fisiks

9 Sekala sa mocheso se fetolelang (sekala sa Celsius Fahrenheit sekala sa Kelvin)

1. 50 ^oC = ….. ^oF?

tharollo

Sebakeng se tloaelehileng sa sepakapaka khatello, ntlha ea ho hoama ea metsi ke 0 ^oC hodima Sekala sa Celsius 'me 32 ^oF ka sekala sa Fahrenheit. Ka kgatello e tloaelehileng ea sepakapaka, ntlha ea ho belisa ea metsi ke 100 ^oC sekaleng sa Celsius le 212 ^oF ka sekala sa Fahrenheit.

0 ^oEA-32-C ^oF le 100 ^oEA-212-C ^oF. Phetoho ea 5 C^o = phetoho ea 9 F^o.

Bakeng sa sekala sa Celsius, sebaka se pakeng tsa 0 ^oC le 100 ^oC e arotsoe ka mekhahlelo e 100 e lekanang. Bakeng sa sekala sa Fahrenheit, sebaka se pakeng tsa 0 ^oC le 100 ^oC e arotsoe ka mekhahlelo e 180 e lekanang.

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 ^oEA-122-C ^oF

2. 86 ^oF = ….. ^oC?

tharollo

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^oEA-30-C

86 ^oF=30 ^oC

3. 50^oC = ….. K ?

tharollo

T = T ^oC + 273

T = 50 + 273

T = 323

50 ^oC= 323 K

4. 212^oF = ….. K ?

tharollo

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^oEA-100-C

212 ^oF=100 ^oC + 273

212 ^oF=373 K

 

5. x ^oC = x ^oF

x = ….. ?

tharollo

1: Ho fetolela sekala sa Celsius ho Fahrenheit

2: Ho fetolela sekala sa Fahrenheit ho ba sekala sa Celsius

6. 122°F = ….. Celsius

tharollo

Phetoho pakeng tsa sekala sa mocheso tse peli e ka ngoloa:

T_C = 5/9 (T_F - 32)

T_C = mocheso ka Celsius, T_F = mocheso ka Fahrenheit

Thempereichara ka Celsius:

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

T_C = 50 ^oC

7. Setšoantšo se ka tlase se bontša tekanyo ea mocheso oa a mokelikeli o nang le thermometer ea sekala sa Fahrenheit! Haeba mocheso oa mokelikeli o lekanngoa ho sebelisoa thermometer ea sekala sa Celsius, joale ke eng mocheso oa metsie.

Tse tsejoang:

Fahrenheit Tekanyo (T_F= 95^oF

Ho batloa: Sekala sa Celsius

Tharollo:

Ka khatello ea 1 atm, sebaka se hatselang sa metsi is 0 °C ha sekala sa Fahrenheit e le 32 ^oF. Ka lehlakoreng le leng, tntlha ea ho belisa ea metsi bakeng sa CElsius sekala ke 100 ^oC ha sekala sa Fahrenheit is 212 ^oF.

Sekala sa Celsius, pakeng tsa 0 °C le 100 °C ho na le 100 ° ha sekala sa Fahrenheit se pakeng tsa 32 °F le 212 °F ho na le 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. Ho latela setšoantšo se ka tlase, fumana tmocheso oa P ho thermometer ea Celsius.

tharollo

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. Haeba mocheso oa sekala sa Celsius joalo ka ha ho bontšitsoe setšoantšong se ka tlase, fumana mocheso oa sekala sa Fahrenheit joalo ka ha ho bontšitsoe setšoantšong se ka tlase.

Tharollo:

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. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

1. Kerafo ea matla (F) khahlanong le ho lelefala (x)) e bontšitsoeng setšoantšong se ka tlase. Fumana se tsitsitseng sa selemo!

tharollo

Molao oa Hooke foromo:

k = F / x

F= lebotho la (Newton)

k = nako e sa fetoheng ea selemo (Newton/mithara)

x = phetoho ea bolelele (limithara)

Nako e tsitsitseng ea selemo:

k = 10 / 0.02 = 20 / 0.04

k = 500 N/m

2. Etsa qeto ea selemo kamehla.

tharollo

Nako e tsitsitseng ea selemo:

k = F / x

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

k = 500 N/m

3. Selemo A se na le bolelele ba pele ba 60 cm mme selemo B se na le bolelele ba pele ba 90 cm. Selemo A se na le botsitso ba 100 N/m, selemo B se na le botsitso ba 200 N/m. Karolelano ea phetoho boleleleng ba selemo A ho ea phetohong ea bolelele ba selemo B ke…

Tse tsejoang:

Nako e sa fetoheng ea selemo A (k)_A) = 100 N/m

Nako e sa fetoheng ea selemo B (k)_B) = 200 N/m

Matla a selemo A (F)_A) = F

Matla a selemo sa B (F)_B) = F

Oa Batla: Δl_A : Δl_B

Tharollo:

Foromo ea molao oa Hooke:

Δl = F / k

Δl = phetoho ea bolelele, F = matla, k = e sa fetoheng

Phetoho boleleleng ba selemo A:

Δl_A =F_A / k_A = F / 100

Phetoho boleleleng ba selemo sa B:

Δl_B =F_B / k_B = F / 200

Karolelano ea phetoho boleleleng ba selemo A ho ea phetohong boleleleng ba selemo B:

Δl_A : Δl_B

F/100 : F/200

1/100: 1/200

1/1: 1/2

2: 1

4. Thapo ea naelone e bolelele ba pele ba 20 cm, e huloa ke matla a 10 N. Phetoho ea bolelele ba khoele ke 2 cm. Fumana boholo ba matla haeba phetoho ea bolelele e le 6 cm.

