwa (c) Canjin tsayi!

Magani:

(a) Damuwa

(b) Matsalar

(c) Canjin tsayi

[irp]

1. Dokar Hooke
2. Damuwa, damuwa, tsarin Young

Karin bayani

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

[irp]

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

[irp]

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

[irp]

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[wpdm_package id='439′]

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

Karin bayani

1. Tayar mai radius 3 0 cm tana juyawa a daidai 5 rad/s ^2. Menene girman hanzarin layi na wani wuri da ke (a) 10 cm daga tsakiya (b) 20 cm daga tsakiya (c) a gefen dabaran?

An sani:

Radius (r) = 30 cm = 0.3 m

Haɓaka kusurwa ( α ) = 5 rad/s ²

Ana so: hanzarin layi (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m

Magani:

Alaƙa tsakanin hanzarin layi (a) da hanzarin kusurwa:

a = rα

(a) hanzarin layi, r = 0.1 m

a = (0.1 m)(5 rad/s ² ) = 0.5 m/s ²

(b) hanzarin layi, r = 0.2 m

a = (0.2 m)(5 rad/s ² ) = 1 m/s ²

(c) hanzarin layi, r = 0.3 m

a = (0.3 m)(5 rad/s ² ) = 1.5 m/s ²

[irp]

2. Kuraje mai tsawon santimita 50 a radius. Idan saurin gudu na layi na wani wuri da ke gefen kuraje shine mita 2/s ² , ƙayyade saurin gudu na kusurwoyin kusurwoyin!

An sani:

Radius (r) = 50 cm = 0,5 m

hanzarin layi (a) = 2 m/s ²

Ana so: hanzarin kusurwa

Magani:

α = a / r = 2 / 0.5 = 4 rad/s ²

3. Ruwan wukake a cikin injin niƙa mai tsawon santimita 20 a radius, da farko a lokacin hutawa. Bayan daƙiƙa 2, ruwan wukake suna juyawa 10 rad/s. A ƙayyade girman saurin layi (a) wani wuri da ke da santimita 10 daga tsakiya (b) wani wuri da ke gefen ruwan wukake.

An sani:

Radius (r) = 20 cm = 0.2 m

_Saurin kusurwa na farko ( ωo ) = 0

Saurin kusurwa na ƙarshe ( ω _{t )} = 10 radians/daƙiƙa

Tazarar lokaci (t) = daƙiƙa 2

Ana so: saurin gudu na layi na wani wuri da ke (a) r = 0.1 m (b) r = 0.2 m

Magani:

ω _t = ω _o + α t

10 = 0 + α (2)

10 = 2 α

α = 10/2

 α = 5 rad/s

(a) hanzarin layi na r = 0.1 m

a = r α = (0.1 m) (5 rad/s ² ) = 0.5 m/s ²

(b) hanzarin layi na r = 0.2 m

a = r α = (0.2 m) (5 rad/s ² ) = 1 m/s ²

[irp]

4. Ana hanzarta tayoyin 20 cm a radius na tsawon daƙiƙa 2 daga 20 rad/s don hutawa. A ƙayyade girman saurin layi (a) wani wuri da ke da nisan 10 cm daga tsakiya (b) wani wuri da ke da nisan 10 cm daga tsakiya.

An sani:

Radius (r) = 20 cm = 0.2 m

Saurin kusurwa na farko ( ωo) = ₂₀ rad/s

_{Gudun kusurwa na ƙarshe} ( ωt ) = 0

Tazarar lokaci (t) = daƙiƙa 2

Ana so: Hanzarin layi (a) r = 0.1 m (b) r = 0.2 m

Magani:

ω _t = ω _o + α t

0 = 20 + α (2)

-20 = 2 α

α = -20 / 2

 α = -10 rad/s

Alamar korau tana nufin saurin kusurwa yana raguwa.

