Physics

9 Kuchinja tembiricha (Celsius scale Fahrenheit scale Kelvin scale)

1. 50 ^oC = ….. ^oF ?

mhinduro

Mumhepo yakajairika kudzvinyirira, nzvimbo yekuomesa mvura ndeye 0 ^oC pane Chikero cheCelsius uye 32 ^oF pachikero cheFahrenheit. Pakumanikidzwa kwemhepo kwakajairika, pombi yekufashaira yemvura i100 ^oC pachikero cheCelsius uye 212 ^oF pachikero cheFahrenheit.

0 ^oC = zana ^oF na 100 ^oC = zana ^oF. Kuchinja kwe5 C^o = shanduko ye9 F^o.

Pachikero cheCelsius, daro riri pakati pe 0 ^oC uye 100 ^oC yakakamurwa kuita zvikamu zana zvakaenzana. Pachikero cheFahrenheit, daro riri pakati pe0 ^oC uye 100 ^oC yakakamurwa kuita zvikamu zana nemakumi masere zvakaenzana.

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

T^oF = (9/5) T^oC + 32

T^oF = (9/5) 50 + 32

T^oF = (9) 10 + 32

T^oF=90 + 32

T^oF=122

50 ^oC = zana ^oF

2. 86 ^oF = ….. ^oC?

mhinduro

T^oC = (100/180)(T)^oF – 32)

T^oC = (5/9)(T)^oF – 32)

T^oC = (5/9)(86 - 32)

T^oC = (5/9)(54)

T^oC = (5)(6)

T^oC = zana

86 ^oF=30 ^oC

3. 50^oC = ….. K ?

mhinduro

T = T ^oC + 273

T = 50 + 273

T = 323

50 ^oC= 323 K

4. 212^oF = ….. K ?

mhinduro

T^oC = (100/180)(T)^oF – 32)

T^oC = (5/9)(T)^oF – 32)

T^oC = (5/9)(212 - 32)

T^oC = (5/9)(180)

T^oC = (5)(20)

T^oC = zana

212 ^oF=100 ^oC + 273

212 ^oF=373 K

 

5. x ^oC = x ^oF

x = ….. ?

mhinduro

1: Kushandura chikero cheCelsius kuita chikero cheFahrenheit

2: Kushandura chikero cheFahrenheit kuita chikero cheCelsius

6. 122°F = ….. Celsius

mhinduro

Kuchinja pakati pezviyero zviviri zvekupisa kunogona kunyorwa seizvi:

T_C = 5/9 (T)_F - 32)

T_C = tembiricha muCelsius, T_F = tembiricha muFahrenheit

Tembiricha muCelsius:

T_C = 5/9 (122 - 32) = T_C = 5/9 (90) = 5 (10)

T_C = 50 ^oC

7. Mufananidzo uri pazasi unoratidza kuyerwa kwekupisa kwe a mvura ine thermometer yechikero cheFahrenheit! Kana tembiricha yemvura ikayerwa uchishandisa thermometer yechikero cheCelsius, saka chii tembiricha yemvurae.

Zvinozivikanwa:

Fahrenheit scale (T_F= = 95^oF

Zvaidiwa: Chikero cheCelsius

Solution:

Pakumanikidzwa kwe1 atm, nzvimbo inotonhora yemvura is 0 °C nepo chikero cheFahrenheit chiri 32 ^oF. Kusiyana neizvi, tpombi yekufashaira yemvura yeCElsius chikero i100 ^oC nepo chikero cheFahrenheit is 212 ^oF.

Pachiyero cheCelsius, pakati pe0 °C ne100 °C pane 100 ° nepo pachiyero cheFahrenheit chiri pakati pe32 °F ne212 °F pane 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^oC

8. Zvichibva pamufananidzo uri pazasi, sarudza ttembiricha P paCelsius thermometer.

mhinduro

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. Kana tembiricha yeCelsius ichienzaniswa nemufananidzo uri pazasi, tsvaga tembiricha yeFahrenheit inoenderana nemufananidzo uri pazasi.

Solution:

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

T^oF = (9/5) T^oC + 32

T^oF = (9/5) 60 + 32

T^oF = (9) 12 + 32

T^oF=108 + 32

T^oF=140

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

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1. Girafu yesimba (F) ichienzaniswa nekureba (x)) inoratidzwa mumufananidzo uri pazasi. Tsvaga chitubu chinoramba chiripo!

mhinduro

Mutemo waHooke formula :

k = F / x

F = simba (Newton)

k = chitubu chisingachinji (Newton/mita)

x = kuchinja kwehurefu (mamita)

Chirimo chinogara kwenguva refu:

k = 10 / 0.02 = 20 / 0.04

k = 500 N/m

2. Sarudza chitubu chinogara.

mhinduro

Chirimo chinogara kwenguva refu:

k = F / x

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

k = 500 N/m

3. Chitubu A chine hurefu hwepakutanga hwe60 cm uye chitubu B chine hurefu hwepakutanga hwe90 cm. Chitubu A chine hurefu hwe100 N/m, chitubu B chine hurefu hwe200 N/m. Chiyero chekuchinja kwehurefu hwechitubu A nekuchinja kwehurefu hwechitubu B ndeche…

Zvinozivikanwa:

Chimiro chechirimo A (k)_A) = 100 N/m

Chimiro chenguva dzose chechirimo B (k)_B) = 200 N/m

Simba pachitubu A (F)_A) = F

Simba pachitubu B (F)_B) = F

Kuda: Δl_A : Δl_B

Solution:

Fomura yemutemo waHooke:

Δl = F / k

Δl = kuchinja kwehurefu, F = simba, k = kusachinja-chinja

Kuchinja kwehurefu hwechitubu A:

Δl_A =F_A / k_A = F / 100

Kuchinja kwehurefu hwechitubu B:

Δl_B =F_B / k_B = F / 200

Chiyero chekuchinja kwehurefu hwechitubu A nekuchinja kwehurefu hwechitubu B:

Δl_A : Δl_B

F/100 : F/200

1/100: 1/200

1/1: 1/2

2: 1

4. Tambo yenylon ine urefu hwepakutanga hwemasendimita makumi maviri, inodhonzwa nesimba re10 N. Kuchinja kwehurefu hwetambo i2 cm. Sarudza hukuru hwesimba kana kuchinja kwehurefu kuri 6 cm.

