Physics

1. Mpira wa 0.2-kg, wolumikizidwa kumapeto kwa chingwe chopingasa, umazunguliridwa mozungulira wozungulira wa mita imodzi ndipo liwiro lalikulu la mpirawo ndi 10 rpm. Kodi kukula kwa mpirawo ndi kotani? kuthamanga kwapakati ndi kukula kwa mphamvu ya kukangana?

Zodziwika:

Misa (m) = 0.2 kg

Ulalo wozungulira (r) = 1 m

Angular velocity (ω) = 10 rev/mphindi = 10 rev/60 s = 0.17 rev/s = (0.17) (6.28 rad)/s = 1 rad/s

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

Akufuna: a_s dani ΣF

Yankho:

(a) Kukula kwa kuthamanga kwa centripetal

(b) Kukula kwa mphamvu ya kukakamira

ΣF = ma

T = ma_s

T = (0.2 kg)(1 m/s²)

T = 0.2 kg m/s²

T = 0.2 N

2. Mpira wa 1 kg kumapeto kwa chingwe ukuzungulira mofanana mu bwalo lozungulira la radius 1 m. Chingwecho chidzasweka pamene mphamvu yake ikupitirira 100 N. Kodi liwiro lalikulu lomwe mpirawo ungakhale nalo ndi lotani?

Zodziwika:

Kulemera (m) = 1 kg

Ulalo wozungulira (r) = mita imodzi

Mphamvu ya kukankhidwa (T) = mphamvu yapakati (ΣF) = 100 N

SE basi: v pazipita

Yankho:

[wpdm_package id='499′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamalo opingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri okhala ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Galimoto yozungulira makona ozungulira. Kodi ngodya ya msewu womwe uli ndi makona ozungulira a mamita 60 ndi liwiro lopangidwa la 20 m/s ndi yotani? Tiyerekeze kuti palibe ayambitsenso pakati pa galimoto ndi msewu.

Anakonza

N= mphamvu yachibadwa

N tchimo θ = gawo lopingasa la mphamvu yachibadwa

N cos θ = gawo loyima la mphamvu yachibadwa

w = mg = ndi kulemera cha galimoto

Msewuwu wapangidwa kuti ukhale ndi magombe kuti uchepetse kudalira kukangana.

Mphamvu yopingasa yopingasa, gawo lopingasa la mphamvu yachibadwa (N tchimo θ), chofunika kuti galimoto iyende mozungulira mozungulira malo okhota.

Timasankha x-axis ngati yopingasa ndi y-axis ngati yoyima, kotero kuti kufulumira kwapakati,_R, ili motsatira njira yopingasa. Mu njira yopingasa, mphamvu yokhayo ndi gawo lopingasa la mphamvu yachibadwa (N tchimo θ), yofunikira kuti ipange kuthamanga kwapakatiN sin θ = mphamvu yapakati.

Gwiritsani ntchito lamulo la Newton la kuyenda molunjika mbali imodzi:

Gwiritsani ntchito lamulo la Newton la kuyenda molunjika mbali yopingasa:

Wosinthakuyika N mu equation 1 mu N mu equation 2 :

[wpdm_package id='497′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Galimoto yolemera makilogalamu 2000 imazungulira msewu wokhotakhota wa radius 150 m. Chiwerengero cha kukangana kosasinthasintha ndi 0.5. Dziwani liwiro lalikulu kwambiri kuti galimoto itsatire njira yokhota komanso kuti isagwedezeke. Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s².

Zodziwika:

Misa (m) = 2000 kg

Ulalo wozungulira (r) = mamita 150

Koyenera ya kukangana kosasinthasintha (μ_s= = 0.5

Kunenepa (w) = mg = (2000 kg)(10 m/s²) = 20,000 kg m/s² = 20,000 n

Mphamvu ya kukangana kosasinthasintha (F)_s) = μ_s N = μ_s w = (0.7)(20,000 N) = 14,000 N

Ankafuna: v

Yankho:

[wpdm_package id='496′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Misa ziwiri m₁ = 2 kg ndi m₂ = 5 kg ali pamtunda wopendekeka ndipo alumikizidwa pamodzi ndi chingwe monga momwe zasonyezedwera pachithunzichi. Coefficient ya kinetic friction pakati pa m₁ ndipo kutsika ndi 0.2 ndipo coefficient ya kukangana kwa kayendedwe ka kayendedwe kake pakati pa m₂ ndipo kutsika ndi 0.1.