(a) hanzarin layi na r = 0.1 m

a = r α = (0.1 m) (-10 rad/s ² ) = -1 m/s ²

(b) hanzarin layi na r = 0.2 m

a = r α = (0.2 m) (-10 rad/s ² ) = -2 m/s ²

[irp]

[wpdm_package id='429′]

[wpdm_package id='439′]

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

Karin bayani

1. Ƙwallo a ƙarshen igiya tana juyawa daidai gwargwado a cikin da'irar kwance ta radius mita 2 a saurin kusurwa mai ɗorewa 10 rad/s. Ka ƙayyade girman saurin layi na wani wuri da ke:

(a) Mita 0.5 daga tsakiya

(b) Mita 1 daga tsakiya

(c) Mita 2 daga tsakiya

An sani:

Radius (r) = mita 0.5 a s, mita 1, mita 3

Gudun kusurwa = 10 radians s / se cond

Ana so: Gudun layi

Magani:

v = r ω

v = saurin layi , r = radius , ω = saurin kusurwa

(a) Gudun layi (v) na wani wuri da ke r = mita 0.5

v = r ω = (mita 0.5 s )(10 rad/s) = mita 5 s / se yanayin

(b) Gudun layi (v) na wani wuri da ke r = mita 1

v = r ω = (mita 1)(10 rad/s) = mita 10 s / se yanayin

(c) Saurin layi (v) na wani wuri da ke r = mita 2 a cikin s

v = r ω = (mita 2 s )(10 rad/s) = mita 20 s / se yanayin

[irp]

2. Ruwan wukake a cikin injin blender suna juyawa a gudun 5000 rpm. Kayyade girman saurin layi:

(a) wani wuri da ke da nisan santimita 5 daga tsakiya

(b) wani wuri da ke da nisan santimita 10 daga tsakiya

An sani:

Radius (r) = 5 cm da 10 cm

Gudun kusurwa (ω) = 5000 juyin juya hali / s 60karshen = 83.3 juyin juya hali / seyanayi = (83.3)(radian 6.28) / seyanayi = 523.3 radianss / seyanayi

Ana so: Girman saurin layi

Magani:

(a) Girman saurin layi na wani wuri da ke da nisan mita 0.05 daga tsakiya

v = r ω = (0.05 m)( 523.3 rad/s) = 26 m/s

(b) Girman saurin layi na wani wuri da ke da nisan mita 0,1 daga tsakiya

v = r ω = (0.1 m)( 523.3 rad/s) = 52 m/s

3. Wani wuri a gefen tayar mai tsawon santimita 30 a radius, a kusa da da'ira a gudun mita 10/dakika.

Menene girman saurin kusurwa?

An sani:

Radius ( r) = 30 cm = mita 0.3 a s

Saurin layi (v) = mita 10 a minti ɗaya

Ana so: saurin kusurwa

Magani:

ω = v / r = 10 / 0.3 = 33 radians s / se cond

[irp]

4. Motar da ke da tayoyi masu diamita santimita 50 tana tafiya mita 10 cikin daƙiƙa 1. Menene saurin kusurwa?

An sani:

Radius (r) = mita 0.25

Gudun layi na wani wuri a gefen tayoyin (v) = mita 10 s / se cond

Ana so: Gudun kusurwa

Magani:

ω = v / r = 10 / 0.25 = 40 radians s / se cond

5. Gudun kusurwa na tayoyin 20 cm a cikin radians shine 120 rpm. Menene nisan idan motar ta yi tafiya cikin daƙiƙa 10.

An sani:

Radius (r) = 20 cm = mita 0.2 a s

Gudun kusurwa = 120 sakewa / 60 secyanayi = 2 sakewa / seyanayi = (2)(6.28) radians / seyanayi = 12.56 radianss / seyanayi

Ana so: nesa

Magani:

Gudun gefen tayoyin:

v = r ω = (mita 0.2 s )(12.56 radians s / se cond ) = mita 2.5 s / se cond

2.5 mitas / second yana nufin wani wuri a gefen tafiyar tayoyin 2.5 mitas kowane daƙiƙa 1. bayan 10 gayanayi, ma'anar tana tafiya 25 mitas.

Don haka nisan shine mita 25 a sakan daya.

