Physics

9 Kutembenuza kutentha (Celsius scale Fahrenheit scale Kelvin scale)

1. 50 ^o C = ….. ^o F ?

Anakonza

Pa kupanikizika kwa mumlengalenga komwe kumafanana ndi mlengalenga , madzi oundana amakhala 0 ^o C pa sikelo ya Celsius ndi 32 ^o F pa sikelo ya Fahrenheit. Pa kupsinjika kwa mumlengalenga komwe kumafanana ndi mlengalenga, kuwira kwa madzi kumakhala 100 ^o C pa sikelo ya Celsius ndi 212 ^o F pa sikelo ya Fahrenheit.

0 ^o C = 32 ^o F ndi 1 00 ^o C = 212 ^o F. Kusintha kwa 5 Co ⁼ kusintha kwa 9 Fo ^o.

Pa sikelo ya Celsius, mtunda wa pakati pa 0 ^o C ndi 100 ^o C umagawidwa m'magawo ofanana 100. Pa sikelo ya Fahrenheit, mtunda wa pakati pa 0 ^o C ndi 100 ^o C umagawidwa m'magawo ofanana 180.

Kufika ^pa F = (180/100) Kufika ^pa C + 32

Kufika ^pa F = (9/5) Kufika ^pa C + 32

Kufika ^pa F = (9/5) 50 + 32

Kufika ^pa F = (9) 10 + 32

Kufika ^pa F = 90 + 32

Kufika ^pa F = 122

50 ^o C = 122 ^o F

[irp]

2. 86 ^o F = ….. ^o C ?

Anakonza

Kufika pa ^o C = (100/180)(Kufika pa ^o F – 32)

Kufika pa ^o C = (5/9)(Kufika pa ^o F – 32)

Kufika ^pa C = (5/9)(86 – 32)

Kufika ^pa C = (5/9)(54)

Kufika ^pa C = (5)(6)

Kufika ^pa C = 30

86 ^o F = 30 ^o C

3. 50 ^o C = ….. K ?

Anakonza

T = Mpaka ^C + 273

T = 50 + 273

T = 323

50 ^o C = 323 K

[irp]

4. 212 ^o F = ….. K ?

Anakonza

Kufika pa ^o C = (100/180)(Kufika pa ^o F – 32)

Kufika pa ^o C = (5/9)(Kufika pa ^o F – 32)

Kufika ^pa C = (5/9)(212 – 32)

Kufika ^pa C = (5/9)(180)

Kufika ^pa C = (5)(20)

Kufika ^pa C = 100

212 ^o F = 100 ^o C + 273

212 ^o F = 373 K

 

5. x ^o C = x ^o F

x = ….. ?

Anakonza

1: Kusintha sikelo ya Celsius kukhala sikelo ya Fahrenheit

2: Kusintha sikelo ya Fahrenheit kukhala sikelo ya Celsius

[irp]

6. 122°F = ….. Celsius

Anakonza

Kusintha pakati pa miyeso iwiri ya kutentha kungalembedwe:

T _C = 5/9 (T _F – 32)

T _C = Kutentha mu Celsius, T _F = kutentha mu Fahrenheit

Kutentha mu Celsius:

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

T _C = 50 ^o C

7. Chithunzi chili pansipa chikuwonetsa muyeso wa kutentha kwa madzi pogwiritsa ntchito thermometer ya Fahrenheit! Ngati kutentha kwa madzi kumayesedwa pogwiritsa ntchito thermometer ya Celsius, ndiye kuti kutentha kwa madzi ndi kotani?

Zodziwika:

Sikelo ya Fahrenheit (T _F ) = 95 ^o F

Kufunidwa: sikelo ya Celsius

Yankho:

Pakupanikizika kwa 1 atm, madzi amaundana ndi 0 °C pomwe Fahrenheit sikelo ndi 32 ^o F. Mosiyana ndi zimenezi, madzi otentha pa sikelo ya Celsius ndi 100 ^o C pomwe Fahrenheit sikelo ndi 212 ^o F.

Pa sikelo ya Celsius, pakati pa 0 °C ndi 100 °C pali 100 ° pomwe pa sikelo ya Fahrenheit pakati pa 32 °F ndi 212 °F pali 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. Kutengera chithunzi chomwe chili pansipa, dziwani kutentha kwa P pa thermometer ya Celsius.

Anakonza

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. Ngati kutentha kwa sikelo ya Celsius monga momwe zasonyezedwera pachithunzi chili pansipa, dziwani kutentha kwa sikelo ya Fahrenheit monga momwe zasonyezedwera pachithunzi chili pansipa.

Yankho:

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

Kufika ^pa F = (9/5) Kufika ^pa C + 32

Kufika ^pa F = (9/5) 60 + 32

Kufika ^pa F = (9) 12 + 32

Kufika ^pa F = 108 + 32

Kufika ^pa F = 140

1. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

1. Chithunzi cha mphamvu (F) motsutsana ndi kutalika (x ) chawonetsedwa pachithunzi chili pansipa. Pezani chokhazikika cha kasupe!

