Physics

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

La yaqaan:

Mass (m) = 0.2 kg

Gacanka (r) = 1 m

Xawaaraha codka (ω) = 10 rev/min = 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 doonayo: a_s dan ΣF

Xalka:

(a) Baaxadda dardargelinta bartamaha dhexe

(b) Baaxadda xoogga xiisadda

ΣF = ma

T = ma_s

T = (0.2 kg)(1 m/s²)

T = 0.2 kg m/s²

T = 0.2 N

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

Xoogga xiisadda (T) = xoogga centripetal (ΣF) = 100 N

SE buska: v ugu badnaan

Xalka:

[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 ee baabuurka

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), waxaa loo baahan yahay in gaariga lagu hayo wareeg 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:

Ku dabaq sharciga dhaqdhaqaaqa ee Newton jihada toosan:

Beddelting N ee isle'egta 1 ilaa N ee isle'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 gacan ah 150 m. khilaaf aan joogto ahayn waa 0.5. Go'aami xawaaraha ugu badan si gaarigu u raaco qalooca oo uusan u simbiriirixan. Dardargelinta cufjiidka awgeed = 10m/s².

La yaqaan:

Mass (m) = 2000 kg

Gacanka (r) = 150 mitir

Isku-darka is-jiidjiid aan joogto ahayn (μ_s= 0.5

Miisaanka (w) = mg = (2000 kg)(10 m/s²) = 20,000 kg m/s² = 20,000N

Xoogga is-jiidjiid aan joogto ahayn (F)_s) = μ_s N = μ_s w = (0.7)(20,000 N) = 14,000 N

La doonayo : v

Xalka:

[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 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

---

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

---

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

[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 qaloocan oo xagal 37 ah.^o ilaa jiifka. Go'aami baaxadda xoogga dibadda ee lagu sameeyay baloogga, si balooggu uusan hoos ugu simbiriirixan diyaaradda. (syn 37)^o = 0.6, cos 37^o = 0.8, g = 10 ms^-2, µ_k = 0.2)

La yaqaan:

Mass (m) = 2 kg

Dardargelinta cufjiidka awgeed (g) = 10 m/s²

Block-yada miisaanka (w) = mg = (2)(10) = 20 Newtons

Dembiga 37^o = 0.6

Lacagta 37^o = 0.8

Isku-dhafka is jiidjiid jiinis ah (µ)_k= 0.2

Qaybta y ee miisaanka (w)_y) = w cs 37^o = (20)(0.8) = 16 Newton

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

xoogga caadiga ah (N) = w_y = 16 Newton

rabay Xoogga dibadda (F)

Solution :

w_x = 12 Newton

Xoogga is-jiidjiidka dhaqdhaqaaqa (f)_k) = µ_k N = (0.1)(16) = 1.6 Newton

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.

2. Cufka baloogga = 2 kg, isku-darka is-jiidjiid aan joogto ahayn µ_s = 0.4 iyo θ = 45^oGo'aami baaxadda xoogga F si balooggu 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/s²

Cufka baloogga (m) = 2 kiilo garaam

Miisaanka baloogga (w) = mg = (2 kg)(10 m/s)²) = 20 kg m/s² = 20 Newton

Qaybta x ee miisaanka (w)_x) = w dembi 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

rabay 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 isku dhaca aan joogtada ahayn :

f_s = µ_s N = (0,4)(10√2) = 4√2

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

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 mass 5 kg ayaa saaran diyaarad u janjeerta xagal 30^oSanduuqa waxaa taageera xadhig. Go'aami xoogga xiisadda (T) iyo xoog caadi ah (N)!

Solution

ΣF_x = 0

T - w sin 30^o = 0

T = w sin 30^o

T = (5 kg)(9.8 m/s²) dembi 30^o

T = (49)(0.5)

T = 24.5 Newtons

ΣF_y = 0

N - w cos 30^o = 0

N = w cos 30^o

N = (49)(0.87)

N = 43 Newton

2. Laba shay oo cuf m ah₁ = m₂ = 2 kg, oo ay ku xiran tahay xarig aan tiro lahayn oo ku dul yaal boolal aan is jiidjiid lahayn. Soo hel xoogga xiisadda T₁ iyo T₂.

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:

ΣF_y = 0

T₁ - w₁ = 0

T₁ = w₁ = m₁ g = (2 kg)(9.8 m/s²) = 19.6 N

Codso Sharciga ugu horreeya ee Newton si loo diido 2:

ΣF_y = 0

T₂ - w₂ = 0

T₂ = w₂ = m₂ g = (2 kg)(9.8 m/s²) = 19.6 N

T₁ =T₂ = 19.6 N.

3. Shay ah miisaanka w_A = 30 N iyo shay miisaan leh w_B = 40 N, waxaa ku xiran xarig khafiif ah oo dul mara boolal aan is jiidjiid lahayn oo ah cufnaan aan la taaban karin. Go'aami isku-dhafka ugu badan khilaaf aan joogto ahayn inta u dhaxaysa w_B iyo dusha sare ee janjeedha, haddii nidaamku nasto.

Solution

(a) Jaantuska jirka ee xorta ah ee shayga w_A (b) Jaantuska jirka ee xorta ah ee shayga w_B

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

ΣF_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) :

ΣF_y = 0

N - w_B cs 45^o = 0

N = w_B cs 45^o = (40)(0.7) = 28 Newton

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

ΣF_x = 0

F_k +w_B aan lahayn 45^o – T = 0

μ_s N + w_B aan lahayn 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

Isku-darka is-jiidjiidka ugu badan ee u dhexeeya w_B iyo dusha sare ee janjeedhsan = 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 xoogga xiisadda T₁, T₂, iyo T₃Iska ilow fiilooyinka mass.

Solution

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

Codso Sharciga ugu horreeya ee Newton shayga:

ΣF_y = 0

T₁ – w = 0

T₁ = w = mg

T₁ = (5 kg) (9.8 m/s²)

T₁ = 49 kg m/s²

T₁ = 49N

Ku dabaq sharciga ugu horreeya ee Newton xadhigga:

ΣF_x = 0

T_3x - T _2x = 0

T₃ cs 30^o - T₂ cs 40^o = 0

0.87 T₃ - 0.77 T₂ = 0

0.87 T₃ = 0.77 T₂

T₂ = 0.87 T₃ / 0.77 = 1.1 T₃ ———- Isle'egta 1aad

-

ΣF_y = 0

T_3y +T_2y - T_1y = 0

T₃ aan lahayn 30^o +T₂ aan lahayn 40^o - T₁ = 0

0.5 T₃ + 0.64 T₂ – 49 N = 0 ———- Isle'egta 2

Beddelka T₂ isle'egta 2aad u gal isle'egta 2aad:

0.5 T₃ + 0.64 (1.1 T)₃) – 49 N = 0

0.5 T₃ + 0.70 T₃ - 49 = 0

1.2 T₃ - 49 = 0

1.2 T₃ = 49

T₃ = 49/1.2

T₃ = 41N

---

T₂ = 1.1 T₃

T₂ = (1.1)(40.8 N)

T₂ = 45N

[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. Mass shay, m = 10 kg, oo ay ku xiran tahay xarig. Soo hel xiisadda ku jirta xarigga!} g = 10 m/s²

La yaqaan:

Cufnaanta (m) = 10 kg

Dardargelinta cufjiidka awgeed (g) = 10 m/s²

La doonayo: Xoogga xiisadda (T)

Xalka:

ΣF_y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s²) = 100 kg m/s²

T = 100 Newtons

2. Cufka shaygu waa 10 kg. Soo hel xiisadda ku jirta xarigga….. Dardargelinta cufisjiidadka = 10 m/s².

Solution

La yaqaan:

Cufnaanta (m) = 10 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s².

La doonayo: Xoogga xiisadda (T)

Xalka:

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

T₁ = xoogga xiisadda 1

_T1x = qaybta x ee xoogga xiisadda 1 = T₁ cs 45^o = 0.7 T₁

_T1y = qaybta y ee xoogga xiisadda 2 = T₁ aan lahayn 45^o = 0.7 T₁

T₂ = xoogga xiisadda 2

_T2x = qaybta x ee xoogga xiisadda 2 = T₂ cs 45^o = 0.7 T₂

_T2y = qaybta y ee xoogga xiisadda 2 = T₂ aan lahayn 45^o = 0.7 T₂

Xaaladda dheelitirka ΣF = 0.

dhidibka y:

ΣF_y = 0

T_1y +T_2y – w = 0

0.7T₁ + 0.7T₂ - 100 = 0

0.7T₁ + 0.7T₂ = 100 —– isla'egta 1

x dhidibka:

ΣF_x = 0

T_2x - T_1x = 0

0.7T₂ – 0.7T₁ = 0

0.7T₂ = 0.7T₁

T₂ =T₁ —– isla'egta 2

Go'aami baaxadda T₁ :

0.7T₁ + 0.7T₁ = 100

1.4T₁ = 100

T₁ = 100/1.4

T₁ = 71.4 Newton

T₁ =T₂ sidaas T₂ = 71.4 Newton

[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 jir cufka xadhigga iyo boolal-gacmeedka iyo is-qabqabsiga ku jira boolal-gacmeedka. Mass sanduuqa 1 = 2 kg, miisaanka sanduuqa 2 = 3 kg, dardargelinta cuf-isjiidadka awgeed = 10m/s². 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/s²

Miisaanka sanduuqa 1aad (w)₁) = m₁ g = (2)(10) = 20 Newton

Miisaanka sanduuqa 2 (w₂) = m₂ g = (3)(10) = 30 Newton

Xalka:

(a) baaxadda iyo jihada dardargelinta

w₂ > w₁ sidaas ah sanduuqa 2aad ayaa hoos u degdegaya sanduuqa 1aadna kor ayuu u kacayaa.

Xoogagga leh jihada isku midka ah ee dardargelinta (w)₂ iyo T₁), calaamaddeedu waa togan. Awoodaha leh jihada lidka ku ah dardargelinta (T₂ iyo w₁), calaamaddeedu waa taban.

ΣF = ma

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

w₂ – T + T – w₁ = (m₁ +m₂) iyo

w₂ - w₁ = (m₁ +m₂) iyo

30 – 20 = (2 + 3) a

10 = 5 a

a = 10/5

a = 2 m/s²

Weynaanta dardargelinta waa 2 m/s².

(b) Xoogga xiisadda

Sanduuqa 2aad:

Waxaa jira laba fal oo xoog leh oo ku yaal sanduuqa 2: marka hore, miisaanka sanduuqa 2 (w₂), waxay tilmaamaysaa hoos si ay u noqoto mid togan. Marka labaad, xoogga xiisadda ayaa lagu sameeyay sanduuqa 2 (T)₂), waxay tilmaamaysaa kor si ay u noqoto mid taban. Ku dabaq Sharciga labaad ee Newton dhaqdhaqaaqa.

ΣF = ma

w₂ - T₂ = m₂ a

30–T₂ = (3)(2)

30–T₂ = 6

T₂ = 30 - 6

T₂ = 24 Newton

Sanduuqa 1aad:

Waxaa jira laba tallaabo oo ku saabsan qodobka 1aad. First, miisaanka sanduuqa 1 (w₁), waxay tilmaamaysaa hoos si ay u noqoto mid taban. labaad, xoogga xiisadda ee lagu sameeyay sanduuqa 1aad (T₁) waxay tilmaamaysaa kor si ay u noqoto mid togan. Ku dhaqan sharciga labaad ee dhaqdhaqaaqa Newton:

ΣF = ma

T₁ - w₁ = m₁ a

T₁ – 20 = (2)(2)

T₁ - 20 = 4

T₁ = 20 + 4

T₁ = 24 Newton

Baaxadda xoogga xiisadda = T₁ =T₂ = T = 24 Newton

2. Shay saaran dusha sare oo siman. Cufka shayga 1 = 2 kg, cufka shayga 2 = 4 kg, dardargelinta cufisjiidadka awgeed = 10 m/s², isku-dhafka is-goysyada taagan = 0.4, isku-dhafka is-goysyada kinetic = 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 (m)₁) = 2 kg

Cufka shayga 2 (m)₂) = 4 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s²

Isku-dhafka khilaaf aan joogto ahayn (μ_s= 0.4

Tirada isku-dhafka dhaqdhaqaaqa (μ_k) = 0.3

Miisaanka shayga 1 (w)₁) = m₁ g = (2)(10) = 20 Newton

Miisaanka shayga 2 (w)₂) = m₂ g = (4)(10) = 40 Newton

xoog caadi ah lagu sameeyay shayga 1 (N) = w₁ = 20 Newton

Xoogga is-jiidjiidka aan joogtada ahayn ee lagu sameeyay shayga 1 (f)_s) = μ_s N = (0.4)(20) = 8 Newton

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

SE buska: dardargelinta (a)

Xalka:

w₂ > f_s (40 Newton > 8 Newton) markaa shayga 2 si toosan ayaa loo dardargeliyaa hoos, shayga 1aadna si toosan ayaa loo dardargeliyaa dhanka midig. Xoogga isjiidjiid ee ku shaqeeya shayada 1 waa xoogga isjiid ..._k) Ku dhaqan sharciga labaad ee dhaqdhaqaaqa Newton:

ΣF = ma

w₂ - ka = (m₁ +m₂) iyo

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s²

Baaxadda xawaaraha = 5.7 m/s²

[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 cufjiidka awgeed = 10m/s²Go'aami xoog caadi ah wiishku ku sameeyay shayga, haddii:

(a) wiishku wuu nasanayaa

(b) wiishku wuxuu hoos ugu socdaa xawaare joogto ah

(c) wiishka oo kor u kacaya dardargelin joogto ah 5 / s²

(d) wiishka oo si xawli ah hoos ugu socda 5 m/s²

(e) wiishka ku jira free-dhaco

Solution

La yaqaan:

Qofka mass (m) = 50 kg

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s²

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

SE buska: 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.

ΣF = 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.

ΣF = ma

N – w = 0

N = w

N = 500 Newton

(c) wiishka oo si joogto ah kor ugu kacaya 5 m/s²

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 oo si xawli ah hoos ugu socda 5 m/s²

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 dhac xor ah macnaheedu waa dardargelinta wiishka waxay la mid tahay dardargelinta cufisjiidadka awgeed. Cabbirka dardargelinta ee cufisjiidadka awgeed waa 9,8 m/s², 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

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

(a) wiishku wuu nasanayaa

(B) wiishka ayaa hoos u degdegay isagoo si joogto ah u socda 5 m/s²

(C) Wiishku wuxuu kor u kacay isagoo si joogto ah u socda 5 m/s²

(d) wiishka xilliga dayrta xorta ah

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s²

Solution

La yaqaan:

Cufka wiishka (m) = 2000 kg

Dardargelinta cufisjiidadka (g) = 10 m/s²

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

La doonayo: Xoogga xiisadda (T)

Xalka:

(a) wiishku wuu nasanayaa

wiish way nasanaysaa markaa ma jirto dardargelin (a = 0)

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

ΣF = ma

T – w = 0

T = w

T = 20,000 Newtons

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

(b) wiishka oo si xawli ah hoos ugu socda 5 m/s²

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/s²

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