Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga - Kugwiritsa ntchito mavuto ndi mayankho a lamulo la Newton la kuyenda

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