Anakonza

Fomula ya lamulo la Hooke :

k = F / x

F = mphamvu (Newton)

k = nthawi yokhazikika ya masika (Newton/mita)

x = kusintha kwa kutalika (mamita)

Chokhazikika cha masika:

k = 10 / 0.02 = 20 / 0.04

k = 500 N/m

[irp]

2. Dziwani nthawi yokhazikika ya kasupe.

Anakonza

Chokhazikika cha masika:

k = F / x

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

k = 500 N/m

[irp]

3. Kasupe A ali ndi kutalika koyambirira kwa 60 cm ndipo kasupe B ali ndi kutalika koyambirira kwa 90 cm. Kasupe A ali ndi 100 N/m yosasinthika, kasupe B ali ndi 200 N/m yosasinthika. Chiŵerengero cha kusintha kwa kutalika kwa kasupe A ndi kusintha kwa kutalika kwa kasupe B ndi…

Zodziwika:

Chokhazikika cha kasupe A (k _A ) = 100 N/m

Chokhazikika cha kasupe B (k _B ) = 200 N/m

Mphamvu pa kasupe A (F _A ) = F

Mphamvu pa kasupe B (F _B ) = F

Akufuna: Δl _A : Δl _B

Yankho:

Fomula ya lamulo la Hooke:

Δl = F / k

Δl = kusintha kwa kutalika, F = mphamvu, k = yosasintha

Kusintha kwa kutalika kwa kasupe A:

Δl _A = F _A / k _A = F / 100

Kusintha kwa kutalika kwa kasupe B:

Δl _B = F _B / k _B = F / 200

Chiŵerengero cha kusintha kwa kutalika kwa kasupe A ndi kusintha kwa kutalika kwa kasupe B:

Δl _A : Δl _B

F/100 : F/200

1/100: 1/200

1/1: 1/2

2: 1

[irp]

4. Chingwe cha nayiloni chokhala ndi kutalika koyambirira kwa masentimita 20, chimakokedwa ndi mphamvu ya 10 N. Kusintha kwa kutalika kwa chingwe ndi masentimita 2. Dziwani kukula kwa mphamvu ngati kusintha kwa kutalika ndi masentimita 6.

Zodziwika:

Mphamvu (F) = 10 N

Kusintha kwa kutalika ( Δl ) = 2 cm = 0.02 m

Kufunidwa: kukula kwa mphamvu (F) ngati Δl = 0.06 m.

Yankho:

Chokhazikika:

k = F / Δl

k = 10 / 0.02 = 500 N/m

Kukula kwa mphamvu (F) ngati Δl = 0.06 m :

F = kx

F = (500)(0.06)

F = 30N

[irp]

[wpdm_package id='689′]

1. Lamulo la Hooke
2. Kupsinjika maganizo, kupsinjika maganizo, modulus ya achinyamata

Werengani zambiri

Mavuto ndi Mayankho a Young's Stress Strain

1. Chingwe cha nayiloni chili ndi mainchesi a 2 mm, chokokedwa ndi mphamvu ya 100 N. Dziwani kupsinjika!

Zodziwika:

Mphamvu (F) = 100 N

M'mimba mwake (d) = 2 mm = 0.002 m

Utali wozungulira (r) = 1 mm = 0.001 m

Kufunidwa: Kupsinjika maganizo

Yankho:

Malo:

A = π r ²

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

A = 3.14 x 10 ^-6 m ²

Kupsinjika maganizo:

[irp]

2. Chingwe chokhala ndi kutalika koyambirira kwa 100 cm chimakokedwa ndi mphamvu. Kusintha kwa kutalika kwa chingwe ndi 2 mm. Dziwani mphamvu!

Zodziwika:

Utali woyambirira (l ₀ ) = 100 cm = 1 m

Kusintha kwa kutalika (Δl) = 2 mm = 0.002 m

Kufunidwa: Mtundu

Yankho:

Sitima ya s :

[irp]

3. Chingwe cha mainchesi 4 mm chili ndi kutalika koyambirira kwa mamita 2. Chingwecho chimakokedwa ndi mphamvu ya 200 N. Ngati kutalika komaliza kwa kasupe ndi 2.02 m, dziwani izi: (a) kupsinjika (b) kupsinjika (c) Young's modulus

Zodziwika:

M'mimba mwake (d) = 4 mm = 0.004 m

Utali wozungulira (r) = 2 mm = 0.002 m

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

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

Mphamvu (F) = 200 N

Utali woyambirira wa kasupe (l ₀ ) = 2 m

Kusintha kwa kutalika (Δl) = 2.02 – 2 = 0.02 m

Kufunidwa: (a) Kupsinjika (b) Kupsinjika c) Modulus ya Young

Yankho:

(a) Kupsinjika maganizo

(b) Kupsinjika

(c) Modulus ya Young

[irp]

4. Chingwe chili ndi mainchesi a 1 cm ndipo kutalika koyambirira kwa 2 m. Chingwecho chimakokedwa ndi mphamvu ya 200 N. Dziwani kusintha kwa kutalika kwa chingwecho! Modulus ya Young ya chingwe = 5 x 10 ⁹ N/m ²

Zodziwika:

Modulus ya Young (E) = 5 x 10 ⁹ N/m ²

Utali woyambirira (l ₀ ) = 2 m

Mphamvu (F) = 200 N

Chidutswa (d) = 1 cm = 0.01 m

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

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

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

Kufunidwa : Kusintha kwa kutalika (Δl)

Yankho:

Fomula ya Young's modulus:

Kusintha kwa kutalika :

[irp]

5. Konkireti ili ndi kutalika kwa mamita 5 ndipo ili ndi gawo la unit la 3 m ³ lothandizira kulemera kwa 30,000 kg. Dziwani (a) Kupsinjika (b) Kupsinjika (c) Kusintha kwa kutalika! Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ² . Young's modulus ya konkireti = 20 x 10 ⁹ N/m ²

Zodziwika:

Modulus ya Young ya konkire = 20 x 10 ⁹ N/m ²

Kutalika koyambirira (l ₀ ) = mamita 5

Malo a gawo (A) = 3 m ²

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

Kufunidwa: (a) Kupsinjika (b) Kupsinjika (c) Kusintha kwa kutalika!