(a) Dziwani zomwe zili mkati mwawo kuthamanga

(b) Dziwani mphamvu ya kukakamira

Zodziwika:

Misa 1 (m₁) = makilogalamu 2

Uzito 2 (m₂) = makilogalamu 4

Koyenera ya kukangana kwa kinetic pakati pa m₁ ndi ndege yopendekera (μ_k1) = 0.2

Koyenera ya kukangana kwa kinetic pakati pa m₂ ndi ndege yopendekera (μ_k2) = 0.1

Kuthamanga chifukwa cha mphamvu yokoka (g) = 9.8 m/s²

a) Kukula ndi komwe kumayambira kuthamanga kwa liwiro

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

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

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

N₁ = The mphamvu yachibadwa pa m₁ = w_1y = 17 Newton

F_k1 = Mphamvu ya kukangana kwa kinetic pa m₁ = μ_k1 N₁ = (0.2)(17 N) = 3.4 Newton

---

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

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

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

N₂ = Mphamvu yachibadwa pa m₂ = w_2y = 19.6 Newton

F_k2 = Mphamvu ya kukangana kwa kinetic pa m₂ = μ_k2 N₂ = (0.1)(19.6 N) = 1.96 Newton

---

Kukula kwa kuthamanga kwa magazi:

∑F_x = ma_x

w_2x > w_1x kotero njira yopititsira patsogolo ndi yofanana ndi njira ya w_2x.

Mphamvu zomwe zimayang'ana pa kuthamanga kwa magazi ndi zabwino ndipo mphamvu zomwe zili ndi mbali yosiyana ndi kuthamanga kwa magazi ndi zoipa.

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

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

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

18.94 N = (6 kg) a_x

a_x = 18.94 N : 6 kg

a_x = 3.16 m/s²

Kukula kwa kuthamanga = 3.16 m/s² . Kuwongolera kwa kuthamanga = njira ya T₁ = malangizo a w_2x

b) Kukula kwa mphamvu ya kukakamira

Gwiritsani ntchito lamulo lachiwiri la Newton pa chinthu 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 n

T₂ = 32.14 N – 12.64 N = 19.5 Newtons

Mphamvu ya kukakamira = T = T₁ = T₂ = 19.5 Newton

2. m₁ = 4 kg, m₂ = 2 kg. Dziwani (a) kukula ndi komwe kumayambira kuthamanga (b) Kukula kwa mphamvu yokakamiza yomwe imalumikiza m₁ ndi m₂ (c) kukula kwa mphamvu yolumikizira pulley ndi denga.

Anakonza

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) Kukula ndi komwe kumayambira kuthamanga kwa liwiro

∑F_y = ma_y

w₁ > w₂ kotero njira ya chinthucho ndi yofanana ndi njira ya kulemera 1 (w₁)Mphamvu zomwe zili ndi mbali yofanana ndi kuthamanga kwa magazi ndi zabwino ndipo mphamvu zomwe zili ndi mbali yosiyana ndi kuthamanga kwa magazi ndi zoipa.

w₁ - T₁ + T₂ - w₂ = (m₁ +m₂) ndi_y

w₁ - w₂ = (m₁ +m₂) ndi_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 = 3.26 m/s²

Kukula kwa kuthamanga = 3.26 m/s². Kuwongolera kwa kufulumira = njira ya w₁ .

b) Kukula kwa mphamvu ya kukakamira yomwe imalumikiza m₁ ndi m₂

Ikani Lamulo lachiwiri la Newton pa m₂ :

∑F_y = ma_y

w₁ - T₁ = m₁ a_y

39.2 N – T₁ = (4 kg)(3.26 m/s²)

39.2 N – T₁ = 13.04 n

T₁ = 39.2 N – 13.04 N

T₁ = 26.16 Newton

Kukula kwa mphamvu yolumikizira zinthu = T = T₁ = T₂ = 26.16 Newton

c) Kukula kwa mphamvu yolumikizira pulley ndi denga.

