Physics

9 Kuchinja tembiricha (Celsius scale Fahrenheit scale Kelvin scale)

1. 50 ^o C = ….. ^o F ?

mhinduro

Pakumanikidzwa kwemhepo kwakajairwa , nzvimbo yekuomesa mvura i0 ^o C pachikero cheCelsius uye 32 ^o F pachikero cheFahrenheit. Pakumanikidzwa kwemhepo kwakajairwa, nzvimbo yekufashaira yemvura i100 ^o C pachikero cheCelsius uye 212 ^o F pachikero cheFahrenheit.

0 ^o C = 32 ^o F uye 1 00 ^o C = 212 ^o F. Kuchinja kwe5 C ⁼ kuchinja kwe9 F ^o.

Pachikero cheCelsius, daro riri pakati pe0 ^o C ne100 ^o C rakakamurwa kuita zvikamu zana zvakaenzana. Pachikero cheFahrenheit, daro riri pakati pe0 ^o C ne100 ^o C rakakamurwa kuita zvikamu zana nemakumi masere zvakaenzana.

Kusvika ^ku F = (180/100) Kusvika ^ku C + 32

Kusvika ^ku F = (9/5) Kusvika ^ku C + 32

Kusvika ^ku F = (9/5) 50 + 32

Kusvika ^pa F = (9) 10 + 32

Kusvika ^paF = 90 + 32

Kusvika ^kuF = 122

50 ^o C = 122 ^o F

[irp]

2. 86 ^o F = ….. ^o C ?

mhinduro

Kusvika ^kuC = (100/180)(Kusvika ^kuF – 32)

Kusvika ^kuC = (5/9)(Kusvika ^kuF – 32)

Kusvika ^kuC = (5/9)(86 - 32)

Kusvika ^kuC = (5/9)(54)

Kusvika ^kuC = (5)(6)

Kusvika ^kuC = 30

86 ^o F = 30 ^o C

3. 50 ^o C = ….. K ?

mhinduro

T = ^Kusvika kuC + 273

T = 50 + 273

T = 323

50 ^o C = 323 K

[irp]

4. 212 ^o F = ….. K ?

mhinduro

Kusvika ^kuC = (100/180)(Kusvika ^kuF – 32)

Kusvika ^kuC = (5/9)(Kusvika ^kuF – 32)

Kusvika ^kuC = (5/9)(212 - 32)

Kusvika ^kuC = (5/9)(180)

Kusvika ^kuC = (5)(20)

Kusvika ^kuC = 100

212 ^o F = 100 ^o C + 273

212 ^o F = 373 K

 

5. x ^o C = x ^o F

x = ….. ?

mhinduro

1: Kushandura chikero cheCelsius kuita chikero cheFahrenheit

2: Kushandura chikero cheFahrenheit kuita chikero cheCelsius

[irp]

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 ^o C

7. Mufananidzo uri pazasi unoratidza kuyerwa kwetembiricha yemvura ine thermometer yechikero cheFahrenheit! Kana tembiricha yemvura ikayerwa uchishandisa thermometer yechikero cheCelsius, saka tembiricha yemvura chii?

Zvinozivikanwa:

Chikero cheFahrenheit (T _F ) = 95 ^o F

Chinodiwa: chikero cheCelsius

Solution:

Pakumanikidzwa kwe1 atm, nzvimbo yekuomesa mvura inenge iri 0 °C nepo chikero cheFahrenheit chiri 32 ^o F. Kusiyana neizvi, nzvimbo yekufashaira yemvura pachikero cheCelsius i100 ^o C nepo chikero cheFahrenheit chiri 212 ^o F.

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 ^o C

8. Zvichibva pamufananidzo uri pazasi, sarudza tembiricha 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 ^o C

9. Kana tembiricha yechikero cheCelsius sezvakaratidzwa pamufananidzo uri pazasi, tsvaga tembiricha yechikero cheFahrenheit sezvakaratidzwa pamufananidzo uri pazasi.

