Laba hay'adood oo leh isla baaxadda dardargelinta - Adeegsiga sharciga Newton ee dhibaatooyinka dhaqdhaqaaqa iyo xalalka

1. Laba cuf m₁ = 2 kg iyo m₂ = 5 kg waxay ku jiraan meel u janjeerta waxaana isku xira xarig sida ku cad sawirka. Isku-dhafka is-jiidjiidka dhaqdhaqaaqa ee u dhexeeya m₁ iyo jilitaanka waa 0.2 iyo isku-dhafka is jiidjiid jiinis ah inta u dhaxaysa m₂ iyo jiirada waa 0.1.

(a) Go'aamintooda dardargelinta

(b) Go'aaminta xoogga xiisadda

La yaqaan:

Mass 1 (m₁) = 2kg

Cufnaanta 2 (m)₂) = 4kg

Isku-darka is-jiidjiidka dhaqdhaqaaqa ee u dhexeeya m₁ iyo diyaarad janjeerta (μ)_k1) = 0.2

Isku-darka is-jiidjiidka dhaqdhaqaaqa ee u dhexeeya m₂ iyo diyaarad u janjeerta (μ)_k2) = 0.1

Dardargelinta cufjiidka awgeed (g) = 9.8 m/s²

a) Cabbirka iyo jihada dardargelinta

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

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

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

N₁ = The xoog caadi ah on m₁ = w_1y = 17 Newton

F_k1 = Xoogga isjiidjiidka dhaqdhaqaaqa m₁ = μ_k1 N₁ = (0.2)(17 N) = 3.4 Newton

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

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

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

N₂ = Xoogga caadiga ah ee m₂ = w_2y = 19.6 Newton

F_k2 = Xoogga isjiidjiidka dhaqdhaqaaqa m₂ = μ_k2 N₂ = (0.1)(19.6 N) = 1.96 Newton

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Baaxadda dardargelinta:

ΣF_x = ma_x

w_2x > w_1x marka jihada dardargelintu waa la mid tahay jihada w_2x.

Awoodaha tilmaamaya dardargelinta waa togan yihiin, xoogagga jihada ka soo horjeeda dardargelintana waa taban yihiin.

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

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

Baaxadda xawaaraha = 3.16 m/s² Jihada dardargelinta = jihada T₁ = jihada w_2x

b) Baaxadda xoogga xiisadda

Ku dabaq sharciga labaad ee Newton shayga 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 = 12.64N

T₂ = 32.14 N – 12.64 N = 19.5 Newtons

Xoogga xiisadda = T = T₁ =T₂ = 19.5 Newton

2. m₁ = 4 kg, m₂ = 2 kg. Go'aami (a) baaxadda iyo jihada dardargelinta (b) Cabbirka xoogga xiisadda ee isku xira m₁ iyo m₂ (c) baaxadda xoogga xiisadda ee isku xira boolal iyo saqaf.

Solution

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) Cabbirka iyo jihada dardargelinta

ΣF_y = ma_y

w₁ > w₂ marka jihada shaygu waxay la mid tahay jihada miisaanka 1 (w₁)Awoodaha leh jihada la mid ah xawaaraha waa togan yihiin, xoogagga leh jihada lidka ku ah xawaarahana waa taban yihiin.

w₁ - T₁ +T₂ - w₂ = (m₁ +m₂) iyo_y

w₁ - w₂ = (m₁ +m₂) iyo_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

Cabbirka xawaaraha = 3.26 m/s²Jihada dardargelinta = jihada w₁ .

b) Cabbirka xoogga xiisadda ee isku xira m₁ iyo m₂

Codso Sharciga labaad ee Newton on m₂ :

ΣF_y = ma_y

w₁ - T₁ = m₁ a_y

39.2 N – T₁ = (4 kg)( 3.26 m/s²)

39.2 N – T₁ = 13.04N

T₁ = 39.2 N – 13.04 N

T₁ = 26.16 Newton

Baaxadda xoogga xiisadda ee isku xira walxaha = T = T₁ =T₂ = 26.16 Newton

c) Cabbirka xoogga xiisadda ee isku xira roogga iyo saqafka.

Pulley wuu nastay:

ΣF_y = ma_y —— a_y = 0

ΣF_y = 0

Ciidamada kor u kacaya waa togan yihiin, kuwa hoos u socdaana waa taban yihiin:

T₃ - T₁ - T₂ = 0

T₃ =T₁ +T₂

T₁ iyo T₂ waxay leeyihiin isla baaxaddaas, T₁ =T₂ = T = 26.16 N:

T₃ = 2T = 2(26.16 N) = 52.32 Newtons

3. Baloogga 1 (m₁ = 10 kg) iyo baloogga 2 (m₂ = 15 kg) oo ay ku xiran tahay xadhig ka sarreeya shabaq aan is jiidjiid lahayn. Isku-xidhka is jiidjiidka taagan ee u dhexeeya baloogga 2 oo leh is jiidjiid = 0.6. Isu-xidhka is jiidjiidka dhaqdhaqaaqa ee u dhexeeya baloogga 2 oo leh is jiidjiid = 0.42. Go'aami (a) Cabbirka xoogga ugu yar ee F ee ku shaqeeya walxaha si walxaha kor loogu kiciyo (b) Go'aami baaxadda xoogga xiisadda.

Solution

w₁ = Miisaanka baloogga 1 = m₁ g = (10 kg)(9.8 m/s²) = 98 Newton

w₂ = Miisaanka baloogga 2 = m₂ g = (15 kg)(9.8 m/s²) = 147 Newton

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

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

N₂ = Xoogga caadiga ah ee ku yaal baloogga 2 = w_2y = 127.89 Newton

F_k2 = Xoogga is-jiidjiidka ee baloogga 2 = μ_k2 N₂ = (0.42)(127.89 N) = 53.7 Newton

F_s2 = Xoogga is-jiidjiid la'aanta taagan ee baloogga 2 = μ_s2 N₂ = (0.6)(127.89 N) = 76.7 Newton

a) Baaxadda xoogga ugu yar ee F ee ku dhacay walxaha si walxaha ay kor ugu kacaan

ΣF_x = ma_x —— a_x = 0

ΣF_x = 0

Ciidamada kor u socda iyo kuwa midig u socda waa kuwo togan, ciidamada hoos u socda iyo kuwa bidix u socda waa kuwo taban.

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) Baaxadda xoogga xiisadda

Ku dabaq sharciga mooshinka ee Newton baloogga 1aad:

ΣF_y = ma_y —— a_y = 0

ΣF_y = 0

T₁ - w₁ = 0

T₁ = w₁ = 98 Newton

Ku dabaq sharciga mooshinka ee Newton baloogga 2aad:

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

Baaxadda xoogga xiisadda = T₁ =T₂ = T = 98 Newton

4. Baloogga 1 (m₁ = 16 kg) waxay ku taal dusha sare ee siman iyo baloogga 2 (m)₂ = 12 kg) waxay ku taal meel siman oo u janjeerta, oo ay ku xiran tahay xarig ka gudbaya boolal yar oo aan is jiidjiid lahayn. Baloogga 3 (m)₃ = 5 kg) wuxuu ku yaal baloogga 2. Isku-dhafka is-jiidjiidka ee u dhexeeya baloogga 2 iyo dusha sare ee toosan waa 0,4. CoefQodobka ugu muhiimsan ee is-jiidjiidka aan joogtada ahayn ee u dhexeeya block 2 iyo block 3 waa 0,3.

(A) Marka nidaamka laga sii daayo nasashada, baloogga 3aad iyo baloogga 2aad wali way isku simbiriirixanayaan?

(B) Haddii uu jiro baloog 3, waa maxay dardargelinta baloogga 1aad iyo baloogga 2aad?

Xalka:

a) Marka nidaamka laga sii daayo nasashada, baloogga 3aad iyo baloogga 2aad wali way isku simbiriirixanayaan?

w₁ = The miisaanka baloogga 1 = m₁ g = (16 kg)(9.8 m/s²) = 156.8 Newton

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

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

N₁ = The xoog caadi ah oo ku socda baloogga 1aad ee diyaaradda janjeedhsan = w_1y = 78.4 Newton

w₃ = The miisaanka baloogga 3 = m₃ g = (5 kg)(9.8 m/s²) = 49 Newton

N₂₃ = The xoog caadi ah oo ku socda baloogga 3 ee baloogga 2 = w₃ = 49 Newton

N₃₂ = nxoog caadi ah oo lagu sameeyay baloogga 2 ee baloogga 3 = N₂₃ = w₃ = 49 Newton

(N₂₃ iyo N₃₂ waa lammaane fal-celin ah)

F_s23 = The xoogga is-jiidjiidka taagan ee ku dhacay baloogga 3 ee baloogga 2 = μ_s N₂₃ = (0.3)(49 N) = 14.7 Newton

F_s32 = The xoogga is-jiidjiidka taagan ee ku dhacay baloogga 2aad ee baloogga 3aad =F_s23 = 14.7 Newton

(F_s23 iyo F_s32 waa lammaane fal-celin ah)

w₂ = The miisaanka baloogga 2 = m₂ g = (12 kg)(9.8 m/s²) = 117.6 Newton

N₂ = The xoog caadi ah oo ku dul sabbaynaya shayga 2 ee dusha sare ee toosan = w₂ + N₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F_k2 = The xoogga is-jiidjiidka ee baloogga 2 = μ_k N₂ = (0.4)(166.6 N) = 66.64 Newton

Ku dabaq sharciga dhaqdhaqaaqa ee Newton baloogga 3aad:

ΣF_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

Xawaaraha ugu badan ee baloogga 3 si baloogga 3 iyo baloogga 2 ay weli isku simbiriirixan yihiin waa 2.94 m/s².

Hadda waxaan xisaabineynaa baaxadda dardargelinta nidaamka ka dib marka laga sii daayo nasashada.

Jihada barokaca baloogga = jihada dardargelinta baloogga = jihada T₂ = jihada w_1x.

ΣF_x = ma_x

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

w_1x - F_k2 = (m₁ +m₂ +m₃ ) iyo_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 waa togan, macnaheedu waa jihada barokaca baloogga ama jihada dardargelinta waxay la mid tahay jihada T₂ ama jihada w_1x.

Baaxadda dardargelintu waa 2.11 m / s² , lka badan deynta 2.94 m / s² markaa waxaan ku soo gabagabeyn karnaa in baloogga 3aad iyo baloogga 2aad ay wali isku simbiriirixanayaan ka dib markii laga sii daayay nasashada.

b) Baaxadda dardargelinta baloogga 1aad iyo baloogga 2aad

ΣF_x = ma_x

w_1x - F_k2 = (m₁ +m₂) iyo_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

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1. Cufka iyo miisaanka
2. xoog caadi ah
3. Sharciga labaad ee dhaqdhaqaaqa Newton
4. Xoogga is-qabqabsiga
5. Dhaqdhaqaaqa dusha sare ee jiifka ah iyada oo aan lahayn xoog is jiidjiid ah
6. Dhaqdhaqaaqa laba jidh oo leh xawaare isku mid ah oo ku yaal dusha sare ee toosan ee qallafsan oo leh xoogga is-jiidjiidka
7. Dhaqdhaqaaqa diyaaradda u janjeerta iyada oo aan lahayn xoog is jiidjiid ah
8. Dhaqdhaqaaqa diyaaradda qallafsan ee u janjeerta oo leh xoogga is jiidjiidka
9. Dhaqdhaqaaqa wiishka
10. Dhaqdhaqaaqa jirka waxaa isku xira fiilooyin iyo boolal
11. Laba jir oo leh xawaare isku mid ah
12. Wareegidda qalooc fidsan - dhaqdhaqaaqa dhaqdhaqaaqa wareegsan
13. Soo koobidda qalooca bangi - dhaqdhaqaaqa dhaqdhaqaaqa wareegsan
14. Dhaqdhaqaaq siman oo goobo jiif ah
15. Xoogga dhexe ee dhaqdhaqaaqa wareegsan ee isku midka ah