Dhibaatooyinka lagu xalliyay Fiisigiska Aasaasiga ah

1. Kubbad 0.2-kg ah, oo ku xiran dhammaadka xarig jiif ah, ayaa lagu wareejinayaa goobaabin 1 mitir ah, xawaaraha ugu badan ee kubbadduna waa 10 rpm. Waa maxay baaxadda dardargelinta dhexe iyo baaxadda xoogga xiisadda?

La yaqaan:

Cufnaanta (m) = 0.2 kg

Gacanka (r) = 1 m

Xawaaraha xagasha (ω) = 10 rev/daqiiqo = 10 rev/60 s = 0.17 rev/s = (0.17)(6.28 rad)/s = 1 rad/s

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

La rabay: a _s iyo Σ F

Xalka:

(a) Baaxadda dardargelinta bartamaha dhexe

(b) Baaxadda xoogga xiisadda

Σ F = ma

T = ma _s

T = (0.2 kg)(1 m/s ² )

T = 0.2 kg m/s ²

T = 0.2 N

[irp]

2. Kubbad 1-kg ah oo dhammaadka xarig ah ayaa si isku mid ah ugu wareegaysa goobaabin siman oo radius ah 1 m. Xadhiggu wuu jabayaa marka xiisadda ku jirta ay dhaafto 100 N. Waa maxay xawaaraha ugu badan ee kubbadu yeelan karto?

La yaqaan:

Cufnaanta (m) = 1 kg

Gacanka (r) = 1 mitir

Xoogaga kacsanaanta (T) = xooga dhexe ( Σ F) = 100 N

La doonayo: v ugu badnaan

Xalka:

[irp]

[wpdm_package id='499′]

1. Cufka iyo miisaanka
2. xoog caadi ah
3. Sharciga labaad ee dhaqdhaqaaqa Newton
4. Xoogga is-qabqabsiga
5. Dhaqdhaqaaq dusha sare oo siman 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 xoog is-jiidjiid ah
7. Dhaqdhaqaaq diyaarad janjeersan 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

Akhri wax dheeraad ah

1. Gaari ku wareegsan qalooc godan. Waa maxay xagal loogu talagalay waddada oo leh qalooc 60 mitir ah oo leh xawaare naqshadeed oo ah 20 m/s? Bal qiyaas inaysan jirin khilaaf inta u dhaxaysa gaariga iyo wadada.

Solution

N= xoog caadi ah

N sin θ = qayb jiif ah oo ka mid ah xoogga caadiga ah

N cos θ = qayb toosan oo ka mid ah xoogga caadiga ah

w = mg = miisaanka gaariga

Wadada waxaa loogu talagalay in lagu xiro si looga takhaluso ku tiirsanaanta is jiidjiidka.

Xoogga siman ee siman, qaybta toosan ee xoogga caadiga ah ( N sin θ) , ayaa looga baahan yahay si gaadhigu ugu socdo goobaabin ku wareegsan qalooca.

Waxaan u doorannaa dhidibka x sida toosan iyo dhidibka y sida toosan, si loo dedejiyo bartamaha, a_R, waxay ku socotaa jihada toosan. Jihada toosan, xoogga kaliya waa qaybta toosan ee xoogga caadiga ah (N sin θ), oo loo baahan yahay in la soo saaro dardargelinta bartamaha. N sin θ = xoogga centripetal.

Ku dabaq sharciga dhaqdhaqaaqa ee Newton jihada toosan:

[irp]

Ku dabaq sharciga dhaqdhaqaaqa ee Newton jihada toosan:

Ku beddel N ee isla'egta 1 N ee isla'egta 2 :

[wpdm_package id='497′]

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

Akhri wax dheeraad ah

1. Gaari 2000-kg ah ayaa ku wareegaya qalooc waddo siman oo radius ah 150 m. Isku-darka is-jiidjiidku waa 0.5. Go'aami xawaaraha ugu badan si gaarigu u raaco qalooca oo uusan u simbiriirixan. Dardargelinta cufisjiidadka awgeed = 10 m/s ².

La yaqaan:

Cufnaanta (m) = 2000 kg

Gacanka (r) = 150 mitir

Isku-darka is-jiidjiid aan joogto ahayn ( μs ₎ = 0.5

Miisaanka (w) = mg = (2000 kg)(10 m/s ² ) = 20,000 kg m/s ² = 20,000 N

Xoogga is jiid-jiidka taagan (F _s ) = μ _s N = μ _s w = (0.7) (20,000 N) = 14,000 N

La doonayo : v

Xalka:

[irp]

[wpdm_package id='496′]

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

Akhri wax dheeraad ah

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.

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

[irp]

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

[irp]

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

[irp]

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

—–> F_s23 = μ_s N₂₃ = μ_s w₃ = μ_s 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

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

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

—–> 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/s ²

[wpdm_package id='493′]

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

Akhri wax dheeraad ah

1. Baloog 2-kg ah ayaa ku yaal meel toosan oo u janjeerta xagal 37 ^{o ah} oo u jirta dhinaca toosan. Go'aami baaxadda xoogga dibadda ee lagu sameeyay baloogga, si balooggu uusan hoos ugu simbirixan diyaaradda. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µ _k = 0.2)

La yaqaan:

Cufnaanta (m) = 2 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

Miisaanka baloogga (w) = mg = (2)(10) = 20 Newtons

Dem 37 ^o = 0.6

Kos 37 ^o = 0.8

Isku-darka is -jiidjiidka dhaqdhaqaaqa (µ _k ) = 0.2

Qaybta y ee miisaanka (w _y ) = w cos 37 ^o = (20)(0.8) = 16 Newtons

Qaybta x ee miisaanka (w _x ) = w sin θ = (20)(dembi 37) = (20)(0.6) = 12 Newtons

xoogga caadiga ah (N) = w _y = 16 Newtons

La Doonayo : Xoogga dibadda (F)

Xalka :

w_x = 12 Newton

Xoogga is-jiidjiidka dhaqdhaqaaqa (f _k ) = µ _k N = (0.1)(16) = 1.6 Newtons

Baaxadda xoogga dibadda F ee ku dhacay baloogga :

F + f _k – w _x = 0

F = w _x – f _k

F = 12 – 1.6

F = 10.4 Newton

Xoogga dibadda F wuxuu ka weyn yahay 10.4 Newtons.

[irp]

2. Cufka baloogga = 2 kg, isku-darka is-jiidjiidka taagan µ _s = 0.4 iyo θ = 45 ^o . Go'aami baaxadda xoogga F si baloogga uu u bilaabo inuu kor u simbirixdo.

La yaqaan:

Isugeynta is-jiidjiidka aan joogtada ahayn (µ _s ) = 0.4

Xagasha (θ) = 45 ^o

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

Cufka baloogga (m) = 2 kiilo garaam

Miisaanka baloogga (w) = mg = (2 kg)(10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Qaybta x ee miisaanka (w _x ) = w sin θ = (20)(dembi 45) = (20)(0.5√2) = 10√2 Newtons

Qaybta y ee miisaanka (w _y ) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newtons

La Doonayo : Baaxadda xoogga F

Xalka:

Balooggu wuxuu bilaabaa inuu kor u simbirixdo, haddii F ≥ w_x + f_s.

Qaybta x ee miisaanka:

w _x = 10√2 Newton

qaybta y ee miisaanka :

w _y = 10√2 Newton

Xoogga caadiga ah :

N = w _y = 10√2 Newton

Xoogga is-jiidjiid la'aanta :

f _s = µ _s N = (0,4) (10√2) = 4√2

Baaxadda xoogga F si balooggu u bilaabo inuu kor u simbirixdo :

F ≥ w _x + f _s

F ≥ 10√2 + 4 √2

F ≥ 14√2 Newton

[wpdm_package id='492′]

1. Walxaha isku dheelitirka hal-cabbir ah
2. Walxaha dheelitirka laba-geesoodka ah
3. Sinnaanta jirka oo ay ku xiran yihiin xadhkaha iyo boolalku
4. Sinnaanta jirka ee diyaaradda u janjeerta

Akhri wax dheeraad ah

1. Sanduuq culeyskiisu yahay 5 kg ayaa saaran diyaarad u janjeerta xagal 30 ^{o ah} . Sanduuqa waxaa taageera xadhig. Go'aami xoogga xiisadda (T) iyo xoogga caadiga ah (N)!

Solution

ΣF_x = 0

T – w sin 30 ^o = 0

T = w sin 30 ^o

T = (5 kg)(9.8 m/s ² ) sin 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

[irp]

2. Laba shay oo cufnaantoodu tahay m ₁ = m ₂ = 2 kg, oo ay ku xiran yihiin xarig aan cufnayn oo dul saaran shaandho aan isqabsanayn. Soo hel xoogagga xiisadda T ₁ iyo T ₂.

Solution

(a) Jaantuska jirka ee xorta ah ee shayga 1 (b) Jaantuska jirka ee xorta ah ee shayga 2

Ku dabaq sharciga ugu horreeya ee Newton diidmada 1aad:

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 N

Ku dabaq sharciga ugu horreeya ee Newton diidmada 2:

∑ F _y = 0

T ₂ – w ₂ = 0

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

T ₁ = T ₂ = 19.6 N.

[irp]

3. Shay miisaan leh w _A = 30 N iyo shay miisaan leh w _B = 40 N, waxaa ku xiran xarig khafiif ah oo ka gudba shaandho aan is jiidjiid lahayn oo ah cuf aan la taaban karin. Go'aami isku-dhafka is jiidjiidka ugu badan ee u dhexeeya w _B iyo dusha sare ee janjeedha, haddii nidaamku nasto.

Solution

(a) Jaantuska jirka ee xorta ah ee walaxda w _A (b) Jaantuska jirka ee xorta ah ee walaxda w _B

Ku dabaq sharciga ugu horreeya ee Newton si aad u diiddo w _A jihada toosan (y):

∑ F _y = 0 (ma jiro dardargelin jihada toosan)

T – w _A = 0

T = w _A = 30 Newton

Ku dabaq sharciga ugu horreeya ee Newton si aad u diiddo w _B jihada toosan (y) :

∑ F _y = 0

N – w _B cos 45 ^o = 0

N = w _B cos 45 ^o = (40)(0.7) = 28 Newtons

Ku dabaq sharciga ugu horreeya ee Newton si aad u diiddo w _B jihada toosan (x):

∑ F _x = 0

F _k + w _B sin 45 ^o – T = 0

μ _s N + w _B dembi 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

Isugeynta is-jiidjiidka ugu badan ee u dhexeeya w _B iyo dusha sare ee janjeedha = 0.07.

[wpdm_package id='490′]

1. Walxaha isku dheelitirka hal-cabbir ah
2. Walxaha dheelitirka laba-geesoodka ah
3. Sinnaanta jirka oo ay ku xiran yihiin xadhkaha iyo boolalku
4. Sinnaanta jirka ee diyaaradda u janjeerta

Akhri wax dheeraad ah

1. Soo hel xoogagga xiisadda T ₁ , T ₂ , iyo T _{3. Iska ilow} cufka xarigga.

Solution

(a) Jaantuska jirka ee xorta ah ee walaxda (b) Jaantuska jirka ee xorta ah ee xadhigga

Ku dabaq sharciga ugu horreeya ee Newton ee shayga:

ΣF _y = 0

T ₁ – w = 0

T ₁ = w = mg

T ₁ = (5 kg)(9.8 m/s ² )

T ₁ = 49 kg m/s ²

T ₁ = 49 N

Ku dabaq sharciga ugu horreeya ee Newton xadhigga:

∑ F _x = 0

T _3x – T _2x = 0

T ₃ cos 30 ^o – T ₂ cos 40 ^o = 0

0.87 T ₃ – 0.77 T ₂ = 0

0.87 T ₃ = 0.77 T ₂

T ₂ = 0.87 T ₃ / 0.77 = 1.1 T ₃ ———- Isle'egta 1

[irp]

-

∑ F _y = 0

T _3y + T _2y – T _1y = 0

T ₃ dembi 30 ^o + T ₂ dembi 40 ^o – T ₁ = 0

0.5 T ₃ + 0.64 T ₂ – 49 N = 0 ———- Isle'egta 2

Ku beddelashada T ₂ ee isla'egta 2 iyo isle'egta 2:

0.5 T ₃ + 0.64 (1.1 T ₃ ) – 49 N = 0

0.5 T ₃ + 0.70 T ₃ – 49 = 0

1.2 T ₃ – 49 = 0

1.2 T ₃ = 49

T ₃ = 49 / 1.2

T ₃ = 41 N

---

T ₂ = 1.1 T ₃

T ₂ = (1.1)(40.8 N)

T ₂ = 45 N

[wpdm_package id='488′]

1. Walxaha isku dheelitirka hal-cabbir ah
2. Walxaha dheelitirka laba-geesoodka ah
3. Sinnaanta jirka oo ay ku xiran yihiin xadhkaha iyo boolalku
4. Sinnaanta jirka ee diyaaradda u janjeerta

Akhri wax dheeraad ah

^{1. Cufka shay, m = 10 kg, oo ay taageerto xadhig. Soo hel xiisadda ku jirta xadhigga!} g = 10 m/s ²

La yaqaan:

Cufnaanta (m) = 10 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

La Doonayo: Xoogga xiisadda (T)

Xalka:

ΣF _y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s ² ) = 100 kg m/s ²

T = 100 Newtons

[irp]

2. Cufka shaygu waa 10 kg. Soo hel xiisadda ku jirta xarigga….. Dardargelinta cufisjiidadka awgeed = 10 m/s ².

Solution

La yaqaan:

Cufnaanta (m) = 10 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ².

La Doonayo: Xoogga xiisadda (T)

Xalka:

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

T ₁ = xoogga xiisadda 1

_{T 1x} = qaybta x ee xoogga xiisadda 1 = T ₁ cos 45 ^o = 0.7 T ₁

_{T 1y} = qaybta y ee xoogga xiisadda 2 = T ₁ sin 45 ^o = 0.7 T ₁

T ₂ = xoogga xiisadda 2

_{T 2x} = qaybta x ee xoogga xiisadda 2 = T ₂ cos 45 ^o = 0.7 T ₂

_{T 2y} = qaybta y ee xoogga xiisadda 2 = T ₂ sin 45 ^o = 0.7 T ₂

Xaaladda dheelitirka ΣF = 0.

dhidibka y:

ΣF _y = 0

T _1y + T _2y – w = 0

0.7T ₁ + 0.7T ₂ – 100 = 0

0.7T ₁ + 0.7T ₂ = 100 —– isla'egta 1

x dhidibka:

ΣF _x = 0

T _2x – T _1x = 0

0.7T ₂ – 0.7T ₁ = 0

0.7T ₂ = 0.7T ₁

T ₂ = T ₁ —– isla'egta 2

Go'aami baaxadda T ₁ :

0.7T ₁ + 0.7T ₁ = 100

1.4T ₁ = 100

T ₁ = 100 / 1.4

T ₁ = 71.4 Newton

T ₁ = T ₂ sidaas darteed T ₂ = 71.4 Newtons

[wpdm_package id='486′]

1. Walxaha isku dheelitirka hal-cabbir ah
2. Walxaha dheelitirka laba-geesoodka ah
3. Sinnaanta jirka oo ay ku xiran yihiin xadhkaha iyo boolalku
4. Sinnaanta jirka ee diyaaradda u janjeerta

Akhri wax dheeraad ah

1. Laba sanduuq ayaa isku xira xadhig ku dul socda boolal. Iska ilow cufka xadhigga iyo boolal iyo wax kasta oo is jiidjiid ah oo ku jira boolal. Cufka sanduuqa 1 = 2 kg, cufka sanduuqa 2 = 3 kg, dardargelinta cufisjiidadka awgeed = 10 m/s ^2. Soo hel (a) Dardargelinta nidaamka (b) Xiisadda ku jirta xadhigga!

Solution

La yaqaan:

Cufka sanduuqa 1 (m1 ₎ = 2 kg

Cufka sanduuqa 2 (m2 ₎ = 3 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

Miisaanka sanduuqa 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Miisaanka sanduuqa 2 (w ₂ ) = m ₂ g = (3)(10) = 30 Newtons

Xalka:

(a) baaxadda iyo jihada dardargelinta

w ₂ > w ₁ markaa sanduuqa 2 wuxuu si degdeg ah hoos ugu socdaa sanduuqa 1aadna kor ayuu u socdaa.

Ciidamada leh jihada isku midka ah ee dardargelinta (w ₂ iyo T ₁ ), calaamadoodu waa togan. Ciidamada leh jihada lidka ku ah dardargelinta (T ₂ iyo w ₁ ), calaamadoodu waa taban.

∑ F = ma

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

w ₂ – T + T – w ₁ = (m ₁ + m ₂ ) a

w ₂ – w ₁ = (m ₁ + m ₂ ) a

30 – 20 = (2 + 3) a

10 = 5 a

a = 10/5

a = 2 m/s ²

Baaxadda xawaaraha waa 2 m/s ².

(b) Xoogga xiisadda

Sanduuqa 2aad:

Waxaa jira laba xoog oo ku yaal sanduuqa 2: marka hore, miisaanka sanduuqa 2 (w ₂ ), wuxuu tilmaamayaa hoos si uu u noqdo mid togan. Marka labaad, xoogga xiisadda ee lagu sameeyay sanduuqa 2 (T ₂ ), wuxuu tilmaamayaa kor si uu u noqdo mid taban. Ku dhaqan sharciga labaad ee dhaqdhaqaaqa ee Newton .

∑ F = ma

w ₂ – T ₂ = m ₂ a

30 – T ₂ = (3)(2)

30 – T ₂ = 6

T ₂ = 30 – 6

T ₂ = 24 Newton

Sanduuqa 1aad:

Waxaa jira laba xoog oo ku yaal sanduuqa 1. Marka hore , miisaanka sanduuqa 1 (w ₁ ), wuxuu tilmaamayaa hoos si uu u noqdo taban. Marka labaad , xoogga xiisadda ee lagu sameeyay sanduuqa 1 (T ₁ ) wuxuu tilmaamayaa kor si uu u noqdo togan. Ku dabaq sharciga labaad ee dhaqdhaqaaqa Newton:

∑ F = ma

T ₁ – w ₁ = m ₁ a

T ₁ – 20 = (2)(2)

T ₁ – 20 = 4

T ₁ = 20 + 4

T ₁ = 24 Newton

Baaxadda xoogga xiisadda = T ₁ = T ₂ = T = 24 Newtons

[irp]

2. Shay saaran dusha sare oo siman oo qallafsan. Cufka shayga 1 = 2 kg, cufka shayga 2 = 4 kg, dardargelinta cufisjiidadka awgeed = 10 m/s ² , isku-dhafka is-jiidjiidka taagan = 0.4, isku-dhafka is-jiidjiidka dhaqdhaqaaqa = 0.3. Nidaamku wuu nasanayaa mise waa la dedejinayaa? Haddii nidaamku la dedejinayo, raadi baaxadda iyo jihada dardargelinta nidaamka!

Solution

La yaqaan:

Cufka shayga 1 (m1 ₎ = 2 kg

Cufka shayga 2 (m2 ₎ = 4 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

Isugeynta is -jiidjiidka aan joogtada ahayn ( μs ₎ = 0.4

Isugeynta is-xoqidda dhaqdhaqaaqa ( μk ₎ = 0.3

Miisaanka shayga 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Miisaanka shayga 2 (w ₂ ) = m ₂ g = (4)(10) = 40 Newtons

Xoogga caadiga ah ee lagu sameeyay shayga 1 (N) = w ₁ = 20 Newtons

Xoogga is-jiidjiidka taagan ee lagu sameeyay shayga 1 (f _s ) = μ _s N = (0.4)(20) = 8 Newtons

Xoogga is-jiidjiidka ee lagu sameeyay shayga 1 (f _k ) = μ _k N = (0.3)(20) = 6 Newtons

La Doonayo: dardargelinta (a)

Xalka:

w ₂ > f _s (40 Newton > 8 Newton) markaa shayga 2 si toosan ayaa loo dardargeliyaa hoos, shayga 1na si toosan ayaa loo dardargeliyaa dhanka midig. Xoogga isjiidjiid ee ku shaqeeya walxaha 1 waa xoogga isjiidjiidjiidjiidjiid (f _k ). Ku dhaqan sharciga labaad ee dhaqdhaqaaqa Newton:

∑ F = ma

w ₂ – the = (m ₁ + m ₂ ) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s ²

Baaxadda xawaaraha = 5.7 m/s ²

[wpdm_package id='484′]

1. Cufka iyo miisaanka
2. xoog caadi ah
3. Sharciga labaad ee dhaqdhaqaaqa Newton
4. Xoogga is-qabqabsiga
5. Dhaqdhaqaaq dusha sare ee jiifa 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

Akhri wax dheeraad ah

1. Qof 50-kg ah oo ku jira wiish. Dardargelinta cufisjiidadka = 10 m/s ^2. Go'aami xoogga caadiga ah ee uu wiishku ku qaado shayga, haddii:

(a) wiishku wuu nasanayaa

(b) wiishku wuxuu hoos ugu socdaa xawaare joogto ah

(c) wiishka oo kor u kacaya xawaare joogto ah 5 / s ²

(d) wiishka ayaa hoos u degdegay isagoo si joogto ah u socda 5 m/s ²

(e) wiishka xilliga dayrta xorta ah

Solution

La yaqaan:

Culeyska qofka (m) = 50 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

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

La Doonayo: Xoogga caadiga ah (N)

Xalka:

(a) wiishku wuu nasanayaa

Wiishku wuu nasanayaa sidaa darteed ma jiro xawaareyn (a = 0)

Waxaan u doorannaa jihada kor u kaca jihada togan iyo jihada hoos u dhaca jihada taban.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(b) wiishku wuxuu hoos ugu socdaa xawaare joogto ah

Xawaaraha joogtada ah sidaa darteed ma jiro dardargelin (a = 0)

Waxaan u doorannaa jihada kor u kaca jihada togan iyo jihada hoos u dhaca jihada taban.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(c) wiishka oo kor u kacaya si joogto ah 5 m/s ²

Jihada dardargelintu waa kor, markaa waxaan u doorannaa jihada togan sida kor.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Qofku wuxuu dareemayaa in dabaqa uu si adag kor ugu riixayo marka loo eego marka wiishku uu taagan yahay ama uu si joogto ah u socdo.

Haddii qofku uu ku istaago miisaan, miisaanku wuxuu akhrinayaa baaxadda xoogga hoos u dhaca ee uu sameeyo qofka miisaanka ku jira. Sida ku cad sharciga saddexaad ee Newton, tani waxay la mid tahay baaxadda xoogga caadiga ah ee kor u kaca ee uu ku sameeyo miisaanku qofka.

(d) wiishka ayaa hoos u degdegay isagoo si joogto ah u socda 5 m/s ²

Jihada dardargelintu waa hoos, markaa waxaan u doorannaa jihada togan inay tahay hoos.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 – 250

N = 250 Newton

Miisaanka qofku waa 250 N, ka yar miisaanka dhabta ah w = 500 N.

(e) wiishka xilliga dayrta xorta ah

Hoos u dhaca xorta ah macnaheedu waa dardargelinta wiishka waxay la mid tahay dardargelinta ay sabab u tahay cufisjiidadka. Cabbirka dardargelinta ee ay sabab u tahay cufisjiidadka waa 9,8 m/s ² , jihada ay u socoto waxay hoos ugu socotaa bartamaha Dhulka. Xawaaruhu si toosan ayuu u kordhaa waqtiga 9,8 m/s ilbiriqsi kasta.

Jihada dardargelintu waa hoos, markaa waxaan u doorannaa jihada togan inay tahay hoos.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 – 500

N = 0

[irp]

2. Go'aami xiisadda fiilada wiishka. Cufka wiishka = 2000 kg.

(a) wiishku wuu nasanayaa

(b) wiishka oo si degdeg ah hoos ugu socda 5 m/s ²

(c) wiishka oo kor u kacaya si joogto ah 5 m/s ²

(d) wiishka xilliga dayrta xorta ah

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

Solution

La yaqaan:

Cufka wiishka (m) = 2000 kg

Dardargelinta cufisjiidadka (g) = 10 m/s ²

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

La Doonayo: Xoogga xiisadda (T)

Xalka:

(a) wiishku wuu nasanayaa

Wiishku wuu nasanayaa sidaa darteed ma jiro xawaareyn (a = 0)

Waxaan u doorannaa jihada kor u kaca jihada togan, jihada hoos u dhacana jihada taban.

Σ F = ma

T – w = 0

T = w

T = 20,000 Newtons

Xiisadda fiilada (T) = miisaanka wiishka (w) = 20,000 Newtons

(b) wiishka oo si degdeg ah hoos ugu socda 5 m/s ²

Jihada dardargelintu waa hoos, markaa waxaan u doorannaa jihada togan inay tahay hoos.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 – 10,000

T = 10,000 Newtons

c) wiishka oo si joogto ah kor ugu kacaya 5 m/s ²

Jihada dardargelintu waa hoos, markaa waxaan u doorannaa jihada togan kor.

T – w = ma

T = w + ma

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

T = 20,000 + 10,000

T = 30,000 Newtons

(d) wiishka xilliga dayrta xorta ah

Jihada dardargelintu waa hoos, markaa waxaan u doorannaa jihada togan inay tahay hoos.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 – 20,000

T = 0

[wpdm_package id='482′]

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 oo qallafsan oo leh xoog is jiidjiid ah
7. Dhaqdhaqaaq diyaarad u janjeera 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

Akhri wax dheeraad ah