Solution:

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

Kusvika ^ku F = (9/5) Kusvika ^ku C + 32

Kusvika ^ku F = (9/5) 60 + 32

Kusvika ^pa F = (9) 12 + 32

Kusvika ^paF = 108 + 32

Kusvika ^kuF = 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 chinoramba chiripo chechitubu!

mhinduro

Fomura yemutemo waHooke :

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

[irp]

2. Sarudza chinoramba chiripo chechirimo.

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

[irp]

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 chenguva dzose 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

Zvaidiwa: Δl _A : Δl _B

Solution:

Fomura yemutemo waHooke:

Δl = F / k

Δl = kuchinja kwehurefu, F = simba, k = nguva dzose

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

[irp]

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

Zvinodiwa: 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

[irp]

[wpdm_package id='689′]

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

Kudiwa: Kushushikana

Solution:

Nzvimbo:

A = π r ²

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

A = 3.14 x 10 ^-6 m ²

Kushushikana:

[irp]

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

Zvinozivikanwa:

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

Kuchinja kwehurefu (Δl) = 2 mm = 0.002 m

Zvinodiwa: Dambudziko

Solution:

Chitima :

[irp]

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

Zvinozivikanwa:

Dhayamita (d) = 4 mm = 0.004 m

Nharaunda (r) = 2 mm = 0.002 m

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

^{Nzvimbo (} A) = 0.00001256 m2 ⁼ 12.56 x 10 ^-6 m2

Simba (F) = 200 N

Kureba kwechitubu chepakutanga (l ₀ ) = 2 m

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

Zvinodiwa: (a) Kushushikana (b) Kumanikidzwa c) Modulus yaYoung

Solution:

(a) Kushushikana

(b) Dambudziko

(c) Modulus yaYoung

[irp]

4. Tambo ine dhayamita ye 1 cm uye kureba kwepakutanga kwemamita maviri. Tambo inodhonzwa nesimba re 200 N. Tsvaga shanduko pakureba kwetambo! Modulus yeYoung yetambo = 5 x 10 ⁹ N/m ²

Zvinozivikanwa:

Modulus yeYoung (E) = 5 x 10 ⁹ N/m ²

Kureba kwekutanga (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 r ² = (3.14)(5 x 10 ^-3 m) ² = (3.14)(25 x 10 ^-6 m ² )

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

Zvinodiwa : Kuchinja kwehurefu (Δl)

Solution:

Fomura ye modulus yaYoung:

Kuchinja kwehurefu :

[irp]

5. Kongiri ine urefu hwemamita mashanu uye ine nzvimbo yeyuniti ye3 m3 ^inotsigira huremu hwe30,000 kg. Tsvaga (a) Kushushikana (b) Kumanikidzwa (c) Kuchinja kwehurefu! Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ² . Young's modulus yekongiri = 20 x 10 ⁹ N/m ²

Zvinozivikanwa:

Modulus yekongiri yaYoung = 20 x 10 ⁹ N/m ²

Kureba kwekutanga (l ₀ ) = mamita mashanu

Nzvimbo yeyuniti (A) = 3 m ²

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

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

Solution:

(a) Kushushikana

(b) Dambudziko

(c) Kuchinja kwehurefu

[irp]

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

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1. Bhora, rakasungirirwa kumagumo kwetambo yakatambanuka, rinotenderedzwa mudenderedzwa reradius 20 cm. Bhora rinotenderera 360 ^o sekondi yega yega. Sarudza hukuru hwekumhanya kwepakati!

Zvinozivikanwa:

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

Nharaunda (r) = 20 cm = 0.2 m

Zvinodiwa: Kukurumidza kwepakati (a _r )

Solution:

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 = kukurumidza kwepakati, v = kumhanya kwakatwasuka, r = radius, ω = kumhanya kwekona

Kukura kwekumhanya kwepakati pesimba :

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

a _r = 1.256 m/s ²

[irp]

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

Zvinodiwa: kukurumidza kwepakati ( a _r ) kwe r = 0.3 m

Solution:

Kukura kwekumhanya kwepakati pesimba:

a _r = r ω ²

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

a _r = 5.65 m/s ²

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

Zvinodiwa : hukuru hwekumhanya kwepakati (a _r )

Solution:

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

[irp]

4. Mota ine mukana wepamusoro wekumhanya pakati pemotokari we10 m/s ² , saka mota inogona kutendeuka isina kutsvedza kubva munzira yakakombama. Kana mota iri kufamba ne108 km/h, muganhu wekona isina kuvharwa ndewei?