[irp]

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[wpdm_package id='439′]

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

Karin bayani

Canza raka'o'in kusurwa (digiri, radian, juyin juya hali)

1. ¼ rev = ….. ^o ( digiri )?

Magani

Juyin juya hali 1 = 360 ^o

½ sake dubawa = 180 ^o

¼ sake dubawa = 90 ^o

2. ½ rev = …….. r ad?

Magani

1 rev = 2 π rad = 2 (3.14) rad = 6.28 rad

½ rev = pi rad = 3.14 rad

3. 180 ^o = ….. sake dubawa?

Magani

Juyin juya hali 360 ^o = juyin juya hali 1

180 ^o = ½ sake dubawa

[irp]

4. 90 ^o = ….. rad ?

Magani

360 ^o = 2 π rad = 2 (3.14) rad = 6.28 ra d

180 ^o = π rad = 3.14 rad

90 ^o = ½ π rad = ½ (3.14) = 1.57

5. 60 rad = ….. sake dubawa?

Magani

6.28 rad = 1 juyi

60 rad/6.28 = 9.55 juyi

6. 40 rad= ….. ^o?

Magani

6.28 rad = 360 ^o

40 rad/6.28 = (6.37) (360 ^o ) = 2292.99 ^o

[irp]

Matsar da kusurwa da kuma ƙaura ta layi

1. Tayar keke mai diamita santimita 60 tana jujjuya radians 10. Menene ma'aunin layi na wani wuri a gefen tayar?

An sani:

Radius (r) = 30 cm = 0.3 m

Kusurwoyi (θ ) = 10 radians

Ana so: matsar layi (l)

Magani:

l = r θ

l = (0.3 m)(10 rad)

l = mita 3

2. Tayar da ke da santimita 50 a radius tana juyawa 360 ^o . Menene ma'aunin layi na wani wuri a gefen tayar?

An sani:

Radius (r) = 50 cm = mita 0.5

Kusurwoyi ( θ ) = 360 ^o = 6.28 radians

Ana so: matsar layi (l)

Magani:

l = r θ

l = (0.5 m)(6.28 rad)

l = mita 3.14

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3. Tayar da ke da santimita 50 a radius tana juyawa sau biyu. Menene canjin layi na wani wuri a gefen tayar?

An sani:

Radius (r) = 50 cm = 0,5 m

Kusurwoyi ( θ ) = Juyi 2 = (2)(radiyoyin 6.28) = radiyoyin 12.56

Ana so: matsar layi (l)?

Magani:

l = r θ

l = (0.5 m)(12.56 rad)

l = 6.28 m

4. Wani wuri a gefen tayoyi mai tsawon mita 2 a radius, yana motsawa mita 100. Ka tantance matsar kusurwa.

An sani:

Radius (r) = ½ (diamita) = ½ (mita 2) = mita 1

Matsar da layi (l) = mita 100

Magani:

(a) Matsar da kusurwa (a cikin radians)

θ = s / r = 100 / 1 = 100 radians

(b) Matsar da kusurwa (a digiri)

1 radian = 360 ^o

Radians 100 = 100(360 ^o ) = Radians 36,000

(c) Matsar da kusurwa (a juyin juya hali)

6.28 radians = juyin juya hali 1

Juyin juya hali 36,000 / 6.28 = juyin juya hali 5732,484

[irp]

5. Ƙwayar zarra tana zagaye da'ira mita 10 kuma tana juyawa 180 ^o . Menene radius ɗin?

An sani:

Matsar da layi (l) = mita 10

Kusurwar ( θ ) = 180 ^o = 3.14 radians

Ana so: radius (r)

Magani:

r = l / θ = 10 / 3.14 = 3.18 mita

[irp]

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

Karin bayani

1. Tayar mita 1 a radius tana sauri daidai gwargwado a 2 rad/s ^2. Kayyade hanzarin kusurwa da saurin kusurwar tayar, bayan daƙiƙa 2.

An sani:

Radius (r) = mita 1

Hanzarin kusurwa (α ) = 2 rad/s ²

Ana so: hanzarin kusurwa da saurin kusurwa bayan daƙiƙa 2.

