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 ho potlaka ha centripetal le boholo ba matla a khatello ke bofe?

Tse tsejoang:

Boima (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

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

Ho batloa: a _s le Σ F

Tharollo:

(a) Boholo ba ho potlaka ha centripetal

(b) Boholo ba matla a khatello

Σ F = ma

T = ma _s

T = (0.2 kg)(1 m/s ² )

T = 0.2 kg m/s ²

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 tsitsipano (T) = matla a bohareng ( Σ F) = 100 N

Ho batloa: v maximum

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

N sin θ = karolo e otlolohileng ea matla a tloaelehileng

N cos θ = karolo e otlolohileng ea matla a tloaelehileng

w = mg = boima ba koloi

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

Matla a ho rapama a letlooa, karolo e rapamang ea matla a tloaelehileng ( N sin θ) , aa hlokahala ho boloka koloi e ntse e tsamaea 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:

Kenya N ho equation ea 1 ho N ho 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 'me e se ke ea thella. Ho potlaka ka lebaka la matla a khoheli = 10 m/s ².

Tse tsejoang:

Boima (m) = 2000 kg

Radius (r) = limithara tse 150

Koefficient ea khohlano e sa fetoheng ( μs ₎ = 0.5

Boima (w) = mg = (2000 kg)(10 m/s ² ) = 20,000 kg m/s ² = 20,000 N

Matla a khohlano e tsitsitseng (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 m ₁ = 2 kg le m ₂ = 5 kg di sekametse mme di hokahantswe mmoho ka thapo jwalo ka ha ho bontshitswe setshwantshong. Koefficient ya kgohlano ya kinetic pakeng tsa m ₁ le ho sekamela ke 0.2 mme koefficient ya kgohlano ya kinetic pakeng tsa m ₂ le ho sekamela ke 0.1.

(a) Fumana hore na li potlaka hakae

(b) Fumana matla a khatello

Tse tsejoang:

Boima ba 1 (m ₁ ) = 2 kg

Boima ba 2 (m2 ₎ = 4 kg

Koefficient ea khohlano ea kinetic pakeng tsa m ₁ le sefofane se sekametseng (μ _k1 ) = 0.2

Koefficient ea khohlano ea kinetic pakeng tsa m2 _le sefofane se sekametseng (μ _k2 ) = 0.1

Ho potlaka ka lebaka la matla a khoheli (g) = 9.8 m/s ²

a) Boholo le tataiso ea ho potlaka

w ₁ = boima 1 = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 Li-Newton

w _1x = w ₁ sin 30 ^o = (19.6 N)(0.5) = 9.8 Newton

w _1y = w ₁ cos 30 ^o = (19.6 N)(0.87) = 17 Newtons

N ₁ = Matla a tloaelehileng ho m ₁ = w _1y = 17 Newtons

F _k1 = Matla a khohlano ea kinetic ho m ₁ = μ _k1 N ₁ = (0.2)(17 N) = 3.4 Li-Newton

---

w ₂ = boima 2 = m ₂ g = (4 kg)(9.8 m/s ² ) = 39.2 Li-Newton

w _2x = w ₂ sebe 60 ^o = (39.2 N) (0.87) = 34.1 Newtons

w _2y = w ₂ cos 60 ^o = (39.2 N)(0.5) = 19.6 Newtons

N ₂ = Matla a tloaelehileng ho m ₂ = w _2y = 19.6 Newtons

F _k2 = Matla a khohlano ea kinetic ho m ₂ = μ _k2 N ₂ = (0.1)(19.6 N) = 1.96 Newtons

---

Boholo ba ho potlaka ha lebelo:

∑ F _x = _max

w _2x > w _1x kahoo tataiso ea ho potlakisa 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 = (m ₁ + m ₂ ) 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) ka _x

a _x = 18.94 N : 6 kg

a _x = 3.16 m/s ²

Boholo ba ho potlaka = 3.16 m/s ^2. Tataiso ea ho potlaka = tataiso ea T ₁ = 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 – T ₂ = m ₂ a _x

34.1 N – 1.96 N – T ₂ = (4 lik’hilograma)(3.16 m/s ² )

32.14 N – T ₂ = 12.64 N

T ₂ = 32.14 N – 12.64 N = 19.5 Newton

Matla a kgatello = T = T ₁ = T ₂ = 19.5 Newtons

2. m ₁ = 4 kg, m ₂ = 2 kg. Fumana (a) boholo le tataiso ea ho potlaka (b) Boholo ba matla a khatello a hokahanyang m ₁ le m ₂ (c) boholo ba matla a khatello a hokahanyang pulley le marulelo.

tharollo

w ₁ = m ₁ g = (4 kg)(9.8 m/s ² ) = 39.2 Li-Newton

w ₂ = m ₂ g = (2 kg)(9.8 m/s ² ) = 19.6 Li-Newton

a) Boholo le tataiso ea ho potlaka

∑ F _y = may _y

w ₁ > w ₂ kahoo tataiso ea ntho e tšoana le tataiso ea boima 1 ( w ₁ ) . 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.

w ₁ – T ₁ + T ₂ – w ₂ = (m ₁ + m ₂ ) a _y

w ₁ – w ₂ = (m ₁ + m ₂ ) a _y

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

19.6 N = (6 kg) ka _y

a _y = 19.6 N : 6 kg

a _y = 3.26 m/s ²

Boholo ba ho potlaka = 3.26 m/s ^2. Tsela ea ho potlaka = tsela ea w ₁.

b) Boholo ba matla a khatello a hokahanyang m ₁ le m ₂

Sebelisa molao oa bobeli oa Newton ho _m2 :

∑ F _y = may _y

w ₁ – T ₁ = m ₁ a _y

39.2 N – T ₁ = (4 lik’hilograma)( 3.26 m/s ² )

39.2 N – T ₁ = 13.04 N

T ₁ = 39.2 N – 13.04 N

T ₁ = 26.16 Newton

Boholo ba matla a khatello a hokahanyang lintho = T = T ₁ = T ₂ = 26.16 Newtons

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

Pulley e phomotse:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

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

T ₃ – T ₁ – T ₂ = 0

T3 = _T1 + _T2

T ₁ le T ₂ li na le boholo bo tšoanang , T ₁ = T ₂ = T = 26.16 N:

T ₃ = 2T = 2(26.16 N) = 52.32 Newton

3. Boloko ba 1 (m ₁ = 10 kg) le boloko ba 2 (m ₂ = 15 kg) tse hokahantsweng ka thapo hodima pulley e se nang khohlano. Khokahano ya khohlano e sa fetoheng pakeng tsa boloko ba 2 ka ho sekamela = 0.6. Khokahano 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

w ₁ = Boima ba boloko 1 = m ₁ g = (10 kg)(9.8 m/s ² ) = 98 Newtons

w ₂ = Boima ba boloko 2 = m ₂ g = (15 kg)(9.8 m/s ² ) = 147 Newtons

w _2y = w ₂ cos 30 ^o = (147 N)(0.87) = 127.89 Li-Newton

w _2x = w ₂ sebe 30 ^o = (147 N) (0.5) = 73.5 Newtons

N ₂ = Matla a tloaelehileng holim'a boloko 2 = w _2y = 127.89 Newtons

F _k2 = Matla a khohlano ea kinetic holim'a block 2 = μ _k2 N ₂ = (0.42)(127.89 N) = 53.7 Newtons

F _s2 = Matla a khohlano e sa fetoheng bolokong 2 = μ _s2 N ₂ = (0.6)(127.89 N) = 76.7 Newtons

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

∑ F _x = max _—— 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 – w ₁ – T ₂ + T ₁ = 0

F – F _k2 – w _2x – w ₁ = 0

F = F _k2 + w _2x + w ₁

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 = may _y —— a _y = 0

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = 98 Newton

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

F – F _k2 – w _2x – T ₂ = 0

T ₂ = F – F _k2 – w _2x

T ₂ = 225.2 N – 53.7 N – 73.5 N

T ₂ = 98 Newton

Boholo ba matla a kgatello = T ₁ = T ₂ = T = 98 Newtons

4. Boloko ba 1 (m ₁ = 16 kg) bo lutse holim'a bokaholimo bo bataletseng 'me boloko ba 2 (m ₂ = 12 kg) bo lutse holim'a sekala se boreleli, se hokahaneng ka thapo e fetang holim'a pulley e nyane, e se nang khohlano. Boloko ba 3 (m ₃ = 5 kg) bo lutse holim'a boloko ba 2. Koefficient ea khohlano ea kinetic pakeng tsa boloko ba 2 le bokaholimo bo bataletseng ke 0,4. Koefficient ea khohlano e sa fetoheng pakeng tsa boloko ba 2 le boloko ba 3 ke 0,3.

(a) Ha sistimi e lokollwa phomolong, boloko ba 3 le boloko ba 2 di ntse di thella mmoho?

(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 lokollwa phomolong, boloko ya 3 le boloko ya 2 di ntse di thella mmoho?

w ₁ = Boima ba boloko 1 = m ₁ g = (16 kg)(9.8 m/s ² ) = 156.8 Newtons

w _1x = w ₁ sin 60 ^o = (156.8 N)(0.87) = 136.4 Newton

w _1y = w ₁ cos 60 ^o = (156.8 N)(0.5) = 78.4 Li-Newton

N ₁ = Matla a tloaelehileng a sebelisoang holim'a boloko ba 1 ke sefofane se sekametseng = w _1y = 78.4 Newtons

w ₃ = Boima ba boloko 3 = m ₃ g = (5 kg)(9.8 m/s ² ) = 49 Newtons

N ₂₃ = Matla a tloaelehileng a sebelisoang holim'a boloko ba 3 ke boloko ba 2 = w ₃ = 49 Newtons

N ₃₂ = Matla a tloaelehileng a sebelisoang holim'a boloko ba 2 ke boloko ba 3 = N ₂₃ = w ₃ = 49 Newtons

(N ₂₃ le N ₃₂ ke para ya karabelo ya ketso )

F _s23 = Matla a khohlano e sa fetoheng e sebediswang hodima boloko ba 3 ke boloko ba 2 = μ _s N ₂₃ = (0.3)(49 N) = 14.7 Newtons

F _s32 = Matla a khohlano e sa fetoheng e sebediswang hodima boloko ba 2 ke boloko ba 3 = F _{s 23} = 14.7 Newtons

(F _s23 le F _s32 ke para ya karabelo ya ketso )

w ₂ = Boima ba boloko 2 = m ₂ g = (12 kg)(9.8 m/s ² ) = 117.6 Li-Newton

N ₂ = Matla a tloaelehileng a sebelisoang nthong ea 2 ke bokaholimo bo otlolohileng = w ₂ + N ₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F _k2 = Matla a kgohlano ya kinetic hodima boloko 2 = μ _k N ₂ = (0.4)(166.6 N) = 66.64 Newtons

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

∑ F _x = _max

F _s23 = m ₃ a _x

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

μ _s m ₃ g = m ₃ a _x

μ _s g = a _x

a _x = (0.3)(9.8 m/s ² ) = 2.94 m/s ²

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/s ².

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

Tsela eo boloko bo fallang ka yona = tsela eo boloko bo potlakang ka yona = tsela eo T _{2 e tsamayang ka yona} = tsela eo w _{1x e tsamayang ka yona}.

∑ F _x = _max

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

w _1x – F _k2 = (m ₁ + m ₂ + m ₃ ) a _x

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

69.76 N = (33 kg) ka _x

a _x = 2.11 m/s ²

a _x e ntle, ho bolelang hore tataiso ea ho falla ha block kapa tataiso ea ho potlaka e tšoana le tataiso ea T ₂ kapa tataiso ea w _1x.

Boholo ba lebelo ke 2.11 m/s ² , bo ka tlase ho 2.94 m/s ² kahoo re ka etsa qeto ea hore boloko ba 3 le boloko ba 2 li ntse li thella hammoho ka mor'a hore li lokolloe phomolong.

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

∑ F _x = _max

w _1x – F _k2 = (m ₁ + m ₂ ) 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 kg + 12 kg) a _x

89.36 N = (28 kg) ka _x

a _x = 89.36 N : 28 kg = 3.19 m/s ²

[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 le leng. Fumana boholo ba matla a kantle a sebelisoang holim'a boloko, e le hore boloko bo se ke ba thella fatše. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µ _k = 0.2)

Tse tsejoang:

Boima (m) = 2 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s ²

Boima ba boloko (w) = mg = (2)(10) = 20 Newtons

Sebe sa 37 ^o = 0.6

Cos 37 ^o = 0.8

Koefficient ea kinetic friction (µ _k ) = 0.2

Karolo ea y ea boima (w _y ) = w cos 37 ^o = (20)(0.8) = 16 Newtons

Karolo ea x ea boima (w _x ) = w sin θ = (20)(sin 37) = (20)(0.6) = 12 Newtons

matla a tloaelehileng (N) = w _y = 16 Newtons

Ho batloa : Matla a kantle (F)

Tharollo :

w_x = 12 Newton

Matla a moferefere wa kinetic (f _k ) = µ _k N = (0.1)(16) = 1.6 Newtons

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 ^o . Fumana boholo ba matla a F e le hore boloko e qale ho thella.

Tse tsejoang:

Koefficient ea khohlano e sa fetoheng (µs ₎ = 0.4

Sekhutlo (θ) = 45 ^o

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s ²

Boima ba Block (m) = 2 kilograma

Boima ba boloko (w) = mg = (2 kg)(10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Karolo ea x ea boima (w _x ) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 Li-Newton

Karolo ea y ea boima (w _y ) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Li-Newton

Ho batloa : 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 hodimo :

F ≥ w _x + f _s

F ≥ 10√2 + 4 √2

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 ba 5 kg le sebakeng se sekametseng ka sekhutlo sa 30 ^o . Lebokose le tshehetswa ke thapo. Fumana matla a kgatello (T) le matla a tlwaelehileng (N)!

tharollo

∑F_x = 0

T – w sin 30 ^o = 0

T = w sin 30 ^o

T = (5 kg)(9.8 m/s ² ) sin 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 tse boima m ₁ = m ₂ = 2 kg, tse hokahaneng ka khoele e se nang boima holim'a pulley e se nang khohlano. Fumana matla a khatello T ₁ le T ₂.

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

T ₁ – w ₁ = 0

T ₁ = w ₁ = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 N

Sebelisa molao oa pele oa Newton ho hanyetsa 2:

∑ F _y = 0

T ₂ – w ₂ = 0

T ₂ = w ₂ = m ₂ g = (2 kg)(9.8 m/s ² ) = 19.6 N

T ₁ = T ₂ = 19.6 N.

3. Ntho e boima 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 kgohlano ya boima bo sa reng letho. Fumana coefficient ya kgohlano e sa fetoheng e phahameng ka ho fetisisa pakeng tsa w _B le bokahodimo 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 tsela e otlolohileng (y):

∑ F _y = 0 (ha ho na ho potlaka ka lehlakoreng le otlolohileng)

T – w _A = 0

T = w _A = 30 Newton

Sebelisa molao oa pele oa Newton ho hanyetsa w _B ka tsela e otlolohileng (y) :

∑ F _y = 0

N – w _B cos 45 ^o = 0

N = w _B cos 45 ^o = (40)(0.7) = 28 Newtons

Sebelisa molao oa pele oa Newton ho hanyetsa w _B ka tsela e otlolohileng (x):

∑ F _x = 0

F _k + w _B sin 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

Koefficient 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 T ₁ , T ₂ , le T _{3. Hlokomoloha} boima ba thapo.

tharollo

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

Sebelisa molao oa pele oa Newton holim'a ntho:

ΣF _y = 0

T ₁ – w = 0

T ₁ = w = mg

T ₁ = (5 kg)(9.8 m/s ² )

T ₁ = 49 kg m/s ²

T ₁ = 49 N

Sebelisa molao oa pele oa Newton holim'a thapo:

∑ F _x = 0

T _3x – T _2x = 0

T ₃ cos 30 ^o – T ₂ cos 40 ^o = 0

0.87 T ₃ – 0.77 T ₂ = 0

0.87 T ₃ = 0.77 T ₂

T ₂ = 0.87 T ₃ / 0.77 = 1.1 T ₃ ———- Tekanyo 1

-

∑ F _y = 0

T _3y + T _2y – T _1y = 0

T ₃ sebe 30 ^o + T ₂ sebe 40 ^o – T ₁ = 0

0.5 T ₃ + 0.64 T ₂ – 49 N = 0 ———- Tekanyo 2

Ho kenya T ₂ ho equation ea 2 ho equation ea 2:

0.5 T ₃ + 0.64 (1.1 T ₃ ) – 49 N = 0

0.5 T ₃ + 0.70 T ₃ – 49 = 0

1.2 T ₃ – 49 = 0

1.2 T ₃ = 49

T ₃ = 49 / 1.2

T ₃ = 41 N

---

T ₂ = 1.1 T ₃

T ₂ = (1.1)(40.8 N)

T ₂ = 45 N

[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. Boima ba ntho, m = 10 kg, e tshehetswang ke thapo. Fumana kgatello ka hara thapo!} g = 10 m/s ²

Tse tsejoang:

Boima (m) = 10 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s ²

Ho batloa: Matla a tsitsipano (T)

Tharollo:

ΣF _y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s ² ) = 100 kg m/s ²

T = 100 Newton

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

tharollo

Tse tsejoang:

Boima (m) = 10 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s ².

Ho batloa: Matla a tsitsipano (T)

Tharollo:

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

T ₁ = matla a khatello ea maikutlo 1

_{T 1x} = karolo ea x ea matla a khatello 1 = T ₁ cos 45 ^o = 0.7 T ₁

_{T 1y} = karolo ea y ea matla a khatello 2 = T ₁ sin 45 ^o = 0.7 T ₁

T ₂ = matla a khatello ea maikutlo 2

_{T 2x} = karolo ea x ea matla a khatello 2 = T ₂ cos 45 ^o = 0.7 T ₂

_{T 2y} = karolo ea y ea matla a khatello 2 = T ₂ sin 45 ^o = 0.7 T ₂

Boemo ba tekano ΣF = 0.

mothapo oa y:

ΣF _y = 0

T _1y + T _2y – w = 0

0.7T ₁ + 0.7T ₂ – 100 = 0

0.7T ₁ + 0.7T ₂ = 100 —– equation 1

mothapo oa x:

ΣF _x = 0

T _2x – T _1x = 0

0.7T ₂ – 0.7T ₁ = 0

0.7T ₂ = 0.7T ₁

T ₂ = T ₁ —– equation 2

Fumana boholo ba T ₁ :

0.7T ₁ + 0.7T ₁ = 100

1.4T ₁ = 100

T ₁ = 100 / 1.4

T ₁ = 71.4 Newton

T ₁ = T ₂ kahoo T ₂ = 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. Boima ba lebokose 1 = 2 kg, boima ba lebokose 2 = 3 kg, ho potlaka ka lebaka la matla a khoheli = 10 m/s ² . Fumana (a) Potlako ea sistimi (b) Khatello ka har'a 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/s ²

Boima ba lebokose 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Boima ba lebokose 2 (w ₂ ) = m ₂ g = (3)(10) = 30 Newtons

Tharollo:

(a) boholo le tataiso ea ho potlaka

w ₂ > w ₁ 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 ho potlaka (w ₂ le T ₁ ), letšoao la bona le letle. Matla a nang le tataiso e fapaneng le ho potlaka (T ₂ le w ₁ ), letšoao la bona le lebe.

∑ F = ma

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

w ₂ – T + T – w ₁ = (m ₁ + m ₂ ) a

w ₂ – w ₁ = (m ₁ + m ₂ ) a

30 – 20 = (2 + 3) a

10 = 5 a

a = 10/5

a = 2 m/s ²

Boholo ba lebelo ke 2 m/s ².

(b) Matla a khatello

Lebokose la 2:

Ho na le matla a mabeli a sebetsang lebokoseng la 2: la pele, boima ba lebokose la 2 (w ₂ ), lintlha tse theohelang tlase kahoo ke tse ntle. La bobeli, matla a khatello a sebelisoang lebokoseng la 2 (T ₂ ), lintlha tse holimo kahoo ke tse mpe. Sebelisa molao oa bobeli oa Newton oa motsamao.

∑ F = ma

w ₂ – T ₂ = m ₂ a

30 – T ₂ = (3)(2)

30 – T ₂ = 6

T ₂ = 30 – 6

T ₂ = 24 Newton

Lebokose la 1:

Ho na le matla a mabeli a etsang lintho ka lebokoseng la 1. Ea pele , boima ba lebokose la 1 (w ₁ ), bo supa tlase kahoo bo na le lintlha tse mpe. Ea bobeli , matla a khatello a sebelisitsoeng lebokoseng la 1 (T ₁ ) a supa holimo kahoo a na le lintlha tse ntle. Sebelisa molao oa bobeli oa Newton oa motsamao:

∑ F = ma

T ₁ – w ₁ = m ₁ a

T ₁ – 20 = (2)(2)

T ₁ – 20 = 4

T ₁ = 20 + 4

T ₁ = 24 Newton

Boholo ba matla a kgatello = T ₁ = T ₂ = T = 24 Newtons

2. Ntho e holim'a sebaka se bataletseng se bataletseng. Boima ba ntho 1 = 2 kg, boima ba ntho 2 = 4 kg, ho potlaka ka lebaka la matla a khoheli = 10 m/s ² , 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/s ²

Koefficient ea khohlano e sa fetoheng ( μs ₎ = 0.4

Koefficient ea ho ferekana ha kinetic ( μk ₎ = 0.3

Boima ba ntho 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Boima ba ntho 2 (w ₂ ) = m ₂ g = (4)(10) = 40 Newtons

Matla a tloaelehileng a sebelisoang nthong 1 (N) = w ₁ = 20 Newtons

Matla a khohlano e sa fetoheng e sebediswang nthong 1 (fs ₎ = μ _s N = (0.4)(20) = 8 Newtons

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

Ho batloa: ho potlakisa (a)

Tharollo:

w ₂ > _fs (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

w ₂ – e = (m ₁ + m ₂ ) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s ²

Boholo ba ho potlaka = 5.7 m/s ²

[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 potlaka ka lebaka la matla a khoheli = 10 m/s ² . Fumana matla a tloaelehileng a sebelisoang nthong ke lifti, haeba:

(a) lifti e phomotse

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

(c) lifti e potlakisitsoeng ho ea holimo ka lebelo le sa fetoheng 5 /s ²

(d) lifti e potlakisitsoeng ho theohela tlase ka lebelo le sa fetoheng la 5 m/s ²

(e) lifti nakong ea ho oa ka bolokolohi

tharollo

Tse tsejoang:

Boima ba motho (m) = 50 kg

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s ²

Boima (w) = mg = (50)(10) = 500 Newtons

Ho batloa: 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.

Σ F = 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.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(c) lifti e potlakisitsoeng ho ea holimo ka lebelo le tsitsitseng la 5 m/s ²

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/s ²

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 wa ha mahala ho bolela hore ho potlaka ha lifti ho tšoana le ho potlaka ho bakoang ke matla a khoheli. Boholo ba ho potlaka ho bakoang ke matla a khoheli ke 9,8 m/s ² , tataiso ea eona e theohela tlase 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 potlakisitsoeng ho theohela tlase ka lebelo le sa fetoheng la 5 m/s ²

(c) lifti e potlakisitsoeng ho ea holimo ka lebelo le tsitsitseng la 5 m/s ²

(d) lifti nakong ea ho oa ka bolokolohi

Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s ²

tharollo

Tse tsejoang:

Boima ba lifti (m) = 2000 kg

Ho potlaka ha matla a khoheli (g) = 10 m/s ²

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

Ho batloa: Matla a tsitsipano (T)

Tharollo:

(a) lifti e phomotse

lifti 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.

Σ F = 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/s ²

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 tsitsitseng la 5 m/s ²

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