Yankho:

(a) Kupsinjika maganizo

(b) Kupsinjika

(c) Kusintha kwa kutalika

[irp]

1. Lamulo la Hooke
2. Kupsinjika maganizo, kupsinjika maganizo, modulus ya achinyamata

Werengani zambiri

1. Mpira, wolumikizidwa kumapeto kwa chingwe chopingasa, umazunguliridwa mozungulira mozungulira 20 cm. Mpirawo umazungulira 360 ^o sekondi iliyonse. Dziwani kukula kwa kuthamanga kwa centripetal!

Zodziwika:

Liwiro la angular (ω ) = 360 ^o /sekondi = 1 revolution/sekondi = 6.28 ma radians/sekondi

Ulalo wozungulira (r) = 20 cm = 0.2 m

Kufunidwa: Kuthamanga kwapakati (a _r )

Yankho:

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 = kuthamanga kwapakati, v = liwiro lolunjika, r = radius, ω = liwiro la angular

Kukula kwa kuthamanga kwa centripetal :

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

a _r = 1.256 m/s ²

[irp]

2. Gudumu la 30 cm mu radius limazungulira pa liwiro la 180 rpm. Dziwani kuthamanga kwa centripetal kwa mfundo yomwe ili m'mphepete mwa gudumu!

Zodziwika:

Utali wozungulira (r) = 30 cm = 0.3 m

Liwiro la angular ( ω ) = ma revolutions 180 / masekondi 60 = ma revolutions 3 / second = (3)(6.28 ma radians) / second = 18.84 ma radians/second

Kufunidwa: kufulumira kwapakati ( a _r ) kwa r = 0.3 m

Yankho:

Kukula kwa kuthamanga kwa centripetal:

a _r = r ω ²

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

a _r = 5.65 m/s ²

3. Galimoto yothamanga imayenda pa msewu wozungulira wa mamita 50. Ngati liwiro la galimotoyo ndi 72 km/h, dziwani kukula kwa liwiro la pakati!

Zodziwika:

Ulalo wozungulira (r) = mamita 50

Liwiro (v) = 72 km/h = (72)(mamita 1000) / masekondi 3600 = mamita 20/sekondi

Kufunidwa : kukula kwa kuthamanga kwa centripetal (a _r )

Yankho:

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

[irp]

4. Galimoto ili ndi liwiro lalikulu la centripetal acceleration la 10 m/s ² , kotero galimotoyo imatha kutembenuka popanda kutsetsereka kuchoka panjira yokhota. Ngati galimotoyo ikuyenda pa liwiro losasintha la 108 km/h, kodi radius ya curve yopanda banki ndi yotani?

Zodziwika:

Kuthamanga kwapakati pa centripetal (a _r ) = 10 m/s ²

Liwiro la galimoto (v) = 108 km/ h = (108)(1000) / 3600 = 30 mamita s /se c on d

Kufunidwa: utali wozungulira (r)

Yankho:

r = v ² / a _r

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

[irp]

[wpdm_package id='433′]

[wpdm_package id='439′]

1. Kusintha mayunitsi a ngodya mavuto a zitsanzo ndi mayankho
2. Mavuto ndi mayankho a zitsanzo za kusamuka kwa angular ndi kusamuka kolunjika
3. Mavuto a chitsanzo cha liwiro la angular ndi liwiro lolunjika ndi mayankho
4. Mavuto a Angular a fast and linear acceleration ndi mayankho
5. Zitsanzo za mavuto ozungulira ofanana ndi mayankho
6. Mavuto a chitsanzo cha Centripetal acceleration ndi mayankho
7. Zitsanzo za mavuto ozungulira osafanana ndi mayankho

Werengani zambiri

1. Gudumu la 3 0 cm mu radius limazungulira pa 5 rad/s yokhazikika ^2. Kodi kukula kwa kufulumira kwa mzere wa mfundo yomwe ili pa (a) 10 cm kuchokera pakati (b) 20 cm kuchokera pakati (c) m'mphepete mwa gudumu ndi kotani?

Zodziwika:

Utali wozungulira (r) = 30 cm = 0.3 m

Kuthamanga kwa angular ( α ) = 5 rad/s ²

Kufunidwa: kufulumira kwa mzere (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m

Yankho:

Ubale pakati pa kufulumira kwa mzere (a) ndi kufulumira kwa angular:

a = r α

(a) kuthamanga kwa mzere, r = 0.1 m

a = (0.1 m)(5 rad/s ² ) = 0.5 m/s ²

(b) kuthamanga kwa mzere, r = 0.2 m

a = (0.2 m)(5 rad/s ² ) = 1 m/s ²

(c) kuthamanga kwa mzere, r = 0.3 m

a = (0.3 m)(5 rad/s ² ) = 1.5 m/s ²

[irp]

2. Pulley ya 50 cm mu radius. Ngati kufulumira kwa mzere wa mfundo yomwe ili m'mphepete mwa pulley ndi 2 m/s ² , dziwani kufulumira kwa angular kwa pulley!

Zodziwika:

Utali wozungulira (r) = 50 cm = 0,5 m

kufulumira kwa mzere (a) = 2 m/s ²

Kufunidwa: kuthamanga kwa angular

Yankho:

α = a / r = 2 / 0.5 = 4 rad/s ²

3. Masamba mu blender 20 cm mu radius, poyamba ali pamalo opumulira. Pambuyo pa masekondi awiri, masambawo amazungulira 10 rad/s. Dziwani kukula kwa liwiro la mzere (a) mfundo yomwe ili pa 10 cm kuchokera pakati (b) mfundo yomwe ili m'mphepete mwa masambawo.

