1. Laba cuf m 1 = 2 kg iyo m 2 = 5 kg ayaa ku yaal meel u janjeerta waxaana isku xira xarig sida ku cad sawirka. Isku-dhafka is-jiidjiidka ee u dhexeeya m 1 iyo u janjeera waa 0.2 isku-dhafka is-jiidjiidka ee u dhexeeya m 2 iyo u janjeera waa 0.1.
(a) Go'aaminta dardargelintooda
(b) Go'aaminta xoogga xiisadda
La yaqaan:
Cufnaanta 1 (m 1 ) = 2 kg
Cufnaanta 2 (m2 ) = 4 kg
Isku-darka is-jiidjiidka dhaqdhaqaaqa ee u dhexeeya m 1 iyo diyaaradda u janjeerta (μ k1 ) = 0.2
Isku-darka is-jiidjiidka dhaqdhaqaaqa ee u dhexeeya m 2 iyo diyaaradda u janjeerta (μ k2 ) = 0.1
Dardargelinta cufisjiidadka awgeed (g) = 9.8 m/s 2
a) Cabbirka iyo jihada dardargelinta
w 1 = miisaan 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 = Xoogga caadiga ah ee m 1 = w 1y = 17 Newtons
F k1 = Xoogga is-jiidjiidka m 1 = μ k1 N 1 = (0.2)(17 N) = 3.4 Newtons
---
w 2 = miisaan 2 = m 2 g = (4 kg)(9.8 m/s 2 ) = 39.2 Newtons
w 2x = w 2 dembi 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 = Xoogga caadiga ah ee m 2 = w 2y = 19.6 Newtons
F k2 = Xoogga is-jiidjiidka m 2 = μ k2 N 2 = (0.1)(19.6 N) = 1.96 Newtons
---
Baaxadda dardargelinta:
∑ F x = ma x
w 2x > w 1x markaa jihada dardargelinta waxay la mid tahay jihada w 2x.
Awoodaha tilmaamaya dardargelinta waa togan yihiin, xoogagga jihada ka soo horjeeda dardargelintana waa taban yihiin.
w2x - Fk2 - T2 +T1 - w1x - Fk1 = (m1 +m2) iyox
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 + 4 kg) a x
18.94 N = (6 kg) a x
a x = 18.94 N: 6 kg
a x = 3.16 m/s 2
Baaxadda dardargelinta = 3.16 m/s 2. Jihada dardargelinta = jihada T 1 = jihada w 2x
b) Baaxadda xoogga xiisadda
Ku dabaq sharciga labaad ee Newton shayga 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
Xoogga xiisadda = T = T 1 = T 2 = 19.5 Newtons
2. m 1 = 4 kg, m 2 = 2 kg. Go'aami (a) baaxadda iyo jihada dardargelinta (b) Cabbirka xoogga xiisadda ee isku xira m 1 iyo m 2 (c) baaxadda xoogga xiisadda ee isku xira pulley iyo saqafka.
Solution
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) Cabbirka iyo jihada dardargelinta
∑ F y = may y
w 1 > w 2 markaa jihada shaygu waa la mid tahay jihada miisaanka 1 ( w 1 ) . Xooggaga leh jihada la mid ah dardargelinta waa togan, xooggaga leh jihada lidka ku ah dardargelintana waa taban.
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
Baaxadda dardargelinta = 3.26 m/s 2. Jihada dardargelinta = jihada w 1.
b) Baaxadda xoogga xiisadda ee isku xira m 1 iyo m 2
Ku dabaq sharciga labaad ee Newton m 2 :
∑ 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
Weynaanta xoogga xiisadda ee isku xira walxaha = T = T 1 = T 2 = 26.16 Newtons
c) Cabbirka xoogga xiisadda ee isku xira roogga iyo saqafka.
Pulley wuu nastay:
∑ F y = may y —— a y = 0
∑ F y = 0
Ciidamada kor u kacaya waa togan yihiin, kuwa hoos u socdaana waa taban yihiin:
T 3 – T 1 – T 2 = 0
T3 = T1 + T2
T 1 iyo T 2 waxay leeyihiin isku cabbir , T 1 = T 2 = T = 26.16 N:
T 3 = 2T = 2(26.16 N) = 52.32 Newtons
3. Baloogga 1 (m 1 = 10 kg) iyo baloogga 2 (m 2 = 15 kg) oo ay ku xiran yihiin xarig ku dul yaal jiid aan is jiidjiid lahayn. Isku-xidhka is jiidjiidka taagan ee u dhexeeya baloogga 2 oo leh is jiidjiidka = 0.6. Isku-xidhka is jiidjiidka dhaqdhaqaaqa ee u dhexeeya baloogga 2 oo leh is jiidjiidka = 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
w 1 = Miisaanka baloogga 1 = m 1 g = (10 kg)(9.8 m/s 2 ) = 98 Newtons
w 2 = Miisaanka baloogga 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 dembi 30 o = (147 N) (0.5) = 73.5 Newtons
N 2 = Xoogga caadiga ah ee ku yaal baloogga 2 = w 2y = 127.89 Newtons
F k2 = Xoogga is-jiidjiidka ee baloogga 2 = μ k2 N 2 = (0.42)(127.89 N) = 53.7 Newtons
F s2 = Xoogga is-jiidjiid la'aanta ah ee baloogga 2 = μ s2 N 2 = (0.6)(127.89 N) = 76.7 Newtons
a) Baaxadda xoogga ugu yar ee F ee ku dhacay walxaha si walxaha ay kor ugu kacaan
∑ F x = max x —— a x = 0
∑ F 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 – 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) Baaxadda xoogga xiisadda
Ku dabaq sharciga mooshinka ee Newton baloogga 1aad:
∑ F y = may y —— a y = 0
∑ F y = 0
T 1 – w 1 = 0
T 1 = w 1 = 98 Newton
Ku dabaq sharciga mooshinka ee Newton baloogga 2aad:
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
Baaxadda xoogga xiisadda = T 1 = T 2 = T = 98 Newtons
4. Baloogga 1 (m 1 = 16 kg) wuxuu ku yaal meel siman oo siman, baloogga 2 (m 2 = 12 kg) wuxuu ku yaal 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. Isugeynta is jiidjiidka dhaqdhaqaaqa ee u dhexeeya baloogga 2 iyo dusha sare ee toosan waa 0,4. Isugeynta is jiidjiidka aan joogtada ahayn ee u dhexeeya baloogga 2 iyo baloogga 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?
w 1 = Miisaanka baloogga 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 = Xoogga caadiga ah ee ku shaqeeya baloogga 1 ee diyaaradda u janjeerta = w 1y = 78.4 Newtons
w 3 = Miisaanka baloogga 3 = m 3 g = (5 kg)(9.8 m/s 2 ) = 49 Newtons
N 23 = Xoogga caadiga ah ee ku shaqeeya baloogga 3 ee baloogga 2 = w 3 = 49 Newtons
N 32 = Xoogga caadiga ah ee ku shaqeeya baloogga 2 ee baloogga 3 = N 23 = w 3 = 49 Newtons
(N 23 iyo N 32 waa labo fal-celin ah )
F s23 = Xoogga is-jiidjiid la'aanta ah ee ku socota baloogga 3 ee baloogga 2 = μ s N 23 = (0.3)(49 N) = 14.7 Newtons
F s32 = Xoogga is-jiidjiid la'aanta ah ee ku socota baloogga 2aad ee baloogga 3 = F s 23 = 14.7 Newtons
(F s23 iyo F s32 waa lammaane fal-celin ah )
w 2 = Miisaanka baloogga 2 = m 2 g = (12 kg)(9.8 m/s 2 ) = 117.6 Newtons
N 2 = Xoogga caadiga ah ee ku shaqeeya shayga 2 ee dusha sare ee toosan = w 2 + N 32 = 117.6 Newtons + 49
Newton = 166.6 Newton
F k2 = Xoogga isjiidjiidka dhaqdhaqaaqa ee baloogga 2 = μ k N 2 = (0.4)(166.6 N) = 66.64 Newtons
Ku dabaq sharciga dhaqdhaqaaqa ee Newton baloogga 3aad:
∑ F x = ma x
F s23 = m 3 a x
—–> Fs23 = μs N23 = μs w3 = μs m3 g
μ s m 3 g = m 3 a x
μ s g = x
a x = (0.3)(9.8 m/s 2 ) = 2.94 m/s 2
Xawaaraha ugu badan ee baloogga 3 si baloogga 3 iyo baloogga 2 ay weli isku simbiriirixan yihiin waa 2.94 m/s 2.
Hadda waxaan xisaabineynaa baaxadda dardargelinta nidaamka ka dib marka laga sii daayo nasashada.
Jihada barokaca baloogga = jihada dardargelinta baloogga = jihada T 2 = jihada w 1x.
∑ F x = ma x
w1x - T1 +T2 - Fk2 - Fs32 +Fs23 = (m1 +m2 +m3) iyox
w 1x – F k2 = (m 1 + m 2 + m 3 ) a x
136.4 N - 66.64 N = (16 kg + 12 kg + 5 kg) a x
69.76 N = (33 kg) a x
a x = 2.11 m/s 2
x waa togan, taasoo la micno ah jihada barokaca baloogga ama jihada dardargelinta waa la mid tahay jihada T 2 ama jihada w 1x.
Baaxadda dardargelintu waa 2.11 m/s 2 , taasoo ka hooseysa 2.94 m/s 2 sidaa darteed waxaan ku soo gabagabeyn karnaa in baloogga 3 iyo baloogga 2 ay wali isku simbiriirixanayaan ka dib markii laga sii daayay nasashada.
b) Baaxadda dardargelinta baloogga 1aad iyo baloogga 2aad
∑ F x = ma x
w 1x – F k2 = (m 1 + m 2 ) a x
—–> Fk2 = μk N2 = μk w2 = μk 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/s 2
[wpdm_package id='493′]
- Cufka iyo miisaanka
- xoog caadi ah
- Sharciga labaad ee dhaqdhaqaaqa Newton
- Xoogga is-qabqabsiga
- Dhaqdhaqaaqa dusha sare ee jiifka ah iyada oo aan lahayn xoog is jiidjiid ah
- Dhaqdhaqaaqa laba jidh oo leh xawaare isku mid ah oo ku yaal dusha sare ee toosan ee qallafsan oo leh xoogga is-jiidjiidka
- Dhaqdhaqaaqa diyaaradda u janjeerta iyada oo aan lahayn xoog is jiidjiid ah
- Dhaqdhaqaaqa diyaaradda qallafsan ee u janjeerta oo leh xoogga is jiidjiidka
- Dhaqdhaqaaqa wiishka
- Dhaqdhaqaaqa jirka waxaa isku xira fiilooyin iyo boolal
- Laba jir oo leh xawaare isku mid ah
- Wareegidda qalooc fidsan - dhaqdhaqaaqa dhaqdhaqaaqa wareegsan
- Soo koobidda qalooca bangi - dhaqdhaqaaqa dhaqdhaqaaqa wareegsan
- Dhaqdhaqaaq siman oo goobo jiif ah
- Xoogga dhexe ee dhaqdhaqaaqa wareegsan ee isku midka ah
