Izinkinga Ezixazululiwe ku-Basic Physics

1. Ibhola elingu-0.2 kg, elinamathiselwe ekugcineni kwentambo evundlile, lizungezwe yindilinga yerediyasi engu-1 imitha kanti isivinini esiphezulu sebhola singu-10 rpm. Ubukhulu bokusheshisa kwe- centripetal kanye nobukhulu bamandla okucindezela buyini?

Kwaziwa:

Isisindo (m) = 0.2 kg

Irediyasi (r) = 1 m

Ijubane le-angular (ω) = 10 rev/min = 10 rev/60 s = 0.17 rev/s = (0.17)(6.28 rad)/s = 1 rad/s

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

Okufunwayo: a _s kanye no -Σ F

Isixazululo:

(a) Ubukhulu bokusheshisa kwe-centripetal

(b) Ubukhulu bamandla okucindezela

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

[irp]

2. Ibhola elingamakhilogremu angu-1 ekugcineni kwentambo lijikeleza ngokulinganayo esiyingini esivundlile esingu-1 m. Intambo izophuka uma ukucindezeleka okukuyo kudlula ama-N angu-100. Yiliphi ijubane elikhulu ibhola elingaba nalo?

Kwaziwa:

Isisindo (m) = 1 kg

Irediyasi (r) = 1 imitha

Amandla okucindezela (T) = amandla amaphakathi ( Σ F) = 100 N

Kufunwa: v esiphezulu

Isixazululo:

[irp]

[wpdm_package id='499′]

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

Funda kabanzi

1. Imoto ezungeza ijika eligobile. Iyini i-engeli yomgwaqo onejika elingamamitha angu-60 elinejubane lomklamo elingama-20 m/s? Ake sithi ayikho friction phakathi kwemoto nomgwaqo.

Isixazululo

N= amandla ajwayelekile

I-N sin θ = ingxenye evundlile yamandla avamile

N cos θ = ingxenye eqondile yamandla avamile

w = mg = isisindo semoto

Umgwaqo wenzelwe ukuba uvalwe ukuze kuqedwe ukuncika ekungqubuzaneni.

Amandla aphelele avundlile, ingxenye evundlile yamandla avamile ( N sin θ) , iyadingeka ukuze imoto iqhubeke ihamba ngendilinga ezungeze ijika.

Sikhetha i-x-axis njengevundlile kanye ne-y-axis njengevundlile, ukuze ukusheshisa okuphakathi nendawo,_R, isendleleni evundlile. Endaweni evundlile, amandla kuphela ingxenye evundlile yamandla avamile (Isono se-N θ), edingekayo ukukhiqiza ukusheshisa okuphakathi. Isono se-N θ = amandla centripetal.

Sebenzisa umthetho kaNewton wokunyakaza ohlangothini oluqondile:

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Sebenzisa umthetho kaNewton wokunyakaza ohlangothini oluvundlile:

Faka u- N esilinganisweni 1 ku-N esilinganisweni 2 :

[wpdm_package id='497′]

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

Funda kabanzi

1. Imoto enesisindo esingamakhilogremu angu-2000 izungeza ijika emgwaqweni oyisicaba ongama-radius angu-150 m. I-coefficient yokungqubuzana okungaguquki ingu-0.5. Thola isivinini esiphezulu ukuze imoto ilandele ijika futhi ingasheleli. Ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s ².

Kwaziwa:

Isisindo (m) = 2000 kg

Irediyasi (r) = amamitha angu-150

I-Coefficient yokungqubuzana okungaguquki ( μs ₎ = 0.5

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

Amandla okungqubuzana okumile (F _s ) = μ _s N = μ _s w = (0.7)(20,000 N) = 14,000 N

Kufunwa: v

Isixazululo:

[irp]

[wpdm_package id='496′]

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

Funda kabanzi

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

---

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

---

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

[wpdm_package id='493′]

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

Funda kabanzi

1. Ibhulokhi elingamakhilogremu angu-2 lilele endizeni ethambekele emaceleni nge-engeli engu-37 ^o kuya endaweni evundlile. Thola ubukhulu bamandla angaphandle asetshenziswa ebhulokhini, ukuze ibhulokhi lingasheleli phansi endizeni. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µ _k = 0.2)

Kwaziwa:

Isisindo (m) = 2 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Isisindo sebhulokhi (w) = mg = (2)(10) = 20 amaNewton

Isono 37 ^o = 0.6

I-Cos 37 ^o = 0.8

I-coefficient ye- kinetic friction (µ _k ) = 0.2

Ingxenye ka-y yesisindo (w _y ) = w cos 37 ^o = (20)(0.8) = 16 Newtons

Ingxenye engu-x yesisindo (w _x ) = w sin θ = (20)(sin 37) = (20)(0.6) = 12 Newtons

amandla avamile (N) = w _y = 16 Newtons

Okufunwayo : Amandla angaphandle (F)

Isixazululo :

w_x = 12 uNewton

Amandla okungqubuzana kwe-kinetic (f _k ) = µ _k N = (0.1)(16) = 1.6 AmaNewton

Ubukhulu bamandla angaphandle u-F asetshenziswe ebhulokini :

F + f _k – w _x = 0

F = w _x – f _k

F = 12 – 1.6

F = 10.4 Newton

Amandla angaphandle u-F makhulu kune-10.4 Newtons.

[irp]

2. Isisindo sebhulokhi = 2 kg, i-coefficient of static friction µ _s = 0.4 kanye no-θ = 45 ^o . Thola ubukhulu bamandla F ukuze ibhulokhi iqale ukushelela phezulu.

Kwaziwa:

I-coefficient yokungqubuzana okungaguquki (µs ₎ = 0.4

I-engeli (θ) = 45 ^o

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Isisindo sebhulokhi (m) = 2 kg

Isisindo sebhulokhi (w) = mg = (2 kg)(10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Ingxenye engu-x yesisindo (w _x ) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 AmaNewton

Ingxenye engu-y yesisindo (w _y ) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 AmaNewton

Okufunwayo : Ubukhulu bamandla F

Isixazululo:

Ibhulokhi iqala ukushelela phezulu, uma F ≥ w_x + f_s.

Ingxenye yesisindo engu-x:

w _x = 10√2 Newton

ingxenye engu-y yesisindo :

w _y = 10√2 Newton

Amandla avamile :

N = w _y = 10√2 Newton

Amandla okungqubuzana okungaguquki :

f _s = µ _s N = (0,4)(10√2) = 4√2

Ubukhulu bamandla F ukuze ibhloko liqale ukushelela phezulu :

F ≥ w _x + f _s

F ≥ 10√2 + 4 √2

F ≥ 14√2 Newton

[wpdm_package id='492′]

1. Izinhlayiya ezilingana ngokulingana okukodwa
2. Izinhlayiya ezilingana ngezindlela ezimbili
3. Ukulingana kwemizimba exhunywe ngezintambo nama-pulley
4. Ukulingana kwemizimba endizeni ethambekele

Funda kabanzi

1. Ibhokisi elinobunzima obungama -5 kg ​​lisendaweni ethambekele ekhoneni elingu-30 ^o . Ibhokisi lisekelwa yintambo. Thola amandla okucindezela (T) kanye namandla ajwayelekile (N)!

Isixazululo

∑F_x = 0

T – w sin 30 ^o = 0

T = w isono 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

[irp]

2. Izinto ezimbili ezinobunzima m ₁ = m ₂ = 2 kg, ezixhunywe ngentambo engenasisindo phezu kwe-pulley engenasiphazamiso. Thola amandla okucindezela T ₁ kanye no-T ₂.

Isixazululo

(a) Umdwebo womzimba okhululekile wento 1 (b) Umdwebo womzimba okhululekile wento 2

Sebenzisa umthetho wokuqala kaNewton ekuphikisweni 1:

∑ F _y = 0

I-T ₁ – w ₁ = 0

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

Sebenzisa umthetho wokuqala kaNewton ekuphikisweni 2:

∑ F _y = 0

I-T ₂ – w ₂ = 0

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

I-T ₁ = I-T ₂ = 19.6 N.

[irp]

3. Into enesisindo w A ₌ 30 N kanye nento enesisindo w _B = 40 N, zixhunywe ngentambo elula edlula phezu kwe-pulley engenasiphazamiso yesisindo esingabalulekile. Nquma i-coefficient yokuphambana okuphezulu okuqinile phakathi kwe-w _B kanye nobuso obuthambekele, uma uhlelo luphumule.

Isixazululo

(a) Umdwebo womzimba okhululekile wento w _A (b) Umdwebo womzimba okhululekile wento w _B

Sebenzisa umthetho wokuqala kaNewton ukuphikisa u-w _A ohlangothini oluqondile (y):

∑ F _y = 0 (akukho ukusheshisa ohlangothini oluqondile)

T – w _A = 0

T = w _A = 30 Newton

Sebenzisa umthetho wokuqala kaNewton ukuphikisa u-w _B ohlangothini oluqondile (y) :

∑ F _y = 0

N – w _B cos 45 ^o = 0

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

Sebenzisa umthetho wokuqala kaNewton ukuphikisa u-w _B ohlangothini oluvundlile (x):

∑ F _x = 0

F _k + w _B sin 45 ^o – T = 0

μ _s N + w _B isono 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

I-coefficient yokungqubuzana okuphezulu okungaguquki phakathi kwe-w _B kanye nobuso obuthambekele = 0.07.

[wpdm_package id='490′]

1. Izinhlayiya ezilingana ngokulingana okukodwa
2. Izinhlayiya ezilingana ngezindlela ezimbili
3. Ukulingana kwemizimba exhunywe ngezintambo nama-pulley
4. Ukulingana kwemizimba endizeni ethambekele

Funda kabanzi

1. Thola amandla okucindezela T ₁ , T ₂ , kanye no-T _{3. Unganaki} isisindo sentambo.

Isixazululo

(a) Umdwebo womzimba okhululekile wento (b) Umdwebo womzimba okhululekile wentambo

Sebenzisa umthetho wokuqala kaNewton entweni:

ΣF _y = 0

I-T ₁ – w = 0

I-T ₁ = w = mg

I-T ₁ = (5 kg)(9.8 m/s ² )

T ₁ = 49 kg m/s ²

I-T ₁ = 49 N

Sebenzisa umthetho wokuqala kaNewton entanjeni:

∑ 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

I-T ₂ = 0.87 I-T ₃ / 0.77 = 1.1 I-T ₃ ———- Isibalo 1

[irp]

-

∑ F _y = 0

T _3y + T _2y – T _1y = 0

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

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

Ukufaka u-T ₂ ku-equation 2 ku-equation 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

I-T ₃ = 49 / 1.2

I-T ₃ = 41 N

---

I-T ₂ = 1.1 I-T ₃

I-T ₂ = (1.1)(40.8 N)

I-T ₂ = 45 N

[wpdm_package id='488′]

1. Izinhlayiya ezilingana ngokulingana okukodwa
2. Izinhlayiya ezilingana ngezindlela ezimbili
3. Ukulingana kwemizimba exhunywe ngezintambo nama-pulley
4. Ukulingana kwemizimba endizeni ethambekele

Funda kabanzi

^{1. Isisindo sento, m = 10 kg, esisekelwe yintambo. Thola ukucindezeleka entanjeni!} g = 10 m/s ²

Kwaziwa:

Isisindo (m) = 10 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Okufunwayo: Amandla okucindezela (T)

Isixazululo:

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

[irp]

2. Isisindo sento singama-10 kg. Thola ukucindezeleka entanjeni….. Ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s ².

Isixazululo

Kwaziwa:

Isisindo (m) = 10 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ².

Okufunwayo: Amandla okucindezela (T)

Isixazululo:

^{w = isisindo = mg = (10 kg)(10 m/s2}) = 100 kg m/s²

T ₁ = amandla okucindezela 1

_{I-T 1x} = ingxenye engu-x yamandla okucindezela 1 = I-T ₁ cos 45 ^o = 0.7 I-T ₁

_{T 1y} = ingxenye ka-y yamandla okucindezela 2 = T ₁ sin 45 ^o = 0.7 T ₁

T ₂ = amandla okucindezela 2

_{I-T 2x} = ingxenye engu-x yamandla okucindezela 2 = I-T ₂ cos 45 ^o = 0.7 I-T ₂

_{T 2y} = ingxenye ka-y yamandla okucindezela 2 = T ₂ sin 45 ^o = 0.7 T ₂

Isimo sokulingana ΣF = 0.

i-axis ka-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 —– isibalo 1

i-axis 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 —– isibalo 2

Thola ubukhulu be-T ₁ :

0.7T ₁ + 0.7T ₁ = 100

1.4T ₁ = 100

I-T ₁ = 100 / 1.4

I-T ₁ = 71.4 Newton

T ₁ = T ₂ ngakho T ₂ = 71.4 amaNewton

[wpdm_package id='486′]

1. Izinhlayiya ezilingana ngokulingana okukodwa
2. Izinhlayiya ezilingana ngezindlela ezimbili
3. Ukulingana kwemizimba exhunywe ngezintambo nama-pulley
4. Ukulingana kwemizimba endizeni ethambekele

Funda kabanzi

1. Amabhokisi amabili axhunywe ngentambo egijima phezu kwe-pulley. Unganaki isisindo sentambo ne-pulley nanoma yikuphi ukungqubuzana ku-pulley. Isisindo sebhokisi 1 = 2 kg, isisindo sebhokisi 2 = 3 kg, ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s ² . Thola (a) Ukusheshisa kwesistimu (b) Ukucindezeleka entanjeni!

Isixazululo

Kwaziwa:

Isisindo sebhokisi 1 (m1 ₎ = 2 kg

Isisindo sebhokisi 2 (m2 ₎ = 3 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Isisindo sebhokisi 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Isisindo sebhokisi 2 (w ₂ ) = m ₂ g = (3)(10) = 30 AmaNewton

Isixazululo:

(a) ubukhulu kanye nesiqondiso sokusheshisa

w ₂ > w ₁ ngakho ibhokisi 2 liyashesha liyehla futhi ibhokisi 1 liyashesha liye phezulu.

Amandla anesiqondiso esifanayo nokusheshisa (w ₂ kanye no-T ₁ ), uphawu lwawo luhle. Amandla anesiqondiso esiphambene nokusheshisa (T ₂ kanye no-w ₁ ), uphawu lwawo luhle.

∑ F = ma

w₂ - T₂ + T₁ - w₁ = (m₁ +m₂) a ——-> 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

Ubukhulu bokusheshisa buyi - 2 m/s ².

(b) Amandla okucindezela

Ibhokisi 2:

Kunezenzo ezimbili zamandla ebhokisini 2: okokuqala, isisindo sebhokisi 2 (w ₂ ), kukhomba phansi ukuze kube kuhle. Okwesibili, amandla okucindezela asebenza ebhokisini 2 (T ₂ ), kukhomba phezulu ukuze kube kubi. Sebenzisa umthetho wesibili wokunyakaza kaNewton .

∑ F = ma

w ₂ – T ₂ = m ₂ a

30 – T ₂ = (3)(2)

30 – T ₂ = 6

Isigaba ₂ = 30 – 6

I-T ₂ = 24 Newton

Ibhokisi 1:

Kunezenzo ezimbili zamandla ebhokisini 1. Okokuqala , isisindo sebhokisi 1 (w ₁ ), sikhomba phansi ngakho-ke singesihle. Okwesibili , amandla okucindezela asebenza ebhokisini 1 (T ₁ ) akhomba phezulu ngakho-ke singesihle. Sebenzisa umthetho wesibili wokunyakaza kaNewton:

∑ F = ma

I-T ₁ – w ₁ = m ₁ a

I-T ₁ – 20 = (2)(2)

Isigaba ₁ – 20 = 4

I-T ₁ = 20 + 4

I-T ₁ = 24 Newton

Ubukhulu bamandla okucindezela = T ₁ = T ₂ = T = 24 Newtons

[irp]

2. Into esendaweni evundlile eqondile. Isisindo sento 1 = 2 kg, isisindo sento 2 = 4 kg, ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s ² , i-coefficient ye-static friction = 0.4, i-coefficient ye-kinetic friction = 0.3. Uhlelo luphumule noma lusheshisiwe? Uma uhlelo lusheshisiwe, thola ubukhulu kanye nesiqondiso sokusheshisa kwesistimu!

Isixazululo

Kwaziwa:

Isisindo sento 1 (m ₁ ) = 2 kg

Isisindo sento 2 (m ₂ ) = 4 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

I-Coefficient yokungqubuzana okungaguquki ( μs ₎ = 0.4

I-coefficient ye-kinetic friction ( μk ₎ = 0.3

Isisindo sento 1 (w ₁ ) = m ₁ g = (2)(10) = 20 AmaNewton

Isisindo sento 2 (w ₂ ) = m ₂ g = (4)(10) = 40 AmaNewton

Amandla avamile asetshenziswa entweni 1 (N) = w ₁ = 20 amaNewton

Amandla okungqubuzana okungaguquki okwenziwa entweni 1 (fs ₎ = μ _s N = (0.4)(20) = 8 Newtons

Amandla okungqubuzana kwe-kinetic asetshenziswa entweni 1 (f _k ) = μ _k N = (0.3)(20) = 6 amaNewton

Okufunwayo: ukusheshisa (a)

Isixazululo:

w ₂ > fs ₍ 40 Newton > 8 Newton) ngakho into 2 isheshiswa ngokuqondile phansi kanti into 1 isheshiswa ngokuqondile ibheke kwesokudla. Amandla okungqubuzana asebenza ezintweni 1 amandla okungqubuzana kwe-kinetic (f _k ). Sebenzisa umthetho wesibili wokunyakaza kaNewton:

∑ F = ma

w ₂ – i = (m ₁ + m ₂ ) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s ²

Ubukhulu bokusheshisa = 5.7 m/s ²

[wpdm_package id='484′]

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

Funda kabanzi

1. Umuntu onesisindo esingama-50 kg ekheshini. Ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s ² . Thola amandla avamile asetshenziswa entweni yikheshi, uma:

(a) ilifti iphumule

(b) ilifti yehla ngesivinini esingaguquki

(c) ilifti esheshiswa phezulu ngokusheshiswa okungaguquki 5 / s ²

(d) ilifti esheshiswa yehla ngesivinini esingaguquki esingu-5 m/s ²

(e) ilifti ekuweni okukhululekile

Isixazululo

Kwaziwa:

Isisindo somuntu (m) = 50 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Isisindo (w) = mg = (50)(10) = 500 amaNewton

Okufunwayo: Amandla avamile (N)

Isixazululo:

(a) ilifti iphumule

Ilifti iphumule ngakho akukho ukusheshisa (a = 0)

Sikhetha indlela eya phezulu ngendlela eyakhayo kanye nendlela eya phansi ngendlela engemihle.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(b) ilifti yehla ngesivinini esingaguquki

Ijubane eliqhubekayo ukuze kungabikho ukusheshisa (a = 0)

Sikhetha indlela eya phezulu ngendlela eyakhayo kanye nendlela eya phansi ngendlela engemihle.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(c) ilifti esheshiswa phezulu ngesivinini esingaguquki esingu-5 m/s ²

Isiqondiso sokusheshisa siphezulu, ngakho-ke sikhetha isiqondiso esihle njengesiphezulu.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Umuntu uzwa iphansi liphakama kakhulu kunalapho ilifti imile noma ihamba ngesivinini esingaguquki.

Uma umuntu emi esikalini, isikali sifunda ubukhulu bamandla aphansi asetshenziswa ngumuntu esikalini. Ngokomthetho wesithathu kaNewton, lokhu kulingana nobukhulu bamandla ajwayelekile aphezulu asetshenziswa yisikali kumuntu.

(d) ilifti esheshiswa yehla ngesivinini esingaguquki esingu-5 m/s ²

Indlela yokusheshisa ibheke phansi, ngakho-ke sikhetha indlela eyakhayo njengeyehlayo.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 – 250

N = 250 Newton

Isisindo somuntu singama-250 N, ngaphansi kwesisindo sangempela w = 500 N.

(e) ilifti ekuweni okukhululekile

Ukuwa kwamahhala kusho ukuthi ukusheshisa kwe-lifti kufana nokusheshisa ngenxa yamandla adonsela phansi. Ubukhulu bokusheshisa ngenxa yamandla adonsela phansi bungu-9,8 m/s ² , isiqondiso sayo sibheke phansi enkabeni yoMhlaba. Ijubane landa ngokulandelana ngesikhathi ngo-9,8 m/s phakathi nomzuzwana ngamunye.

Indlela yokusheshisa ibheke phansi, ngakho-ke sikhetha indlela eyakhayo njengeyehlayo.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 – 500

N = 0

[irp]

2. Thola ukucindezeleka ekhebula le-lifti. Isisindo se-lifti = 2000 kg.

(a) ilifti iphumule

(b) ilifti esheshiswa yehla ngesivinini esingaguquki esingu-5 m/s ²

(c) ilifti esheshiswa phezulu ngesivinini esingaguquki esingu-5 m/s ²

(d) ilifti ekuweni okukhululekile

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Isixazululo

Kwaziwa:

Isisindo se-elevator (m) = 2000 kg

Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s ²

isisindo (w) = mg = (2000)(10) = 20,000 amaNewton

Okufunwayo: Amandla okucindezela (T)

Isixazululo:

(a) ilifti iphumule

ilifti iphumule ngakho akukho ukusheshisa (a = 0)

Sikhetha indlela eya phezulu njengesiqondiso esihle kanye nendlela eya phansi njengesiqondiso esibi.

Σ F = ma

T – w = 0

T = w

T = 20,000 Newton

Ukucindezeleka kwekhebula (T) = isisindo se-elevator (w) = ama-Newton angu-20,000

(b) ilifti esheshiswa yehla ngesivinini esingaguquki esingu-5 m/s ²

Indlela yokusheshisa ibheke phansi, ngakho-ke sikhetha indlela eyakhayo njengeyehlayo.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 – 10,000

T = 10,000 Newton

c) ilifti isheshiswe phezulu ngesivinini esingaguquki esingu-5 m/s ²

Indlela yokusheshisa ibheke phansi, ngakho-ke sikhetha indlela enhle njengeyaphezulu.

T – w = ma

T = w + ma

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

T = 20,000 + 10,000

T = 30,000 Newton

(d) ilifti ekuweni okukhululekile

Indlela yokusheshisa ibheke phansi, ngakho-ke sikhetha indlela eyakhayo njengeyehlayo.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 – 20,000

T = 0

[wpdm_package id='482′]

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

Funda kabanzi