Zodziwika:

Utali wozungulira (r) = 20 cm = 0.2 m

Liwiro loyambirira la _{angular (} ωo ) = 0

Liwiro lomaliza la angular ( ω _{t )} = 10 radians/second

Nthawi yopuma (t) = masekondi 2

Kufunidwa: kufulumira kwa mzere wa mfundo yomwe ili pa (a) r = 0.1 m (b) r = 0.2 m

Yankho:

ω _t = ω _o + α t

10 = 0 + α (2)

10 = 2 α

α = 10 / 2

 α = 5 rad/s

(a) kuthamanga kwa mzere wa r = 0.1 m

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

(b) kuthamanga kwa mzere wa r = 0.2 m

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

[irp]

4. Gudumu la 20 cm mu radius limafulumizitsidwa kwa masekondi awiri kuchokera pa 20 rad/s kuti lipumule. Dziwani kukula kwa kufulumizitsa kwa mzere (a) mfundo yomwe ili pa 10 cm kuchokera pakati (b) mfundo yomwe ili pa 10 cm kuchokera pakati.

Zodziwika:

Utali wozungulira (r) = 20 cm = 0.2 m

Liwiro loyambirira la angular ( ω _o ) = 20 rad/s

_{Liwiro lomaliza la angular} ( ωt ) = 0

Nthawi yopuma (t) = masekondi 2

Kufunidwa: Kuthamanga kwa mzere (a) r = 0.1 m (b) r = 0.2 m

Yankho:

ω _t = ω _o + α t

0 = 20 + α (2)

-20 = 2 α

α = -20 / 2

 α = -10 rad/s

Chizindikiro chotsutsa chimatanthauza kuti liwiro la angular likuchepa.

(a) kuthamanga kwa mzere wa r = 0.1 m

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

(b) kuthamanga kwa mzere wa 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. Kusintha mayunitsi a ngodya mavuto a zitsanzo ndi mayankho
2. Mavuto ndi mayankho a zitsanzo za kusamuka kwa angular ndi kusamuka kolunjika
3. Mavuto a chitsanzo cha liwiro la angular ndi liwiro lolunjika ndi mayankho
4. Mavuto a Angular a fast and linear acceleration ndi mayankho
5. Zitsanzo za mavuto ozungulira ofanana ndi mayankho
6. Mavuto a chitsanzo cha Centripetal acceleration ndi mayankho
7. Zitsanzo za mavuto ozungulira osafanana ndi mayankho

Werengani zambiri

1. Mpira kumapeto kwa chingwe ukuzungulira mofanana mu bwalo lozungulira la radius mamita awiri pa liwiro lokhazikika la angular 10 rad/s. Dziwani kukula kwa liwiro la mzere wa mfundo yomwe ili:

(a) mamita 0.5 kuchokera pakati

(b) mita imodzi kuchokera pakati

(c) mamita awiri kuchokera pakati

Zodziwika:

Ulalo wozungulira (r) = 0.5 mamita s, mita 1, mamita 3

Liwiro la angular = 10 radians s /se cond

Kufunidwa: Liwiro lolunjika

Yankho:

v = r ω

v = liwiro lolunjika , r = utali wozungulira , ω = liwiro la angular

(a) Liwiro lolunjika (v) la mfundo yomwe ili pa r = mamita 0.5

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

(b) Liwiro lolunjika (v) la mfundo yomwe ili pa r = mita imodzi

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

(c) Liwiro lolunjika (v) la mfundo yomwe ili pa r = 2 mamita s

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

[irp]

2. Masamba mu blender amazungulira pa liwiro la 5000 rpm. Dziwani kukula kwa liwiro la mzere:

(a) mfundo yomwe ili pamtunda wa 5 cm kuchokera pakati

(b) mfundo yomwe ili pamtunda wa masentimita 10 kuchokera pakati

Zodziwika:

Ulalo wozungulira (r) = 5 cm ndi 10 cm

Liwiro la angular (ω) = 5000 kusintha / masekondi 60econds = 83.3 kusintha / sechikhalidwe = (83.3)(6.28 ma radians) / sechikhalidwe = 523.3 radians / sechikhalidwe

Kufunidwa: Kukula kwa liwiro la mzere

Yankho:

(a) Kukula kwa liwiro la mzere wa mfundo yomwe ili pa 0.05 m kuchokera pakati

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

(b) Kukula kwa liwiro la mzere wa mfundo yomwe ili pa 0,1 m kuchokera pakati

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

3. Mfundo m'mphepete mwa gudumu la 30 cm mu radius, kuzungulira bwalo pa liwiro losasintha la mamita 10/sekondi.

Kodi liwiro la angular ndi lalikulu bwanji?

Zodziwika:

Ulalo wozungulira ( r) = 30 cm = 0.3 mamita s

Liwiro lolunjika (v) = mamita 10 s / se cond

Kufunidwa: liwiro la angular

Yankho:

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

[irp]

4. Galimoto yokhala ndi matayala a mainchesi 50 imayenda mamita 10 mu sekondi imodzi . Kodi liwiro lake ndi lotani?

Zodziwika:

Ulalo wozungulira (r) = mamita 0.25

Liwiro lolunjika la mfundo m'mphepete mwa matayala (v) = 10 mita s / se cond

Kufunidwa: Liwiro la angular

Yankho:

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

5. Liwiro la gudumu la 20 cm mu ma radians ndi 120 rpm. Kodi mtunda wake ndi wotani ngati galimotoyo ikuyenda mu masekondi 10?