Magani:

(a) Hanzar kusurwa cikin daƙiƙa 2

Haɓaka kusurwa yana dawwama, don haka bayan daƙiƙa 2, haɓaka kusurwar ƙafafun shine 2 rad/s ².

(b) Saurin kusurwa cikin daƙiƙa 2

Haɓaka kusurwa 2 rad/s ² yana nufin saurin kusurwa yana ƙaruwa da radians 2 a kowace daƙiƙa 1. Bayan daƙiƙa 1, saurin kusurwa = radians 2 a kowace daƙiƙa. Bayan daƙiƙa 2, saurin kusurwa = radians 4 a kowace daƙiƙa.

[irp]

2. Ƙwayar cuta tana hanzartawa daidai gwargwado daga hutawa zuwa rpm 60 cikin daƙiƙa 10. Kayyade girman hanzarin kusurwa!

An sani:

Saurin kusurwa na farko (ωo ₎ = 0

Saurin kusurwa na ƙarshe ( ω _t ) = 60 rpm = juyin juya hali 60 / daƙiƙa 60 = juyin juya hali 1 / daƙiƙa = 6,28 radians/daƙiƙa

Tazarar lokaci (t) = daƙiƙa 10

Ana so: Hanzarin kusurwa ( α )

Magani:

ω _o = saurin kusurwa na farko, ω _t = saurin kusurwa na ƙarshe, α = hanzarin kusurwa, t = tazara ta lokaci, θ = kusurwa.

ω _t = ω _o + α t

6.28 = 0 + α (10)

6.28 = 10 α

α = 6.28 / 10

α = 0.628 rad/s ²

Girman hanzarin kusurwa = 0.628 rad/s ²

3. Abu yana raguwa daga 20 rad/s zuwa 10 rad/s cikin daƙiƙa 4. Kayyade girman hanzarin kusurwa!

An sani:

Tazarar lokaci (t) = daƙiƙa 4

Saurin kusurwa na farko ( ωo ₎ = 20 rad/s

Saurin kusurwa na ƙarshe ( ω _t ) = 10 rad/s

Ana so : girman hanzarin kusurwa (α )

Magani:

ω _t = ω _o + α t

10 = 20 + α (4)

10 – 20 = 4 α

-10 = 4 α

α = -10 / 4

α = – 2.5 rad/s ²

Girman hanzarin kusurwa shine -2.5 rad/s ^2. Alamar mara kyau tana nufin abu yana raguwa. Saurin gudu = saurin kusurwa yana ƙaruwa, raguwa = saurin kusurwa yana raguwa.

[irp]

4. Ana hanzarta abu na tsawon daƙiƙa 2 daga 10 rad/s zuwa 2 rad/s ^2. Kayyade kusurwar da aka zagaye ta hanyar abin!

An sani:

saurin kusurwa na farko ( ωo ₎ = 10 rad/s

hanzarin kusurwa (α ) = 2 rad/s ²

tazara ta lokaci (t) = daƙiƙa 2

Ana so: kusurwa (θ)

Magani:

θ = ω _o + ½ α t ²

θ = (10)(2) + ½ (2)(2 ² )

θ = 20 + (1)(4) = 20 + 4

θ = 24 radians

5. Tayar mota tana raguwa daga 20 rad/s zuwa hutawa bayan zagaye na 20 radians. Kayyade girman saurin kusurwa na tayar!

An sani:

saurin kusurwa na farko ( ωo ₎ = 20 rad/s

_{Gudun kusurwa na ƙarshe} ( ωt ) = 0

Kusurwoyi ( θ ) = 20 radians

Ana so: girman hanzarin kusurwa (α )

Magani:

ω _t ² = ω _o ² + 2 α θ

0 = 20 ² + 2 α (20)

0 = 400 + 40 α

400 = – 40 α

α = – 400 / 40

α = – 10 rad/s ²

6. Sanda mai tsawon santimita 60 tana juyawa game da maki Q a matsayin ma'aunin juyawa da PQ a matsayin radius na da'ira. Sanda mai saurin PQ daga hutawa zuwa 0.3 rad/s ^2. Menene saurin layi na maki P a t = daƙiƙa 10, idan matsayin kusurwar farko shine 0.