Zvinozivikanwa:

Simba (F) = 10 N

Kuchinja kwehurefu (Δl) = 2 cm = 0.02 m

Zvaidiwa: hukuru hwesimba (F) kana Δl = 0.06 m.

Solution:

Nguva dzose:

k = F / Δl

k = 10 / 0.02 = 500 N/m

Hukuru hwesimba (F) kana Δl = 0.06 m :

F = kx

F = (500)(0.06)

F = 30N

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1. Mutemo waHooke
2. Kushushikana, kushushikana, modulus yeYoung

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Kushungurudzika Kwepfungwa Modulus yeYoung - Matambudziko neMhinduro

1. Tambo yenylon ine dhayamita ye 2 mm, inodhonzwa nesimba re 100 N. Tsvaga kushushikana!

Zvinozivikanwa:

simba (F) = 100 N

Dhayamita (d) = 2 mm = 0.002 m

Nharaunda (r) = 1 mm = 0.001 m

Zvaidiwa: Kushushikana

Solution:

Nzvimbo:

A = π r²

A = (3.14)(0.001 m)² = 0.00000314 XNUMX m²

A = 3.14 x 10^-6 m²

Kushushikana:

2. Tambo ine hurefu hwepakutanga hwemasendimita zana (100 cm) inodhonzwa nesimba. Kuchinja kwehurefu hwetambo i2 mm. Sarudza kuti tambo yacho yakamanikidzwa sei!

Zvinozivikanwa:

Kureba kwepakutanga (l)₀) = 100 cm = 1 m

Kuchinja kwehurefu (Δl) = 2 mm = 0.002 m

Zvaidiwa: Dambudziko racho

Solution:

Iyo schitima:

3. Tambo ine dhayamita ye4 mm ine hurefu hwepakutanga hwemamita maviri. Tambo yacho inodhonzwa nesimba re200 N. Kana hurefu hwekupedzisira hwechitubu huri 2.02 m, sarudza: (a) kushushikana (b) kushushikana (c) Kushanda kweYoung's modulus

Zvinozivikanwa:

Dhayamita (d) = 4 mm = 0.004 m

Nharaunda (r) = 2 mm = 0.002 m

Nzvimbo (A) = π r² = (3.14)(0.002 m)²

Nzvimbo (A) = 0.00001256 m² = 12.56 x gumi^-6 m²

Simba (F) = 200 N

Hurefu hwepakutanga hwechitubu (l)₀) = 2 m

Kuchinja kwehurefu (Δl) = 2.02 – 2 = 0.02 m

Zvaidiwa: (a) Kushushikana (b) Kushushikana c) Modulus yaYoung

Solution:

(a) Zvikamutress

(b) Dambudziko

(C) Modulus wechidiki

4. Tambo ine dhayamita ye 1 cm uye kureba kwepakutanga kwemamita maviri. Tambo inodhonzwa nesimba re 200 N. Tsvaga shanduko pakureba kwetambo! Modulus yaYoung yetambo = 5 x 10⁹ N / m²

Zvinozivikanwa:

Modulus yemudiki (E) = 5 x 10⁹ N / m²

Kureba kwepakutanga (l)₀) = 2 m

Simba (F) = 200 N

Dhayamita (d) = 1 cm = 0.01 m

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

Nzvimbo (A) = π r² = (3.14)(5 x 10^-3 m)² = (3.14)(25 x 10^-6 m²)

Nzvimbo (A) = 78.5 x 10^-6 m² = 7.85 x gumi^-5 m²

Wanted : Kuchinja kwehurefu (Δl)

Solution:

Fomura ye modulus yaYoung:

Kuchinja kwehurefu :

5. Konkriti ine urefu hwemamita mashanu uye ine nzvimbo ye3 m³ inotsigira a uremu ye30,000 kg. Tsvaga (a) Kushushikana (b) Kumanikidzwa (c) Kuchinja kwehurefu! Kuwedzera nekuda kwegiravhiti (g) = 10 m/s². Modulus yekongiri yaYoung = 20 x 10⁹ N / m²

Zvinozivikanwa:

Modulus yekongiri yaYoung = 20 x 10⁹ N / m²

Kureba kwekutanga (l)₀) = mamita makumi matanhatu

Nzvimbo yeyuniti (A) = 3 m²

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

Zvaidiwa: (a) Kushushikana (b) Kumanikidzwa (c) Kuchinja kwehurefu!

Solution:

(a) Kushushikana

(b) Dambudziko

(c) Kuchinja kwehurefu

1. Mutemo waHooke
2. Kushushikana, kushushikana, modulus yeYoung

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1. Bhora, rakasungirirwa kumagumo kwetambo yakatambanudzwa, rinotenderedzwa mudenderedzwa reradius 20 cm. Bhora iri rinotenderera 360 cm.^o Sekondi yega yega. Sarudza hukuru hwe kukurumidza kwepakati!