Pulley yapuma:

∑F_y = ma_y —— a_y = 0

∑F_y = 0

Mphamvu zakukwera ndi zabwino, mphamvu zakutsika ndi zoipa:

T₃ - T₁ - T₂ = 0

T₃ = T₁ + T₂

T₁ ndi T₂ ali ndi kukula kofanana, T₁ = T₂ = T = 26.16 N :

T₃ = 2T = 2(26.16 N) = 52.32 Newtons

3. Buloko 1 (m₁ = 10 kg) ndi chipika 2 (m₂ = 15 kg) yolumikizidwa ndi chingwe pamwamba pa pulley yopanda kukangana. Koefficient ya kukangana kosasinthasintha pakati pa block 2 yokhala ndi kupendekera = 0.6. Koefficient ya kukangana kwa kinetic pakati pa block 2 yokhala ndi kupendekera = 0.42. Dziwani (a) Kukula kwa mphamvu yocheperako F yomwe imagwiritsidwa ntchito pazinthuzo kotero kuti zinthuzo zifulumizitse kupita mmwamba (b) Dziwani kukula kwa mphamvu yokangana.

Anakonza

w₁ = Kulemera kwa chipika 1 = m₁ g = (10 kg)(9.8 m/s²) = 98 Newton

w₂ = Kulemera kwa chipika 2 = m₂ g = (15 kg)(9.8 m/s²) = 147 Newton

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

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

N₂ = Mphamvu yachibadwa pa chipika 2 = w_2y = 127.89 Newton

F_k2 = Mphamvu ya kukangana kwa kinetic pa block 2 = μ_k2 N₂ = (0.42)(127.89 N) = 53.7 Newton

F_s2 = Mphamvu ya kukangana kosasinthasintha pa chipika 2 = μ_s2 N₂ = (0.6)(127.89 N) = 76.7 Newton

a) Kukula kwa mphamvu yochepa kwambiri ya F yomwe imagwiritsidwa ntchito pazinthuzo kotero kuti zinthuzo zidakwera mofulumira

∑F_x = ma_x —— a_x = 0

∑F_x = 0

Mphamvu zakumtunda ndi zakumanja ndi zabwino, mphamvu zakutsika ndi zakumanzere ndi zoipa.

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) Kukula kwa mphamvu ya kukangana

Gwiritsani ntchito lamulo la Newton la kayendedwe pa block 1:

∑F_y = ma_y —— a_y = 0

∑F_y = 0

T₁ - w₁ = 0

T₁ = w₁ = 98 Newton

Gwiritsani ntchito lamulo la Newton la kayendedwe pa block 2:

F – F_k2 - w_2x - T₂ = 0

T₂ = F – F_k2 - w_2x

T₂ = 225.2 N – 53.7 N – 73.5 N

T₂ = 98 Newton

Kukula kwa mphamvu ya kukakamira = T₁ = T₂ = T = 98 Newton

4. Buloko 1 (m₁ = 16 kg) ili pamalo opingasa ndipo chipika 2 (m₂ = 12 kg) ili pamalo osalala, olumikizidwa ndi chingwe chomwe chimadutsa pa pulley yaying'ono, yopanda kukangana. Block 3 (m₃ = 5 kg) ili pa boloko 2. Chiwerengero cha kukangana kwa kinetic pakati pa boloko 2 ndi malo opingasa ndi 0,4. CoefChiyerekezo cha kukangana kosasinthasintha pakati pa chipika 2 ndi chipika 3 ndi 0,3.

(a) Pamene dongosololi latulutsidwa kuchokera pamalo opumulira, chipika 3 ndi chipika 2 zimangoyendabe pamodzi?

(b) Ngati pali chipika 3, kodi kuthamanga kwa chipika 1 ndi chipika 2 ndi kotani?

Yankho:

a) Pamene dongosololi latulutsidwa kuchokera pamalo opumulira, chipika 3 ndi chipika 2 zimangoyendabe pamodzi?

w₁ = The kulemera kwa chipikacho 1 = m₁ g = (16 kg)(9.8 m/s²) = 156.8 Newton

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

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

N₁ = The mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa block 1 ndi ndege yopendekera = w_1y = 78.4 Newton

w₃ = The kulemera kwa chipikacho 3 = m₃ g = (5 kg)(9.8 m/s²) = 49 Newton

N₂₃ = The mphamvu yachibadwa yogwiritsidwa ntchito pa chipika 3 ndi chipika 2 = w₃ = 49 Newton

