1. Cufka sanduuqa 1 waa 2 kg, cufka sanduuqa 2 waa 4 kg, dardargelinta cuf-isjiidadka waa 10 m/s 2 , cufnaanta xoogga F waa 40 Newtons. Isugeynta isjiidadka kinetic-ga ee u dhexeeya sanduuqa 1 iyo dabaqa waa 0.2 iyo isku-dhafka isjiidadka kinetic-ga ee u dhexeeya sanduuqa 2 iyo dabaqa waa 0.3. Soo hel (a) Cabbirka iyo jihada dardargelinta sanduuqa (b) Cabbirka xoogga uu sameeyo sanduuqa 1 ee sanduuqa 2 (F 12 ) iyo baaxadda xoogga uu sameeyo sanduuqa 2 ee sanduuqa 1 (F 21 ).

Solution

La yaqaan:
Cufka sanduuqa 1 (m1 ) = 2 kg
Cufka sanduuqa 2 (m2 ) = 4 kg
Dardargelinta cufisjiidadka (g) = 10 m/s 2 ,
Xoogga F = 40 Newton,
Isku-darka is-jiidjiidka ee u dhexeeya sanduuqa 1 iyo dabaqa ( μ k1 ) = 0.2
Isku-darka is-jiidjiidka ee u dhexeeya sanduuqa 2 iyo dabaqa ( μ k2 ) = 0.3
Miisaanka sanduuqa 1 (w 1 ) = m 1 g = (2) ( 10) = 20 Newtons
Miisaanka sanduuqa 2 (w 2 ) = m 2 g = (4)(10) = 40 Newtons
Xoogga caadiga ah ee lagu sameeyay sanduuqa 1 (N 1 ) = w 1 = 20 Newtons
Xoogga caadiga ah ee lagu sameeyay sanduuqa 2 (N 2 ) = w 2 = 40 Newtons
Xoogga is-jiidjiidka ee lagu sameeyay sanduuqa 1 (f k1 ) = ( μ k1 )(N 1 ) = (0.2)(20) = 4 Newtons
Xoogga is-jiidjiidka ee lagu sameeyay sanduuqa 2 (f k2 ) = ( μ k1 )(N 2 ) = (0.3)(40) = 12 Newtons
Xalka:
(a) Cabbirka iyo jihada xawaaraha sanduuqa
ΣF = ma
F – f k1 – f k2 = (m 1 + m 2 ) a
40 – 4 – 12 = (2 + 4) a
24 = 6 a
a = 24/6
a = 4 m/s 2
Jihada dardargelinta = jihada xoogga saafiga ah = dhanka midig.
(b) Cabbirka xoogga uu sameeyay sanduuqa 1 ee sanduuqa 2 (F 12 ) iyo baaxadda xoogga uu sameeyay sanduuqa 2 ee sanduuqa 1 (F 21 ).
Xisaabi baaxadda F 12 :
ΣF = ma
F 12 – f k2 = (m 2 ) a
F 12 – 12 = (4)(4)
F 12 – 12 = 16
F 12 = 16 + 12
F12 = 28 Newtons
F 12 iyo F 21 waa xoogag ficil iyo falgal ah oo ka shaqeeya walxaha kala duwan. F 12 iyo F 21 waxay leeyihiin isku cabbir iyo jiho ka soo horjeeda.
F 12 = 28 Newtons = F 21 = 28 Newtons.
2. Cufka sanduuqa 1 waa 2 kg, cufka sanduuqa 2 waa 4 kg, dardargelinta cuf-isjiidadka waa 10 m/s 2 , xoogga F waa 40 N. Isku-dhafka is-jiidadka ee u dhexeeya sanduuqa 1 iyo dabaqa waa 0.2 iyo isku-dhafka is-jiidadka ee u dhexeeya sanduuqa 2 iyo dabaqa waa 0.3. Go'aami (a) Cabbirka iyo jihada is-jiidadka (b) Xiisadda ku jirta xarigga isku xiraya sanduuqyada. Iska ilow cufka xarigga.

La yaqaan:
Cufka sanduuqa 1 (m1 ) = 2 kg
Cufka sanduuqa 2 (m2 ) = 4 kg
Dardargelinta cufisjiidadka (g) = 10 m/s 2 ,
Xoogga F = 40 Newton,
Isku-darka is-jiidjiidka ee u dhexeeya sanduuqa 1 iyo dabaqa waa 0.2 ( μ k1 ) = 0.2
Isku-darka is-jiidjiidka ee u dhexeeya sanduuqa 2 iyo dabaqa waa 0.2 ( μ k2 ) = 0.3
Miisaanka sanduuqa 1 (w 1 ) = m 1 g = (2)(10) = 20 Newtons
Miisaanka sanduuqa 2 (w 2 ) = m 2 g = (4)(10) = 40 Newtons
Xoogga caadiga ah ee lagu sameeyay sanduuqa 1 (N 1 ) = w 1 = 20 Newtons
Xoogga caadiga ah ee lagu sameeyay sanduuqa 2 (N 2 ) = w 2 = 40 Newtons
Xoogga is-jiidjiidka ee lagu sameeyay sanduuqa 1 (f k1 ) = ( μ k1 )(N 1 ) = (0.2)(20) = 4 Newtons
Xoogga is-jiidjiidka ee lagu sameeyay sanduuqa 2 (f k2 ) = ( μ k1 )(N 2 ) = (0.3)(40) = 12 Newtons
Xalka:
(a) baaxadda iyo jihada dardargelinta
ΣF = ma
F – f k1 – f k2 = (m 1 + m 2 ) a
40 – 4 – 12 = (2 + 4) a
24 = 6 a
a = 24/6
a = 4 m/s 2
Baaxadda dardargelintu waa 4 m/s 2 , jihada dardargelinta = jihada xoogga saafiga ah = dhanka midig.
(b) Xiisadda fiilada
Xoogagga ku shaqeeya sanduuqa 1 ee jihada toosan waa xiisadda 1 (T 1 ) dhanka midig iyo xoogga isjiidjiidka kinetic 1 (f k1 ) dhanka bidix. Ku dabaq sharciga labaad ee Newton:
ΣF = ma
T 1 – f k1 = m 1 a
T 1 – 4 = (2)(4)
T 1 – 4 = 8
T 1 = 8 + 4 = 12 Newton
Xoogagga ka shaqeeya sanduuqa 2 ee jihada toosan waa xiisadda 2 (T 2 ) dhanka bidix iyo xoogga is-jiidjiidka dhaqdhaqaaqa 2 (f k2 ) dhanka midig. Ku dabaq sharciga labaad ee Newton :
ΣF = ma
F – T 2 – f k2 = m 2 a
40 – T 2 – 12 = (4)(4)
28 – T 2 = 16
T 2 = 28 – 16 = 12 Newton
Xiisadda ku jirta xarigga isku xiraya sanduuqyada = T 1 = T 2 = T = 12 Newtons.
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