Tse tsejoang:

Matla (F) = 10 N

Phetoho ea bolelele (Δl) = 2 cm = 0.02 m

Ho batloa: boholo ba matla (F) haeba Δl = 0.06 m.

Tharollo:

Kamehla:

k = F / Δl

k = 10 / 0.02 = 500 N/m

Boholo ba matla (F) haeba Δl = 0.06 m :

F = kx

F = (500)(0.06)

F = 30N

[ID ea sephutheloana sa wpdm='689′]

1. Molao oa Hooke
2. Khatello ea maikutlo, khatello, modulus ea Young

Bala haholoanyane

Khatello ea Khatello ea Kelello Modulus ea Young - Mathata le Litharollo

1. Thapo ea nylon e na le bophara ba 2 mm, e huloang ke matla a 100 N. Fumana khatello!

Tse tsejoang:

Etsa matla (F) = 100 N

Bophara (d) = 2 mm = 0.002 m

Radius (r) = 1 mm = 0.001 m

Ho batloa: Khatello ea maikutlo

Tharollo:

Sebaka:

A = π r²

A = (3.14)(0.001 m)² = 0.00000314 limithara²

A = 3.14 x 10^-6 m²

Khatello ea maikutlo:

2. Thapo e bolelele ba pele ba 100 cm e huloa ke matla. Phetoho ea bolelele ba thapo ke 2 mm. Fumana khatello!

Tse tsejoang:

Bolelele ba mantlha (l)₀) = 100 cm = 1 m

Phetoho ea bolelele (Δl) = 2 mm = 0.002 m

Ho batloa: Moferefere

Tharollo:

Likarolo tsa sterene:

3. Khoele e bophara ba 4 mm e na le bolelele ba pele ba limithara tse 2. Khoele e huloa ka matla a 200 N. Haeba bolelele ba ho qetela ba selemo e le 2.02 m, fumana: (a) khatello ea maikutlo (b) khatello ea maikutlo (c) Modulus ea Young

Tse tsejoang:

Bophara (d) = 4 mm = 0.004 m

Radius (r) = 2 mm = 0.002 m

Sebaka (A) = π r² = (3.14)(0.002 m)²

Sebaka (A) = 0.00001256 m² = 12.56x10^-6 m²

Matla (F) = 200 N

Bolelele ba pele ba selemo (l)₀) = 2 m

Phetoho ea bolelele (Δl) = 2.02 – 2 = 0.02 m

Ho batloa: (a) Kgatelelo ya maikutlo (b) Kgatelelo ya maikutlo c) Modulus ya Young

Tharollo:

(a) Li-stsietsi

(b) Moferefere

(C) Modulus ea bacha

4. Khoele e na le bophara ba 1 cm 'me bolelele ba pele ba 2 m. Khoele e huloa ke matla a 200 N. Fumana phetoho boleleleng ba khoele! Modulus ea Young ea khoele = 5 x 10⁹ N / limithara²

Tse tsejoang:

Modulus ea Young (E) = 5 x 10⁹ N / limithara²

Bolelele ba mantlha (l)₀) = 2 m

Matla (F) = 200 N

Bophara (d) = 1 cm = 0.01 m

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

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

Sebaka (A) = 78.5 x 10^-6 m² = 7.85x10^-5 m²

o ne a batla : Phetoho ea bolelele (Δl)

Tharollo:

Foromo ea modulus ea Young:

Phetoho ea bolelele :

5. Konkreite e na le bophahamo ba limithara tse 5 mme e na le sebaka sa yuniti sa limithara tse 3³ tšehetsa a boima ea 30,000 kg. Fumana (a) Khatello ea maikutlo (b) Khatello (c) Phetoho ea bolelele! Ho potlakisa ka baka la matla a khoheli (g) = 10 m/s²Modulus ea Young ea konkreite = 20 x 10⁹ N / limithara²

Tse tsejoang:

Modulus ea Young ea konkreite = 20 x 10⁹ N / limithara²

Bolelele ba qalong (l)₀) = limithara tse 5

Sebaka sa yuniti (A) = 3 m²

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

Ho batloa: (a) Kgatelelo ya maikutlo (b) Kgatelelo ya maikutlo (c) Phetoho ya bophahamo!

Tharollo:

(a) Khatello ea maikutlo

(b) Moferefere

(c) Phetoho ea bophahamo

1. Molao oa Hooke
2. Khatello ea maikutlo, khatello, modulus ea Young

Bala haholoanyane

1. Bolo, e hoketsoeng pheletsong ea thapo e rapameng, e potoloha ka selikalikoe sa radius ea 20 cm. Bolo e ka ba 360^o motsotsoana o mong le o mong. Fumana boholo ba ho potlaka ha bohareng!

Tse tsejoang:

Lebelo la angular (ω= 360^o/motsotswana = phetohelo e le 1/motsotswana = 6.28 radians/motsotswana

Radius (r) = 20 cm = 0.2 limithara

Ho batloa: Ho potlaka ha centripetal (a_r)

Tharollo:

a_r = v² /r —> v = r ω

a_r = (r ω)² / r = r² ω² /r

a_r =r ω²

a_s = ho potlaka ha bohareng, v = lebelo le otlolohileng, r = radius, ω = lebelo la maqhubu

Boholo ba ho potlaka ha centripetal :

a_r =r ω² a_r = (0,2 m)(6.28 rad/s)

a_r = 1.256 m/s²

2. Lebili la 30 cm ka radius le potoloha ka lebelo la 180 rpm. Fumana lebelo la bohareng ba ntlha e ka lehlakoreng la lebili!