N₃₂ = Nmphamvu yachibadwa yogwiritsidwa ntchito pa chipika chachiwiri ndi chipika chachitatu = N₂₃ = w₃ = 49 Newton

(N₂₃ ndi N₃₂ ndi mawiri a zochita ndi zochita)

F_s23 = The mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chipika 3 ndi chipika 2 = μ_s N₂₃ = (0.3)(49 N) = 14.7 Newton

F_s32 = The mphamvu ya kukangana kosasinthasintha komwe kumachitika pa block 2 ndi block 3 =F_s23 = 14.7 Newton

(F_s23 ndi F_s32 ndi mawiri a zochita ndi zochita)

w₂ = The kulemera kwa chipika 2 = m₂ g = (12 kg)(9.8 m/s²) = 117.6 Newton

N₂ = The mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chinthu 2 ndi malo opingasa = w₂ +N₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F_k2 = The mphamvu ya kukangana kwa kinetic pa block 2 = μ_k N₂ = (0.4)(166.6 N) = 66.64 Newton

Gwiritsani ntchito lamulo la Newton la kayendetsedwe ka zinthu pa bolodi 3:

∑F_x = ma_x

F_s23 =m₃ a_x

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

μ_s m₃ g = m₃ a_x

μ_s g = a_x

a_x = (0.3)(9.8 m/s²) = 2.94 m/s²

Kuthamanga kwakukulu kwa chipika 3 kotero kuti chipika 3 ndi chipika 2 zipitirire kutsetsereka pamodzi ndi 2.94 m/s².

Tsopano tikuwerengera kukula kwa kuthamanga kwa dongosololi pambuyo poti latulutsidwa kuchoka pamalo opumulira.

Kulunjika kwa kusuntha kwa block = komwe kumayenda mofulumira kwa block = komwe kumayenda kwa T₂ = njira ya w_1x.

∑F_x = ma_x

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

w_1x - F_k2 = (m₁ +m₂ +m₃ ) ndi_x

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

69.76 N = (33 kg) a_x

a_x = 2.11 m/s²

a_x ndi zabwino, zikutanthauza kuti njira yolowera kusuntha kwa block kapena njira yothamangira ndi yofanana ndi njira ya T₂ kapena malangizo a w_1x.

Kukula kwa kuthamanga kwa liwiro ndi 2.11 m / s² , lmphamvu kuposa 2.94 m / s² kotero tinganene kuti chipika 3 ndi chipika 2 zimangoyenda pamodzi zitatulutsidwa m'malo opumulira.

b) Kukula kwa kuthamanga kwa chipika 1 ndi chipika 2

∑F_x = ma_x

w_1x - F_k2 = (m₁ +m₂) ndi_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. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Chipolopolo cha makilogalamu awiri chili pamalo otsetsereka mopingasa pa ngodya 37^o kupita mopingasa. Dziwani kukula kwa mphamvu yakunja yomwe imagwiritsidwa ntchito pa chipikacho, kuti chipikacho chisagwedezeke pansi. (syn 37^o = 0.6, cos 37^o = 0.8, g = 10 ms^-2, µ_k = 0.2)

Zodziwika:

Misa (m) = 2 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Block's kulemera (w) = mg = (2)(10) = 20 Newtons

Tchimo 37^o = 0.6

kodi 37^o = 0.8

Koyefifiti ya kukangana kwa kayendedwe ka kayendedwe kake (µ_k= = 0.2

Gawo la y la kulemera (w)_y) = w 37^o = (20)(0.8) = 16 Newtons

Chigawo cha x cha kulemera (w_x) = w uchimo θ = (20)(tchimo 37) = (20)(0.6) = 12 Newtons

mphamvu yachibadwa (N) = w_y = 16 Newton

anafuna Mphamvu yakunja (F)

Anakonza :

w_x = 12 Newton

Mphamvu ya kukangana kwa kinetic (f)_k) = µ_k N = (0.1)(16) = 1.6 Newtons

Kukula kwa mphamvu yakunja ya F yomwe imagwiritsidwa ntchito pa block :

F + f_k - w_x = 0

F = w_x - f_k

F = 12 – 1.6

F = 10.4 Newton

Mphamvu yakunja ya F ndi yaikulu kuposa 10.4 Newtons.