An sani:

Tsawon sandar PQ = radius na da'ira (r) = 60 cm = 60/100 m = 0.60 m

Saurin kusurwa na farko (ω _o ) = 0 rad/s

Haɓaka kusurwa (α) = 0.3 rad s ^-2

Matsayin kusurwa na farko (θ _o ) = 0

Ana so: Gudun layi (v) na maki P a t = daƙiƙa 10

Magani:

Saurin kusurwa na ƙarshe bayan daƙiƙa 10:

ω _t = ω _o + α t = 0 rad/s + (0.3 rad s ^-2 )(10 s) = 3 rad/s

Saurin layi na ƙarshe bayan daƙiƙa 10:

v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s

[irp]

7. Abu yana juyawa da saurin farko na 4 rad/s kuma saurin kusurwa shine 0.5 rad/s ^2. Menene saurin abu bayan daƙiƙa 4.

An sani:

Saurin kusurwa na farko (ω _o ) = 4 rad/s

Hanzarin kusurwa (α) = 0.5 rad/s ²

Tazarar lokaci (t) = daƙiƙa 4

Ana so: Saurin abu bayan daƙiƙa 4 (ω _t )

Magani:

ω _t = ω _o + α t

ω _t = 4 + (0.5)(4)

ω _t = 4 + 2

ω _t = 6 rad/s

8. Agogon bango mai diamita na santimita 10 yana da allurai uku, kowannensu don nuna awanni, mintuna da daƙiƙa. Kwatanta adadin zagaye na allurar sa'a: allurar minti: allurar ta biyu.

A. 1: 3: 180

B. 1: 12: 720

C. 4: 12: 180

D. 4: 12: 720

An sani:

Awa 1 = mintuna 60

Awa 12 = (12)(minti 60) = mintuna 720

Gudun kusurwa na awa na allura = juyin juya hali 1 / awanni 12 = juyin juya hali 1 / mintuna 720

Gudun kusurwa na mintuna allura = juyin juya hali 1 / awa 1 = juyin juya hali 1 / minti 60

Saurin kusurwa na allura ta biyu = juyin juya hali 1 / minti 1

Ana so: Kwatanta adadin zagaye na allurar sa'a: allurar minti: allurar ta biyu

Magani:

Daidaiton motsi na zagaye:

Gudun kusurwa = adadin juyin juya hali / tazara lokaci

Adadin juyin juya hali = saurin kusurwa x tazara lokaci

A cikin tazara lokaci ɗaya, misali, minti 1, sau nawa juyawar allurar awa, allurar minti, da allurar ta biyu.

Adadin juyawar allurar sa'a = saurin kusurwa x tazara ta lokaci = (juyi 1 / mintuna 720)(minti 1) = juyawa 1/720

Adadin juyawar allurar minti = saurin kusurwa x tazara lokaci = (juyi 1 / mintuna 60)(minti 1) = juyawa 1/60

Adadin juyawar allura ta biyu = saurin kusurwa x tazara ta lokaci = (juyi 1 / minti 1)(minti 1) = 1/1 juyawa

Kwatanta juyin juya hali da dama:

Adadin juyin juya halin allurar sa'a: adadin juyin juya halin allurar minti: adadin juyin juya halin allurar ta biyu.

1/720: 1/60: 1/1

1/720: 12/720: 720/720

1: 12: 720

Amsar da ta dace ita ce B.

9. Ƙwallo da aka ɗaure da igiya. Ana juya ƙwallon ta yadda za ta motsa a cikin jirgin sama mai zagaye daidai da saman duniya. A cikin wannan motsi, ƙwallon yana ƙaruwa saboda…..