Tse tsejoang:

Radius (r) = 30 cm = 0.3 m

Lebelo la angular (ω) = Diphetoho tse 180 / Metsotsoana e 60 = Diphetoho tse 3 / Motsotsoana = (3)(Di-radian tse 6.28) / Motsotsoana = Di-radian tse 18.84/Motsotsoana

Ho batloa: ho potlaka ha bohareng (a_r) ea r = 0.3 m

Tharollo:

Boholo ba ho potlaka ha centripetal:

a_r =r ω²

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

a_r = 5.65 m/s²

3. Koloi ea mabelo e tsamaea tseleng e chitja ea radius ea limithara tse 50. Haeba lebelo la koloi e le 72 km/h, fumana boholo ba lebelo la centripetal!

Tse tsejoang:

Radius (r) = limithara tse 50

Lebelo (v) = 72 km/h = (72)(limithara tse 1000) / metsotsoana e 3600 = limithara tse 20/motsotsoana

o ne a batla : boholo ba ho potlaka ha centripetal (a_r)

Tharollo:

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

4. Koloi e na le lebelo le phahameng ka ho fetisisa la bohareng ba 10 m/s², e le hore koloi e ka reteleha ntle le ho thella tseleng e kobehileng. Haeba koloi e tsamaya ka lebelo le sa fetoheng la 108 km/h, radius ya sekhutlo se sa kobehang ke efe?

Tse tsejoang:

Ho potlaka ha centripetal (a_r) = 10 m/s²

Lebelo la koloi (v) = 108 km/h = (108)(1000) / 3600 = limithara tse 30s/second

Ho batloa: radius (r)

Tharollo:

r = v² / a_r

r = 30² / 10 = 900 / 10 = limithara tse 90s

[ID ea sephutheloana sa wpdm='433′]

[ID ea sephutheloana sa wpdm='439′]

1. Mathata a sampole a diyuniti tsa dikhutlo a fetolang ka ditharollo
2. Mathata le litharollo tsa sampole ea ho falla ka mokhoa o otlolohileng le oa ho falla ka mokhoa o otlolohileng
3. Mathata a sampole ea lebelo la angular le lebelo le otlolohileng ka litharollo
4. Mathata a mohlala oa ho potlakisa ka mokhoa o otlolohileng le oa ho potlakisa ka litharollo
5. Mehlala ea mathata a metsamao e chitja e tšoanang ka litharollo
6. Mathata a sampole ea ho potlakisa centripetal ka litharollo
7. Mathata a sampole ea metsamao e chitja e sa tšoanelang ka litharollo

Bala haholoanyane

1. Koloi e nang le mabili a mararo0 cm ka har'a radius e potoloha ka mokhoa o sa fetoheng 5 rad/s²Boholo ba ho potlaka ka mola ntlha e fumanehang ho (a) 10 cm ho tloha bohareng (b) 20 cm ho tloha bohareng (c) pheletsong ea lebili?

Tse tsejoang:

Radius (r) = 30 cm = 0.3 m

Ho potlaka ha Angular (α) = 5 rad/s²

Ho batloa: ho potlaka ka mola (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m

Tharollo:

Kamano pakeng tsa ho potlaka ka mola o otlolohileng (a) le ho potlaka ka angular:

a = r α

(A) ho potlaka ka mola, r = 0.1 m

a = (0.1 m)(5 rad/s²) = 0.5 m/s²

(B) ho potlaka ka mola, r = 0.2 m

a = (0.2 m)(5 rad/s²) = 1 m/s²

(C) ho potlaka ka mola, r = 0.3 m

a = (0.3 m)(5 rad/s²) = 1.5 m/s²

2. Pulley ea 50 cm ka radius. Haeba lebelo le otlolohileng la ntlha e fumanehang moeling oa pulley e le 2 m/s², fumana lebelo la angular la pulley!

Tse tsejoang:

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

ho potlaka ka mola o otlolohileng (a) = 2 m/s²

Ho batloa: ho potlaka ha angular

Tharollo:

α = ho / r = 2 / 0.5 = 4 rad/s²

3. Mahare ka har'a blender a bolelele ba 20 cm ka har'a radius, qalong a phomotse. Kamora metsotsoana e 2, mahare a potoloha ka 10 rad/s. Fumana boholo ba lebelo le otlolohileng (a) ntlha e fumanehang ho 10 cm ho tloha bohareng (b) ntlha e fumanehang moeling oa mahare.

Tse tsejoang:

Radius (r) = 20 cm = 0.2 m

Lebelo la pele la angular (ω_o) = 0

Lebelo la ho qetela la angular (ω_t) = 10 radians/motsotsoana

Nako ea ho arohana (t) = metsotsoana e 2

Ho batloa: sefuthumatsi se otlolohilengntlha e fumanehang ho (a) r = 0.1 m (b) r = 0.2 m

Tharollo:

ω_t = ω_o + α t

10 = 0 + α (2)

10 = 2 α

α = 10 / 2

 α = 5 rad/s

(A) ho potlaka ha mola oa r = 0.1 m

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

(B) ho potlaka ha mola oa r = 0.2 m

a =r α = (0.2 m)(5 rad/s²) = 1 m/s²

4. Lebili la 20 cm ka radius le potlakiswa metsotsoana e 2 ho tloha ho 20 rad/s ho ya phomolong. Fumana boholo ba potlakiso e otlolohileng (a) ntlha e fumanehang ho 10 cm ho tloha bohareng (b) ntlha e fumanehang ho 10 cm ho tloha bohareng.

Tse tsejoang:

Radius (r) = 20 cm = 0.2 m

Lebelo la pele la angular (ω_o) = 20 rad/s

Lebelo la ho qetela la angular (ω_t= 0

Nako ea ho arohana (t) = metsotsoana e 2

Ho batloa: Ho potlaka ho otlolohileng (a) r = 0.1 m (b) r = 0.2 m

Tharollo:

ω_t = ω_o + α t

0 = 20 + α (2)

-20 = 2 α

α = -20 / 2

 α = -10 rad/s

Letšoao le fosahetseng le bolela lebelo la angular e fokotseha.