Zvinozivikanwa:

Kukurumidza kwepakati (a _r ) = 10 m/s ²

Kumhanya kwemota (v) = 108 km/ h = (108)(1000) / 3600 = 30 metres s /se c on d

Zvinodiwa: radius (r)

Solution:

r = v ² / a _r

r = 30 ² / 10 = 900 / 10 = 90 mamita s

[irp]

[wpdm_package id='433′]

[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. Vhiri re3 0 cm mu radius rinotenderera pa 5 rad/s ² . Chii chiri kukura kwekumhanya kwemutsara kwenzvimbo iri pa (a) 10 cm kubva pakati (b) 20 cm kubva pakati (c) pamucheto wevhiri?

Zvinozivikanwa:

Nharaunda (r) = 30 cm = 0.3 m

Kukurumidza kwekona ( α ) = 5 rad/s ²

Zvinodiwa: kumhanyisa kwakatwasuka (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) kumhanyisa kwakatwasuka, r = 0.1 m

a = (0.1 m)(5 rad/s ² ) = 0.5 m/s ²

(b) kumhanyisa kwakatwasuka, r = 0.2 m

a = (0.2 m)(5 rad/s ² ) = 1 m/s ²

(c) kumhanyisa kwakatwasuka, r = 0.3 m

a = (0.3 m)(5 rad/s ² ) = 1.5 m/s ²

[irp]

2. Pulley ine 50 cm mu radius. Kana kumhanyisa kwemutsara kwenzvimbo iri pamucheto wepulley kuri 2 m/s ² , tsvaga kumhanyisa kwekona kwepulley!

Zvinozivikanwa:

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

kumhanya kwakatwasuka (a) = 2 m/s ²

Zvinodiwa: kukurumidza kwekona

Solution:

α = a / r = 2 / 0.5 = 4 rad/s ²

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} ( ωo ) = 0

Kumhanya kwekupedzisira kwekona ( ωt ₎ = 10 radians/ _sekondi

Nguva yepakati (t) = masekondi gumi nemashanu

Zvinodiwa: kumhanyisa kwakanangana kwenzvimbo 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) kumhanyisa kwakanangana kwe r = 0.1 m

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

(b) kumhanyisa kwakanangana kwe r = 0.2 m

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

[irp]

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} ( ωt ) = 0

Nguva yepakati (t) = masekondi gumi nemashanu

Zvinodiwa: Kukurumidza kwakatwasuka (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 chekusaratidza kuti kumhanya kwekona kuri kudzikira.

(a) kumhanyisa kwakanangana kwe r = 0.1 m

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

(b) kumhanyisa kwakanangana kwe 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. 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 metres s, 1 mita, 3 metres

Kumhanya kwekona = 10 radians s /se cond

Zvinodiwa: Kumhanya kwakatwasuka

Solution:

v = r ω

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

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

v = r ω = (0.5 mamita s )(10 rad/s) = 5 mamita s /se cond

(b) Kumhanya kwakanangana (v) kwenzvimbo iri pa r = mita imwe

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

(c) Kumhanya kwakanangana (v) kwenzvimbo iri pa r = 2 metres s

v = r ω = (2 mamita s )(10 rad/s) = 20 mamita s /se cond

[irp]

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 cm

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

Zvinodiwa: Hukuru hwekumhanya kwemutsara

Solution:

(a) Hukuru hwekumhanya kwemutsara wepoindi iri 0.05 m kubva pakati

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

(b) Hukuru hwekumhanya kwemutsara wepoindi iri 0,1 m kubva pakati

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

3. Nzvimbo iri pamucheto wevhiri ine 30 cm mu radius, yakatenderedza denderedzwa nekumhanya kwakafanana kwemamita gumi pasekondi.

Chii chinonzi angular velocity?

Zvinozivikanwa:

Nharaunda ( r) = 30 cm = 0.3 mamita s

Kumhanya kwemutsetse (v) = 10 metres s /se cond

Zvinodiwa: kumhanya kwekona

Solution:

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

[irp]

4. Mota ine matayi ane dhayamita ye50 cm inofamba mamita gumi musekondi imwe chete . Chii chinonzi angler speed?

Zvinozivikanwa:

Nharaunda (r) = 0.25 mamita

Kumhanya kwakanangana kwepoindi iri pamucheto wematayi (v) = 10 metres s /se cond

Kudiwa: Kumhanya kwekona

Solution:

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

5. Kumhanya kwevhiri re20 cm muma radians i120 rpm. Ndeipi daro kana mota ichifamba mumasekonzi gumi.

Zvinozivikanwa:

Nharaunda (r) = 20 cm = 0.2 mita s

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

Zvinodiwa: kure

Solution:

Kumhanya kwemucheto wevhiri:

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

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 daro racho i25 metres s.