A. Gogayya ta iska

B. Nauyin ƙwallon

C. Ƙarfin tashin hankali

D. Ƙarfin nauyi

Magani:

Dokar motsi ta biyu ta Newton ta bayyana cewa abu yana hanzarta idan akwai ƙarfin da ya haifar. Ana haɗa ƙwallon da igiyar kuma lokacin da igiyar ta juya, ƙwallon ma tana juyawa. Lokacin da ƙwallon ta juya (ƙwallon yana motsawa a cikin da'ira), ƙwallon tana yin saurin centripetal. Duk abubuwan da ke motsawa suna da saurin centripetal. Haɓaka centripetal yana faruwa ne ta hanyar ƙarfin centripetal . Ƙarfin centripetal na wannan yanayin shine ƙarfin tashin hankali.

Madaidaicin amsar ita ce C.

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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

Karin bayani

1. Abu yana motsawa a cikin da'ira tare da saurin kusurwa mai 10 rad/s. Ƙayyade (a) Saurin kusurwa bayan daƙiƙa 10 (b) Saurin kusurwa bayan daƙiƙa 10.

An sani:

Gudun kusurwa (ω) = 10 rad/s

Ana so:

(a) Saurin kusurwa (ω) bayan daƙiƙa 10.

(b) Kusurwa (θ) bayan daƙiƙa 10

Magani:

(a) Saurin kusurwa (ω) bayan daƙiƙa 10

Abu a cikin motsi na zagaye iri ɗaya don gudun kusurwa ya kasance daidai, 10 rad/s.

(b) Matsar da kusurwa (θ)

Gudun kusurwa mai daidaito 10 radians/daƙiƙa yana nufin abu mai kusan radians 10 a kowace daƙiƙa. Bayan daƙiƙa 10, abu mai kusan radians 10 x 10 = radians 100.

[irp]

2. Ƙwayar cuta tana motsawa a cikin da'ira mai saurin mita 10/s. Radius na da'ira = mita 1. Ƙayyade (a) Gudun ƙwayar cuta bayan daƙiƙa 5 (b) Motsa ƙwayar cuta bayan daƙiƙa 5 (c) Hanzarta ta tsakiya.

An sani:

Radius na da'ira (r) = mita 1

Gudun barbashi (v) = 10 m/s

Magani:

(a) Saurin barbashi bayan daƙiƙa 5

Motsin abin yana cikin motsi mai zagaye iri ɗaya don haka gudun ya kasance mai daidaito, 10 m/s.

(b) Fitar da ƙwayoyin cuta bayan daƙiƙa 5

Mita 10/daƙiƙa yana nufin kowace daƙiƙa 1, ƙaurar ƙwayar cuta = mita 10. Bayan daƙiƙa 5, ƙaurar ƙwayar cuta = mita 5 x 10 = mita 50.

(c) Hanzarin tsakiya (a _r )

a _r = v ² / r = 10 ² / 1 = 100 / 1 = 100 m/s ²

3. An juya ƙwallon da aka makala a ƙarshen igiya a cikin da'ira mai radius na mita 2 a gudun da ba ya canzawa na rpm 60. A ƙayyade (a) girman saurin kusurwa bayan daƙiƙa 2 (b) canjin kusurwa bayan minti 1.

An sani:

Radius na da'ira (r) = mita 2

Gudun kusurwa (ω) = 60 rpm = juyin juya hali 60 / minti 1

= Juyi 60 / daƙiƙa 60 = Juyi 1 / daƙiƙa = 2π radians / daƙiƙa

= 2(3.14) radians / daƙiƙa = 6.28 radians / daƙiƙa

Magani:

(a) Saurin kusurwa (ω) bayan daƙiƙa 2

Gudun kusurwar yana da daidaito don haka bayan daƙiƙa 2, saurin kusurwar (ω) = 6.28 radians / daƙiƙa

(b) Matsar da kusurwa (θ)

Saurin kusurwa = juyin juya hali 1/daƙiƙa yana nufin kowace daƙiƙa 1, ƙwallon tana fuskantar juyin juya hali 1. Bayan daƙiƙa 60, ƙwallon tana motsa juyin juya hali 60.

Gudun kusurwa = radians 6.28/daki yana nufin kowace dakika 1, ƙwallon yana motsawa da kusurwar radians 6.28. Bayan dakika 60, ƙwallon yana motsawa radians 376.8.

[irp]

4. Tayar keke tana juyawa sau 120 cikin daƙiƙa 60. Menene saurin kusurwa?

Magani:

(a) juyin juya hali a minti daya (rpm)

Juyin juya hali 120 / daƙiƙa 60 = juyi 120 / minti 1 = juyi 120 / minti = 120 rpm

(b) digiri a kowace daƙiƙa ( ^o / s)

Juyin juya hali 1 = 360 ^o , Juyin juya hali 120 = 43200 ^o

Juyawa 120 / daƙiƙa 60 = (120)(360 ^o ) / daƙiƙa 60 = 43200 ^o / daƙiƙa 60 = 720 ^o / daƙiƙa

(c) radians a kowace daƙiƙa (rad/s)

Juyin juya hali 1 = 6.28 radians

Juyawa 120 / daƙiƙa 60 = (120)(6.28) radians / daƙiƙa 60 = 753.6 radians / daƙiƙa 60 = 12.56 radians/daƙiƙa.

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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

Karin bayani

1. An yi amfani da ƙwallon 0. 1-kg, wadda aka haɗa a ƙarshen igiyar kwance, a cikin da'irar radius 50 cm da kuma saurin kusurwar ƙwallon s 4 rad s -1 . Menene girman ^ƙarfin centripetal?

An sani:

Nauyi (m) = gram 100 = 100/1000 kg = 1/10 kg = 0.1 kg

Gudun kusurwa ( ω) = 4 radians/se cond

Radius (r) = 50 cm = 50/100 m = 0.5 m

Ana nema: Ƙarfin tsakiya

Magani:

Ƙarfin centripetal shine ƙarfin da ke samar da hanzarin centripetal :

∑ F = ma _r

∑ F = mv ² /r = m ω ² r

∑ F = ƙarfin net = ƙarfin centripetal , m = taro , v = gudu , ω = saurin kusurwa , r = radius

∑ F = m ω ² r = (0.1)(4) ² (0.5) = (0.1)(16)(0,5) = 0.8 Newtons

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2. Kwallo tana juyawa daidai gwargwado a cikin da'irar kwance. Idan saurin ya canza zuwa sau huɗu na ƙimar farko, menene girman ƙarfin centripetal…..

An sani:

Nauyi = m

Sauri = v

Saurin farko = v _o

Radius (r) = r

Ana nema: Girman ƙarfin centripetal

Magani:

3. An tsara lanƙwasa mai kusurwa huɗu na radius R ta yadda motar da ke tafiya a gudun 12 ms ^–1 za ta iya daidaita juyawar lafiya. Matsakaicin gogayya tsakanin mota da hanya = 0.4. Menene radius R. Hawan nauyi saboda nauyi ( g ) = 10 ms ^–2.

An sani:

Gudun (v) = 12 m/s

Ma'aunin gogayya mai tsauri ( μs ₎ = 0.4

Saurin gudu saboda nauyi (g) = 10 m/s ²

Ana nema: Radius (R)

Magani:

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1. Nauyi da nauyi
2. ƙarfin al'ada
3. Dokar motsi ta biyu ta Newton
4. Ƙarfin gogayya
5. Motsi a kan saman kwance ba tare da ƙarfin gogayya ba
6. Motsin gawawwaki biyu tare da hanzari iri ɗaya a kan saman kwance mai tsauri tare da ƙarfin gogayya
7. Motsi a kan jirgin sama mai karkata ba tare da ƙarfin gogayya ba
8. Motsi a kan jirgin sama mai karkata da ƙarfin gogayya
9. Motsi a cikin lif
10. Motsin jikin mutum yana da alaƙa da igiyoyi da kuma ƙwallo
11. Jikuna biyu masu girman gudu iri ɗaya
12. Zagaye lanƙwasa mai faɗi - yanayin motsi na zagaye
13. Zagaye lanƙwasa mai banked - yanayin motsi na zagaye
14. Motsi iri ɗaya a cikin da'irar kwance
15. Ƙarfin tsakiya a cikin motsi na zagaye iri ɗaya

Karin bayani