Zvinozivikanwa:

Kumhanya kwekona (ω)= = 360^o/yechipiri = 1 revolution/yechipiri = 6.28 radians/yechipiri

Nharaunda (r) = 20 cm = 0.2 M

Zvaidiwa: Kukurumidza kwepakati pepakati (a_r)

Solution:

a_r =v² /r —> v = r ω

a_r = (r ω)² / r = r² ω² /r

a_r =r ω²

a_s = kukurumidza kwepakati, v = kumhanya kwakatwasuka, r = dhayasi, ω = angular velocity

Kukura kwekumhanya kwepakati pepakati :

a_r =r ω² a_r = (0,2 m)(6.28 rad/s)

a_r = 1.256 m/s²

2. Vhiri re30 cm mu radius rinotenderera ne 180 rpm. Tsvaga kuti centripetal acceleration yepoindi iri pamucheto wevhiri iri kutenderera sei!

Zvinozivikanwa:

Nharaunda (r) = 30 cm = 0.3 m

Kumhanya kwekona (ω) = 180 revolutions / 60 seconds = 3 revolutions / second = (3)(6.28 radians) / second = 18.84 radians/second

Zvaidiwa: kukurumidza kwepakati (a_r) ye r = 0.3 m

Solution:

Kukura kwekumhanya kwepakati pesimba:

a_r =r ω²

a_r = (0.3 m)(18.84 rad / s)

a_r = 5.65 m/s²

3. Motokari yemujaho inofamba panzira yakatenderera ine radius yemamita makumi mashanu. Kana kumhanya kwemotokari kuri 72 km/awa, tarisa kukura kwekumhanya kwepakati!

Zvinozivikanwa:

Nharaunda (r) = 50 mamita

Kumhanya (v) = 72 km/awa = (72)(mamita 1000) / 3600 masekondi = 20 mamita/sekondi

Wanted : hukuru hwekumhanya kwepakati pesimba (a_r)

Solution:

a_r =v² / r = 20² / 50 = 400 / 50 = 8 m/s²

4. Mota ine kumhanya kwakanyanya kwepakati pe10 m/s², kuitira kuti mota ikwanise kutendeuka isina kutsvedza kubva munzira yakakombama. Kana mota iri kufamba ne108 km/awa, muganhu wekona isina kuvharwa ndewei?

Zvinozivikanwa:

Kukurumidza kwepakati (a_r) = 10 m/s²

Kumhanya kwemotokari (v) = 108 km/h = (108)(1000) / 3600 = mamita makumi matatus/second

Zvaidiwa: radius (r)

Solution:

r =v² / ivo_r

r = 30² / 10 = 900 / 10 = 90 mamitas

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1. Kuchinja mayuniti emakona emuenzaniso matambudziko nemhinduro
2. Matambudziko emuenzaniso wekutama kweAngular uye linear displacement uye mhinduro
3. Matambudziko emuenzaniso wekumhanya kweAngular uye kumhanya kwemutsara ane mhinduro
4. Matambudziko emuenzaniso wekumhanyisa kweAngular uye wekumhanyisa mutsara ane mhinduro
5. Muenzaniso wematambudziko ekufamba kwakatenderera kwakafanana nemhinduro
6. Matambudziko emuenzaniso wekumhanyisa kweCentripetal nemhinduro
7. Matambudziko emhando dzakasiyana dzemafambiro edenderedzwa ane mhinduro dzakasiyana

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1. Motokari ine mavhiri matatu0 cm mu radius inotenderera panguva imwe chete 5 rad/s². Hukuru hwei hwe kukurumidza kwakanangana yenzvimbo iri pa (a) 10 cm kubva pakati (b) 20 cm kubva pakati (c) pamucheto wevhiri?

Zvinozivikanwa:

Nharaunda (r) = 30 cm = 0.3 m

Kukurumidzisa kwekona (α) = 5 rad/s²

Zvaidiwa: kukurumidza kwakanangana (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m

Solution:

Hukama huripo pakati pekumhanyisa kwemutsara (a) uye kumhanyisa kwekona:

a = r α

(A) kumhanya kwakatwasuka, r = 0.1 m

a = (0.1 m)(5 rad/s²) = 0.5 m/s²

(B) kumhanya kwakatwasuka, r = 0.2 m

a = (0.2 m)(5 rad/s²) = 1 m/s²

(C) kumhanya kwakatwasuka, r = 0.3 m

a = (0.3 m)(5 rad/s²) = 1.5 m/s²

2. Pureji ine 50 cm mu radius. Kana kumhanyisa kwemutsara kwenzvimbo iri pamucheto wepureji kuri 2 m/s², sarudza kukurumidza kwekona kwepulley!

Zvinozivikanwa:

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

kukurumidza kwakanangana (a) = 2 m/s²

Zvaidiwa: kukurumidza kwekona

Solution:

α = a / r = 2 / 0.5 = 4 rad/s²

3. Mapadza ari mublender ane 20 cm mu radius, pakutanga ari pakuzorora. Mushure memasekonzi maviri, mapadza anotenderera 10 rad/s. Sarudza hukuru hwekumhanya kwakatwasuka (a) poindi iri pa10 cm kubva pakati (b) poindi iri pamucheto wemapadza.

Zvinozivikanwa:

Nharaunda (r) = 20 cm = 0.2 m

Kumhanya kwekutanga kwekona (ω_o) = 0

Kumhanya kwekupedzisira kwekona (ω_t) = 10 radians/sekondi

Nguva yepakati (t) = masekondi gumi nemashanu

Zvaidiwa: chinokurudzira mutsaranzvimbo iri pa (a) r = 0.1 m (b) r = 0.2 m

Solution:

ω_t = ω_o + α t

10 = 0 + α (2)

10 = 2 α

α = 10 / 2

 α = 5 rad/s

(A) kumhanya kwakanangana kwe r = 0.1 m

a = r α = (0.1 m)(5 rad/s²) = 0.5 m/s²

(B) kumhanya kwakanangana kwe r = 0.2 m

a =r α = (0.2 m)(5 rad/s²) = 1 m/s²

4. Vhiri re 20 cm mu radius rinokurumidziswa kwemasekonzi maviri kubva pa 20 rad/s kusvika razorora. Sarudza hukuru hwekukurumidzisa kwakanangana (a) poindi iri pa 10 cm kubva pakati (b) poindi iri pa 10 cm kubva pakati.