[irp]

[wpdm_package id='427′]

[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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Kushandura mayuniti ekona (dhigirii, radian, revolution)

1. ¼ rev = ….. ^o ( dhigirii )?

mhinduro

Chimurenga chimwe = 360 ^o

½ rev = 180 ^o

¼ rev = 90 ^o

2. ½ rev = …….. r ad?

mhinduro

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

½ rev = pi rad = 3.14 rad

3. 180 ^o = ….. rev ?

mhinduro

360 ^o = 1 chimurenga

180 ^o = ½ rev

[irp]

4. 90 ^o = ….. rad ?

mhinduro

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

180 ^o = π rad = 3.14 rad

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

[irp]

Kutama kwekona uye kutamiswa kwakatwasuka

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

Zvinozivikanwa:

Nharaunda (r) = 30 cm = 0.3 m

Angle (θ ) = 10 radians

Zvinodiwa: kutama kwakatwasuka (l)

Solution:

l = r θ

l = (0.3 m)(10 rad)

l = mamita matatu

2. Vhiri re50 cm mu radius rinotenderera 360 ^o . Chii chinonzi linear displacement yepoindi iri pamucheto wevhiri?

Zvinozivikanwa:

Nharaunda (r) = 50 cm = 0.5 mamita

Angle ( θ ) = 360 ^o = 6.28 radians

Zvinodiwa: kutama kwakatwasuka (l)

Solution:

l = r θ

l = (0.5 m)(6.28 rad)

l = mamita matatu

[irp]

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

Zvinodiwa: kutama kwemutsara (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 ) = 36,000 ma radians

(c) Kutamiswa kwekona (mukuchinja)

6.28 radians = 1 revolution

36,000 / 6.28 = 5732,484 ma revolutions

[irp]

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

Zvinozivikanwa:

Kufamba kwemutsetse (l) = mamita gumi

Angle ( θ ) = 180 ^o = 3.14 radians

Zvinodiwa: radius (r)

Solution:

r = l / θ = 10 / 3.14 = 3.18 mamita

[irp]

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 rine mita imwe muradius rinokurumidza zvakaenzana pa2 rad/s ^2. Sarudza kumhanyisa kwekona uye kumhanya kwekona kwevhiri, mushure memasekonzi maviri.

Zvinozivikanwa:

Nharaunda (r) = mita imwe

Kukurumidza kwekona (α ) = 2 rad/s ²

Zvinodiwa: kumhanyisa kwekona uye kumhanya kwekona mushure memasekonzi maviri.

Solution:

(a) Kukurumidza kwekona mumasekondi maviri

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

(b) Kumhanya kwekona mumasekondi maviri

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

[irp]

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 ( ωt ₎ = 60 rpm = 60 revolutions / 60 seconds = 1 revolution / second = 6,28 radians/second

Nguva yepakati (t) = masekondi gumi nemashanu

Zvinodiwa: Kukurumidza kwekona ( α )

Solution:

ω _o = kumhanya kwekutanga kwekona, ω _t = kumhanya kwekona kwekupedzisira, α = kukurumidza kwekona, t = nguva, 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/s ²

Hukuru hwekumhanya kwekona = 0.628 rad/s ²

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 ( ωt ) = 10 rad/ _s

Zvinodiwa : 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/s ²

Hukuru hwekumhanya kwekona ndeye -2.5 rad/s ^2. Chiratidzo chekunega chinoreva kuti chinhu chiri kudzika. Kumhanya = kumhanya kwekona kunowedzera, kudzika = kumhanya kwekona kuderera.

[irp]

4. Chinhu chinokurumidziswa kwemasekonzi maviri kubva pa10 rad/s kusvika pa2 rad/s . ^2. Sarudza kona yakatenderedzwa nechinhu chacho!

Zvinozivikanwa:

kumhanya kwekutanga kwekona ( ω _o ) = 10 rad/s

kukurumidza kwekona (α ) = 2 rad/s ²

nguva (t) = masekondi maviri

Zvinodiwa: kona (θ)

Solution:

θ = ω _o + ½ α t ²

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} ( ωt ) = 0

Angle ( θ ) = 20 radians

Zvinodiwa: hukuru hwekumhanya kwekona (α )

Solution:

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. Rod PQ ine urefu hwe60 cm inotenderera panosvika point Q se axis yekutenderera uye PQ se radius yedenderedzwa. Rod PQ yakawedzera kubva pakuzorora kusvika pa 0.3 rad/s ² . Ndeipi linear speed yepoint P pa t = 10 seconds, kana angular initial position 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

Zvinodiwa: 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

[irp]

7. Chinhu chinotenderera nekumhanya kwekutanga kwe4 rad/s uye angular acceleration iri 0.5 rad/s ^2. Chii chinonzi kumhanya kwechinhu mushure memasekonzi mana.

Zvinozivikanwa:

Kumhanya kwekutanga kwekona (ω _o ) = 4 rad/s

Kukurumidza kwekona (α) = 0.5 rad/s ²

Nguva yepakati (t) = masekondi gumi nemashanu

Zvinodiwa: 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. 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

Zvinodiwa: Kuenzanisa huwandu hwemarounds etsono yeawa: tsono yemaminitsi: 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. Kukweshana kwemhepo

B. Kurema kwebhora

C. Simba rekukakavadzana

D. Simba regiravhiti

Solution:

Mutemo wechipiri waNewton wekufamba unotaura kuti chinhu chinokurumidziswa kana paine simba rinobuda. Bhora rakabatana netambo uye kana tambo yatenderera, bhora rinotendererawo. Kana bhora ratenderera (bhora richifamba mudenderedzwa), bhora rinokurumidziswa nepakati penzira. Zvinhu zvese zvinofamba zvinotenderera nepakati penzira. Kukurumidziswa kwepakati penzira kunokonzerwa nesimba repakati penzira . Simba repakati penzira pachiitiko ichi isimba rekumanikidzwa.

Mhinduro chaiyo ndeinoti C.

[irp]

[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. Tsvaga (a) Kumhanya kwekona mushure memasekonzi gumi (b) Kufamba kwekona mushure memasekonzi gumi.

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 maviri

Chinhu chakafanana nekufamba kwedenderedzwa kuitira kuti kumhanya kwekona kugare kwakasimba, 10 rad/s.

(b) Kufamba 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.

[irp]

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

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

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 / second = 2π radians / second

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

Solution:

(a) Kumhanya kwekona (ω) mushure memasekonzi maviri

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.

[irp]

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 mhirizhonga = 43200 ^o

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

(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.

[irp]

[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. Bhora re 0.1 kg, rakasungirirwa kumagumo kwetambo yakatambanudzwa, rinotenderedzwa mudenderedzwa re radius ye 50 cm uye kumhanya kwebhora kuri s 4 rad s ^-1 . Simba repakati pebhora rakakura sei?

Zvinozivikanwa:

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

Kumhanya kwekona ( ω) = 4 radians/se cond

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

Chinodiwa: Simba repakati

Solution:

Simba repakati (centripetal force) isimba rinokonzera kukurumidza kwepakati (centripetal acceleration ):

∑ F = ma _r

∑ F = mv ² /r = m ω ² r

∑ F = simba repakati = simba repakati , m = uremu , v = kumhanya , ω = kumhanya kwekona , r = dhayasi

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

[irp]

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

Zvinozivikanwa:

Huremu = m

Kumhanya = v

Kumhanya kwekutanga = v _o

Nharaunda (r) = r

Zvinodiwa: Hukuru hwesimba repakati

Solution:

3. Mutsetse we radius R wakagadzirwa kuitira kuti mota inofamba nekumhanya kwe 12 ms ^-1 igone kutenderera zvakachengeteka. Chiyero chekukakavadzana kwemotokari nemugwagwa = 0.4. Chii chinonzi radius R. Kukurumidza kunokonzerwa negiravhiti ( g ) = 10 ms ^-2.

Zvinozivikanwa:

Kumhanya (v) = 12 m/s

Koefficient yekukweshana kwestatic ( μs ₎ = 0.4

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Kudiwa: Radius (R)

Solution:

[irp]

[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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