(A) ho potlaka ha mola oa r = 0.1 m

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

(B) ho potlaka ha mola oa r = 0.2 m

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

[ID ea sephutheloana sa wpdm='429′]

[ID ea sephutheloana sa wpdm='439′]

1. Mathata a sampole a diyuniti tsa dikhutlo a fetolang ka ditharollo
2. Mathata le litharollo tsa sampole ea ho falla ka mokhoa o otlolohileng le oa ho falla ka mokhoa o otlolohileng
3. Mathata a sampole ea lebelo la angular le lebelo le otlolohileng ka litharollo
4. Mathata a mohlala oa ho potlakisa ka mokhoa o otlolohileng le oa ho potlakisa ka litharollo
5. Mehlala ea mathata a metsamao e chitja e tšoanang ka litharollo
6. Mathata a sampole ea ho potlakisa centripetal ka litharollo
7. Mathata a sampole ea metsamao e chitja e sa tšoanelang ka litharollo

Bala haholoanyane

1. Bolo qetellong ea khoele e potoloha ka ho lekana selikalikoeng se bataletseng sa radius ea limithara tse 2 ka lebelo le sa fetoheng la angular la 10 rad/s. Fumana boholo ba lebelo le otlolohileng la ntlha e fumanehang:

(a) Limithara tse 0.5 ho tloha bohareng

(b) mithara e le 1 ho tloha bohareng

(c) limithara tse 2 ho tloha bohareng

Tse tsejoang:

Radius (r) = 0.5 mithas, mithara e le 1, limithara tse 3

Lebelo la angular = mahlaseli a 10s/seboemo

Ho batloa: The lebelo le otlolohileng

Tharollo:

v = r ω

v = lebelo le otlolohileng, r = radius, ω = lebelo la angular

(A) Lebelo le otlolohileng (v) la ntlha e fumanehang ho r = 0.5 metres

v = r ω = (Limithara tse 0.5s)(10 rad/s) = limithara tse 5s/seboemo

(B) Lebelo le otlolohileng (v) ea ntlha e fumanehang ho r = mithara e le 1

v = r ω = (mithara e le 1)(10 rad/s) = limithara tse 10s/seboemo

(C) Lebelo le otlolohileng (v) ea ntlha e fumanehang ho r = mithara e le 2s

v = r ω = (Limithara tse 2s)(10 rad/s) = limithara tse 20s/seboemo

2. Mahare a ka har'a blender a potoloha ka lebelo la 5000 rpm. Fumana boholo ba lebelo le otlolohileng:

(A) ntlha e fumanehang 5 cm ho tloha bohareng

(B) ntlha e fumanehang 10 cm ho tloha bohareng

Tse tsejoang:

Radius (r) = 5 cm le 10 cm,

Lebelo la angular (ω) = 5000 liphetohelo / 60 seconds = 83.3 liphetohelo / seboemo = (83.3)(6.28 radians) / seboemo = mahlaseli a 523.3s / seboemo

Ho batloa: Boholo ba lebelo le otlolohileng

Tharollo:

(A) Boholo ba lebelo le otlolohileng la ntlha e fumanehang 0.05 m ho tloha bohareng

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

(B) Boholo ba lebelo le otlolohileng la ntlha e fumanehang 0,1 m ho tloha bohareng

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

3. Ntlha e ka lehlakoreng la lebili 30 cm, ka har'a radius, ho potoloha selikalikoe ka lebelo le sa fetoheng Limithara tse 10 ka motsotsoana.

Boholo ba lebelo la angular ke bofe?

Tse tsejoang:

Radius (r) = 30 cm = 0.3 limitharas

Lebelo le otlolohileng (v) = limithara tse 10s/seboemo

Ho batloa: lebelo la angular

Tharollo:

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

4. Koloi e nang le mabili a bophara ba 50 cm moetillimithara tse 10 ka hare 1 sa bobeli. Lebelo la angular ke lefe?

Tse tsejoang:

Radius (r) = limithara tse 0.25

Lebelo le otlolohileng la ntlha e ka lehlakoreng la thaere (v) = limithara tse 10s/seboemo

Oa Batla: Lebelo la angular

Tharollo:

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

5. Lebelo le potolohang la lebili la 20 cm ka radians ke 120 rpm. Ke eng distanta haeba koloi e tsamaea ka metsotsoana e 10.

Tse tsejoang:

Radius (r) = 20 cm = 0.2 limitharas

Lebelo la angular = 120 Tšen / 60 semaemo = 2 Tšen / seboemo = (2)(6.28) radians / seboemo = mahlaseli a 12.56s / seboemo

Ho batloa: distanta

Tharollo:

Velocity ea lehlakore la lebili:

v = r ω = (limithara tse 0.2s)(12.56 radians/seboemo) = limithara tse 2.5s/seboemo

Monyetla oa 2.5s / second e bolela ntlha e ka lehlakoreng la leeto la mabili Monyetla oa 2.5s motsotsoana o mong le o mong. Ka mor'a hore 10maemo, ntlha e tsamaea Monyetla oa 25s.

Kahoo sebaka se joalo Monyetla oa 25s.

[ID ea sephutheloana sa wpdm='427′]

[ID ea sephutheloana sa wpdm='439′]

1. Mathata a sampole a diyuniti tsa dikhutlo a fetolang ka ditharollo
2. Mathata le litharollo tsa sampole ea ho falla ka mokhoa o otlolohileng le oa ho falla ka mokhoa o otlolohileng
3. Mathata a sampole ea lebelo la angular le lebelo le otlolohileng ka litharollo
4. Mathata a mohlala oa ho potlakisa ka mokhoa o otlolohileng le oa ho potlakisa ka litharollo
5. Mehlala ea mathata a metsamao e chitja e tšoanang ka litharollo
6. Mathata a sampole ea ho potlakisa centripetal ka litharollo
7. Mathata a sampole ea metsamao e chitja e sa tšoanelang ka litharollo

Bala haholoanyane

Ho fetola diyuniti tsa angle (degree, radian, revolution)

1. ¼ Tšen = ….. ^o (tekanyo)?

tharollo

1 Tšen = 360^o

½ Tšen = 180^o

¼ Tšen = 90^o

2. ½ Tšen = …….. rad ?

tharollo

1 Tšen = 2π lera = 2(3.14) lera = 6.28 lera

½ Tšen = pi rad = 3.14 rad

3. 180^o = ….. phetolelo?

tharollo

360^o = 1 Tšen

180^o = ½ Tšen

4. 90^o = ….. rad ?

tharollo

360^o = 2π lera = 2(3.14) lera = 6.28 lerad

180^o = π lera = 3.14 lera

90^o = ½ π lera = ½ (3.14) = 1.57

5. 60 rad = ….. Tšen ?

tharollo

6.28 rad = 1 Tšen

60 rad/6.28 = 9.55 Tšen

6. 40 rad= ….. ^o ?

tharollo

6.28 rad = 360^o

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

Ho falla ha angular le ho falla ha linear

1. Lebili la baesekele le bophara ba 60 cm le potoloha di-radian tse 10. Ke eng ho falla ka mola ntlha e ka lehlakoreng la lebili?

Tse tsejoang:

Radius (r) = 30 cm = 0.3 m

Angle (θ)) = li-radian tse 10

Ho batloa: ho falla ha mola (l)

Tharollo:

l = r θ

l = (0.3 m)(10 rad)

l = limithara tse 3

2. Lebili la 50 cm ka radius le potoloha 360^o. Ho falla ha ntlha e lebaneng le lebili ke eng?

Tse tsejoang:

Radius (r) = 50 cm = 0.5 metres

Sekhutlo (θ= 360^o = 6.28 radians

Ho batloa: ho falla ha mola (l)

Tharollo:

l = r θ

l = (0.5 m)(6.28 rad)

l = limithara tse 3.14

3. Lebili la 50 cm ka radius le potoloha diphetoho tse 2. Ho falla ha ntlha e moeding wa lebili ke eng?

Tse tsejoang:

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

Sekhutlo (θ) = 2 diphetoho = (2)(6.28 radians) = 12.56 radians

Ho batloa: ho falla ha mola (l) ?

Tharollo:

l = r θ

l = (0.5 m)(12.56 rad)

l = 6.28 m

4. Ntlha e ka lehlakoreng la lebili e bolelele ba limithara tse 2 ka har'a radius, e tsamaea limithara tse 100. Fumana ho falla ha khoele.

Tse tsejoang:

Radius (r) = ½ (bophara) = ½ (limithara tse 2) = 1 mithara

ho falla ha mola (l) = limithara tse 100

Tharollo:

(a) Ho falla ha Angular (ka mahlaseli)

θ = s / r = 100 / 1 = 100 radians

(b) Ho falla ha Angular (ka likhato)

Radian e le 1 = 360^o

Li-radian tse 100 = 100 (360)^o) = li-radian tse 36,000

(c) Ho falla ha Angular (phetohelong)

Li-radian tse 6.28 = phetohelo e le 'ngoe

36,000 / 6.28 = 5732,484 diphetoho

5. Phatsa e potoloha selikalikoe sa limithara tse 10 ebe e potoloha 180^o. Radius ke eng?

Tse tsejoang:

Ho falla ha mola (l) = limithara tse 10

Sekhutlo (θ= 180^o = 3.14 radians

Ho batloa: radius (r)

Tharollo:

r = l / θ = 10 / 3.14 = limithara tse 3.18

1. Mathata a sampole a diyuniti tsa dikhutlo a fetolang ka ditharollo
2. Mathata le litharollo tsa sampole ea ho falla ka mokhoa o otlolohileng le oa ho falla ka mokhoa o otlolohileng
3. Mathata a sampole ea lebelo la angular le lebelo le otlolohileng ka litharollo
4. Mathata a mohlala oa ho potlakisa ka mokhoa o otlolohileng le oa ho potlakisa ka litharollo
5. Mehlala ea mathata a metsamao e chitja e tšoanang ka litharollo
6. Mathata a sampole ea ho potlakisa centripetal ka litharollo
7. Mathata a sampole ea metsamao e chitja e sa tšoanelang ka litharollo

Bala haholoanyane

1. Lebili la mithara e le 'ngoe ka har'a radius le potlakisa ka ho lekana ho 2 rad/s². Fumana hore na lebelo la angular le lebelo la angular ea lebili, metsotsoana e 2 hamorao.

Tse tsejoang:

Radius (r) = 1 mithara

Ho potlaka ha Angular (α)) = 2 rad/s²

Oa Batla: ho potlaka ha angular le lebelo la angular kamora metsotsoana e 2.

Tharollo:

(A) Ho potlaka ha Angular ka metsotsoana e 2

Ho potlaka ha Angular ho tsitsitse, kahoo kamora metsotsoana e 2, ho potlaka ha Angular ha lebili ke 2 rad/s².

(B) Lebelo la Angular ka metsotsoana e 2

Ho potlaka ha Angular 2 rad/s² ho bolela hore lebelo la angular le eketsa di-radian tse 2/motsotswana o mong le o mong. Kamora motsotsoana o le mong, lebelo la angular = di-radian tse 2/motsotswana. Kamora metsotsoana e 2, lebelo la angular = di-radian tse 4/motsotswana.