Zodziwika:

Ulalo wozungulira (r) = 20 cm = 0.2 mita s

Liwiro la angular = 120 rev / 60 semikhalidwe = 2 rev / sechikhalidwe = (2)(6.28) radians / sechikhalidwe = 12.56 radians / sechikhalidwe

Akufuna: mtunda

Yankho:

Liwiro la m'mphepete mwa gudumu:

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

Mphindi wa 2.5s / second amatanthauza mfundo yomwe ili m'mphepete mwa kuyenda kwa mawilo Mphindi wa 2.5s sekondi imodzi iliyonse. pambuyo 10mikhalidwe, mfundo ikuyenda Mphindi wa 25s.

Kotero mtunda ndi mamita 25.

[irp]

[wpdm_package id='427′]

[wpdm_package id='439′]

1. Kusintha mayunitsi a ngodya mavuto a zitsanzo ndi mayankho
2. Mavuto ndi mayankho a zitsanzo za kusamuka kwa angular ndi kusamuka kolunjika
3. Mavuto a chitsanzo cha liwiro la angular ndi liwiro lolunjika ndi mayankho
4. Mavuto a Angular a fast and linear acceleration ndi mayankho
5. Zitsanzo za mavuto ozungulira ofanana ndi mayankho
6. Mavuto a chitsanzo cha Centripetal acceleration ndi mayankho
7. Zitsanzo za mavuto ozungulira osafanana ndi mayankho

Werengani zambiri

Mayunitsi osinthira ngodya (digiri, radian, revolution)

1. ¼ rev = ….. ^o ( digiri ) ?

Anakonza

Kusintha 1 = 360 ^o

½ rev = 180 ^o

¼ rev = 90 ^o

2. ½ rev = …….. r ad?

Anakonza

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

½ rev = pi rad = 3.14 rad

3. 180 ^o = ….. rev ?

Anakonza

360 ^o = 1 revolution

180 ^o = ½ rev

[irp]

4. 90 ^o = ….. rad ?

Anakonza

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?

Anakonza

6.28 rad = 1 rev

60 rad/6.28 = 9.55 rev

6. 40 rad= ….. ^o?

Anakonza

6.28 rad = 360 ^o

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

[irp]

Kusamuka kwa ngodya ndi kusamuka kolunjika

1. Gudumu la njinga la mainchesi 60 limazungulira ma radians 10. Kodi kusuntha kwa mzere wa mfundo yomwe ili m'mphepete mwa gudumu ndi kotani?

Zodziwika:

Utali wozungulira (r) = 30 cm = 0.3 m

Ngodya (θ ) = ma radians 10

Kufunidwa: kusamuka kolunjika (l)

Yankho:

l = r θ

l = (0.3 m)(10 rad)

l = mamita atatu

2. Gudumu la 50 cm mu radius limazungulira 360 ^o . Kodi kusuntha kwa mzere wa mfundo yomwe ili m'mphepete mwa gudumu ndi kotani?

Zodziwika:

Ulalo wozungulira (r) = 50 cm = 0.5 mamita

Ngodya ( θ ) = 360 ^o = 6.28 ma radians

Kufunidwa: kusamuka kolunjika (l)

Yankho:

l = r θ

l = (0.5 m)(6.28 rad)

l = mamita atatu

[irp]

3. Gudumu la 50 cm mu radius limazungulira maulendo awiri. Kodi kusuntha kwa mzere wa mfundo yomwe ili m'mphepete mwa gudumu ndi kotani?

Zodziwika:

Utali wozungulira (r) = 50 cm = 0,5 m

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

Kufunidwa: kusamuka kolunjika (l)?

Yankho:

l = r θ

l = (0.5 m)(12.56 rad)

l = 6.28 m

4. Mfundo yomwe ili m'mphepete mwa gudumu mamita awiri mu radius, imayenda mamita 100. Dziwani kusuntha kwa ngodya.

Zodziwika:

Ulalo wozungulira (r) = ½ (m'mimba mwake) = ½ (mamita awiri) = mita imodzi

kusamuka kolunjika (l) = mamita 100

Yankho:

(a) Kusuntha kwa ngodya (mu ma radians)

θ = s / r = 100 / 1 = ma radians 100

(b) Kusuntha kwa ngodya (mu madigiri)

1 radian = 360 ^o

Ma radians 100 = 100(360 ^o ) = ma radians 36,000

(c) Kusamuka kwa ngodya (mu kusintha)

Ma radians 6.28 = 1 revolution

36,000 / 6.28 = ma revolution 5732,484

[irp]

5. Tinthu tating'onoting'ono timazungulira mamita 10 ndikuzungulira ^madigiri 180. Kodi radius ndi chiyani?

Zodziwika:

Kusamuka kwa mzere (l) = mamita 10

Ngodya ( θ ) = 180 ^o = 3.14 ma radians

Kufunidwa: utali wozungulira (r)

Yankho:

r = l / θ = 10 / 3.14 = 3.18 mamita

[irp]

1. Kusintha mayunitsi a ngodya mavuto a zitsanzo ndi mayankho
2. Mavuto ndi mayankho a zitsanzo za kusamuka kwa angular ndi kusamuka kolunjika
3. Mavuto a chitsanzo cha liwiro la angular ndi liwiro lolunjika ndi mayankho
4. Mavuto a Angular a fast and linear acceleration ndi mayankho
5. Zitsanzo za mavuto ozungulira ofanana ndi mayankho
6. Mavuto a chitsanzo cha Centripetal acceleration ndi mayankho
7. Zitsanzo za mavuto ozungulira osafanana ndi mayankho

Werengani zambiri

1. Gudumu la mita imodzi mu radius limathamanga mofanana pa 2 rad/s ^2. Dziwani liwiro la angular ndi liwiro la angular la gudumu, masekondi awiri pambuyo pake.

