fisiks

1. Bolo ea 0.2-kg, e hoketsoeng qetellong ea thapo e rapameng, e potoloha ka selikalikoe sa radius ea mithara e le 'ngoe 'me lebelo le phahameng ka ho fetisisa la bolo ke 10 rpm. Boholo ba eona ke bofe ho potlaka ha bohareng le boholo ba matla a tsitsipano?

Tse tsejoang:

Boholo (m) = 0.2 kg

Radius (r) = 1 m

Lebelo la angular (ω) = 10 rev/min = 10 rev/60 s = 0.17 rev/s = (0.17) (6.28 rad)/s = 1 rad/s

Velocity (v) = r ω = (1 m)(1 rad/s) = 1 m/s

Ho batloa: a_s dan tao ΣF

Tharollo:

(a) Boholo ba ho potlaka ha centripetal

(b) Boholo ba matla a khatello

ΣF = ma

T = ma_s

T = (0.2 kg)(1 m/s²)

T = 0.2 kg m/s²

T = 0.2 N

2. Bolo ea 1-kg qetellong ea khoele e potoloha ka ho lekana selikalikoeng se bataletseng sa radius ea 1 m. Thapo e tla robeha ha khatello e ho eona e feta 100 N. Lebelo le phahameng ka ho fetisisa leo bolo e ka bang le lona ke lefe?

Tse tsejoang:

Boima (m) = 1 kg

Radius (r) = 1 mithara

Matla a kgatello (T) = matla a bohareng (ΣF) = 100 N

Oa Batla: boholo ba v

Tharollo:

[ID ea sephutheloana sa wpdm='499′]

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 sefofaneng 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

1. Koloi e potolohang moedi o kobehileng. Sekhutlo sa tsela e nang le moedi o kobehileng wa radius wa dimithara tse 60 ka lebelo la moralo wa 20 m/s ke sefe? A re re ha ho na khohlano pakeng tsa koloi le tsela.

tharollo

N= matla a tloaelehileng

Sebe sa N θ = karolo e otlolohileng ea matla a tloaelehileng

N cos θ = karolo e otlolohileng ea matla a tloaelehileng

w = mg = e boima ba 'mele ea koloi

Tsela e etselitsoe ho ba le libanka ho felisa ho itšetleha ka khohlano.

Matla a ho rapama a letlooa, karolo e otlolohileng ea matla a tloaelehileng (Sebe sa N θ), ho hlokahala ho boloka koloi e ntse e tsamaya ka selikalikoe ho potoloha mothinya.

Re khetha x-axis e le e otlolohileng le y-axis e le e otlolohileng, e le hore ho potlakisoa ha centripetal, e be_R, e ka lehlakoreng le otlolohileng. Ka lehlakoreng le otlolohileng, matla feela ke karolo e otlolohileng ea matla a tloaelehileng (Sebe sa N θ), e hlokahalang ho hlahisa ho potlaka ha bohareng. N sin θ = matla a bohareng.

Sebelisa molao oa Newton oa motsamao ka lehlakoreng le otlolohileng:

Sebelisa molao oa Newton oa motsamao ka lehlakoreng le otlolohileng:

Moemeliho kenya N ka har'a equation ea 1 ho ea ho N ka har'a equation ea 2 :

[ID ea sephutheloana sa wpdm='497′]

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

1. Koloi ea boima ba lik'hilograma tse 2000 e potoloha mothinya tseleng e bataletseng ea radius ea 150 m. Coefficient ea khohlano e sa fetoheng ke 0.5. Fumana lebelo le phahameng ka ho fetisisa e le hore koloi e latele mothinya mme e se ke ea thella. Ho potlakisa ka baka la matla a khoheli = 10 m/s².

Tse tsejoang:

Boholo (m) = 2000 kg

Radius (r) = limithara tse 150

Khokahano ea khohlano e sa fetoheng (μ_s= 0.5

Weight (w) = mg = (2000 kg)(10 m/s²) = 20,000 kg m/s² = 20,000N

Matla a khohlano e sa fetoheng (F)_s) = μ_s N = μ_s w = (0.7)(20,000 N) = 14,000 N

Ho batloa: v

Tharollo:

[ID ea sephutheloana sa wpdm='496′]

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

1. Boima bo habeli m₁ = 2 kg le m₂ = 5 kg di sebakeng se sekametseng mme di hokahantswe mmoho ka thapo jwalo ka ha ho bontshitswe setshwantshong. Koefficient ya kgatello ya kinetic pakeng tsa m₁ 'me ho sekamela ke 0.2 'me coefficient ea khohlano ea kinetic pakeng tsa m₂ 'me ho sekamela ke 0.1.