2. Phatsa e potlaka ka ho lekana ho tloha phomolong ho isa ho 60 rpm ka metsotsoana e 10. Fumana boholo ba potlakiso ea angular!

Tse tsejoang:

Lebelo la pele la angular (ω_o= 0

Lebelo la ho qetela la angular (ω_t) = 60 rpm = diphetoho tse 60 / metsotsoana e 60 = phetoho e le 1 / motsotsoana = di-radian tse 6,28/motsotswana

Nako ea ho arohana (t) = metsotsoana e 10

Ho batloa: Ho potlaka ha Angular (α)

Tharollo:

ω_o = lebelo la pele la angular, ω_t = lebelo la ho qetela la angular, α = ho potlaka ha angular, t = nako e sa fellang, θ = sekhutlo.

ω_t = ω_o + α t

6.28 = 0 + α (10)

6.28 = 10 α

α = 6.28/10

α = 0.628 rad/s²

Boholo ba ho potlaka ha angular = 0.628 rad/s²

3. Ntho e fokotsa lebelo ho tloha ho 20 rad/s ho isa ho 10 rad/s ka metsotsoana e 4. Fumana boholo ba lebelo la angular!

Tse tsejoang:

Nako ea ho arohana (t) = metsotsoana e 4

Lebelo la pele la angular (ω_o ) = 20 rad/s

Lebelo la ho qetela la angular (ω_t) = 10 rad/s

o ne a batla : boholo ba ho potlaka ha angular (α)

Tharollo:

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

Boholo ba ho potlaka ha angular ke -2.5 rad/s²Letšoao le fosahetseng le bolela hore ntho e ntse e fokotseha. Ho potlaka = lebelo la angular lea eketseha, ho fokotseha = lebelo la angular lea fokotseha.

4. Ntho e potlakiswa ka metsotsoana e 2 ho tloha ho 10 rad/s ho isa ho 2 rad/s²Fumana sekhutlo se chitja ke ntho!

Tse tsejoang:

lebelo la pele la angular (ω_o ) = 10 rad/s

ho potlaka ha angular (α) = 2 rad/s²

nako e sa fellang (t) = metsotsoana e 2

Ho batloa: sekhutlo (θ)

Tharollo:

θ = ω_o + ½ α t²

θ = (10)(2) + ½ (2)(2²)

θ = 20 + (1)(4) = 20 + 4

θ = mahlasedi a 24

5. Lebili la koloi le fokotsa lebelo ho tloha ho 20 rad/s ho ea phomola kamora ho potoloha 20 radians. Fumana boholo ba lebelo le potolohang la lebili!

Tse tsejoang:

lebelo la pele la angular (ω_o) = 20 rad/s

lebelo la ho qetela la angular (ω_t= 0

Sekhutlo (θ) = li-radian tse 20

Ho batloa: boholo ba ho potlaka ha angular (α)

Tharollo:

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 e bolelele ba 60 cm e potoloha hoo e ka bang ntlha Q e le axis ea potoloho le PQ e le radius ea selikalikoe. Rod PQ e potlakile ho tloha phomolong ho ea ho 0.3 rad/s²Lebelo le otlolohileng la ntlha P ke lefe ho t = metsotsoana e 10, haeba boemo ba pele ba angular e le 0.

Tse tsejoang:

Bolelele ba thupa PQ = radius ea selikalikoe (r) = 60 cm = 60/100 m = 0.60 m

Lebelo la pele la angular (ω_o) = 0 rad/s

Ho potlaka ha Angular (α) = 0.3 rad s^-2

Boemo ba pele ba angular (θ_o= 0

Ho batloa: Lebelo la mola (v) la ntlha P ho t = metsotsoana e 10

Tharollo:

Lebelo la ho qetela la angular kamora metsotsoana e 10:

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

Lebelo la ho qetela le otlolohileng kamora metsotsoana e 10:

v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s

7. Ntho e potoloha ka lebelo la pele la 4 rad/s mme lebelo la angular ke 0.5 rad/s². Lebelo la ntho ke lefe ka mora metsotswana e 4?

Tse tsejoang:

Lebelo la pele la angular (ω_o) = 4 rad/s

Ho potlaka ha Angular (α) = 0.5 rad/s²

Nako ea ho arohana (t) = metsotsoana e 4

Ho batloa: Lebelo la ntho ka mora metsotsoana e 4 (ω_t)

Tharollo:

ω_t = ω_o + α t

ω_t = 4 + (0.5)(4)

ω_t = 4 + 2

ω_t = 6 rad/s

8. A Oache ea lebota e bophara ba 10 cm e na le linalete tse tharo, e 'ngoe le e 'ngoe e bontša lihora, metsotso le metsotsoana. Papiso ea palo ea lipotoloho tsa nale ea hora: nale ea motsotso: nale ea bobeli.

A. 1: 3: 180

B. 1 : 12 : 720

C. 4: 12: 180

D. 4: 12: 720

Tse tsejoang:

Hora e le 1 = metsotso e 60

Lihora tse 12 = (12)(metsotso e 60) = metsotso e 720

Lebelo la angular la nale ea hora = phetoho e le 'ngoe / lihora tse 12 = phetoho e le 'ngoe / metsotso e 720

Lebelo la motsotso la nale = phetoho e le 'ngoe / hora e le 'ngoe = phetoho e le 'ngoe / metsotso e 60

Lebelo la nale ea bobeli le potolohang = phetohelo e le 'ngoe / motsotso o le mong

Oa Batla: Papiso ea palo ea lipotoloho tsa nale ea hora: nale ea motsotso: nale ea bobeli

Tharollo:

Tekanyo ea motsamao o chitja:

Lebelo la Angular = palo ea liphetohelo / nako e sa fellang

Palo ea liphetohelo = lebelo la angular x nako e sa fellang

Ka nako e tšoanang, mohlala, motsotso o le mong, ke liphetoho tse kae tsa nale ea hora, nale ea motsotso, le nale ea bobeli.

Palo ea liphetohelo tsa nale ea hora = lebelo la angular x nako ea karohano = (phetohelo e le 'ngoe / metsotso e 720) (motsotso o le mong) = liphetohelo tse 1/720

Palo ea liphetohelo tsa nale ea motsotso = lebelo la angular x nako ea karohano = (phetohelo e le 'ngoe / metsotso e 60) (motsotso o le mong) = liphetohelo tse 1/60

Palo ea liphetohelo tsa nale ea bobeli = lebelo la angular x nako ea nako = (phetohelo e le 'ngoe / motsotso o le mong) (motsotso o le mong) = phetoho ea 1/1

Papiso ea liphetohelo tse 'maloa:

Palo ea liphetohelo tsa nale ea hora: palo ea liphetohelo tsa nale ea motsotso: palo ea liphetohelo tsa nale ea bobeli.

1/720: 1/60: 1/1

1/720: 12/720: 720/720

1:12:720

Karabo e nepahetseng ke B.

9. Bolo e tlamiloeng ka thapo. Bolo e potoloha e le hore e tsamaee ka tsela e chitja e bapileng le bokaholimo ba lefatše. Motsamaong ona, bolo e potlaka hobane…..

A. Khohlano ea moea

B. Weight ea bolo

C. Matla a kgatello

D. Matla a khoheli

Tharollo:

Molao oa bobeli oa Newton oa ho sisinyeha e bolela hore ntho e potlakiswa haeba ho na le matla a hlahang. Bolo e hokahantsoe le thapo mme ha thapo e potoloha, bolo le yona e a potoloha. Ha bolo e potoloha (bolo e tsamaya ka sedikadikwe), bolo e feta potlakisong ya centripetal. Dintho tsohle tse tsamayang ke potlakiso e chitja ya centripetal. Ho potlaka ha centripetal e bakoa ke matla a boharengMatla a bohareng bakeng sa nyeoe ena ke matla a khatello.

Karabo e nepahetseng ke C.

[ID ea sephutheloana sa wpdm='437′]

[ID ea sephutheloana sa wpdm='439′]

1. Mathata a sampole a diyuniti tsa dikhutlo a fetolang ka ditharollo
2. Mathata le litharollo tsa sampole ea ho falla ka mokhoa o otlolohileng le oa ho falla ka mokhoa o otlolohileng
3. Mathata a sampole ea lebelo la angular le lebelo le otlolohileng ka litharollo
4. Mathata a mohlala oa ho potlakisa ka mokhoa o otlolohileng le oa ho potlakisa ka litharollo
5. Mehlala ea mathata a metsamao e chitja e tšoanang ka litharollo
6. Mathata a sampole ea ho potlakisa centripetal ka litharollo
7. Mathata a sampole ea metsamao e chitja e sa tšoanelang ka litharollo

Bala haholoanyane

1. Ntho e tsamaya ka sedikadikwe ka lebelo le sa fetoheng la di-rad/s tse 10. Fumana (a) Lebelo la angular kamora metsotsoana e 10 (b) Ho falla ha Angular kamora metsotsoana e 10.

Tse tsejoang:

Lebelo la angular (ω) =10 rad/s

Ho batloa:

(a) Lebelo la Angular (ω) kamora metsotsoana e 10.

(b) Sekhutlo (θ) kamora metsotsoana e 10

Tharollo:

(A) Lebelo la angular (ω) kamora metsotsoana e 10

Ntho e ka hare motsamao o chitja o tšoanang e le hore lebelo la angular le lule le tsitsitse, 10 rad/s.

(b) Ho falla ha Angle (θ)

Lebelo le sa fetoheng la angular 10 radians/motsotswana le bolela ntho e potolohileng 10 radians ka motsotsoana. Kamora metsotsoana e 10, ntho e potolohileng 10 x 10 radians = 100 radians.

2. Phatsa e tsamaya ka sedikadikwe ka lebelo le sa fetoheng la 10 m/s. Radius ya sedikadikwe = mithara e le 1. Fumana (a) Lebelo la phatsa ka mora metsotswana e 5 (b) Phatsa ho baleha kamora metsotsoana e 5 (c) Ho potlaka ha centripetal.

Tse tsejoang:

Radius ea selikalikoe (r) = 1 meter

Lebelo la karoloana (v) = 10 m/s

Tharollo:

(A) Lebelo la karoloana ka mor'a metsotsoana e 5

Motsamao oa ntho o ka har'a motsamao o chitja o tšoanang e le hore lebelo le lule le tsitsitse, 10 m/s.

(B) Ho falla ha karoloana ka mor'a metsotsoana e 5

Limithara tse 10 ka motsotsoana li bolela motsotsoana o mong le o mong, ho falla ha karoloana = limithara tse 10. Kamora metsotsoana e 5, ho falla ha karoloana = limithara tse 5 x 10 = limithara tse 50.

(C) Ho potlaka ha centripetal (a_r)

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

3. Bolo e hoketsweng pheletsong e 'ngoe ea thapo, e potoloha ka selikalikoe se nang le radius ea limithara tse 2 ka lebelo le sa fetoheng la 60 rpm. Fumana (a) boholo ba lebelo la angular kamora metsotsoana e 2 (b) ho falla ha angular kamora motsotso o le mong.

Tse tsejoang:

Radius ea selikalikoe (r) = limithara tse 2

Lebelo la Angular (ω) = 60 rpm = diphetoho tse 60 / motsotso o le 1

= Diphetoho tse 60 / Metsotsoana e 60 = Phetoho e le 1 / Motsotsoana = 2π mahlaseli / motsotsoana

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

Tharollo:

(A) Lebelo la angular (ω) kamora metsotsoana e 2

Lebelo la angular ha le fetohe kahoo kamora metsotsoana e 2, lebelo la angular (ω) = 6.28 radians / motsotsoana

(B) Ho falla ha Angular (θ)

Lebelo la angular = phetohelo e le 'ngoe/motsotswana le bolela hore motsotsoana o mong le o mong, bolo e ba le phetoho e le 'ngoe. Kamora metsotsoana e 60, bolo e tsamaea ka makhetlo a 60.

Lebelo la angular = 6.28 radians/motsotswana le bolela hore motsotsoana o mong le o mong, bolo e tsamaya ka sekhutlo sa 6.28 radians. Kamora metsotsoana e 60, bolo e tsamaya ka 376.8 radians.

4. Lebili la baesekele le potoloha diphetoho tse 120 ka metsotswana e 60. Lebelo le nang le dikhutlo tse pedi ke lefe?

Tharollo:

(a) diphetoho ka motsotso (rpm)

Liphetoho tse 120 / metsotsoana e 60 = liphetoho tse 120 / motsotso o le 1 = liphetoho tse 120 / motsotso = 120 rpm

(B) likhato ka motsotsoana (^o/ s)

Phetohelo e le 'ngoe = 360^o, diphetoho tse 120 = 43200^o

Liphetohelo tse 120 / metsotsoana e 60 = (120)(360^o) / metsotsoana e 60 = 43200^o / Metsotsoana e 60 = 720^o/motsotsoana

(C) radians ka motsotsoana (rad/s)

Phetoho e le 'ngoe = li-radian tse 6.28

Diphetoho tse 120 / metsotsoana e 60 = (120)(6.28) di-radian / metsotsoana e 60 = di-radian tse 753.6 / metsotsoana e 60 = di-radian tse 12.56/motsotswana.

[ID ea sephutheloana sa wpdm='432′]

[ID ea sephutheloana sa wpdm='439′]

1. Mathata a sampole a diyuniti tsa dikhutlo a fetolang ka ditharollo
2. Mathata le litharollo tsa sampole ea ho falla ka mokhoa o otlolohileng le oa ho falla ka mokhoa o otlolohileng
3. Mathata a sampole ea lebelo la angular le lebelo le otlolohileng ka litharollo
4. Mathata a mohlala oa ho potlakisa ka mokhoa o otlolohileng le oa ho potlakisa ka litharollo
5. Mehlala ea mathata a metsamao e chitja e tšoanang ka litharollo
6. Mathata a sampole ea ho potlakisa centripetal ka litharollo
7. Mathata a sampole ea metsamao e chitja e sa tšoanelang ka litharollo

Bala haholoanyane

1. A 0.1Bolo ea -kg, e khomaretsoeng pheletsong ea thapo e rapameng, e potoloha ka selikalikoe sa radius 50 cm, le tsa bolo lebelo la angular is Li-rad tse 4^-1Boholo ba centripetal ke bofe matla?

Tse tsejoang:

Boholo (m) = digrama tse 100 = 100/1000 kg = 1/10 kg = 0.1 kg

Lebelo la angular (ω) = 4 radians/sboemo

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

Ho batloa: Matla a bohareng

Tharollo:

Matla a bohareng ke matla a sa hlokeng letho a hlahisang ho potlaka ha bohareng :

∑F = ma_r

∑F = mv²/r = m ω² r

∑F= matla a letlooa = matla a bohareng, m = boima, v = lebelo, ω = lebelo la angular, r = radius

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

2. Bolo e potoloha ka ho lekana ka selikalikoe se rapameng. Haeba lebelo le fetoha ho ba le boleng ba pele bo fetang makgetlo a mane, boholo ba matla a bohareng ke bofe…..

Tse tsejoang:

Boholo = m

lebelo = v

Lebelo la pele = v_o

Radius (r) =r

Oa Batla: Boholo ba matla a bohareng

Tharollo:

3. Sekotwana sa radius R se entsoe ka tsela eo koloi e tsamaeang ka lebelo la 12 ms^-1 e ka buisana ka ho reteleha ka mokhoa o sireletsehileng. Coefficient ea khohlano e sa fetoheng pakeng tsa koloi le tsela = 0.4. Radius ke eng R. Ho potlakisa ka baka la matla a khoheli (g) = 10 ms^-2.

Tse tsejoang:

lebelo (v) = 12 m/s

Khokahano ea khohlano e sa fetoheng (μ_s) = 0.4

Ho potlakisa ka baka la matla a khoheli (g) = 10 m/s²

Oa Batla: Radius (R)

Tharollo:

[ID ea sephutheloana sa wpdm='501′]

1. Boima le boima
2. Matla a tloaelehileng
3. Molao oa bobeli oa Newton oa ho sisinyeha
4. Matla a khohlano
5. Ho sisinyeha holim'a bokaholimo bo otlolohileng ntle le matla a khohlano
6. Motsamao oa 'mele e 'meli e nang le lebelo le tšoanang holim'a bokaholimo bo bataletseng bo bataletseng ka matla a khohlano
7. Ho sisinyeha ha sefofane se sekametseng ntle le matla a khohlano
8. Motsamao sefofaneng se sekametseng ka thata ka matla a khohlano
9. Motsamao ka lifting
10. Motsamao oa 'mele o hokahantsoe ka lithapo le li-pulleys
11. 'Mele e 'meli e nang le boholo bo tšoanang ba ho potlaka
12. Ho potoloha mothapo o bataletseng - matla a motsamao o chitja
13. Ho potoloha mothapo o kobehileng - matla a motsamao o chitja
14. Motsamao o tšoanang ka selikalikoe se otlolohileng
15. Matla a bohareng a motsamao o chitja o tšoanang

Bala haholoanyane