Zvinozivikanwa:

Nharaunda (r) = 20 cm = 0.2 m

Kumhanya kwekutanga kwekona (ω_o) = 20 rad/s

Kumhanya kwekupedzisira kwekona (ω_t= = 0

Nguva yepakati (t) = masekondi gumi nemashanu

Zvaidiwa: Kukurumidza kwakanangana (a) r = 0.1 m (b) r = 0.2 m

Solution:

ω_t = ω_o + α t

0 = 20 + α (2)

-20 = 2 α

α = -20 / 2

 α = -10 rad/s

Chiratidzo chekuramba chinoreva kumhanya kwekona kuri kuderera.

(A) kumhanya kwakanangana kwe r = 0.1 m

 a =r α = (0.1 m)(-10 rad/s²) = -1 m/s²

(B) kumhanya kwakanangana kwe r = 0.2 m

a = r α = (0.2 m)(-10 rad/s²) = -2 m/s²

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1. Kuchinja mayuniti emakona emuenzaniso matambudziko nemhinduro
2. Matambudziko emuenzaniso wekutama kweAngular uye linear displacement uye mhinduro
3. Matambudziko emuenzaniso wekumhanya kweAngular uye kumhanya kwemutsara ane mhinduro
4. Matambudziko emuenzaniso wekumhanyisa kweAngular uye wekumhanyisa mutsara ane mhinduro
5. Muenzaniso wematambudziko ekufamba kwakatenderera kwakafanana nemhinduro
6. Matambudziko emuenzaniso wekumhanyisa kweCentripetal nemhinduro
7. Matambudziko emhando dzakasiyana dzemafambiro edenderedzwa ane mhinduro dzakasiyana

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1. Bhora riri kumagumo kwetambo riri kutenderera zvakaenzana mudenderedzwa rakatwasuka reradius 2 metres ne angle speed 10 rad/s. Sarudza hukuru hwe linear velocity yenzvimbo iri :

(a) 0.5 metres kubva pakati

(b) mita imwe kubva pakati

(c) mamita maviri kubva pakati

Zvinozivikanwa:

nharaunda (r) = 0.5 mitas, mita imwe, mamita matatu

Kumhanya kwekona = 10 radians/semamiriro

Zvaidiwa: The kumhanya kwakatwasuka

Solution:

v = r ω

v= kumhanya kwakanangana, r = radius, ω = kumhanya kwekona

(A) Kumhanya kwemutsetse (v) kwenzvimbo iri pa r = 0.5 metres

v = r ω = (Mamita 0.5s)(10 rad/s) = mamita mashanus/semamiriro

(B) Kumhanya kwakanangana (v) yenzvimbo iri pa r = mita imwe

v = r ω = (mita imwe)(10 rad/s) = mamita gumis/semamiriro

(C) Kumhanya kwakanangana (v) yenzvimbo iri pa r = mita imwes

v = r ω = (Mamita 2s)(10 rad/s) = mamita mashanus/semamiriro

2. Mapazi ari mublender anotenderera ne5000 rpm. Sarudza hukuru hwemutsara wekukurumidza:

(A) nzvimbo iri 5 cm kubva pakati

(B) nzvimbo iri 10 cm kubva pakati

Zvinozivikanwa:

nharaunda (r) = 5 cm uye 10 masendimita

Kumhanya kwekona (ω) = 5000 kumukira / masekondi makumi matanhatueconds = 83.3 kumukira / semamiriro = (83.3)(6.28 radians) / semamiriro = 523.3 radians / semamiriro

Zvaidiwa: Hukuru hwekumhanya kwakanangana

Solution:

(A) Ukuru hwekumhanya kwemutsara wepoindi iri 0.05 m kubva pakati

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

(B) Ukuru hwekumhanya kwemutsara wepoindi iri 0,1 m kubva pakati

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

3. Poindi iri pamucheto wevhiri 30 masendimita muredhiyo, kutenderera denderedzwa nekumhanya kwakasimba Mamita gumi/sekondi.

Chii chinonzi angular velocity?

Zvinozivikanwa:

Nharaunda (r) = 30 cm = 0.3 mamitas

Kumhanya kwakanangana (v) = mamita gumis/semamiriro

Zvaidiwa: kumhanya kwekona

Solution:

ω = v / r = 10 / 0.3 = 33 radianss/semamiriro

4. Mota ine matayi ane dhayamita ye50 cm mufambols 10 metres mu 1 Chepiri. Chii chinonzi kona yekumhanya?

Zvinozivikanwa:

nharaunda (r) = mamita 0.25

Kumhanya kwakanangana kwe nzvimbo iri pamucheto wevhiri (v) = mamita gumis/semamiriro

Kuda: Kumhanya kwekona

Solution:

ω = v / r = 10 / 0.25 = 40 radianss/semamiriro

5. Kumhanya kwevhiri re20 cm muma radians kuri 120 rpm. Chii chinonzi mufambo kana mota ikafamba mumasekonzi gumi.

Zvinozivikanwa:

nharaunda (r) = 20 cm = 0.2 mamitas

Kumhanya kwekona = 120 rev / 60 semamiriro ezvinhu = 2 rev / semamiriro = (2)(6.28) radians / semamiriro = 12.56 radians / semamiriro

Zvaidiwa: mufambo

Solution:

Velocity yemucheto wevhiri:

v = r ω = (0.2 mamitas)(12.56 radians/semamiriro) = 2.5 mamitas/semamiriro

2.5 mamitas / second zvinoreva nzvimbo iri pamucheto wekufamba nevhiri 2.5 mamitas sekondi imwe neimwe. pashure 10mamiriro ezvinhu, pfungwa yacho inofamba 25 mamitas.

