I-physics

1. Ibhola elingamakhilogremu angu-0.2, elinamathiselwe ekugcineni kwentambo evundlile, lizungezwe yindilinga yerediyasi engu-1 imitha kanti isivinini esiphezulu sebhola singama-10 rpm. Ubukhulu balo buyini? ukusheshisa okuphakathi kanye nobukhulu bamandla okucindezela?

Kwaziwa:

Imisa (m) = 0.2 kg

Irediyasi (r) = 1 m

I-angular velocity (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

Kufunwa: a_s dan ΣF

Isixazululo:

(a) Ubukhulu bokusheshisa kwe-centripetal

(b) Ubukhulu bamandla okucindezela

ΣF = ma

T = ma_s

T = (0.2 kg)(1 m/s²)

T = 0.2 kg m/s²

T = 0.2 N

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 centripetal (ΣF) = 100 N

Okufunayo: ubukhulu be-v

Isixazululo:

[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

Isono se-N θ = ingxenye evundlile yamandla avamile

I-N cos θ = ingxenye eqondile yamandla avamile

w = mg = i isisindo yemoto

Umgwaqo wenzelwe ukuba uvalwe ukuze kuqedwe ukuncika ekungqubuzaneni.

Amandla aphelele avundlile, ingxenye evundlile yamandla avamile (Isono se-N θ), okudingekayo ukuze imoto iqhubeke ihamba nxazonke.

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:

Sebenzisa umthetho kaNewton wokunyakaza ohlangothini oluvundlile:

Ukushintshaukufaka u-N ku-equation 1 ku-N ku-equation 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 ijikeleza ijika emgwaqweni oyisicaba ongama-radius angu-150 m. I-coefficient ye ukungqubuzana okungaguquki ingu-0.5. Thola isivinini esiphezulu ukuze imoto ilandele ijika futhi ingasheleli. Ukusheshisa ngenxa yamandla adonsela phansi = 10m/s².

Kwaziwa:

Imisa (m) = 2000 kg

Irediyasi (r) = amamitha angu-150

Isilinganiso sokungqubuzana okungaguquki (μ_s= = 0.5

Isisindo (w) = mg = (2000 kg)(10 m/s²) = 20,000 kg m/s² = 20,000 uN

Amandla okungqubuzana okungaguquki (F)_s) = μ_s N = μ_s w = (0.7)(20,000 N) = 14,000 N

Kufunwa: v

Isixazululo:

[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 m₁ = 2 kg kanye ne-m₂ = 5 kg zisendizeni ethambekele futhi zixhunywe ndawonye ngentambo njengoba kuboniswe esithombeni. I-coefficient ye-kinetic friction phakathi kuka-m₁ futhi ukuthambekela kungu-0.2 kanye ne-coefficient ye ukungqubuzana kwe-kinetic phakathi kuka-m₂ futhi ukuthambekela kungu-0.1.

(a) Thola ukuthi bangobani ukusheshisa

(b) Thola amandla okucindezela

Kwaziwa:

Imisa 1 (m₁) = 2kg

Isisindo 2 (m₂) = 4kg

I-coefficient yokungqubuzana kwe-kinetic phakathi kuka-m₁ futhi indiza ethambekele (μ_k1) = 0.2

I-coefficient yokungqubuzana kwe-kinetic phakathi kuka-m₂ kanye nendiza ethambekele (μ_k2) = 0.1

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 9.8 m/s²

a) Ubukhulu kanye nesiqondiso sokusheshisa

w₁ = isisindo 1 = m₁ g = (2 kg)(9.8 m/s²) = 19.6 Newton

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

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

N₁ = I amandla ajwayelekile ku-m₁ = w_1y = 17 uNewton

F_k1 = Amandla okungqubuzana kwe-kinetic ku-m₁ = μ_k1 N₁ = (0.2)(17 N) = 3.4 Newton

---

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

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

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

N₂ = Amandla avamile ku-m₂ = w_2y = 19.6 uNewton

F_k2 = Amandla okungqubuzana kwe-kinetic ku-m₂ = μ_k2 N₂ = (0.1)(19.6 N) = 1.96 Newton

---

Ubukhulu bokusheshisa:

∑F_x = umama_x

w_2x > w_1x ngakho-ke isiqondiso sokusheshisa sifana nesiqondiso sika-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 = (m₁ +m₂ ) futhi_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 = 3.16m/s²

Ubukhulu bokusheshisa = 3.16 m/s² . Isiqondiso sokusheshisa = isiqondiso se-T₁ = isiqondiso se-w_2x

b) Ubukhulu bamandla okucindezela

Sebenzisa umthetho wesibili kaNewton entweni 2:

w_2x - F_k2 - T₂ = m₂ a_x

34.1 N – 1.96 N – T₂ = (4 kg)(3.16 m/s²)

32.14 N – T₂ = 12.64 uN

T₂ = 32.14 N – 12.64 N = 19.5 Newtons

Amandla okucindezela = T = T₁ =T₂ = 19.5 uNewton

2. m₁ = 4 kg, m₂ = 2 kg. Thola (a) ubukhulu kanye nesiqondiso sokusheshisa (b) Ubukhulu bamandla okucindezela axhumanisa u-m₁ kanye no-m₂ (c) ubukhulu bamandla okucindezela axhumanisa i-pulley nophahla.

Isixazululo

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) Ubukhulu kanye nesiqondiso sokusheshisa

∑F_y = umama_y

w₁ > w₂ ngakho-ke isiqondiso sento sifana nesiqondiso sesisindo 1 (w₁)Amandla anesiqondiso esifanayo nokusheshisa amahle kanti amandla anesiqondiso esiphambene nokusheshisa angemabi.

w₁ - T₁ + T₂ - w₂ = (m₁ +m₂) futhi_y

w₁ - w₂ = (m₁ +m₂) futhi_y

39.2 N – 19.6 N = (4 kg + 2 kg) a_y

19.6 N = (6 kg) a_y

a_y = 19.6 N : 6 kg

a_y = 3.26m/s²

Ubukhulu bokusheshisa = 3.26 m/s². Isiqondiso sokusheshisa = isiqondiso sika-w₁ .

b) Ubukhulu bamandla okucindezela axhumanisa u-m₁ kanye no-m₂

Faka isicelo Umthetho wesibili kaNewton ku-m₂ :

∑F_y = umama_y

w₁ - T₁ = m₁ a_y

39.2 N – T₁ = (4 kg)(3.26 m/s²)

39.2 N – T₁ = 13.04 uN

T₁ = 39.2 N – 13.04 N

T₁ = 26.16 uNewton

Ubukhulu bamandla okucindezela axhumanisa izinto = T = T₁ =T₂ = 26.16 uNewton

c) Ubukhulu bamandla okucindezela axhumanisa i-pulley nophahla.

I-Pulley iphumule:

∑F_y = umama_y —— a_y = 0

∑F_y = 0

Amandla aphezulu amahle, amandla aphansi awabi:

T₃ - T₁ - T₂ = 0

T₃ =T₁ + T₂

T₁ no-T₂ banobukhulu obufanayo, T₁ =T₂ = T = 26.16 N:

T₃ = 2T = 2(26.16 N) = 52.32 amaNewton

3. Ibhulokhi 1 (m₁ = 10 kg) kanye nebhulokhi 2 (m₂ = 15 kg) exhunywe ngentambo phezu kwe-pulley engenakho ukungqubuzana. I-Coefficient yokungqubuzana okungaguquki phakathi kwebhulokhi 2 ene-inclination = 0.6. I-coefficient yokungqubuzana kwe-kinetic phakathi kwebhulokhi 2 ene-inclination = 0.42. Thola (a) Ubukhulu bamandla amancane u-F asetshenziswa ezintweni ukuze izinto zisheshise phezulu (b) Thola ubukhulu bamandla okucindezela.

Isixazululo

w₁ = Isisindo sebhloko 1 = m₁ g = (10 kg)(9.8 m/s²) = 98 Newton

w₂ = Isisindo sebhloko 2 = m₂ g = (15 kg)(9.8 m/s²) = 147 Newton

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

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

N₂ = Amandla avamile ebhulokini 2 = w_2y = 127.89 uNewton

F_k2 = Amandla okungqubuzana kwe-kinetic kubhlokhi 2 = μ_k2 N₂ = (0.42)(127.89 N) = 53.7 Newton

F_s2 = Amandla okungqubuzana okungaguquki kubhlokhi 2 = μ_s2 N₂ = (0.6)(127.89 N) = 76.7 Newton

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

∑F_x = umama_x —— a_x = 0

∑F_x = 0

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

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) Ubukhulu bamandla okucindezela

Sebenzisa umthetho kaNewton wokunyakaza kubhlokhi 1:

∑F_y = umama_y —— a_y = 0

∑F_y = 0

T₁ - w₁ = 0

T₁ = w₁ = 98 uNewton

Sebenzisa umthetho kaNewton wokunyakaza kubhlokhi 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 uNewton

Ubukhulu bamandla okucindezela = T₁ =T₂ = T = 98 Newton

4. Ibhulokhi 1 (m₁ = 16 kg) ilele endaweni evundlile kanye nebhulokhi 2 (m₂ = 12 kg) ilele endaweni ebushelelezi ethambekele, exhunywe ngentambo edlula phezu kwe-pulley encane, engenakho ukungqubuzana. Ibhloko 3 (m)₃ = 5 kg) ilele kubhlokhi 2. I-coefficient yokungqubuzana kwe-kinetic phakathi kwebhlokhi 2 kanye nobuso obuvundlile ingu-0,4. I-coefIsilinganiso sokungqubuzana okungaguquki phakathi kwebhulokhi 2 nebhulokhi 3 ngu-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?

w₁ = I isisindo sebhulokhi 1 = m₁ g = (16 kg)(9.8 m/s²) = 156.8 Newton

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

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

N₁ = I amandla avamile asetshenziswa ebhulokini 1 yindiza ethambekele = w_1y = 78.4 uNewton

w₃ = I isisindo sebhulokhi 3 = m₃ g = (5 kg)(9.8 m/s²) = 49 Newton

N₂₃ = I amandla avamile asetshenziswa kubhlokhi 3 yibhlokhi 2 = w₃ = 49 uNewton

N₃₂ = I-namandla avamile asetshenziswa kubhlokhi 2 yibhlokhi 3 = N₂₃ = w₃ = 49 uNewton

(N₂₃ futhi N₃₂ ziyizibhangqwana zokusabela ngesenzo)

F_s23 = I amandla okungqubuzana okungaguquki okwenziwa kubhlokhi 3 yibhlokhi 2 = μ_s N₂₃ = (0.3)(49 N) = 14.7 Newton

F_s32 = I amandla okungqubuzana okungaguquki okwenziwa kubhlokhi 2 yibhlokhi 3 =F_s23 = 14.7 uNewton

(F_s23 futhi F_s32 ziyizibhangqwana zokusabela ngesenzo)

w₂ = I isisindo sebhulokhi 2 = m₂ g = (12 kg)(9.8 m/s²) = 117.6 Newton

N₂ = I amandla avamile asetshenziswa entweni 2 ngendawo evundlile = w₂ + N₃₂ = 117.6 Newtons + 49

I-Newton = 166.6 I-Newton

F_k2 = I amandla okungqubuzana kwe-kinetic kubhlokhi 2 = μ_k N₂ = (0.4)(166.6 N) = 66.64 Newton

Sebenzisa umthetho kaNewton wokunyakaza kubhlokhi 3:

∑F_x = umama_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

Ukusheshisa okuphezulu kwebhulokhi 3 ukuze ibhulokhi 3 kanye nebhulokhi 2 kusashelela ndawonye kungu-2.94 m/s².

Manje sibala ubukhulu bokusheshisa kwesistimu ngemva kokukhululwa ekuphumuleni.

Isiqondiso sokufuduka kwebhulokhi = isiqondiso sokusheshisa kwebhulokhi = isiqondiso se-T₂ = isiqondiso se-w_1x.

∑F_x = umama_x

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

w_1x - F_k2 = (m₁ +m₂ +m₃ ) futhi_x

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

69.76 N = (33 kg) a_x

a_x = 2.11m/s²

a_x kuyinto enhle, kusho ukuthi isiqondiso sokufuduka kwebhulokhi noma isiqondiso sokusheshisa sifana nesiqondiso se-T₂ noma isiqondiso se-w_1x.

Ubukhulu bokusheshisa bungu 2.11 m / s² , lamandla kune 2.94 m / s² ngakho-ke singaphetha ngokuthi ibhlogo 3 nebhlogo 2 zisashelela ndawonye ngemva kokukhululwa ekuphumuleni.

b) Ubukhulu bokusheshisa kwebhulokhi 1 kanye nebhulokhi 2

∑F_x = umama_x

w_1x - F_k2 = (m₁ +m₂) futhi_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/s²

[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 ama-2 lilele endaweni ethambekele emaceleni nge-engeli engu-37^o kuya endaweni evundlile. Thola ubukhulu bamandla angaphandle asetshenziswa ebhulokini, ukuze ibhulokhi lingasheleli phansi endizeni. (syn 37^o = 0.6, cos 37^o = 0.8, g = 10 ms^-2, µ_k = 0.2)

Kwaziwa:

Imisa (m) = 2 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

Amabhulokhi isisindo (w) = mg = (2)(10) = 20 AmaNewton

Ngaphandle kwama-37^o = 0.6

ICos 37^o = 0.8

I-Coefficient ye ukungqubuzana kwe-kinetic (µ_k= = 0.2

Ingxenye yesisindo engu-y (w)_y) = w ibe 37^o = (20)(0.8) = 16 Newton

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

amandla avamile (N) = w_y = 16 uNewton

wayefuna : Amandla angaphandle (F)

Isixazululo :

w_x = 12 uNewton

Amandla okungqubuzana kwe-kinetic (f)_k) = µ_k N = (0.1)(16) = 1.6 Newton

Ubukhulu bamandla angaphandle u-F asetshenziswa 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.

2. Isisindo sebhulokhi = 2 kg, i-coefficient yokungqubuzana okungaguquki µ_s = 0.4 kanye no-θ = 45^oThola ubukhulu bamandla u-F ukuze ibhloko liqale ukushelela phezulu.

Kwaziwa:

I-coefficient yokungqubuzana okungaguquki (µ_s= = 0.4

I-engeli (θ) = 45^o

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

Isisindo sebhulokhi (m) = 2 kg

Isisindo sebhulokhi (w) = mg = (2 kg)(10 m/s²) = 20 kg m/s² = 20 uNewton

Ingxenye yesisindo engu-x (w)_x) = w isono θ = (20)(isono 45) = (20)(0.5√2) = 10√2 Amathoni amasha

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

wayefuna : Ubukhulu bamandla F

Isixazululo:

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

Ingxenye yesisindo engu-x:

w_x = 10√2 uNewton

ingxenye yesisindo engu-y :

w_y = 10√2 uNewton

Amandla avamile :

N = w_y = 10√2 uNewton

Amandla okungqubuzana okungaguquki :

f_s = µ_s N = (0,4)(10√2) = 4√2

Ubukhulu bamandla u-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 le- Mass Ama-5 kg ​​abekwe endaweni ethambekele ekhoneni lama-30^o. Ibhokisi lisekelwa yintambo. Thola amandla okucindezela (T) kanye amandla ajwayelekile (N)!

Isixazululo

∑F_x = 0

T – w isono 30^o = 0

T = w isono 30^o

T = (5 kg)(9.8 m/s²) isono 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. Izinto ezimbili ezinobunzima m₁ = m₂ = 2 kg, exhunywe ngentambo engenasisindo phezu kwe-pulley engenasiphazamiso. Thola amandla okucindezela u-T₁ no-T₂.

Isixazululo

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

Sebenzisa umthetho wokuqala kaNewton ekuphikisweni 1:

∑F_y = 0

T₁ - w₁ = 0

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

Faka isicelo Umthetho wokuqala kaNewton ukuphikisa 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. Into ye isisindo w_A = 30 N kanye nento enesisindo u-w_B = 40 N, zixhunywe ngentambo elula edlula phezu kwe-pulley engenakuphikiswana yesisindo esingabalulekile. Nquma i-coefficient ye-maximum ukungqubuzana okungaguquki phakathi kuka-w_B kanye nobuso obuthambekele, uma uhlelo luphumule.

Isixazululo

(a) Umdwebo womzimba okhululekile wento u-w_A (b) Umdwebo womzimba okhululekile wento u-w_B

Sebenzisa umthetho wokuqala kaNewton ekuphikiseni u-w_A ohlangothini oluqondile (y):

∑F_y = 0 (akukho ukusheshisa ohlangothini oluqondile)

T – w_A = 0

T = w_A = 30 uNewton

Sebenzisa umthetho wokuqala kaNewton ekuphikiseni u-w_B ohlangothini oluqondile (y) :

∑F_y = 0

N – w_B ibe 45^o = 0

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

Sebenzisa umthetho wokuqala kaNewton ekuphikiseni u-w_B ngendlela evundlile (x):

∑F_x = 0

F_k +w_B ngaphandle 45^o -T = 0

μ_s N + w_B ngaphandle 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 okuqinile phakathi kuka-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 u-T₁, T₂, kanye noT₃. Unganaki izintambo Mass.

Isixazululo

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

Faka isicelo se Umthetho wokuqala kaNewton entweni:

ΣF_y = 0

T₁ – w = 0

T₁ = w = mg

T₁ = (5 kg)(9.8 m/s²)

T₁ = 49 kg m/s²

T₁ = 49 uN

Sebenzisa umthetho wokuqala kaNewton entanjeni:

∑F_x = 0

T_3x - T _2x = 0

T₃ ibe 30^o - T₂ ibe 40^o = 0

I-0.87 T₃ - 0.77 T₂ = 0

I-0.87 T₃ = 0.77 T₂

T₂ = 0.87 T₃ / 0.77 = 1.1 T₃ ———- Isibalo 1

-

∑F_y = 0

T_3y + T_2y - T_1y = 0

T₃ ngaphandle 30^o + T₂ ngaphandle 40^o - T₁ = 0

I-0.5 T₃ + 0.64 T₂ – 49 N = 0 ———- Isibalo 2

Ukufaka esikhundleni se-T₂ ku-equation 2 ku-equation 2:

I-0.5 T₃ + 0.64 (1.1 T₃) – 49 N = 0

I-0.5 T₃ + 0.70 T₃ - 49 = 0

I-1.2 T₃ - 49 = 0

I-1.2 T₃ = 49

T₃ = 49/1.2

T₃ = 41 uN

---

T₂ = 1.1 T₃

T₂ = (1.1)(40.8 N)

T₂ = 45 uN

[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. Imisa kwento, m = 10 kg, esekelwa yintambo. Thola ukucindezeleka entanjeni!} g = 10 m/s²

Kwaziwa:

Isisindo (m) = 10 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

Kufunwa: Amandla okucindezela (T)

Isixazululo:

ΣF_y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s²) = 100 kg m/s²

T = 100 Newton

2. Isisindo sento singama-10 kg. Thola ukucindezeleka entanjeni….. Ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s².

Isixazululo

Kwaziwa:

Isisindo (m) = 10 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s².

Kufunwa: Amandla okucindezela (T)

Isixazululo:

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

T₁ = amandla okucindezela 1

_T1x = ingxenye engu-x yamandla okucindezela 1 = T₁ ibe 45^o = 0.7 T₁

_T1y = ingxenye ka-y yamandla okucindezela 2 = T₁ ngaphandle 45^o = 0.7 T₁

T₂ = amandla okucindezela 2

_T2x = ingxenye engu-x yamandla okucindezela 2 = T₂ ibe 45^o = 0.7 T₂

_T2y = ingxenye ka-y yamandla okucindezela 2 = T₂ ngaphandle 45^o = 0.7 T₂

Isimo sokulingana ΣF = 0.

i-axis ka-y:

ΣF_y = 0

T_1y + T_2y – w = 0

I-0.7T₁ + 0.7T₂ - 100 = 0

I-0.7T₁ + 0.7T₂ = 100 —– isibalo 1

i-axis x:

ΣF_x = 0

T_2x - T_1x = 0

I-0.7T₂ – 0.7T₁ = 0

I-0.7T₂ = 0.7T₁

T₂ =T₁ —– isibalo 2

Nquma ubukhulu be-T₁ :

I-0.7T₁ + 0.7T₁ = 100

I-1.4T₁ = 100

T₁ = 100/1.4

T₁ = 71.4 uNewton

T₁ =T₂ ngakho-ke u-T₂ = 71.4 uNewton

[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 ubunzima bentambo ne-pulley nanoma yikuphi ukungqubuzana ku-pulley. Imisa kwebhokisi 1 = 2 kg, isisindo sebhokisi 2 = 3 kg, ukusheshisa ngenxa yamandla adonsela phansi = 10m/s². 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/s²

Isisindo kwebhokisi 1 (w₁) = m₁ g = (2)(10) = 20 Newton

Isisindo sebhokisi 2 (w₂) = m₂ g = (3)(10) = 30 Newton

Isixazululo:

(a) ubukhulu kanye nesiqondiso sokusheshisa

w₂ > w₁ ngakho-ke ibhokisi 2 liyasheshisa liyehla kanti ibhokisi 1 liyasheshisa liye phezulu.

Amandla anesiqondiso esifanayo sokusheshisa (w₂ no-T₁), uphawu lwayo luhle. Amandla anesiqondiso esiphambene nokusheshisa (T₂ kanye w₁), uphawu lwayo luyi-negative.

∑F = ma

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

w₂ – T + T – w₁ = (m₁ +m₂) futhi

w₂ - w₁ = (m₁ +m₂) futhi

30 – 20 = (2 + 3) a

10 = 5 a

a = 10/5

a = 2 m/s²

Ubukhulu be- ukusheshisa ingu-2 m/s².

(b) Amandla okucindezela

Ibhokisi 2:

Kunezenzo ezimbili zamandla ebhokisini 2: okokuqala, isisindo sebhokisi 2 (w₂), ikhomba phansi ukuze kube kuhle. Okwesibili, amandla okucindezela asebenza ebhokisini 2 (T₂), ikhomba phezulu ukuze ibe negative. Faka Umthetho wesibili kaNewton ukunyakaza.

∑F = ma

w₂ - T₂ = m₂ a

30 - T₂ = (3)(2)

30 - T₂ = 6

T₂ = 30 - 6

T₂ = 24 uNewton

Ibhokisi 1:

Kunezenzo ezimbili zamandla ebhokisini 1. Okokuqala, isisindo sebhokisi 1 (w₁), ikhomba phansi ngakho-ke ayilungile. Okwesibili, amandla okucindezela asebenza ebhokisini 1 (T₁) ikhomba phezulu ukuze kube kuhle. Sebenzisa umthetho wesibili wokunyakaza kaNewton:

∑F = ma

T₁ - w₁ = m₁ a

T₁ – 20 = (2)(2)

T₁ - 20 = 4

T₁ = 20 + 4

T₁ = 24 uNewton

Ubukhulu bamandla okucindezela = T₁ =T₂ = T = 24 Newton

2. Into esendaweni evundlile eqondile. Isisindo sento 1 = 2 kg, isisindo sento 2 = 4 kg, ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s², i-coefficient ye-static friction = 0.4, i-coefficient ye-kinetic friction = 0.3. Uhlelo luphumulile noma lusheshisiwe? Uma uhlelo lusheshisiwe, thola ubukhulu kanye nesiqondiso sokusheshiswa kwesistimu!

Isixazululo

Kwaziwa:

Isisindo sento 1 (m₁) = 2 kg

Isisindo sento 2 (m₂) = 4 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

I-Coefficient ye ukungqubuzana okungaguquki (μ_s= = 0.4

I-coefficient yokungqubuzana kwe-kinetic (μ_k) = 0.3

Isisindo sento 1 (w₁) = m₁ g = (2)(10) = 20 Newton

Isisindo sento 2 (w₂) = m₂ g = (4)(10) = 40 Newton

amandla ajwayelekile okufakwe entweni 1 (N) = w₁ = 20 uNewton

Amandla okungqubuzana okungaguquki okwenziwa entweni 1 (f_s) = μ_s N = (0.4)(20) = 8 Newton

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

Okufunayo: ukusheshisa (a)

Isixazululo:

w₂ > f_s (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)_kSebenzisa umthetho wesibili kaNewton wokunyakaza:

∑F = ma

w₂ - the = (m₁ +m₂) futhi

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s²

Ubukhulu bokusheshisa = 5.7 m/s²

[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 esingamakhilogremu angu-50 e-lifti. Ukusheshisa ngenxa yamandla adonsela phansi = 10m/s². Nquma amandla ajwayelekile okufakwa entweni eduze kwe-lifti, uma:

(a) ilifti iphumule

(b) ilifti yehla ngesivinini esiphezulu ijubane elingaguquki

(c) ilifti isheshiswe phezulu ku-a ukusheshisa okuqhubekayo 5 /s²

(d) ilifti esheshiswa yehla ngesivinini esingaguquki esingu-5 m/s²

(e) ilifti ku- ukuwa kwamahhala

Isixazululo

Kwaziwa:

Okomuntu Mass (m) = 50 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

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

Okufunayo: 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.

ΣF = umama

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.

ΣF = umama

N – w = 0

N = w

N = 500 Newton

(c) ilifti esheshiswa phezulu ngesivinini esingaguquki esingu-5 m/s²

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/s²

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 buyi-9,8 m/s², isiqondiso sayo sibheke phansi enkabeni yoMhlaba. Ijubane landa ngokulandelana ngesikhathi ngama-9,8 m/s ngomzuzwana 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

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

(a) ilifti iphumule

(B) ilifti isheshiswe yehla ngesivinini esingaguquki esingu-5 m/s²

(C) I-elevator isheshise phezulu ngesivinini esingaguquki esingu-5 m/s²

(d) ilifti ekuweni okukhululekile

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

Isixazululo

Kwaziwa:

Isisindo se-elevator (m) = 2000 kg

Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s²

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

Kufunwa: Amandla okucindezela (T)

Isixazululo:

(a) ilifti iphumule

ikheshi iphumule ngakho akukho ukusheshisa (a = 0)

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

ΣF = umama

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/s²

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/s²

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