(a) Fumana hore na ba ho potlaka

(b) Fumana matla a khatello

Tse tsejoang:

Boholo 1 (m₁) = 2 kg

Boima ba 2 (m₂) = 4 kg

Khokahano ea kinetic pakeng tsa m₁ 'me sefofane se sekametseng (μ_k1) = 0.2

Khokahano ea kinetic pakeng tsa m₂ le sefofane se sekametseng (μ_k2) = 0.1

Ho potlakisa ka baka la matla a khoheli (g) = 9.8 m/s²

a) Boholo le tataiso ea ho potlaka

w₁ = boima ba 'mele 1 = m₁ g = (2 kg)(9.8 m/s²) = 19.6 Newton

w_1x = w₁ sebe 30^o = (19.6 N)(0.5) = 9.8 Newton

w_1y = w₁ Cos 30^o = (19.6 N)(0.87) = 17 Newton

N₁ = E matla a tloaelehileng ka m₁ = w_1y = 17 Newton

F_k1 = Matla a moferefere oa kinetic ho m₁ = μ_k1 N₁ = (0.2)(17 N) = 3.4 Newton

---

w₂ = boima 2 = m₂ g = (4 kg)(9.8 m/s²) = 39.2 Newton

w_2x = w₂ sebe 60^o = (39.2 N)(0.87) = 34.1 Newton

w_2y = w₂ Cos 60^o = (39.2 N)(0.5) = 19.6 Newton

N₂ = Matla a tloaelehileng ho m₂ = w_2y = 19.6 Newton

F_k2 = Matla a moferefere oa kinetic ho m₂ = μ_k2 N₂ = (0.1)(19.6 N) = 1.96 Newton

---

Boholo ba ho potlaka ha lebelo:

∑F_x = ma_x

w_2x > w_1x kahoo tataiso ea ho potlaka e tšoana le tataiso ea w_2x.

Matla a supang ho potlaka a matle mme matla a fapaneng le ho potlaka a mabe.

w_2x - F_k2 - T₂ +T₁ - w_1x - F_k1 = (m₁ +m₂) a_x

w_2x - F_k2 - w_1x - F_k1 = (m₁ +m₂ ) a_x

34.1 N – 1.96 N – 9.8 N – 3.4 N = (2 kg + 4 kg) a_x

18.94 N = (6 kg) a_x

a_x = 18.94 N : 6 kg

a_x = 3.16 m/s²

Boholo ba ho potlaka = 3.16 m/s² . Tataiso ea ho potlaka = tataiso ea T₁ = tataiso ea w_2x

b) Boholo ba matla a khatello

Sebelisa molao oa bobeli oa Newton holim'a ntho ea 2:

w_2x - F_k2 - T₂ = m₂ a_x

34.1 N – 1.96 N – T₂ = (4 lik'hilograma)(3.16 m/s²)

32.14 N – T₂ = 12.64N

T₂ = 32.14 N – 12.64 N = 19.5 Newton

Matla a tsitsipano = T = T₁ = T₂ = 19.5 Newton

2. m₁ = 4 kg, m₂ = 2 kg. Fumana (a) boholo le tataiso ea ho potlaka (b) Boholo ba matla a khatello a hokahanyang m₁ le m₂ (c) boholo ba matla a kgatello a hokahanyang pulley le marulelo.

tharollo

w₁ = m₁ g = (4 kg)(9.8 m/s²) = 39.2 Newton

w₂ = m₂ g = (2 kg)(9.8 m/s²) = 19.6 Newton

a) Boholo le tataiso ea ho potlaka

∑F_y = ma_y

w₁ > w₂ kahoo tataiso ea ntho e tšoana le tataiso ea boima ba 1 (w₁)Matla a nang le tataiso e tšoanang le ea ho potlaka a matle 'me matla a nang le tataiso e fapaneng le ea ho potlaka a mabe.

w₁ - T₁ +T₂ - w₂ = (m₁ +m₂) a_y

w₁ - w₂ = (m₁ +m₂) a_y

39.2 N - 19.6 N = (4 lik'hilograma + 2 lik'hilograma) a_y

19.6 N = (6 kg) a_y

a_y = 19.6 N : 6 kg

a_y = 3.26 m/s²

Boholo ba ho potlaka = 3.26 m/s². Tataiso ea ho potlaka = tataiso ea w₁ .

b) Boholo ba matla a khatello a hokahanyang m₁ le m₂

Etsa kopo Molao oa bobeli oa Newton ka m₂ :

∑F_y = ma_y

w₁ - T₁ = m₁ a_y

39.2 N – T₁ = (4 kg)(3.26 m/s²)

39.2 N – T₁ = 13.04N

T₁ = 39.2 N – 13.04 N

T₁ = 26.16 Newton

Boholo ba matla a khatello a hokahanyang lintho = T = T₁ = T₂ = 26.16 Newton

c) Boholo ba matla a kgatello a hokahanyang pulley le marulelo.

Pulley e phomotse:

∑F_y = ma_y —— a_y = 0

∑F_y = 0

Matla a holimo a matle, matla a theohelang tlase a mabe:

T₃ - T₁ - T₂ = 0

T₃ = T₁ +T₂

T₁ le T₂ li na le boholo bo tšoanang, T₁ = T₂ = T = 26.16 N :

T₃ = 2T = 2(26.16 N) = 52.32 Li-Newton

3. Boloko ea 1 (m₁ = 10 kg) le boloko ba 2 (m₂ = 15 kg) e hokahantswe ka thapo hodima pulley e se nang khohlano. Khoefithara ya khohlano e sa fetoheng pakeng tsa boloko ba 2 ka ho sekamela = 0.6. Khoefithara ya khohlano ya kinetic pakeng tsa boloko ba 2 ka ho sekamela = 0.42. Fumana (a) Boholo ba matla a bonyane F a sebediswang hodima dintho e le hore dintho di potlakise ho ya hodimo (b) Fumana boholo ba matla a kgatello.

tharollo

w₁ = Boima ba boloko 1 = m₁ g = (10 kg)(9.8 m/s²) = 98 Newton

w₂ = Boima ba boloko 2 = m₂ g = (15 kg)(9.8 m/s²) = 147 Newton

w_2y = w₂ Cos 30^o = (147 N)(0.87) = 127.89 Newton

w_2x = w₂ sebe 30^o = (147 N)(0.5) = 73.5 Newton

N₂ = Matla a tloaelehileng holim'a boloko 2 = w_2y = 127.89 Newton

F_k2 = Matla a moferefere wa kinetic hodima boloko 2 = μ_k2 N₂ = (0.42)(127.89 N) = 53.7 Newton

F_s2 = Matla a khohlano e sa fetoheng bolokong 2 = μ_s2 N₂ = (0.6)(127.89 N) = 76.7 Newton

a) Boholo ba matla a fokolang a F a sebelisitsoeng linthong kahoo lintho li ile tsa potlaka ho ea holimo

∑F_x = ma_x —— a_x = 0

∑F_x = 0

Matla a eang holimo le a eang ka letsohong le letona a matle, matla a theohelang le a eang ka letsohong le letšehali a mabe.

F – F_k2 - w_2x - w₁ - T₂ +T₁ = 0

F – F_k2 - w_2x - w₁ = 0

F = F_k2 +w_2x +w₁

F = 53.7 N + 73.5 N + 98 N

F = 225.2 Newton

b) Boholo ba matla a khatello ea maikutlo

Sebelisa molao oa Newton oa ho sisinyeha holim'a boloko ba 1:

∑F_y = ma_y —— a_y = 0

∑F_y = 0

T₁ - w₁ = 0

T₁ = w₁ = 98 Newton

Sebelisa molao oa Newton oa ho sisinyeha holim'a boloko ba 2:

F – F_k2 - w_2x - T₂ = 0

T₂ = F – F_k2 - w_2x

T₂ = 225.2 N – 53.7 N – 73.5 N

T₂ = 98 Newton

Boholo ba matla a khatello = T₁ = T₂ = T = 98 Newton

4. Boloko ea 1 (m₁ = 16 kg) e lutse holim'a bokaholimo bo bataletseng 'me boloko ba 2 (m₂ = 12 kg) e robetse sebakeng se sekametseng hantle, e hokahantsoe ka thapo e fetang holim'a pulley e nyane, e se nang khohlano. Block 3 (m₃ = 5 kg) e lutse holim'a boloko 2. Koefficient ea khohlano ea kinetic pakeng tsa boloko 2 le bokaholimo bo otlolohileng ke 0,4. CoefKhohlano e sa fetoheng pakeng tsa boloko ba 2 le boloko ba 3 ke 0,3.

(A) Ha sistimi e lokollotsoe phomolong, boloko ea 3 le boloko ea 2 li ntse li thella hammoho?

(B) Haeba ho na le boloko ba 3, ho potlaka ha boloko ba 1 le boloko ba 2 ke eng?

Tharollo:

a) Ha sistimi e lokollotsoe phomolong, boloko ea 3 le boloko ea 2 li ntse li thella hammoho?

w₁ = E boima ba boloko 1 = m₁ g = (16 kg)(9.8 m/s²) = 156.8 Newton

w_1x = w₁ sebe 60^o = (156.8 N)(0.87) = 136.4 Newton

w_1y = w₁ Cos 60^o = (156.8 N)(0.5) = 78.4 Newton

N₁ = E matla a tloaelehileng a sebelisoang bolokong ba 1 ke sefofane se sekametseng = w_1y = 78.4 Newton

w₃ = E boima ba boloko 3 = m₃ g = (5 kg)(9.8 m/s²) = 49 Newton

N₂₃ = E matla a tloaelehileng a sebelisoang holim'a boloko ba 3 ke boloko ba 2 = w₃ = 49 Newton

N₃₂ = Nmatla a tloaelehileng a sebelisoang holim'a boloko ba 2 ke boloko ba 3 = N₂₃ = w₃ = 49 Newton

(N₂₃ 'me N₃₂ ke lipara tsa karabelo ea ketso)

F_s23 = E Matla a khohlano e sa fetoheng e sebediswang hodima boloko ba 3 ke boloko ba 2 = μ_s N₂₃ = (0.3)(49 N) = 14.7 Newton

F_s32 = E Matla a khohlano e sa fetoheng e sebediswang hodima boloko ba 2 ke boloko ba 3 =F_s23 = 14.7 Newton

(F_s23 'me F_s32 ke lipara tsa karabelo ea ketso)

w₂ = E boima ba boloko 2 = m₂ g = (12 kg)(9.8 m/s²) = 117.6 Newton

N₂ = E matla a tloaelehileng a sebelisoang nthong ea 2 ke bokaholimo bo otlolohileng = w₂ +N₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F_k2 = E Matla a khohlano ea kinetic holim'a block 2 = μ_k N₂ = (0.4)(166.6 N) = 66.64 Newton

Sebelisa molao oa Newton oa ho sisinyeha holim'a boloko ba 3:

∑F_x = ma_x

F_s23 =m₃ a_x

—–> F_s23 = μ_s N₂₃ = μ_s w₃ = μ_s m₃ g

μ_s m₃ g = m₃ a_x

μ_s g = a_x

a_x = (0.3)(9.8 m/s²) = 2.94 m/s²

Lebelo le phahameng ka ho fetisisa la boloko ba 3 e le hore boloko ba 3 le boloko ba 2 li ntse li thella hammoho ke 2.94 m/s².

Jwale re bala boholo ba ho potlaka ha sistimi ka mora ho lokollwa phomolong.

Tsela eo boloko bo fallang ka yona = tsela eo bo potlakisang ka yona = tsela eo T e tsamayang ka yona₂ = tataiso ea w_1x.

∑F_x = ma_x

w_1x - T₁ +T₂ - F_k2 - F_s32 +F_s23 = (m₁ +m₂ +m₃) a_x

w_1x - F_k2 = (m₁ +m₂ +m₃ ) a_x

136.4 N – 66.64 N = (16 kg + 12 kg + 5 kg) a_x

69.76 N = (33 kg) a_x

a_x = 2.11 m/s²

a_x e ntle, e bolela hore tataiso ea ho falla ha boloko kapa tataiso ea ho potlaka e tšoana le tataiso ea T₂ kapa tataiso ea w_1x.

Boholo ba ho potlaka ke 2.11 limithara / s² , lmatla ho feta 2.94 limithara / s² kahoo re ka etsa qeto ea hore boloko ba 3 le boloko ba 2 li ntse li thella hammoho ka mor'a ho lokolloa phomolong.

b) Boholo ba ho potlaka ha boloko 1 le boloko 2

∑F_x = ma_x

w_1x - F_k2 = (m₁ +m₂) a_x

—–> F_k2 = μ_k N₂ = μ_k w₂ = μ_k m₂ g = (0.4)(12 kg)(9.8 m/s²) = 47.04 Newton

136.4 N - 47.04 N = (16 lik'hilograma + 12 lik'hilograma) a_x

89.36 N = (28 kg) a_x

a_x = 89.36 N : 28 kg = 3.19 m/s²

[ID ea sephutheloana sa wpdm='493′]

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

1. Boloko ba 2-kg bo lutse sebakeng se sekametseng ka lehlakoreng la 37^o ho ea ho e otlolohileng. Fumana boholo ba matla a kantle a sebelisoang holim'a boloko, e le hore boloko bo se ke ba thella fatše. (syn 37^o = 0.6, cos 37^o = 0.8, g = 10 ms^-2, µ_k = 0.2)

Tse tsejoang:

Boholo (m) = 2 kg

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

Li-block boima ba 'mele (w) = mg = (2)(10) = 20 Li-Newton

Sebe sa 37^o = 0.6

Tše 37^o = 0.8

Koefficient ea khohlano ea kinetic (µ_k= 0.2

Karolo ea y ea boima (w_y) = w Cos 37^o = (20)(0.8) = 16 Newton

Karolo ea x ea boima (w_x) = w sebe θ = (20)(sebe 37) = (20)(0.6) = 12 Newtons

matla a tloaelehileng (N) = w_y = 16 Newton

o ne a batla Matla a kantle (F)

tharollo :

w_x = 12 Newton

Matla a moferefere oa kinetic (f)_k) = µ_k N = (0.1)(16) = 1.6 Newton

Boholo ba matla a kantle a F a sebelisitsoeng holim'a boloko :

F + f_k - w_x = 0

F = w_x - f_k

F = 12 – 1.6

F = 10.4 Newton

Matla a kantle a F a feta 10.4 Newtons.

2. Boima ba boloko = 2 kg, coefficient ea khohlano e sa fetoheng µ_s = 0.4 le θ = 45^oFumana boholo ba matla a F e le hore boloko e qale ho thella.

Tse tsejoang:

Koefficient ea khohlano e sa fetoheng (µ_s= 0.4

Sekhutlo (θ) = 45^o

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s²

Boima ba Block (m) = 2 kilograma

Boima ba boloko (w) = mg = (2 kg)(10 m/s²) = 20 kg m/s² = 20 Newton

Karolo ea x ea boima (w_x) = w sebe θ = (20)(sebe 45) = (20)(0.5√2) = 10√2 Newtons

Karolo ea y ea boima (w_y) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newtons

o ne a batla : Boholo ba matla F

Tharollo:

Boloko bo qala ho thella, haeba F ≥ w_x + f_s.

Karolo ea x ea boima:

w_x = 10√2 Newton

karolo ea y ea boima :

w_y = 10√2 Newton

Matla a tloaelehileng :

N = w_y = 10√2 Newton

Matla a khohlano e sa fetoheng :

f_s = µ_s N = (0,4)(10√2) = 4√2

Boholo ba matla a F hoo boloko bo qalang ho thella :

F ≥ w_x + f_s

F ≥ 10√2 + 42

F ≥ 14√2 Newton

[ID ea sephutheloana sa wpdm='492′]

1. Likaroloana tse leka-lekaneng la ntlha e le 'ngoe
2. Likaroloana tse nang le tekano ea mahlakore a mabeli
3. Tekano ea 'mele e hokahaneng ka lithapo le li-pulley
4. Tekano ea 'mele e sekametseng

Bala haholoanyane

1. Lebokose la boima 5 kg e sekametse ka lehlakoreng la 30^oLebokose le tshehetswa ke thapo. Fumana matla a kgatello (T) le matla a tloaelehileng (Hantle)!

tharollo

∑F_x = 0

T – w sin 30^o = 0

T = w sebe 30^o

T = (5 kg)(9.8 m/s²) sebe sa 30^o

T = (49)(0.5)

T = 24.5 Newton

∑F_y = 0

N – w cos 30^o = 0

N = w cos 30^o

N = (49)(0.87)

N = 43 Newton

2. Lintho tse peli tsa boima m₁ = m₂ = 2 kg, e hokahantswe ka thapo e se nang boima hodima pulley e se nang khohlano. Fumana matla a kgatello T₁ le T₂.

tharollo

(a) Setšoantšo sa 'mele o lokolohileng bakeng sa ntho ea 1 (b) Setšoantšo sa 'mele o lokolohileng bakeng sa ntho ea 2

Sebelisa molao oa pele oa Newton ho hanyetsa 1:

∑F_y = 0

T₁ - w₁ = 0

T₁ = w₁ = m₁ g = (2 kg)(9.8 m/s²) = 19.6 N

Etsa kopo Molao oa pele oa Newton ho hanyetsa 2:

∑F_y = 0

T₂ - w₂ = 0

T₂ = w₂ = m₂ g = (2 kg)(9.8 m/s²) = 19.6 N

T₁ = T₂ = 19.6 N.

3. Ntho ea boima ba 'mele w_A = 30 N le ntho e boima w_B = 40 N, di hoketswe ka thapo e bobebe e fetang hodima pulley e se nang ho kgohlano ya boima bo sa reng letho. Fumana coefficient ya maximum khohlano e sa fetoheng pakeng tsa w_B le bokaholimo bo sekametseng, haeba sistimi e phomotse.

tharollo

(a) Setšoantšo sa 'mele o lokolohileng bakeng sa ntho w_A (b) Setšoantšo sa 'mele o lokolohileng bakeng sa ntho w_B

Sebelisa molao oa pele oa Newton ho hanyetsa w_A ka lehlakoreng le otlolohileng (y):

∑F_y = 0 (ha ho potlakiso ka lehlakoreng le otlolohileng)

T – w_A = 0

T = w_A = 30 Newton

Sebelisa molao oa pele oa Newton ho hanyetsa w_B ka lehlakoreng le otlolohileng (y) :

∑F_y = 0

N – w_B Cos 45^o = 0

N = w_B Cos 45^o = (40)(0.7) = 28 Newton

Sebelisa molao oa pele oa Newton ho hanyetsa w_B ka lehlakoreng le otlolohileng (x):

∑F_x = 0

F_k +w_B sebe 45^o - T = 0

μ_s N + w_B sebe 45^o - T = 0

μ_s (28) + (40)(0.7) – 30 = 0

μ_s (28) + 28 – 30 = 0

μ_s (28) = 30 – 28

μ_s (28) = 2

μ_s = 2/28

μ_s = 0.07

Coefficient ea khohlano e sa fetoheng e phahameng ka ho fetisisa pakeng tsa w_B le bokaholimo bo sekametseng = 0.07.

[ID ea sephutheloana sa wpdm='490′]

1. Likaroloana tse leka-lekaneng la ntlha e le 'ngoe
2. Likaroloana tse nang le tekano ea mahlakore a mabeli
3. Tekano ea 'mele e hokahaneng ka lithapo le li-pulley
4. Tekano ea 'mele e sekametseng

Bala haholoanyane

1. Fumana matla a khatello ea maikutlo T₁, T₂, le T₃Hlokomoloha likhoele tsa khoele boima.

tharollo

(a) Setšoantšo sa 'mele o lokolohileng bakeng sa ntho (b) Setšoantšo sa 'mele o lokolohileng bakeng sa thapo

Etsa kopo ea Molao oa pele oa Newton hodima ntho:

ΣF_y = 0

T₁ – w = 0

T₁ = w = mg

T₁ = (5 lik'hilograma)(9.8 m/s²)

T₁ = 49 kg m/s²

T₁ = 49N

Sebelisa molao oa pele oa Newton holim'a thapo:

∑F_x = 0

T_3x - T _2x = 0

T₃ Cos 30^o - T₂ Cos 40^o = 0

0.87 T₃ – 0.77 T₂ = 0

0.87 T₃ = 0.77 T₂

T₂ = 0.87 T₃ / 0.77 = 1.1 T₃ ———- Tekanyo ea 1

-

∑F_y = 0

T_3y +T_2y - T_1y = 0

T₃ sebe 30^o +T₂ sebe 40^o - T₁ = 0

0.5 T₃ + 0.64 T₂ – 49 N = 0 ———- Tekanyo ea 2

Ho nkela T sebaka₂ ho equation ea 2 ho equation ea 2:

0.5 T₃ + 0.64 (1.1 T₃) – 49 N = 0

0.5 T₃ + 0.70 T₃ - 49 = 0

1.2 T₃ - 49 = 0

1.2 T₃ = 49

T₃ = 49/1.2

T₃ = 41N

---

T₂ = 1.1 T₃

T₂ = (1.1)(40.8 N)

T₂ = 45N

[ID ea sephutheloana sa wpdm='488′]

1. Likaroloana tse leka-lekaneng la ntlha e le 'ngoe
2. Likaroloana tse nang le tekano ea mahlakore a mabeli
3. Tekano ea 'mele e hokahaneng ka lithapo le li-pulley
4. Tekano ea 'mele e sekametseng

Bala haholoanyane

^{1. Boholo ea ntho, m = 10 kg, e tšehelitsoeng ke thapo. Fumana khatello ka har'a thapo!} g = 10 m/s²

Tse tsejoang:

Boima (m) = 10 kg

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

Ho batloa: Matla a khatello ea maikutlo (T)

Tharollo:

ΣF_y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s²) = 100 kg m/s²

T = 100 Newton

2. Boima ba ntho ke 10 kg. Fumana kgatello thapong….. Ho potlaka ka lebaka la matla a khoheli = 10 m/s².

tharollo

Tse tsejoang:

Boima (m) = 10 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s².

Ho batloa: Matla a khatello ea maikutlo (T)

Tharollo:

^{w = boima ba 'mele = mg = (10 kg)(10 m/s2}) = 100 kg m/s²

T₁ = matla a khatello ea maikutlo 1

_T1x = karolo ea x ea matla a khatello 1 = T₁ Cos 45^o = 0.7 T₁

_T1y = karolo ea y ea matla a khatello 2 = T₁ sebe 45^o = 0.7 T₁

T₂ = matla a khatello ea maikutlo 2

_T2x = karolo ea x ea matla a khatello 2 = T₂ Cos 45^o = 0.7 T₂

_T2y = karolo ea y ea matla a khatello 2 = T₂ sebe 45^o = 0.7 T₂

Boemo ba tekano ΣF = 0.

mothapo oa y:

ΣF_y = 0

T_1y +T_2y – w = 0

0.7T₁ + 0.7T₂ - 100 = 0

0.7T₁ + 0.7T₂ = 100 —– equation 1

mothapo oa x:

ΣF_x = 0

T_2x - T_1x = 0

0.7T₂ – 0.7T₁ = 0

0.7T₂ = 0.7T₁

T₂ = T₁ —– equation 2

Fumana boholo ba T₁ :

0.7T₁ + 0.7T₁ = 100

1.4T₁ = 100

T₁ = 100/1.4

T₁ = 71.4 Newton

T₁ = T₂ kahoo T₂ = 71.4 Newton

[ID ea sephutheloana sa wpdm='486′]

1. Likaroloana tse leka-lekaneng la ntlha e le 'ngoe
2. Likaroloana tse nang le tekano ea mahlakore a mabeli
3. Tekano ea 'mele e hokahaneng ka lithapo le li-pulley
4. Tekano ea 'mele e sekametseng

Bala haholoanyane

1. Mabokose a mabeli a hokahantsoe ka thapo e mathang holim'a pulley. Hlokomoloha boima ba thapo le pulley le khohlano efe kapa efe ka har'a pulley. Boholo ea lebokose 1 = 2 kg, boima ba lebokose 2 = 3 kg, ho potlaka ka lebaka la matla a khoheli = 10 m/s². Fumana (a) Ho potlaka ha sistimi (b) Kgatelelo ka hara thapo!

tharollo

Tse tsejoang:

Boima ba lebokose 1 (m₁) = 2 kg

Boima ba lebokose 2 (m₂) = 3 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s²

Weight ea lebokose la 1 (w₁) = m₁ g = (2)(10) = 20 Newton

Boima ba lebokose 2 (w₂) = m₂ g = (3)(10) = 30 Newton

Tharollo:

(a) boholo le tataiso ea ho potlaka

w₂ > w₁ kahoo lebokose la 2 le potlakisa ho theohela tlase mme lebokose la 1 le potlakisa ho ya hodimo.

Matla a nang le tataiso e tšoanang le ea ho potlaka (w₂ le T₁), letšoao la eona le letle. Matla a nang le tsela e fapaneng le ho potlaka (T₂ le w₁), letshwao la yona ke le lebe.

∑F = ma

w₂ - T₂ +T₁ - w₁ = (m₁ +m₂) e ——-> T₁ = T₂ = T

w₂ – T + T – w₁ = (m₁ +m₂) a

w₂ - w₁ = (m₁ +m₂) a

30 – 20 = (2 + 3) a

10 = 5 a

a = 10/5

a = 2 m/s²

Boholo ba ho potlaka ke 2 m/s².

(b) Matla a khatello

Lebokose la 2:

Ho na le liketso tse peli tsa matla lebokoseng la 2: la pele, boima ba lebokose la 2 (w₂), e supa tlase kahoo e ntle. Ea bobeli, matla a khatello a sebelisitsoeng lebokoseng la 2 (T₂), e supa hodimo kahoo e le negative. E tshase Molao oa bobeli oa Newton ea motsamao.

∑F = ma

w₂ - T₂ = m₂ a

30 – T₂ = (3)(2)

30 – T₂ = 6

T₂ = 30 - 6

T₂ = 24 Newton

Lebokose la 1:

Ho na le liketso tse peli tsa matla lebokoseng la 1. First, boima ba lebokose 1 (w₁), e supa tlase kahoo e le mpe. ea bobeli, matla a tsitsipano a sebelisitsoeng lebokoseng la 1 (T₁) e supa hodimo kahoo e ntle. Sebedisa molao wa bobedi wa Newton wa motsamao:

∑F = ma

T₁ - w₁ = m₁ a

T₁ – 20 = (2)(2)

T₁ - 20 = 4

T₁ = 20 + 4

T₁ = 24 Newton

Boholo ba matla a khatello = T₁ = T₂ = T = 24 Newton

2. Ntho e holim'a bokaholimo bo bataletseng bo bataletseng. Boima ba ntho 1 = 2 kg, boima ba ntho 2 = 4 kg, ho potlaka ka lebaka la matla a khoheli = 10 m/s², coefficient ea khohlano e sa fetoheng = 0.4, coefficient ea khohlano ea kinetic = 0.3. Sistimi e phomotse kapa e potlakile? Haeba sistimi e potlakile, fumana boholo le tataiso ea ho potlaka ha sistimi!

tharollo

Tse tsejoang:

Boima ba ntho 1 (m₁) = 2 kg

Boima ba ntho 2 (m₂) = 4 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s²

Koefficient ea khohlano e sa fetoheng (μ_s= 0.4

Coefficient ea moferefere oa kinetic (μ_k) = 0.3

Boima ba ntho 1 (w₁) = m₁ g = (2)(10) = 20 Newton

Boima ba ntho 2 (w₂) = m₂ g = (4)(10) = 40 Newton

Matla a tloaelehileng e sebedisitsweng nthong 1 (N) = w₁ = 20 Newton

Matla a khohlano e sa fetoheng e sebediswang nthong 1 (f_s) = μ_s N = (0.4)(20) = 8 Newton

Matla a khohlano ea kinetic e sebelisoang nthong ea 1 (f)_k) = μ_k N = (0.3)(20) = 6 Newton

Oa Batla: ho potlakisa (a)

Tharollo:

w₂ > f_s (40 Newton > 8 Newton) kahoo ntho ea 2 e potlakisoa ka ho otloloha ho ea tlase 'me ntho ea 1 e potlakisoa ka ho otloloha ho ea ka ho le letona. Matla a khohlano a sebetsang linthong tsa 1 ke matla a khohlano ea kinetic (f)_k). Sebelisa molao oa bobeli oa Newton oa motsamao:

∑F = ma

w₂ - the = (m₁ +m₂) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s²

Boholo ba ho potlaka = 5.7 m/s²

[ID ea sephutheloana sa wpdm='484′]

1. Boima le boima
2. Matla a tloaelehileng
3. Molao oa bobeli oa Newton oa ho sisinyeha
4. Matla a khohlano
5. Motsamao 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

1. Motho ea boima ba lik'hilograma tse 50 ka har'a lifti. Ho potlakisa ka baka la matla a khoheli = 10 m/s². Fumana hore na matla a tloaelehileng e behetsoeng nthong e haufi le lifti, haeba:

(a) lifti e phomotse

(b) lifti e theohela tlase ho lebelo le sa fetoheng

(c) lifti e potlakisitsoe ho ea holimo ka lebelo ho potlaka ho sa khaotseng 5 /s²

(d) lifti e potlakisitsoeng ho theohela tlase ka lebelo le sa fetoheng la 5 m/s²

(e) lifti ka har'a ho oela mahala

tharollo

Tse tsejoang:

Ea motho boima (m) = 50 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s²

Weight (w) = mg = (50)(10) = 500 Li-Newton

Oa Batla: Matla a tloaelehileng (N)

Tharollo:

(a) lifti e phomotse

Lifti e phomotse kahoo ha ho na ho potlaka (a = 0)

Re khetha tsela e eang holimo ka lehlakoreng le letle le tsela e eang tlase ka lehlakoreng le lebe.

ΣF = ma

N – w = 0

N = w

N = 500 Newton

(b) lifti e theohela tlase ka lebelo le sa fetoheng

Lebelo le sa fetoheng kahoo ha ho na ho potlaka (a = 0)

Re khetha tsela e eang holimo ka lehlakoreng le letle le tsela e eang tlase ka lehlakoreng le lebe.

ΣF = ma

N – w = 0

N = w

N = 500 Newton

(c) lifti e potlakisitsoeng ho ea holimo ka lebelo le sa fetoheng la 5 m/s²

Tsela eo lebelo le tswelang ka yona e ya hodimo, kahoo re kgetha tsela e ntle jwalo ka tsela e yang hodimo.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Motho o utloa mokatong o sutumelletsoa holimo ka matla ho feta ha lifti e eme kapa e tsamaea ka lebelo le sa fetoheng.

Haeba motho a eme sekaleng, sekala se bala boholo ba matla a theohelang a sebelisoang ke motho sekaleng. Ho ea ka molao oa boraro oa Newton, sena se lekana le boholo ba matla a tloaelehileng a holimo a sebelisoang ke sekala ho motho.

(d) lifti e potlakisitsoeng ho theohela tlase ka lebelo le sa fetoheng la 5 m/s²

Tsela eo lebelo le potlakileng le shebileng ho yona e theohela tlase, kahoo re kgetha tsela e ntle e le e theohelang tlase.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 – 250

N = 250 Newton

Boima ba motho ke 250 N, e leng boima bo ka tlase ho boima ba 'nete w = 500 N.

(e) lifti nakong ea ho oa ka bolokolohi

Ho oa ha mahala ho bolela hore ho potlaka ha lifti ho tšoana le ho potlaka ka lebaka la matla a khoheli. Boholo ba ho potlaka ka lebaka la matla a khoheli ke 9,8 m/s², tataiso ea eona e theohela tlase ho ea bohareng ba Lefatše. Lebelo le eketseha ka tatellano ka 9,8 m/s motsotsoana o mong le o mong.

Tsela eo lebelo le potlakileng le shebileng ho yona e theohela tlase, kahoo re kgetha tsela e ntle e le e theohelang tlase.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 – 500

N = 0

2. Fumana kgatello ka hara thapo ya lifti. Boima ba lifti = 2000 kg.

(a) lifti e phomotse

(B) lifti e potlakisitse ho theohela tlase ka lebelo le sa fetoheng la 5 m/s²

(C) Lifti e potlakisitse ho ea holimo ka lebelo le sa fetoheng la 5 m/s²

(d) lifti nakong ea ho oa ka bolokolohi

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s²

tharollo

Tse tsejoang:

Boima ba lifti (m) = 2000 kg

Ho potlaka ha matla a khoheli (g) = 10 m/s²

boima (w) = mg = (2000)(10) = 20,000 Newtons

Ho batloa: Matla a khatello ea maikutlo (T)

Tharollo:

(a) lifti e phomotse

holo e phomotse kahoo ha ho na ho potlaka (a = 0)

Re khetha tsela e eang holimo e le tsela e ntle le tsela e eang tlase e le tsela e mpe.

ΣF = ma

T – w = 0

T = w

T = 20,000 Newton

Khatello ka har'a thapo (T) = boima ba lifti (w) = 20,000 Newtons

(b) lifti e potlakisitsoeng ho theohela tlase ka lebelo le sa fetoheng la 5 m/s²

Tsela eo lebelo le potlakileng le shebileng ho yona e theohela tlase, kahoo re kgetha tsela e ntle e le e theohelang tlase.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 – 10,000

T = 10,000 Newton

c) lifti e potlakisitsoeng ho ea holimo ka lebelo le sa fetoheng la 5 m/s²

Tsela eo lebelo le potlakileng le shebileng ka yona e theohela tlase, kahoo re kgetha tsela e ntle e le e yang hodimo.

T – w = ma

T = w + ma

T = 20,000 + (2000)(5)

T = 20,000 + 10,000

T = 30,000 Newton

(d) lifti nakong ea ho oa ka bolokolohi

Tsela eo lebelo le potlakileng le shebileng ho yona e theohela tlase, kahoo re kgetha tsela e ntle e le e theohelang tlase.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 – 20,000

T = 0

[ID ea sephutheloana sa wpdm='482′]

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 sebaka se bataletseng se bataletseng ka matla a khohlano
7. Motsamao sefofaneng 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