Zodziwika:

Ulalo wozungulira (r) = mita imodzi

Kuthamanga kwa angular (α ) = 2 rad/s ²

Kufunidwa: kuthamanga kwa angular ndi liwiro la angular pambuyo pa masekondi awiri.

Yankho:

(a) Kuthamanga kwa ngodya mu masekondi awiri

Kuthamanga kwa angular kumakhala kosalekeza, motero pakatha masekondi awiri, kuthamanga kwa angular kwa gudumu ndi 2 rad/s ².

(b) Liwiro la ngodya mu masekondi awiri

Kuthamanga kwa angular 2 rad/s ² kumatanthauza kuti liwiro la angular limawonjezera ma radians awiri/sekondi iliyonse. Pambuyo pa sekondi imodzi, liwiro la angular = ma radians awiri/sekondi. Pambuyo pa masekondi awiri, liwiro la angular = ma radians anayi/sekondi.

[irp]

2. Tinthu tating'onoting'ono timathamanga mofanana kuchokera pa mpumulo mpaka 60 rpm mu masekondi 10. Dziwani kukula kwa kuthamanga kwa angular!

Zodziwika:

Liwiro loyambirira la angular (ω _o ) = 0

Liwiro lomaliza la angular ( ωt ) = 60 rpm = ma revolutions 60 / masekondi 60 = revolution 1 / second = 6,28 ma radians/ _second

Nthawi yopuma (t) = masekondi 10

Kufunidwa: Kuthamanga kwa angular ( α )

Yankho:

ω _o = liwiro loyambirira la angular, ω _t = liwiro lomaliza la angular, α = kuthamanga kwa angular, t = nthawi yopuma, θ = ngodya.

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

Kukula kwa kuthamanga kwa angular = 0.628 rad/s ²

3. Chinthu chimachedwetsa liwiro kuchoka pa 20 rad/s kufika pa 10 rad/s mu masekondi 4. Dziwani kukula kwa kuthamanga kwa angular!

Zodziwika:

Nthawi yopuma (t) = masekondi 4

Liwiro loyambirira la angular ( ω _o ) = 20 rad/s

Liwiro lomaliza la angular ( ω _t ) = 10 rad/s

Kufunidwa : kukula kwa kuthamanga kwa angular (α )

Yankho:

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

Kukula kwa kufulumira kwa angular ndi -2.5 rad/s ^2. Chizindikiro chotsutsa chimatanthauza kuti chinthucho chikuchepa. Kuthamanga = liwiro la angular likuwonjezeka, kutsika = liwiro la angular likuchepa.

[irp]

4. Chinthu chimafulumizitsidwa kwa masekondi awiri kuchokera pa 10 rad/s mpaka 2 rad/s . ^2. Dziwani ngodya yozunguliridwa ndi chinthucho!

Zodziwika:

liwiro loyambirira la angular ( ω _o ) = 10 rad/s

kuthamanga kwa angular (α ) = 2 rad/s ²

nthawi yopuma (t) = masekondi awiri

Akufuna: ngodya (θ)

Yankho:

θ = ω _o + ½ α t ²

θ = (10)(2) + ½ (2)(2 ² )

θ = 20 + (1)(4) = 20 + 4

θ = ma radians 24

5. Gudumu la galimoto limachepa kuchoka pa 20 rad/s kuti lipumule pambuyo pa ma radians ozungulira 20. Dziwani kukula kwa liwiro la angular la gudumu!

Zodziwika:

liwiro loyambirira la angular ( ω _o ) = 20 rad/s

liwiro lomaliza la _{angular (} ωt ) = 0

Ngodya ( θ ) = ma radians 20

Kufunidwa: kukula kwa kuthamanga kwa angular (α )

Yankho:

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 yokhala ndi kutalika kwa 60 cm imazungulira mozungulira point Q ngati axis of rotation ndi PQ ngati radius ya circle. Rod PQ imathamanga kuchokera pamalo opumulira mpaka 0.3 rad/s ² . Kodi liwiro la linear la point P pa t = 10 seconds ndi liti, ngati angular initial position ndi 0.

Zodziwika:

Kutalika kwa ndodo PQ = radius ya bwalo (r) = 60 cm = 60/100 m = 0.60 m

Liwiro loyambirira la angular (ω _o ) = 0 rad/s

Kuthamanga kwa angular (α) = 0.3 rad s ^-2

Malo oyamba a angular (θ _o ) = 0

Kufunidwa: Liwiro la mzere (v) la mfundo P pa t = masekondi 10

Yankho:

Liwiro lomaliza la angular pambuyo pa masekondi 10:

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

Liwiro lomaliza la mzere pambuyo pa masekondi 10:

v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s

[irp]

7. Chinthu chimazungulira ndi liwiro loyambirira la 4 rad/s ndipo kufulumira kwa angular ndi 0.5 rad/s ^2. Kodi liwiro la chinthucho ndi lotani pakatha masekondi 4?

Zodziwika:

Liwiro loyambirira la angular (ω _o ) = 4 rad/s

Kuthamanga kwa angular (α) = 0.5 rad/s ²

Nthawi yopuma (t) = masekondi 4

Kufunidwa: Liwiro la chinthucho pambuyo pa masekondi 4 (ω _t )

Yankho:

ω _t = ω _o + α t

ω _t = 4 + (0.5)(4)

ω _t = 4 + 2

ω _t = 6 rad/s

8. Wotchi ya pakhoma yokhala ndi mainchesi 10 imakhala ndi singano zitatu, iliyonse kusonyeza maola, mphindi ndi masekondi. Kuyerekeza chiwerengero cha maulendo a singano ya ola: singano ya mphindi: singano yachiwiri.