Saka chinhambwe chacho 25 mamitas.

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1. Kuchinja mayuniti emakona emuenzaniso matambudziko nemhinduro
2. Matambudziko emuenzaniso wekutama kweAngular uye linear displacement uye mhinduro
3. Matambudziko emuenzaniso wekumhanya kweAngular uye kumhanya kwemutsara ane mhinduro
4. Matambudziko emuenzaniso wekumhanyisa kweAngular uye wekumhanyisa mutsara ane mhinduro
5. Muenzaniso wematambudziko ekufamba kwakatenderera kwakafanana nemhinduro
6. Matambudziko emuenzaniso wekumhanyisa kweCentripetal nemhinduro
7. Matambudziko emhando dzakasiyana dzemafambiro edenderedzwa ane mhinduro dzakasiyana

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Kushandura mayuniti ekona (dhigirii, radian, revolution)

1. ¼ rev = ….. ^o (degree)?

mhinduro

1 rev = 360^o

½ rev = 180^o

¼ rev = 90^o

2. ½ rev = …….. rad ?

mhinduro

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

½ rev = pi rad = 3.14 rad

3. 180^o = ….. rev?

mhinduro

360^o = 1 rev

180^o = ½ rev

4. 90^o = ….. rad ?

mhinduro

360^o = 2π radhi = 2(3.14) radhi = 6.28 rad

180^o = π radhi = 3.14 radhi

90^o = ½ π rad = ½ (3.14) = 1.57

5. 60 rad = ….. rev ?

mhinduro

6.28 rad = 1 rev

60 rad/6.28 = 9.55 rev

6. 40 rad= ….. ^o ?

mhinduro

6.28 rad = 360^o

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

Kutama kwekona uye kutamiswa kwakatwasuka

1. Vhiri rebhasikoro rine dhayamita ye60 cm rinotenderera ma radians gumi. Chii chinonzi kutama kwakanangana yenzvimbo iri pamucheto wevhiri?

Zvinozivikanwa:

Nharaunda (r) = 30 cm = 0.3 m

Angle (θ)) = ma radians gumi

Zvaidiwa: kutama kwakatwasuka (l)

Solution:

l = r θ

l = (0.3 m)(10 rad)

l = mamita matatu

2. Vhiri re50 cm mu radius rinotenderera 360^oChii chinonzi kusuduruka kwemutsara wepoindi iri pamucheto wevhiri?

Zvinozivikanwa:

Nharaunda (r) = 50 cm = 0.5 mamita

Angle (θ= = 360^o = 6.28 radians

Zvaidiwa: kutama kwakatwasuka (l)

Solution:

l = r θ

l = (0.5 m)(6.28 rad)

l = mamita matatu

3. Vhiri re50 cm mu radius rinotenderera kaviri. Chii chinonzi linear displacement yenzvimbo iri pamucheto wevhiri?

Zvinozivikanwa:

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

Angle (θ) = 2 revolutions = (2)(6.28 radians) = 12.56 radians

Zvaidiwa: kuchinjika kwemutsetse (l) ?

Solution:

l = r θ

l = (0.5 m)(12.56 rad)

l = 6.28 m

4. Poindi iri pamucheto wevhiri ine mamita maviri muradius, inofamba mamita zana. Tsvaga nzvimbo ine kona.

Zvinozivikanwa:

Nharaunda (r) = ½ (dhayamita) = ½ (mamita maviri) = mita imwe

kutama kwakatwasuka (l) = mamita zana

Solution:

(a) Kufamba kwekona (muma radians)

θ = s / r = 100 / 1 = 100 radians

(b) Kuchinja kwekona (mumadhigirii)

1 radian = 360^o

Ma radians zana = 100 (360)^o) = ma radians gumi

(c) Kutamiswa kwekona (mukuchinja)

6.28 radians = 1 revolution

36,000 / 6.28 = 5732,484 ma revolutions

5. Chidimbu chinotenderera denderedzwa remamita gumi uye chinotenderera 180^oChii chinonzi radius?

Zvinozivikanwa:

Kufamba kwemutsetse (l) = mamita gumi

Angle (θ= = 180^o = 3.14 radians

Zvaidiwa: nharaunda (r)

Solution:

r = l / θ = 10 / 3.14 = 3.18 mamita

1. Kuchinja mayuniti emakona emuenzaniso matambudziko nemhinduro
2. Matambudziko emuenzaniso wekutama kweAngular uye linear displacement uye mhinduro
3. Matambudziko emuenzaniso wekumhanya kweAngular uye kumhanya kwemutsara ane mhinduro
4. Matambudziko emuenzaniso wekumhanyisa kweAngular uye wekumhanyisa mutsara ane mhinduro
5. Muenzaniso wematambudziko ekufamba kwakatenderera kwakafanana nemhinduro
6. Matambudziko emuenzaniso wekumhanyisa kweCentripetal nemhinduro
7. Matambudziko emhando dzakasiyana dzemafambiro edenderedzwa ane mhinduro dzakasiyana

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1. Vhiri re 1 mita mu radius rinomhanya zvakaenzana pa 2 rad/s²Sarudza kuti angular acceleration uye kumhanya kwekona yevhiri, masekondi maviri gare gare.

Zvinozivikanwa:

Nharaunda (r) = mita imwe

Kukurumidzisa kwekona (α)) = 2 rad/s²

Kuda: kukurumidza kwekona uye kumhanya kwekona mushure memasekonzi maviri.

Solution:

(A) Kukurumidza kwekona mumasekonzi maviri

Kukurumidza kwevhiri (angular acceleration) kunogara kuripo, saka mushure memasekonzi maviri, kukurumidza kwevhiri (angular acceleration) kuri 2 rad/s.².

(B) Kumhanya kwekona mumasekonzi maviri

Kukurumidza kwekona 2 rad/s² zvinoreva kuti kumhanya kwekona kunowedzera ma radians maviri/sekondi imwe neimwe. Mushure mesekondi imwe, kumhanya kwekona = ma radians maviri/sekondi. Mushure memasekonzi maviri, kumhanya kwekona = ma radians mana/sekondi.

2. Chidimbu chimwe chinomhanyisa zvakafanana kubva pakuzorora kusvika pa60 rpm mumasekonzi gumi. Tsvaga hukuru hwekumhanya kwekona!

Zvinozivikanwa:

Kumhanya kwekutanga kwekona (ω)_o= = 0

Kumhanya kwekupedzisira kwekona (ω_t) = 60 rpm = 60 revolutions / 60 seconds = 1 revolution / second = 6,28 radians/second

Nguva yepakati (t) = masekondi gumi nemashanu

Zvaidiwa: Kukurumidzisa kwekona (α)

Solution:

ω_o = kumhanya kwekutanga kwekona, ω_t = kumhanya kwekupedzisira kwekona, α = kukurumidza kwekona, t = nguva yekupfuura, θ = kona.

ω_t = ω_o + α t

6.28 = 0 + α (10)

6.28 = 10 α

α = 6.28/10

α = 0.628 rad/s²

Kukura kwekumhanya kwekona = 0.628 rad/s²

3. Chinhu chinononoka kubva pa20 rad/s kusvika pa10 rad/s mumasekonzi mana. Tsvaga hukuru hwekumhanya kwekona!

Zvinozivikanwa:

Nguva yepakati (t) = masekondi gumi nemashanu

Kumhanya kwekutanga kwekona (ω_o ) = 20 rad/s

Kumhanya kwekupedzisira kwekona (ω_t) = 10 rad/s

Wanted : hukuru hwekumhanya kwekona (α))

Solution:

ω_t = ω_o + α t

10 = 20 + α (4)

10 - 20 = 4 α

-10=4 α

α = -10 / 4

α = – 2.5 rad/s²

Hukuru hwekumhanya kwekona ndeye -2.5 rad/s²Chiratidzo chekunega chinoreva kuti chinhu chiri kudzika. Kukurumidza = kumhanya kwekona kunowedzera, kudzikira = kumhanya kwekona kuderera.

4. Chinhu chinokurumidziswa kwemasekonzi maviri kubva pa10 rad/s kusvika pa2 rad/s²Sarudza kona yakatenderedzwa nechinhu chacho!

Zvinozivikanwa:

kumhanya kwekutanga kwekona (ω_o ) = 10 rad/s

kukurumidza kwekona (α) = 2 rad/s²

nguva (t) = masekondi maviri

Zvaidiwa: kona (θ)

Solution:

θ = ω_o + ½ α t²

θ = (10)(2) + ½ (2)(2)²)

θ = 20 + (1)(4) = 20 + 4

θ = 24 radians

5. Vhiri remotokari rinodzikira kubva pa20 rad/s kusvika razorora mushure mekutenderera maradian makumi maviri. Tsvaga hukuru hwekumhanya kwevhiri!

Zvinozivikanwa:

kumhanya kwekutanga kwekona (ω_o) = 20 rad/s

kumhanya kwekupedzisira kwekona (ω_t= = 0

Angle (θ) = ma radians gumi

Zvaidiwa: hukuru hwekumhanya kwekona (α))

Solution:

ω_t² = ω_o² + 2 α θ

0 = 20² + 2 α (20)

0 = 400 + 40 α

400 = – 40 α

α = – 400 / 40

α = – 10 rad/s²

6. Rod PQ ine urefu hwe60 cm inotenderera panosvika point Q se axis yekutenderera uye PQ se radius yedenderedzwa. Rod PQ inomhanyisa kubva pakuzorora kusvika pa 0.3 rad/s²Chii chinonzi linear speed yepoindi P pa t = 10 seconds, kana nzvimbo yekutanga ye angular iri 0.

Zvinozivikanwa:

Kureba kwetsvimbo PQ = radius yedenderedzwa (r) = 60 cm = 60/100 m = 0.60 m

Kumhanya kwekutanga kwekona (ω_o) = 0 rad/s

Kukurumidza kwekona (α) = 0.3 rad s^-2

Nzvimbo yekutanga yekona (θ_o= = 0

Zvaidiwa: Kumhanya kwemutsetse (v) kwepoindi P pa t = masekondi gumi

Solution:

Kumhanya kwekupedzisira kwekona mushure memasekonzi gumi:

ω_t = ω_o + α t = 0 rad/s + (0.3 rad s^-2)(10 s) = 3 rad/s

Kumhanya kwekupedzisira kwemutsara mushure memasekonzi gumi:

v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s

7. Chinhu chinotenderera nekumhanya kwekutanga kwe4 rad/s uye kumhanyisa kwekona kuri 0.5 rad/s²Chii chinonzi kumhanya kwechinhu mushure memasekonzi mana?

Zvinozivikanwa:

Kumhanya kwekutanga kwekona (ω_o) = 4 rad/s

Kukurumidza kwekona (α) = 0.5 rad/s²

Nguva yepakati (t) = masekondi gumi nemashanu

Zvaidiwa: Kumhanya kwechinhu mushure memasekonzi mana (ω_t)

Solution:

ω_t = ω_o + α t

ω_t = 4 + (0.5)(4)

ω_t = 4 + 2

ω_t = 6 rad/s

8. A Wachi yemadziro ine dhayamita ye10 cm ine tsono nhatu, imwe neimwe ichiratidza maawa, maminetsi nemasekonzi. Kuenzanisa huwandu hwemadenderedzwa etsono yeawa: tsono yeminiti: tsono yechipiri.

A. 1: 3: 180

B. 1 : 12 : 720

C. 4 : 12 : 180

D. 4 : 12 : 720

Zvinozivikanwa:

Awa imwe = maminetsi makumi matanhatu

Maawa gumi nemaviri = (12)(maminitsi makumi matanhatu) = maminitsi mazana manomwe nemakumi maviri

Kumhanya kwetsono yeawa = 1 revolution / maawa gumi nemaviri = 1 revolution / maminitsi mazana manomwe nemakumi maviri

Kumhanya kwekona kwetsono yemaminitsi = 1 revolution / awa imwe = 1 revolution / maminitsi makumi matanhatu

Kumhanya kwetsono yechipiri kwekona = 1 revolution / 1 miniti

Kuda: Kuenzanisa kwenhamba yemarounds etsono yeawa: tsono yeminiti: tsono yechipiri

Solution:

Kuenzanisa kwekufamba kwedenderedzwa:

Kumhanya kwekona = nhamba yekutenderera / nguva yekupindira

Nhamba yekuchinja = kona yekumhanya x nguva yekupindirana

Munguva imwe chete, semuenzaniso, miniti imwe chete, kuti tsono yeawa inotenderera kangani, tsono yeminiti, uye tsono yechipiri inotenderera kangani.

Huwandu hwemapinduko etsono yeawa = kona yekumhanya x nguva yekupindira = (1 revolution / 720 minutes)(1 miniti) = 1/720 revolutions

Huwandu hwemapinduko etsono yeminiti = kona yekumhanya x nguva yekupindira = (1 revolution / 60 minutes)(1 miniti) = 1/60 revolutions

Huwandu hwemapindukiro etsono yechipiri = kona yekumhanya x nguva yekupindira = (1 revolution / 1 minute)(1 minute) = 1/1 revolution

Kuenzanisa kwezvimurenga zvakawanda:

Huwandu hwemapinduko etsono yeawa: huwandu hwemapinduko etsono yeminiti: huwandu hwemapinduko etsono yechipiri.

1/720: 1/60: 1/1

1/720: 12/720: 720/720

1: 12: 720

Mhinduro chaiyo ndeiyi B.

9. Bhora rakasungwa netambo. Bhora rinotenderedzwa kuitira kuti rifambe rakatenderera rakafanana nepamusoro penyika. Mukufamba uku, bhora rinomhanya nekuti…..

A. Friction yemhepo

B. uremu yebhora

C. Simba rekukakavadzana

D. Simba regiravhiti

Solution:

Mutemo wechipiri wekufamba waNewton inoti chinhu chinokurumidziswa kana paine simba rinobuda. Bhora rakabatana netambo uye kana tambo yatenderera, bhora rinotendererawo. Kana bhora ratenderera (bhora richifamba mudenderedzwa), bhora rinokurumidziswa nepakati nepakati. Zvinhu zvese zvinofamba zvinotenderera nepakati nepakati. Kukurumidza kwepakati inokonzerwa na simba repakatiSimba repakati penyaya iyi ndiro simba rekumanikidza.

Mhinduro chaiyo ndeinoti C.

[wpdm_package id='437′]

[wpdm_package id='439′]

1. Kuchinja mayuniti emakona emuenzaniso matambudziko nemhinduro
2. Matambudziko emuenzaniso wekutama kweAngular uye linear displacement uye mhinduro
3. Matambudziko emuenzaniso wekumhanya kweAngular uye kumhanya kwemutsara ane mhinduro
4. Matambudziko emuenzaniso wekumhanyisa kweAngular uye wekumhanyisa mutsara ane mhinduro
5. Muenzaniso wematambudziko ekufamba kwakatenderera kwakafanana nemhinduro
6. Matambudziko emuenzaniso wekumhanyisa kweCentripetal nemhinduro
7. Matambudziko emhando dzakasiyana dzemafambiro edenderedzwa ane mhinduro dzakasiyana

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1. Chinhu chinofamba mudenderedzwa chine kumhanya kwekona kunogara kuripo kwe10 rad/s. Sarudza (a) Kumhanya kwekona mushure memasekonzi gumi (b) Kutama kwekona mushure memasekonzi mashanu.

Zvinozivikanwa:

Kumhanya kwekona (ω) =10 rad/s

Zvaidiwa:

(a) Kumhanya kwekona (ω) mushure memasekonzi gumi.

(b) Angle (θ) mushure memasekonzi gumi

Solution:

(A) Kumhanya kwekona (ω) mushure memasekonzi gumi

Chinhu chiri mukati kufamba kwakafanana kwedenderedzwa saka kumhanya kwekona hakuchinji, 10 rad/s.

(b) Kutamiswa kwekona (θ)

Kumhanya kwekona nguva dzose kwemaradians gumi pasekondi zvinoreva chinhu chakakomberedza maradians gumi pasekondi. Mushure memasekonzi gumi, chinhu chakakomberedza maradians gumi pasekondi imwe chete = maradians zana.

2. Chidimbu chinofamba mudenderedzwa chine kumhanya kunogara kuripo kwe10 m/s. Nharaunda yedenderedzwa = mita imwe. Tsvaga (a) Kumhanya kwechikamu mushure memasekonzi mashanu (b) Chidimbu kudzingiswa mushure memasekonzi mashanu (c) Kukurumidza kwepakati.

Zvinozivikanwa:

Nharaunda yedenderedzwa (r) = mita imwe

Kumhanya kwechikamu (v) = 10 m/s

Solution:

(A) Kumhanya kwechikamu mushure memasekonzi mashanu

Kufamba kwechinhu chacho kuri mukufamba kwakafanana kwedenderedzwa kuitira kuti kumhanya kurambe kuripo, 10 m/s.

(B) Kufamba kwechikamu chezvimedu mushure memasekonzi mashanu

Mamita gumi pasekondi zvinoreva sekondi imwe chete yega yega, kusuduruka kwezvikamu = mamita gumi. Mushure memasekonzi mashanu, kusuduruka kwezvikamu = 5 x 10 mamita = mamita makumi mashanu.

(C) Kukurumidza kwepakati pepakati (a_r)

a_r =v² / r = 10² / 1 = 100 / 1 = 100 m/s²

3. Bhora rakasungirirwa kumucheto mumwe wetambo, rinotenderedzwa mudenderedzwa rine radius yemamita maviri nekumhanya kwakafanana kwe60 rpm. Tsvaga (a) hukuru hwekumhanya kwekona mushure memasekonzi maviri (b) kutenderera kwekona mushure meminiti imwe.

Zvinozivikanwa:

Nharaunda yedenderedzwa (r) = mamita maviri

Kumhanya kwekona (ω) = 60 rpm = 60 revolutions / 1 miniti

= 60 revolutions / 60 seconds = 1 revolution / sekondi = 2π radians / sekondi

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

Solution:

(A) Kumhanya kwekona (ω) mushure memasekonzi gumi

Kumhanya kwekona hakuchinji saka mushure memasekonzi maviri, kumhanya kwekona (ω) = 6.28 radians / sekondi

(B) Kufamba kwekona (θ)

Kumhanya kwekona = 1 revolution/sekondi zvinoreva kuti pasekondi imwe chete yega yega, bhora rinoita revolution imwe chete. Mushure memasekonzi makumi matanhatu, bhora rinofamba revolution makumi matanhatu.

Kumhanya kwekona = 6.28 radians/sekondi zvinoreva kuti sekondi imwe chete yega yega, bhora rinofamba nekona ye6.28 radians. Mushure memasekonzi makumi matanhatu, bhora rinofamba 376.8 radians.

4. Vhiri rebhasikoro rinotenderera ma revolution zana nemakumi maviri mumasekonzi makumi matanhatu. Chii chinonzi angler speed?

Solution:

(a) kutenderera paminiti (rpm)

Kutenderera 120 / masekondi 60 = 120 kutenderera / miniti 1 = 120 kutenderera / miniti = 120 rpm

(B) madhigirii pasekondi (^o/ s)

Chimurenga chimwe = 360^o, 120 revolutions = 43200^o

Kutenderera kwe120 / masekondi makumi matanhatu = (120)(360^o) / masekondi makumi matanhatu = 43200^o / Masekondi makumi matanhatu = 720^o/Chepiri

(C) radians pasekondi (rad/s)

Chimurenga chimwe chete = 6.28 radians

Kutenderera 120 / masekondi 60 = (120)(6.28) radians / masekondi 60 = 753.6 radians / masekondi 60 = 12.56 radians/sekondi.

[wpdm_package id='432′]

[wpdm_package id='439′]

1. Kuchinja mayuniti emakona emuenzaniso matambudziko nemhinduro
2. Matambudziko emuenzaniso wekutama kweAngular uye linear displacement uye mhinduro
3. Matambudziko emuenzaniso wekumhanya kweAngular uye kumhanya kwemutsara ane mhinduro
4. Matambudziko emuenzaniso wekumhanyisa kweAngular uye wekumhanyisa mutsara ane mhinduro
5. Muenzaniso wematambudziko ekufamba kwakatenderera kwakafanana nemhinduro
6. Matambudziko emuenzaniso wekumhanyisa kweCentripetal nemhinduro
7. Matambudziko emhando dzakasiyana dzemafambiro edenderedzwa ane mhinduro dzakasiyana

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1. A 0.1Bhora re -kg, rakasungirirwa kumagumo kwetambo yakatambanuka, rinotenderedzwa mudenderedzwa reradius 50 masendimita uye bhora kumhanya kwekona is 4 rad s^-1. Hukuru hwepakati pechikamu (centripetal) hwakaita sei? simba?

Zvinozivikanwa:

Misa (m) = magiramu zana = 100/1000 kg = 1/10 kg = 0.1 kg

Kumhanya kwekona (ω) = 4 radians/smamiriro

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

Zvaidiwa: Simba repakati

Solution:

Simba repakati (centripetal force) isimba rinobva mukugadzira kukurumidza kwepakati :

∑F = ma_r

∑F = mv²/r = m ω² r

∑F = simba remagetsi = simba repakati, m = uremu, v = havukavu, ω = kumhanya kwekona, r = radius

∑F = m ω² r = (0.1)(4)² (0.5) = (0.1)(16)(0,5) = 0.8 Newtons

2. Bhora riri kutenderera zvakaenzana mudenderedzwa rakatwasuka. Kana kumhanya kukachinja kusvika pakapetwa kana kupfuura kukosha kwekutanga, simba repakati penyika rinoita sei…..

Zvinozivikanwa:

Misa = m

havukavu =v

Kumhanya kwekutanga = v_o

Radhiyasi (r) =r

Kuda: Hukuru hwesimba repakati

Solution:

3. Mutsetse we radius R wakagadzirwa nenzira yekuti mota ifambe nekumhanya kwe 12 ms^-1 inogona kutaurirana zvakachengeteka. Chiyero che kukweshana kwemamiriro ezvinhu pakati pemotokari nemugwagwa = 0.4. Chii chinonzi radius R. Kuwedzera nekuda kwegiravhiti (g) = 10 ms^-2.

Zvinozivikanwa:

havukavu (v) = 12 m/s

Kukweshana kwekusagadzikana (μ_s) = 0.4

Kuwedzera nekuda kwegiravhiti (g) = 10 m/s²

Kuda: Nharaunda (R)

Solution:

[wpdm_package id='501′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba panzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakakotama pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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