Imizimba emibili enesivinini esifanayo – Ukusetshenziswa kwezinkinga nezixazululo zomthetho kaNewton wokunyakaza

1. Isisindo ezimbili m ₁ = 2 kg kanye m ₂ = 5 kg zisendizeni ethambekele futhi zixhunywe ndawonye ngentambo njengoba kuboniswe esithombeni. I-coefficient ye-kinetic friction phakathi kwe-m ₁ kanye ne-inclination ingu-0.2 kanti i-coefficient ye- kinetic friction phakathi kwe-m ₂ kanye ne-inclination ingu-0.1.

(a) Nquma ukusheshisa kwazo

(b) Thola amandla okucindezela

Kwaziwa:

Isisindo 1 (m ₁ ) = 2 kg

Isisindo 2 (m2 ₎ = 4 kg

I-coefficient yokungqubuzana kwe-kinetic phakathi kwe-m ₁ kanye nendiza ethambekele (μ _k1 ) = 0.2

I-coefficient yokungqubuzana kwe-kinetic phakathi kwe-m2 _kanye nendiza ethambekele (μ _k2 ) = 0.1

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 9.8 m/s ²

a) Ubukhulu kanye nesiqondiso sokusheshisa

w ₁ = isisindo 1 = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 AmaNewton

w _1x = w ₁ isono 30 ^o = (19.6 N)(0.5) = 9.8 amaNewton

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

N ₁ = Amandla avamile ku-m ₁ = w _1y = 17 Newtons

F _k1 = Amandla okungqubuzana kwe-kinetic ku-m ₁ = μ _k1 N ₁ = (0.2)(17 N) = 3.4 AmaNewton

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w ₂ = isisindo 2 = m ₂ g = (4 kg)(9.8 m/s ² ) = 39.2 AmaNewton

w _2x = w ₂ isono 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 = Amandla avamile ku-m ₂ = w _2y = 19.6 Newtons

F _k2 = Amandla okungqubuzana kwe-kinetic ku-m ₂ = μ _k2 N ₂ = (0.1)(19.6 N) = 1.96 AmaNewton

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Ubukhulu bokusheshisa:

∑ F _x = _max

w _2x > w _1x ngakho-ke isiqondiso sokusheshisa sifana nesiqondiso se-w _2x.

Amandla akhomba ukusheshisa amahle kanti amandla anesiqondiso esiphambene nokusheshisa angemabi.

w_2x - F_k2 - T₂ + T₁ - w_1x - F_k1 = (m₁ +m₂) futhi_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) a _x

a _x = 18.94 N : 6 kg

a _x = 3.16 m/s ²

Ubukhulu bokusheshisa = 3.16 m/s ^2. Isiqondiso sokusheshisa = isiqondiso se-T ₁ = isiqondiso se-w _2x

b) Ubukhulu bamandla okucindezela

Sebenzisa umthetho wesibili kaNewton entweni 2:

w _2x – F _k2 – T ₂ = m ₂ a _x

34.1 N – 1.96 N – T ₂ = (4 kg)(3.16 m/s ² )

32.14 N – T ₂ = 12.64 N

I-T ₂ = 32.14 N – 12.64 N = 19.5 Newtons

Amandla okucindezela = T = T ₁ = T ₂ = 19.5 Newtons

[irp]

2. m ₁ = 4 kg, m ₂ = 2 kg. Thola (a) ubukhulu kanye nesiqondiso sokusheshisa (b) Ubukhulu bamandla okucindezela axhumanisa m ₁ kanye m ₂ (c) ubukhulu bamandla okucindezela axhumanisa i-pulley nophahla.

Isixazululo

w ₁ = m ₁ g = (4 kg)(9.8 m/s ² ) = 39.2 AmaNewton

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

a) Ubukhulu kanye nesiqondiso sokusheshisa

∑ F _y = may _y

w ₁ > w ₂ ngakho-ke isiqondiso sento sifana nesiqondiso sesisindo 1 ( w ₁ ) . Amandla anesiqondiso esifanayo nokusheshisa amahle kanti amandla anesiqondiso esiphambene nokusheshisa angemabi.

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 kg + 2 kg) a _y

19.6 N = (6 kg) _ngonyaka

a _y = 19.6 N : 6 kg

a _y = 3.26 m/s ²

Ubukhulu bokusheshisa = 3.26 m/s ^2. Isiqondiso sokusheshisa = isiqondiso se-w ₁.

b) Ubukhulu bamandla okucindezela axhumanisa u-m ₁ no-m ₂

Sebenzisa umthetho wesibili kaNewton ku- _m2 :

∑ F _y = may _y

w ₁ – T ₁ = m ₁ a _y

39.2 N – T ₁ = (4 kg)( 3.26 m/s ² )

39.2 N – T ₁ = 13.04 N

I-T ₁ = 39.2 N – 13.04 N

I-T ₁ = 26.16 Newton

Ubukhulu bamandla okucindezela axhumanisa izinto = T = T ₁ = T ₂ = 26.16 AmaNewton

c) Ubukhulu bamandla okucindezela axhumanisa i-pulley nophahla.

I-Pulley iphumule:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

Amandla aphezulu amahle, amandla aphansi awabi:

I-T ₃ – I-T ₁ – I-T ₂ = 0

T3 = _T1 + _T2

I-T ₁ kanye ne-T ₂ zinobukhulu obufanayo , i-T ₁ = T ₂ = T = 26.16 N:

I-T ₃ = 2T = 2(26.16 N) = 52.32 AmaNewton

[irp]

3. Ibhloko 1 (m ₁ = 10 kg) kanye nebhloko 2 (m ₂ = 15 kg) exhunywe ngentambo phezu kwe-pulley engenakho ukungqubuzana. I-Coefficient yokungqubuzana okungaguquki phakathi kwebhloko 2 ene-inclination = 0.6. I-coefficient yokungqubuzana kwe-kinetic phakathi kwebhloko 2 ene-inclination = 0.42. Thola (a) Ubukhulu bamandla amancane u-F asetshenziswa ezintweni ukuze izinto zisheshise phezulu (b) Thola ubukhulu bamandla okucindezela.

Isixazululo

w ₁ = Isisindo sebhloko 1 = m ₁ g = (10 kg)(9.8 m/s ² ) = 98 Newtons

w ₂ = Isisindo sebhloko 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 AmaNewton

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

N ₂ = Amandla avamile ebhulokini 2 = w _2y = 127.89 Newtons

F _k2 = Amandla okungqubuzana kwe-kinetic kubhlokhi 2 = μ _k2 N ₂ = (0.42)(127.89 N) = 53.7 AmaNewton

F _s2 = Amandla okungqubuzana okungaguquki kubhlokhi 2 = μ _s2 N ₂ = (0.6)(127.89 N) = 76.7 AmaNewton

a) Ubukhulu bamandla amancane u-F asetshenziswa ezintweni ukuze izinto zisheshise phezulu

∑ F _x = max _—— a _x = 0

∑ F _x = 0

Amandla aphezulu kanye namandla angakwesokudla alungile, amandla aphansi kanye namandla angakwesokunxele angalungile.

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) Ubukhulu bamandla okucindezela

Sebenzisa umthetho kaNewton wokunyakaza kubhlokhi 1:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

I-T ₁ – w ₁ = 0

I-T ₁ = w ₁ = 98 Newton

Sebenzisa umthetho kaNewton wokunyakaza kubhlokhi 2:

F – F _k2 – w _2x – T ₂ = 0

T ₂ = F – F _k2 – w _2x

I-T ₂ = 225.2 N – 53.7 N – 73.5 N

I-T ₂ = 98 Newton

Ubukhulu bamandla okucindezela = T ₁ = T ₂ = T = 98 Newtons

[irp]

4. Ibhloko 1 (m ₁ = 16 kg) lilele endaweni evundlile kanti ibhloko 2 (m ₂ = 12 kg) lilele endaweni ebushelelezi ethambekele, exhunywe ngentambo edlula phezu kwe-pulley encane, engenakho ukungqubuzana. Ibhloko 3 (m ₃ = 5 kg) lilele kubhloko 2. I-coefficient ye-kinetic friction phakathi kwebhloko 2 kanye nendawo evundlile ingu-0,4. I-coefficient ye -static friction phakathi kwebhloko 2 nebhloko 3 ingu-0,3.

(a) Uma uhlelo lukhishwa ekuphumuleni, ibhulokhi 3 kanye nebhulokhi 2 kusashelela ndawonye?

(b) Uma kukhona ibhlogo 3, kuyini ukusheshisa kwebhlogo 1 kanye nebhlogo 2?

Isixazululo:

a) Uma uhlelo lukhishwa ekuphumuleni, ibhulokhi 3 kanye nebhulokhi 2 kusashelela ndawonye?

w ₁ = Isisindo sebhloko 1 = m ₁ g = (16 kg)(9.8 m/s ² ) = 156.8 Newtons

w _1x = w ₁ isono 60 ^o = (156.8 N)(0.87) = 136.4 amaNewton

w _1y = w ₁ cos 60 ^o = (156.8 N)(0.5) = 78.4 AmaNewton

N ₁ = Amandla avamile asetshenziswa kubhlokhi 1 ngendiza ethambekele = w _1y = 78.4 Newtons

w ₃ = Isisindo sebhloko 3 = m ₃ g = (5 kg)(9.8 m/s ² ) = 49 Newtons

N ₂₃ = Amandla avamile asetshenziswa kubhlokhi 3 yibhlokhi 2 = w ₃ = 49 Newtons

N ₃₂ = Amandla avamile asetshenziswa kubhlokhi 2 yibhlokhi 3 = N ₂₃ = w ₃ = 49 Newtons

(I-N ₂₃ kanye ne -N ₃₂ ziyibhangqa lokusabela kwesenzo )

F _s23 = Amandla okungqubuzana okungaguquki asebenza kubhlokhi 3 yibhlokhi 2 = μ _s N ₂₃ = (0.3)(49 N) = 14.7 AmaNewton

F _s32 = Amandla okungqubuzana okungaguquki asebenza kubhlokhi 2 yibhlokhi 3 = F _{s 23} = 14.7 amaNewton

(I-F _s23 kanye ne -F _s32 ziyibhangqa lokusabela kwesenzo )

w ₂ = Isisindo sebhloko 2 = m ₂ g = (12 kg)(9.8 m/s ² ) = 117.6 AmaNewton

N ₂ = Amandla avamile asetshenziswa entweni 2 ngendawo evundlile = w ₂ + N ₃₂ = 117.6 Newtons + 49

I-Newton = 166.6 I-Newton

F _k2 = Amandla okungqubuzana kwe-kinetic kubhlokhi 2 = μ _k N ₂ = (0.4)(166.6 N) = 66.64 AmaNewton

Sebenzisa umthetho kaNewton wokunyakaza kubhlokhi 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

Ukusheshisa okuphezulu kwebhulokhi 3 ukuze ibhulokhi 3 kanye nebhulokhi 2 kusashelela ndawonye kungu-2.94 m/s ².

Manje sibala ubukhulu bokusheshisa kwesistimu ngemva kokukhululwa ekuphumuleni.

Isiqondiso sokufuduka kwebhulokhi = isiqondiso sokusheshisa kwebhulokhi = isiqondiso se-T ₂ = isiqondiso se-w _1x.

∑ F _x = _max

w_1x - T₁ + T₂ - F_k2 - F_s32 +F_s23 = (m₁ +m₂ +m₃) futhi_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) a _x

a _x = 2.11 m/s ²

u-a _x ulungile, okusho ukuthi isiqondiso sokufuduka kwebhulokhi noma isiqondiso sokusheshisa sifana nesiqondiso se-T ₂ noma isiqondiso se-w _1x.

Ubukhulu bokusheshisa bungu- 2.11 m/s ² , bungaphansi kuka- 2.94 m/s ² ngakho-ke singaphetha ngokuthi ibhulokhi 3 kanye nebhulokhi 2 kusashelela ndawonye ngemva kokukhululwa ekuphumuleni.

b) Ubukhulu bokusheshisa kwebhulokhi 1 kanye nebhulokhi 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) a _x

a _x = 89.36 N : 28 kg = 3.19 m/s ²

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1. Isisindo kanye nesisindo
2. amandla ajwayelekile
3. Umthetho wesibili wokunyakaza kukaNewton
4. Amandla okungqubuzana
5. Ukunyakaza endaweni evundlile ngaphandle kwamandla okungqubuzana
6. Ukunyakaza kwemizimba emibili ngokusheshisa okufanayo endaweni evundlile eqinile ngamandla okungqubuzana
7. Ukunyakaza endizeni ethambekele ngaphandle kwamandla okungqubuzana
8. Ukunyakaza endizeni ethambekele emangelengele ngamandla okungqubuzana
9. Ukunyakaza e-lifti
10. Ukunyakaza kwemizimba kuxhunywe ngezintambo nama-pulleys
11. Imizimba emibili enesilinganiso esifanayo sokusheshisa
12. Ukuzungeza ijika eliyisicaba - amandla okunyakaza okujikelezayo
13. Ukuzungeza ijika eligobile - amandla okunyakaza okujikelezayo
14. Ukunyakaza okufanayo kumbuthano ovundlile
15. Amandla aphakathi ahambisanayo ajikelezayo