A. 1: 3: 180

B. 1 : 12 : 720

C. 4 : 12 : 180

D. 4 : 12 : 720

Zodziwika:

Ola limodzi = mphindi 60

Maola 12 = (12) (mphindi 60) = mphindi 720

Liwiro la singano ya ola = kuzungulira 1 / maola 12 = kuzungulira 1 / mphindi 720

Liwiro la singano ya mphindi = kuzungulira 1 / ola 1 = kuzungulira 1 / mphindi 60

Liwiro la singano yachiwiri = kuzungulira 1 / mphindi 1

Kufunidwa: Kuyerekeza chiwerengero cha maulendo a singano ya ola limodzi: singano ya mphindi imodzi: singano yachiwiri

Yankho:

Kuyerekeza kwa kayendedwe kozungulira:

Liwiro la angular = chiwerengero cha ma revolutions / nthawi yopuma

Chiwerengero cha ma revolutions = angular speed x nthawi yopuma

Mu nthawi yomweyi, mwachitsanzo, mphindi imodzi, kuchuluka kwa ma revolutions a singano ya ola, singano ya mphindi, ndi singano yachiwiri.

Chiwerengero cha ma revolutions a singano ya ola = angular speed x time interval = (1 revolution / 720 minutes)(1 minute) = 1/720 revolutions

Chiwerengero cha ma revolutions a singano ya mphindi = angular speed x time interval = (1 revolution / 60 minutes) (1 minute) = 1/60 revolutions

Chiwerengero cha kusintha kwa singano yachiwiri = liwiro la angular x nthawi yopuma = (kusintha 1 / mphindi 1) (mphindi 1) = kusintha 1/1

Kuyerekeza kwa ma revolution angapo:

Chiwerengero cha ma revolutions a singano ya ola: chiwerengero cha ma revolutions a singano ya mphindi: chiwerengero cha ma revolutions a singano yachiwiri.

1/720: 1/60: 1/1

1/720: 12/720: 720/720

1: 12

Yankho lolondola ndi B.

9. Mpira womangidwa ndi chingwe. Mpirawo umazunguliridwa kuti uyende mozungulira molingana ndi pamwamba pa dziko lapansi. Mu mayendedwe awa, mpirawo umathamanga chifukwa…..

A. Kukangana kwa mpweya

B. Kulemera kwa mpira

C. Mphamvu ya kukangana

D. Mphamvu yokoka

Yankho:

Lamulo lachiwiri la Newton loyendetsa likunena kuti chinthu chimathamanga ngati pali mphamvu yochokerapo. Mpira umalumikizidwa ndi chingwe ndipo chingwe chikazungulira, mpirawo umazunguliranso. Mpira ukazungulira (mpirawo umayenda mozungulira), mpirawo umadutsa mu liwiro la pakati. Zinthu zonse zoyenda zimakhala zozungulira ndi liwiro la pakati. Kuthamanga kwa pakati kumachitika chifukwa cha mphamvu ya pakati . Mphamvu ya pakati pa nkhaniyi ndi mphamvu ya kukakamira.

Yankho lolondola ndi C.

[irp]

[wpdm_package id='437′]

[wpdm_package id='439′]

1. Kusintha mayunitsi a ngodya mavuto a zitsanzo ndi mayankho
2. Mavuto ndi mayankho a zitsanzo za kusamuka kwa angular ndi kusamuka kolunjika
3. Mavuto a chitsanzo cha liwiro la angular ndi liwiro lolunjika ndi mayankho
4. Mavuto a Angular a fast and linear acceleration ndi mayankho
5. Zitsanzo za mavuto ozungulira ofanana ndi mayankho
6. Mavuto a chitsanzo cha Centripetal acceleration ndi mayankho
7. Zitsanzo za mavuto ozungulira osafanana ndi mayankho

Werengani zambiri

1. Chinthu chimayenda mozungulira ndi liwiro losasintha la angular la 10 rad/s. Dziwani (a) Liwiro la angular pambuyo pa masekondi 10 (b) Kusuntha kwa angular pambuyo pa masekondi 10.

Zodziwika:

Liwiro la angular (ω) = 10 rad/s

Akufuna:

(a) Liwiro la angular (ω) pambuyo pa masekondi 10.

(b) Ngodya (θ) pambuyo pa masekondi 10

Yankho:

(a) Liwiro la angular (ω) pambuyo pa masekondi awiri

Chinthucho chimayenda mozungulira mofanana kotero kuti liwiro la angular likhale losasintha, 10 rad/s.

(b) Kusuntha kwa ngodya (θ)

Liwiro lokhazikika la angular 10 radians/sekondi limatanthauza chinthu chozungulira ma radians 10 pa sekondi. Pambuyo pa masekondi 10, chinthucho chozungulira ma radians 10 x 10 = ma radians 100.

[irp]

2. Tinthu tating'onoting'ono timayendayenda mozungulira ndi liwiro losasintha la 10 m/s. Ma radius a bwalo = mita 1. Dziwani (a) Liwiro la tinthu tating'onoting'ono pambuyo pa masekondi 5 (b) Kusuntha kwa tinthu tating'onoting'ono pambuyo pa masekondi 5 (c) Kuthamanga kwapakati.

Zodziwika:

Ulalo wozungulira (r) = mita imodzi

Liwiro la tinthu (v) = 10 m/s

Yankho:

(a) Liwiro la tinthu tating'onoting'ono pambuyo pa masekondi 5

Kuyenda kwa chinthucho kuli kozungulira mofanana kotero kuti liwiro limakhala losasintha, 10 m/s.

(b) Kusuntha kwa tinthu tating'onoting'ono patatha masekondi 5

Mamita 10/sekondi amatanthauza sekondi imodzi iliyonse, kusamuka kwa tinthu tating'onoting'ono = mamita 10. Pambuyo pa masekondi 5, kusamuka kwa tinthu tating'onoting'ono = mamita 5 x 10 = mamita 50.

(c) Kuthamanga kwapakati pa centripetal (a _r )

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

3. Mpira womangiriridwa kumapeto kwa chingwe, umazunguliridwa mozungulira ndi utali wa mamita awiri pa liwiro losasintha la 60 rpm. Dziwani (a) kukula kwa liwiro la angular pambuyo pa masekondi awiri (b) kusuntha kwa angular pambuyo pa mphindi imodzi.

Zodziwika:

Ulalo wozungulira (r) = mamita awiri

Liwiro la angular (ω) = 60 rpm = ma revolutions 60 / mphindi imodzi

= ma revolution 60 / masekondi 60 = revolution 1 / sekondi = ma radians 2π / sekondi

= 2(3.14) ma radians / yachiwiri = ma radians 6.28 / yachiwiri

Yankho:

(a) Liwiro la angular (ω) pambuyo pa masekondi awiri

Liwiro la angular ndi losasintha kotero pambuyo pa masekondi awiri, liwiro la angular (ω) = 6.28 radians / sekondi

(b) Kusuntha kwa ngodya (θ)

Liwiro la angular = 1 revolution/sekondi limatanthauza kuti sekondi imodzi iliyonse, mpira umakumana ndi revolution imodzi. Pambuyo pa masekondi 60, mpira umasuntha ma revolution 60.

Liwiro la angular = 6.28 radians/sekondi limatanthauza kuti sekondi imodzi iliyonse, mpira umayenda ndi ngodya ya 6.28 radians. Pambuyo pa masekondi 60, mpira umasuntha ma radians 376.8.

[irp]

4. Gudumu la njinga limazungulira maulendo 120 mu masekondi 60. Kodi liwiro lake ndi lotani?

Yankho:

(a) kusintha kwa mphindi (rpm)

Ma revolutions 120 / masekondi 60 = ma revolutions 120 / mphindi imodzi = ma revolutions 120 / mphindi = 120 rpm

(b) madigiri pa sekondi ( ^o / s)

Kusinthana 1 = 360 ^o , kusinthana 120 = 43200 ^o

Ma revolution 120 / masekondi 60 = (120)(360 ^o ) / masekondi 60 = 43200 ^o / masekondi 60 = 720 ^o /sekondi

(c) ma radians pa sekondi (rad/s)

Chisinthiko chimodzi = ma radians 6.28

Ma revolution 120 / masekondi 60 = (120)(6.28) ma radians / masekondi 60 = ma radians 753.6 / masekondi 60 = ma radians 12.56/sekondi.

[irp]

[wpdm_package id='432′]

[wpdm_package id='439′]

1. Kusintha mayunitsi a ngodya mavuto a zitsanzo ndi mayankho
2. Mavuto ndi mayankho a zitsanzo za kusamuka kwa angular ndi kusamuka kolunjika
3. Mavuto a chitsanzo cha liwiro la angular ndi liwiro lolunjika ndi mayankho
4. Mavuto a Angular a fast and linear acceleration ndi mayankho
5. Zitsanzo za mavuto ozungulira ofanana ndi mayankho
6. Mavuto a chitsanzo cha Centripetal acceleration ndi mayankho
7. Zitsanzo za mavuto ozungulira osafanana ndi mayankho

Werengani zambiri

1. Mpira wa 0.1 kg, wolumikizidwa kumapeto kwa chingwe chopingasa, umazunguliridwa mu bwalo la radius 50 cm ndipo liwiro la angular la mpira ndi s 4 rad s ^-1 . Kodi kukula kwa mphamvu ya centripetal ndi kotani?

Zodziwika:

Kulemera (m) = magalamu 100 = 100/1000 kg = 1/10 kg = 0.1 kg

Liwiro la angular ( ω ) = 4 radians/se cond

Ulalo wozungulira (r) = 50 cm = 50/100 m = 0.5 m

Kufunidwa: Mphamvu yapakati

Yankho:

Mphamvu yapakati ndi mphamvu yeniyeni yomwe imapangitsa kuti kuthamanga kwapakati kukhale kofanana ndi :

∑ F = ma _r

∑ F = mv ² /r = m ω ² r

∑ F = mphamvu yeniyeni = mphamvu yapakati , m = kulemera , v = liwiro , ω = liwiro la angular , r = radius

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

[irp]

2. Mpira ukuzungulira mofanana mu bwalo lozungulira. Ngati liwiro lasintha kufika kanayi kuposa mtengo woyamba, kodi mphamvu ya pakati ndi yotani…..

Zodziwika:

Misa = m

Liwiro = v

Liwiro loyambirira = v _o

Ulalo wozungulira (r) = r

Kufunidwa: Kukula kwa mphamvu yapakati

Yankho:

3. Mzere wozungulira wa radius R wapangidwa kuti galimoto yoyenda pa liwiro la 12 ms ^-1 itha kuyendetsa bwino kutembenuka. Chiŵerengero cha kukangana kosasinthasintha pakati pa galimoto ndi msewu = 0.4. Kodi radius R ndi chiyani? Kuthamanga chifukwa cha mphamvu yokoka ( g ) = 10 ms ^-2.

Zodziwika:

Liwiro (v) = 12 m/s

Koyefifiti ya kukangana kosasinthasintha ( μs ₎ = 0.4

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Akufuna: Radius (R)

Yankho:

[irp]

[wpdm_package id='501′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamalo opingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri