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

1. Zidutswa ziwiri m ₁ = 2 kg ndipo m _{2 = 5 kg} zili pamalo opendekera ndipo zalumikizidwa pamodzi ndi chingwe monga momwe zasonyezedwera pachithunzichi. Chiŵerengero cha chi _...

(a) Dziwani kufulumira kwawo

(b) Dziwani mphamvu ya kukakamira

Zodziwika:

Kulemera 1 (m ₁ ) = 2 kg

Kulemera 2 (m2 ₎ = 4 kg

Koefficient ya kinetic friction pakati pa m ₁ ndi plane yopendekeka (μ _k1 ) = 0.2

Koefficient ya kinetic friction pakati pa m2 _ndi plane yopendekeka (μ _k2 ) = 0.1

Kuthamanga chifukwa cha mphamvu yokoka (g) = 9.8 m/s ²

a) Kukula ndi komwe kumayambira kuthamanga kwa liwiro

w ₁ = kulemera 1 = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 Newtons

w _1x = w ₁ sin 30 ^o = (19.6 N)(0.5) = 9.8 Newtons

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

N ₁ = Mphamvu yachibadwa pa m ₁ = w _1y = 17 Newtons

F _k1 = Mphamvu ya kukangana kwa kinetic pa m ₁ = μ _k1 N ₁ = (0.2)(17 N) = 3.4 Newtons

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w ₂ = kulemera 2 = m ₂ g = (4 kg)(9.8 m/s ² ) = 39.2 Newtons

w _2x = w ₂ tchimo 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 = Mphamvu yachibadwa pa m ₂ = w _2y = 19.6 Newtons

F _k2 = Mphamvu ya kukangana kwa kinetic pa m ₂ = μ _k2 N ₂ = (0.1)(19.6 N) = 1.96 Newtons

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Kukula kwa kuthamanga kwa magazi:

∑ F _x = _max

w _2x > w _1x kotero njira yoyendetsera liwiro 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 = (m ₁ + m ₂ ) a _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/s ²

Kukula kwa kuthamanga = 3.16 m/s ^2. Kuwongolera kuthamanga = njira ya T ₁ = njira ya w _2x

b) Kukula kwa mphamvu ya kukakamira

Gwiritsani ntchito lamulo lachiwiri la Newton pa chinthu 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

T ₂ = 32.14 N – 12.64 N = 19.5 Newtons

Mphamvu ya kukakamira = T = T ₁ = T ₂ = 19.5 Newtons

[irp]

2. m ₁ = 4 kg, m ₂ = 2 kg. Dziwani (a) kukula ndi komwe kumayambira kuthamanga (b) Kukula kwa mphamvu yokakamiza yomwe imalumikiza m ₁ ndi m ₂ (c) kukula kwa mphamvu yokakamiza yomwe imalumikiza pulley ndi denga.

Anakonza

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

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

a) Kukula ndi komwe kumayambira kuthamanga kwa liwiro

∑ F _y = may _y

w ₁ > w ₂ kotero kuti njira ya chinthucho ndi yofanana ndi njira ya kulemera 1 ( w ₁ ) . Mphamvu zomwe zili ndi njira yofanana ndi njira yofulumira ndi zabwino ndipo mphamvu zomwe zili ndi njira yosiyana ndi njira yothamangira ndi zoipa.

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) a _y

a _y = 19.6 N : 6 kg

a _y = 3.26 m/s ²

Kukula kwa kuthamanga = 3.26 m/s ^2. Kuwongolera kuthamanga = kulunjika kwa w ₁.

b) Kukula kwa mphamvu ya kukakamira yomwe imagwirizanitsa m ₁ ndi m ₂

Gwiritsani ntchito lamulo lachiwiri la Newton pa _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

T ₁ = 39.2 N – 13.04 N

T ₁ = 26.16 Newton

Kukula kwa mphamvu yolumikizira zinthu = T = T ₁ = T ₂ = 26.16 Newtons

c) Kukula kwa mphamvu yolumikizira pulley ndi denga.

Pulley yapuma:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

Mphamvu zakukwera ndi zabwino, mphamvu zakutsika ndi zoipa:

T ₃ – T ₁ – T ₂ = 0

T3 = _T1 + _T2

T ₁ ndi T ₂ zili ndi kukula kofanana , T ₁ = T ₂ = T = 26.16 N:

T ₃ = 2T = 2(26.16 N) = 52.32 Newtons

[irp]

3. Block 1 (m ₁ = 10 kg) ndi block 2 (m ₂ = 15 kg) zolumikizidwa ndi chingwe pamwamba pa pulley yopanda kukangana. Coefficient ya kukangana kosasinthasintha pakati pa block 2 yokhala ndi kupendekera = 0.6. Coefficient ya kukangana kwa kinetic pakati pa block 2 yokhala ndi kupendekera = 0.42. Dziwani (a) Kukula kwa mphamvu yocheperako F yomwe imagwiritsidwa ntchito pazinthu kuti zinthuzo zifulumizitse kupita mmwamba (b) Dziwani kukula kwa mphamvu yokangana.

Anakonza

w ₁ = Kulemera kwa chipika 1 = m ₁ g = (10 kg)(9.8 m/s ² ) = 98 Newtons

w ₂ = Kulemera kwa chipika 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 Newtons

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

N ₂ = Mphamvu yachibadwa pa boloko 2 = w _2y = 127.89 Newtons

F _k2 = Mphamvu ya kukangana kwa kinetic pa block 2 = μ _k2 N ₂ = (0.42)(127.89 N) = 53.7 Newtons

F _s2 = Mphamvu ya kukangana kosasinthasintha pa chipika 2 = μ _s2 N ₂ = (0.6)(127.89 N) = 76.7 Newtons

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

∑ F _x = max _—— a _x = 0

∑ F _x = 0

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

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) Kukula kwa mphamvu ya kukangana

Gwiritsani ntchito lamulo la Newton la kayendedwe pa block 1:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = 98 Newton

Gwiritsani ntchito lamulo la Newton la kayendedwe pa block 2:

F – F _k2 – w _2x – T ₂ = 0

T ₂ = F – F _k2 – w _2x

T ₂ = 225.2 N – 53.7 N – 73.5 N

T ₂ = 98 Newton

Kukula kwa mphamvu ya kukakamira = T ₁ = T ₂ = T = 98 Newtons

[irp]

4. Block 1 (m ₁ = 16 kg) ili pamalo opingasa ndipo block 2 (m ₂ = 12 kg) ili pamalo osalala, olumikizidwa ndi chingwe chomwe chimadutsa pa pulley yaying'ono, yopanda kukangana. Block 3 (m ₃ = 5 kg) ili pa block 2. Coefficient ya kinetic friction pakati pa block 2 ndi malo opingasa ndi 0,4. Coefficient ya static friction pakati pa block 2 ndi block 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) Dongosolo likatulutsidwa kuchokera pamalo opumulira, chipika 3 ndi chipika 2 zimangoyendabe pamodzi?

w ₁ = Kulemera kwa chipika 1 = m ₁ g = (16 kg)(9.8 m/s ² ) = 156.8 Newtons

w _1x = w ₁ sin 60 ^o = (156.8 N)(0.87) = 136.4 Newtons

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

N ₁ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa block 1 ndi ndege yopendekera = w _1y = 78.4 Newtons

w ₃ = Kulemera kwa chipika 3 = m ₃ g = (5 kg)(9.8 m/s ² ) = 49 Newtons

N ₂₃ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chipika 3 ndi chipika 2 = w ₃ = 49 Newtons

N ₃₂ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chipika 2 pafupi ndi chipika 3 = N ₂₃ = w ₃ = 49 Newtons

(N ₂₃ ndi N ₃₂ ndi awiri a zochita-zochita )

F _s23 = Mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chipika 3 ndi chipika 2 = μ _s N ₂₃ = (0.3)(49 N) = 14.7 Newtons

F _s32 = Mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chipika chachiwiri ndi chipika chachitatu = F _{s 23} = 14.7 Newtons

(F _s23 ndi F _s32 ndi awiri a zochita-zochita )

w ₂ = Kulemera kwa chipika 2 = m ₂ g = (12 kg)(9.8 m/s ² ) = 117.6 Newtons

N ₂ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chinthu 2 ndi malo opingasa = w ₂ + N ₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F _k2 = Mphamvu ya kukangana kwa kinetic pa block 2 = μ _k N ₂ = (0.4)(166.6 N) = 66.64 Newtons

Gwiritsani ntchito lamulo la Newton la kayendetsedwe ka zinthu pa bolodi 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

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

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

Kulunjika kwa kusuntha kwa block = njira ya kufulumira kwa block = njira ya T ₂ = njira ya w _1x.

∑ F _x = _max

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

w _1x – F _k2 = (m ₁ + m ₂ + m ₃ ) a _x

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

69.76 N = (33 kg) a _x

a _x = 2.11 m/s ²

a _x ndi yabwino, kutanthauza kuti njira yolowera kusuntha kwa block kapena njira yolowera kufulumira ndi yofanana ndi njira ya T ₂ kapena njira ya w _1x.

Kukula kwa kuthamanga kwa mpweya ndi 2.11 m/s ² , kochepera 2.94 m/s ² kotero titha kunena kuti chipika 3 ndi chipika 2 zimangoyenda pamodzi zitatulutsidwa pamalo opumulira.

b) Kukula kwa kuthamanga kwa chipika 1 ndi chipika 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 = (16kg + 12kg) 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. 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