2. Kulemera kwa chipika = 2 kg, coefficient of static friction µ_s = 0.4 ndi θ = 45^oDziwani kukula kwa mphamvu F kuti chipikacho chiyambe kutsetsereka mmwamba.

Zodziwika:

Chiwerengero cha kukangana kosasinthasintha (µ)_s= = 0.4

Ngodya (θ) = 45^o

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Kulemera kwa Block (m) = 2 kilogalamu

Kulemera kwa chipika (w) = mg = (2 kg)(10 m/s²) = 20 kg m/s² = 20 Newton

Chigawo cha x cha kulemera (w_x) = w tchimo θ = (20)(tchimo 45) = (20)(0.5√2) = 10√2 Newtons

Gawo la y la kulemera (w)_y) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newtons

anafuna : Kukula kwa mphamvu F

Yankho:

Block imayamba kutsetsereka, ngati F ≥ w_x + f_s.

Chigawo cha x cha kulemera:

w_x = 10√2 Newton

gawo la y la kulemera :

w_y = 10√2 Newton

Mphamvu yachibadwa :

N = w_y = 10√2 Newton

Mphamvu ya kukangana kosasinthasintha :

f_s = µ_s N = (0,4)(10√2) = 4√2

Kukula kwa mphamvu F kotero kuti chipikacho chimayamba kutsetsereka :

F ≥ w_x + f_s

F ≥ 10√2 + 4.2

F ≥ 14√2 Newton

[wpdm_package id='492′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

1. Bokosi la Unyinji 5 kg ili pa mtunda wopendekeka pa ngodya 30^oBokosilo limathandizidwa ndi chingwe. Dziwani mphamvu ya kukanikizana (T) ndi mphamvu yachibadwa (N)!

Anakonza

∑F_x = 0

T – w sin 30^o = 0

T = w sin 30^o

T = (5 kg)(9.8 m/s²) tchimo 30^o

T = (49)(0.5)

T = 24.5 Newtons

∑F_y = 0

N – w cos 30^o = 0

N = w cos 30^o

N = (49)(0.87)

N = 43 Newton

2. Zinthu ziwiri zolemera m₁ = m₂ = 2 kg, yolumikizidwa ndi chingwe chopanda unyinji pamwamba pa pulley yopanda kukangana. Pezani mphamvu yokakamiza T₁ ndi T₂.

Anakonza

(a) Chithunzi cha thupi lopanda kanthu pa chinthu 1 (b) Chithunzi cha thupi lopanda kanthu pa chinthu 2

Gwiritsani ntchito lamulo loyamba la Newton potsutsa 1:

∑F_y = 0

T₁ - w₁ = 0

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

Ikani Lamulo loyamba la Newton kutsutsa 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. Chinthu cha kulemera w_A = 30 N ndi chinthu cholemera w_B = 40 N, zimamangiriridwa ndi chingwe chopepuka chomwe chimadutsa pa pulley yopanda kukangana ya kulemera kochepa. Dziwani coefficient ya maximum kukangana kosasinthasintha pakati pa w_B ndi pamwamba popendekeka, ngati dongosololo lili pamalo opumulira.

Anakonza

(a) Chithunzi cha thupi lopanda kanthu cha chinthu w_A (b) Chithunzi cha thupi lopanda kanthu cha chinthu w_B

Gwiritsani ntchito lamulo loyamba la Newton potsutsa w_A molunjika (y):

∑F_y = 0 (palibe kuthamanga kolunjika molunjika)

T – w_A = 0

T = w_A = 30 Newton

Gwiritsani ntchito lamulo loyamba la Newton potsutsa w_B molunjika (y) :

∑F_y = 0

N – w_B 45^o = 0

N = w_B 45^o = (40)(0.7) = 28 Newtons

Gwiritsani ntchito lamulo loyamba la Newton potsutsa w_B molunjika (x):

∑F_x = 0

F_k +w_B tchimo 45^o -T = 0

μ_s N + w_B tchimo 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

Chokwanira cha kukangana kwakukulu kosasinthasintha pakati pa w_B ndi malo opendekera = 0.07.

[wpdm_package id='490′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

1. Pezani mphamvu ya kukakamira T₁, T₂, ndi T₃Osanyalanyaza chingwe Unyinji.

Anakonza

(a) Chithunzi cha thupi lopanda kanthu (b) Chithunzi cha thupi lopanda kanthu cha chingwe

Ikani Lamulo loyamba la Newton pa chinthucho:

ΣF_y = 0

T₁ – w = 0

T₁ = w = mg

T₁ = (5 kg)(9.8 m/s²)

T₁ = 49 kg m/s²

T₁ = 49 n

Gwiritsani ntchito lamulo loyamba la Newton pa chingwe:

∑F_x = 0

T_3x - T _2x = 0

T₃ 30^o - T₂ 40^o = 0

0.87 T₃ – 0.77 T₂ = 0

0.87 T₃ = 0.77 T₂

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

-

∑F_y = 0

T_3y + T_2y - T_1y = 0

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

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

Kulowa m'malo mwa T₂ mu equation 2 mu equation 2:

0.5 T₃ + 0.64 (1.1 T)₃) – 49 N = 0

0.5 T₃ + 0.70 T₃ - 49 = 0

1.2 T₃ - 49 = 0

1.2 T₃ = 49

T₃ = 49/1.2

T₃ = 41 n

---

T₂ = 1.1 T₃

T₂ = (1.1)(40.8 N)

T₂ = 45 n

[wpdm_package id='488′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

^{1. Misa ya chinthu, m = 10 kg, chothandizidwa ndi chingwe. Pezani mphamvu mu chingwe!} g = 10 m/s²

Zodziwika:

Kulemera (m) = 10 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Akufuna: Mphamvu ya kukakamira (T)

Yankho:

ΣF_y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s²) = 100 kg m/s²

T = 100 Newtons

2. Kulemera kwa chinthucho ndi 10 kg. Pezani mphamvu mu chingwe….. Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s².

Anakonza

Zodziwika:

Kulemera (m) = 10 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s².

Akufuna: Mphamvu ya kukakamira (T)

Yankho:

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

T₁ = mphamvu ya kukakamira 1

_T1x = gawo la x la mphamvu yokakamiza 1 = T₁ 45^o = 0.7 T₁

_T1y = gawo la y la mphamvu yokakamiza 2 = T₁ tchimo 45^o = 0.7 T₁

T₂ = mphamvu ya kukakamira 2

_T2x = gawo la x la mphamvu yokakamiza 2 = T₂ 45^o = 0.7 T₂

_T2y = gawo la y la mphamvu yokakamiza 2 = T₂ tchimo 45^o = 0.7 T₂

Mkhalidwe wa mgwirizano ΣF = 0.

mzere wa y:

ΣF_y = 0

T_1y + T_2y – w = 0

0.7T₁ + 0.7T₂ - 100 = 0

0.7T₁ + 0.7T₂ = 100 —– equation 1

mzere wa x:

ΣF_x = 0

T_2x - T_1x = 0

0.7T₂ – 0.7T₁ = 0

0.7T₂ = 0.7t₁

T₂ = T₁ —– equation 2

Dziwani kukula kwa T₁ :

0.7T₁ + 0.7T₁ = 100

1.4T₁ = 100

T₁ = 100/1.4

T₁ = 71.4 Newton

T₁ = T₂ kotero T₂ = 71.4 Newton

[wpdm_package id='486′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

1. Mabokosi awiri amalumikizidwa ndi chingwe chomwe chikuyenda pamwamba pa pulley. Musanyalanyaze kulemera kwa chingwe ndi pulley ndi kukangana kulikonse mu pulley. Misa ya bokosi 1 = 2 kg, kulemera kwa bokosi 2 = 3 kg, kuthamanga chifukwa cha mphamvu yokoka = 10 m/s². Pezani (a) Kuthamanga kwa dongosolo (b) Kukanika kwa chingwe!

Anakonza

Zodziwika:

Kulemera kwa bokosi 1 (m₁) = 2 kg

Kulemera kwa bokosi 2 (m₂) = 3 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Kunenepa ya bokosi 1 (w₁) = m₁ g = (2)(10) = 20 Newton

Kulemera kwa bokosi 2 (w)₂) = m₂ g = (3)(10) = 30 Newton

Yankho:

(a) kukula ndi njira ya kuthamanga kwa liwiro

w₂ > w₁ kotero bokosi lachiwiri limathamanga pansi ndipo bokosi loyamba limathamanga mmwamba.

Mphamvu zomwe zili ndi mbali imodzi ndi kuthamanga (w₂ ndi T₁), chizindikiro chake ndi chabwino. Mphamvu zomwe zili ndi mbali yosiyana ndi kuthamanga (T₂ ndi w₁), chizindikiro chake ndi choipa.

∑F = ma

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

w₂ – T + T – w₁ = (m₁ +m₂) ndi

w₂ - w₁ = (m₁ +m₂) ndi

30 – 20 = (2 + 3) a

10 = 5 a

a = 10 / 5

a = 2 m/s²

Kukula kwa kuthamanga ndi 2 m/s².

(b) Mphamvu ya kukakamira

Bokosi 2:

Pali mphamvu ziwiri zomwe zimachitika pa bokosi 2: choyamba, kulemera kwa bokosi 2 (w₂), imaloza pansi kotero kuti ndi yabwino. Chachiwiri, mphamvu yamphamvu yomwe ikugwiritsidwa ntchito pa bokosi 2 (T₂), imaloza mmwamba kotero kuti ndi yoipa. Ikani Lamulo lachiwiri la Newton za kuyenda.

∑F = ma

w₂ - T₂ = m₂ a

30 – T₂ = (3)(2)

30 – T₂ = 6

T₂ = 30-6

T₂ = 24 Newton

Bokosi 1:

Pali mphamvu ziwiri zomwe zimachitika pa bokosi 1. Choyamba, kulemera kwa bokosi 1 (w₁), imaloza pansi kotero kuti ndi yoipa. Chachiwirimphamvu ya kukanikizana yomwe imagwiritsidwa ntchito pa bokosi 1 (T₁) imaloza mmwamba kotero kuti ndi yabwino. Gwiritsani ntchito lamulo lachiwiri la Newton la kayendedwe:

∑F = ma

T₁ - w₁ = m₁ a

T₁ – 20 = (2)(2)

T₁ - 20 = 4

T₁ = 20 + 4

T₁ = 24 Newton

Kukula kwa mphamvu ya kukakamira = T₁ = T₂ = T = 24 Newton

2. Chinthu chomwe chili pamalo opingasa. Kulemera kwa chinthucho 1 = 2 kg, kulemera kwa chinthucho 2 = 4 kg, kuthamanga chifukwa cha mphamvu yokoka = 10 m/s², coefficient ya static friction = 0.4, coefficient ya kinetic friction = 0.3. Dongosolo lili pamalo opumira kapena lafulumira? Ngati dongosololi lafulumira, pezani kukula ndi komwe dongosololi lathamangira!

Anakonza

Zodziwika:

Kulemera kwa chinthu 1 (m₁) = 2 kg

Kulemera kwa chinthu 2 (m₂) = 4 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Koyefifiti ya kukangana kosasinthasintha (μ_s= = 0.4

Kuchuluka kwa kupsinjika kwa kinetic (μ_k) = 0.3

Kulemera kwa chinthu 1 (w)₁) = m₁ g = (2)(10) = 20 Newton

Kulemera kwa chinthu 2 (w)₂) = m₂ g = (4)(10) = 40 Newton

mphamvu yachibadwa yogwiritsidwa ntchito pa chinthu 1 (N) = w₁ = 20 Newton

Mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chinthu 1 (f)_s) = μ_s N = (0.4)(20) = 8 Newtons

Mphamvu ya kupsinjika kwa kinetic komwe kumachitika pa chinthu 1 (f)_k) = μ_k N = (0.3)(20) = 6 Newtons

SE basi: kufulumizitsa (a)

Yankho:

w₂ > f_s (40 Newton > 8 Newton) kotero chinthu 2 chimafulumizitsidwa molunjika pansi ndipo chinthu 1 chimafulumizitsidwa molunjika kumanja. Mphamvu yokangana yomwe imagwira ntchito pa zinthu 1 ndi mphamvu ya kukangana kwa kinetic (f)._kGwiritsani ntchito lamulo lachiwiri la Newton la kayendedwe:

∑F = ma

w₂ - pa = (m₁ +m₂) ndi

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s²

Kukula kwa kuthamanga = 5.7 m/s²

[wpdm_package id='484′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamalo opingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Munthu wolemera makilogalamu 50 mu elevator. Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s²Dziwani mphamvu yachibadwa choyikidwa pa chinthucho pafupi ndi elevator, ngati:

(a) elevator ili pamalo opumulira

(b) chikepicho chikutsika pansi pa liwiro losasintha

(c) chikepe chokwera mmwamba kuthamanga kosalekeza 5 /mphindi²

(d) chikepe chotsika mofulumira pa liwiro losasintha la 5 m/s²

(e) chikepi mu kugwa kwaulere

Anakonza

Zodziwika:

Za munthu Unyinji (m) = 50 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

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

SE basi: Mphamvu yachibadwa (N)

Yankho:

(a) elevator ili pamalo opumulira

Chikepe chili pamalo opumulirako kotero palibe kuthamanga (a = 0)

Timasankha njira yopita mmwamba m'njira yabwino ndi njira yopita pansi m'njira yoipa.

ΣF = ma

N – w = 0

N = w

N = 500 Newton

(b) chikepe chikuyenda pansi pa liwiro losasintha

Liwiro lokhazikika kotero palibe kufulumira (a = 0)

Timasankha njira yopita mmwamba m'njira yabwino ndi njira yopita pansi m'njira yoipa.

ΣF = ma

N – w = 0

N = w

N = 500 Newton

(c) chikepe chokwera mmwamba pa liwiro losasintha la 5 m/s²

Njira yopititsira patsogolo liwiro ndi yokwera, kotero timasankha njira yabwino ngati mmwamba.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Munthuyo amamva pansi likukwera mmwamba kwambiri kuposa pamene elevator ili pamalo amodzi kapena ikuyenda ndi liwiro losalekeza.

Ngati munthuyo aima pa sikelo, sikeloyo imawerenga kukula kwa mphamvu yotsika yomwe munthuyo ali pa sikeloyo amagwiritsa ntchito. Malinga ndi lamulo lachitatu la Newton, izi zikufanana ndi kukula kwa mphamvu yokwera yomwe munthuyo ali nayo pa sikeloyo.

(d) chikepe chotsika mofulumira pa liwiro losasintha la 5 m/s²

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 - 250

N = 250 Newton

Kulemera kwa munthuyo ndi 250 N, komwe ndi kochepa kuposa kulemera kwenikweni w = 500 N.

(e) chikepe mu kugwa kwaulere

Kugwa kwaulere kumatanthauza kuti kuthamanga kwa elevator kuli kofanana ndi kuthamanga chifukwa cha mphamvu yokoka. Kukula kwa kuthamanga chifukwa cha mphamvu yokoka ndi 9,8 m/s², njira yake ili pansi kupita pakati pa Dziko Lapansi. Liwiro limawonjezeka molunjika munthawi ndi 9,8 m/s pa sekondi iliyonse.

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 - 500

N = 0

2. Dziwani mphamvu ya chingwe cha elevator. Kulemera kwa elevator = 2000 kg.

(a) elevator ili pamalo opumulira

(b) elevator imatsika mofulumira pa liwiro losasintha la 5 m/s²

(c) Elevator imakwera mmwamba pa liwiro losasintha la 5 m/s²

(d) chikepe mu kugwa kwaulere

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Anakonza

Zodziwika:

Kulemera kwa elevator (m) = 2000 kg

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

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

Akufuna: Mphamvu ya kukakamira (T)

Yankho:

(a) elevator ili pamalo opumulira

chikepe ali pa mpumulo kotero palibe kuthamanga (a = 0)

Timasankha njira yopita mmwamba ngati njira yabwino ndi njira yopita pansi ngati njira yoipa.

ΣF = ma

T – w = 0

T = w

T = 20,000 Newtons

Kupsinjika kwa chingwe (T) = kulemera kwa elevator (w) = 20,000 Newtons

(b) chikepe chotsika mofulumira pa 5 m/s²

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 – 10,000

T = 10,000 Newtons

c) chikepe chokwera mmwamba pa liwiro losasintha la 5 m/s²

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati mmwamba.

T – w = ma

T = w + ma

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

T = 20,000 + 10,000

T = 30,000 Newtons

(d) chikepe mu kugwa kwaulere

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 – 20,000

T = 0

[wpdm_package id='482′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri ndi kuthamanga komweko pamalo opingasa ozungulira ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri