10 Dynamics Object da aka haɗa ta hanyar igiya akan injin Atwood - Matsaloli da Magani
1. Toshe A mai nauyin kilogiram 5, an sanya shi a kan jirgin sama mai santsi a kwance. Toshe B mai nauyin kilogiram 3 a rataye a ƙarshen igiyar da aka haɗa da toshe A a kan injin jan ƙarfe. Saurin gudu saboda nauyi shine 10 m/s 2. Menene saurin gudu na toshe biyu?
An sani:
Nauyin toshe A (m)A) = 5 kg
Nauyin tubalin B (m B ) = 3 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin toshe B (w B ) = m B g = (3)(10) = Newtons 30
Ana nema: Haɓaka tubalan biyu (a)
Magani:
Jirgin kwance yana da santsi don haka babu ƙarfin gogayya. Ƙarfin da ke hanzarta tubalan biyu shine nauyin tubalan B.
ΣF = ma
w B = (m A + m B ) a
30 = (5 + 3) a
30 = 8 a
a = 30/8
a = 3.75 m/s 2
2.
Dangane da hoton da ke sama, 
(1) hanzarta abu = 0
(2) abin yana motsawa a daidai lokacin gudu
(3) abu a hutawa
(4) abin yana motsawa idan nauyin abin ya fi ƙanƙanta fiye da ƙarfin da ke jan abin.
Magani:
(1) Hanzarta abu = 0.
Ƙarfin da aka samu:
∑ F = ma –> hanzari (a) = 0
∑ F = 0
F 1 + F 2 – F 3 = 12 + 24 – 36 = 36 – 36 = 0 N
(2) Abu yana motsawa a daidai gudun da ba ya canzawa
Babu hanzari yana nufin abu a hutawa ko motsi a cikin saurin da ba ya canzawa.
(3) abu a hutawa
Babu ƙarfin da ke sama yana nufin abu a lokacin hutawa.
(4) abin yana motsawa idan nauyin abin ya fi ƙanƙanta fiye da ƙarfin da ke jan abin.
Nauyi yana aiki ne a kan alkiblar tsaye, yayin da ƙarfin ja ke aiki a kan alkiblar kwance.
Abu yana motsawa a kwance don haka ƙarfin kwance ne kawai ke aiki akan abu
3. Idan ma'aunin gogayya tsakanin toshe A da saman teburi shine 0.1. Saurin da aka samu sakamakon nauyi shine 10 m/s2, to menene ƙarfin da ke aiki akan toshe A don haka tsarin ya koma hagu a cikin 2 m/s 2.
An sani:
Nauyin toshe A (m)A) = 30 kg
Nauyin tubalin A (w A ) = (30 kg)(10 m/s 2 ) = 300 kg m/s 2 ko 300 Newtons
Nauyin tubalin B (m B ) = 20 kg
Nauyin tubalin B (w B ) = (20 kg)(10 m/s 2 ) = 200 kg m/s 2 ko 200 Newtons
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ma'aunin gogayya ta motsi ( μk ) = 0.1
Haɓaka tsarin (a) = 2 m/s 2 (zuwa hagu)
Ƙarfin gogayya ta motsi (f k ) = μ k N = μ k w A = (0.1)(300) = 30 Newtons
Ana so: Girman ƙarfin F
Magani:
Dokar Newton ta biyu:
ΣF = ma
Abu A yana motsawa zuwa hagu:
F – f k – w B = (m A + m B ) a
F – 30 – 200 = (30 + 20)(2)
F – 230 = (50)(2)
F – 230 = 100
F = 230 + 100
F = 330 Newton
4. Abubuwa biyu, A = 2 kg da B = 6 kg, an haɗa su a ƙarshen igiya ɗaya a kan wani abin jan ƙarfe, kamar yadda aka nuna a cikin hoton da ke ƙasa. Idan hanzarin da aka samu saboda nauyi shine 10 ms -2 to menene hanzarin abu B.
An sani:
Nauyin abu A (m)A) = 2 kg, mB = 6 kg, g = 10 m/s2
nauyin abu A (w A ) = (m A )(g) = (2)(10) = 20 N
nauyin abu B (w B ) = (m B )(g) = (6)(10) = 60 N
Ana so: Haɓaka abu b (haɓaka tsarin).
Magani:
w B > w A don haka wannan abu B yana motsawa ƙasa, abu A yana motsawa sama
ΣF = ma
w B – w A = (m A + m B ) a
60 – 20 = (2 + 6) a
40 = (8) a
a = 5 m/s 2
5. Abubuwa biyu da aka haɗa ta hanyar igiya a kan wani santsi mai laushi, kamar yadda aka nuna a cikin hoton da ke ƙasa. Idan m 1 = 1 kg, m 2 = 2 kg, kuma hanzarin da aka samu saboda nauyi shine 10 ms -2 , to menene ƙarfin tashin hankali T.
An sani:
Nauyin abu 1 (m1) = 1 kg
Nauyin abu 2 (m2 ) = 2 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin abu 1 (w 1 ) = m 1 g = (1 kg)(10 m/s 2 ) = 10 kg m/s 2 ko 10 Newtons
Nauyin abu 2 (w 2 ) = m 2 g = (2 kg)(10 m/s 2 ) = 20 kg m/s 2 ko 20 Newtons
Ana so: Ƙarfin tashin hankali (T)?
Magani:
w 2 > w 1 don haka m 2 yana motsawa ƙasa , m 1 yana motsawa sama.
Dokar motsi ta biyu ta Newton :
ΣF = ma
w 2 – w 1 = (m 1 + m 2 ) a
20 – 10 = (1 + 2) a
10 = (3) a
a = 3.3 m/s 2
Saurin tsarin = 3.3 m/s 2.
m 2 yana tafiya ƙasa:
w 2 – T 2 = m 2 a
20 – T 2 = (2)(3.33)
20 – T 2 = 6.66
T 2 = 20 – 6.66
T 2 = 13.3 Newton
m 1 yana tafiya sama:
T 1 – w 1 = m 1 a
T 1 – 10 = (1)(3.3)
T 1 – 10 = 3.33
T 1 = 10 + 3.33
T 1 = 13.3 Newton
Ƙarfin tashin hankali (T) = 13.3 Newtons.
6. Nauyin m 1 = 6 kg da nauyin m 2 = 4 kg. Saman kwance yana da santsi. Saurin nauyi saboda nauyi shine 10 m/s 2. Menene saurin tsarin.
An sani:
Nauyin m1 = 6kg
nauyin m2 = 4 kg
hanzari saboda nauyi (g) = 10 m/s 2
nauyin w 1 = m 1 g = (kilogiram 6)(mita 10/s 2 ) = kilogiram 60 m/s 2 ko 60 Newtons
nauyin w 2 = m 2 g = (kilogiram 4)(m 10/s 2 ) = kg 40 m/s 2 ko 40 Newtons
Ana so: Haɓaka tsarin (a)
Magani:
m 1 a kan jirgin sama mai santsi a kwance ba tare da gogayya ba don haka tsarin yana hanzarta ta hanyar nauyin toshe 2.
Yi amfani da dokar Newton ta biyu:
∑ F = ma
w 2 = (m 1 + m 2 ) a
40 N = (kilogiram 6 + kilogiram 4) a
40 N = (10 kg) a
a = 40 N / 10 kg
a = 4 m/s 2
7. Tubalai biyu, kowanne tubali yana da nauyin kilogiram 2, wanda aka haɗa ta hanyar igiya a kan kura, kamar yadda aka nuna a cikin hoton da ke ƙasa. Jirgin kwance da kura suna da santsi. Idan an ja kura ta B ta hanyar ƙarfin kwance na Newtons 40, to menene saurin kura ta. Saurin gudu saboda nauyi shine 10 m/s 2.
An sani:
nauyin toshe A (m)A) = nauyin toshe B (mB) = 2 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ƙarfin F = 40 N
nauyin abu A (w A ) = mg = (2)(10) = 20 N
Ana so: Haɓaka tsarin (a)?
Magani:
Yi amfani da dokar Newton ta biyu:
∑ F = ma
F – w A = (m A + m B ) a
40 – 20 = (2 + 2) a
20 = (4) a
a = 20/4
a = 5 m/s 2
8. Nauyin tubalin A = 2 kg da nauyin tubalin B = 1 kg. Toshe B da farko yana hutawa, sannan ya yi sauri ƙasa har sai ya faɗi ƙasa. Saurin gudu saboda nauyi shine 10 m/s 2. Menene girman ƙarfin tashin hankali.
An sani:
Nauyin toshe A (m)A) = 2 kg
Nauyin tubalin B (m B ) = 1 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin toshe B (w B ) = m B g = (1)(10) = Newtons 10
Ana so: Girman ƙarfin tashin hankali (T)
Magani:
Ka yi watsi da ƙarfin gogayya.
Haɓaka tsarin (a)
∑ F = ma
w B = (m A + m B ) a
10 = (2 + 1) a
10 = 3 a
a = 10/3
Ƙarfin tashin hankali (T)
Ƙarfin tashin hankali a kan tubalin A:
∑ F = ma
T = m A a = (2)(10/3) = 20/3 = 6.7 Newtons
Ƙarfin tashin hankali a kan tubalin B:
∑ F = ma
w B – T = m B a
10 – T = (1)(10/3)
10 – T = 3.3
T = 10 – 3.3 = 6.7 Newtons
Ƙarfin tashin hankali (T) = 6.7 Newtons
9. Nauyin tubalan A = 2 kg da nauyin tubalan B = 1 kg. Ƙarfin gogayya tsakanin abu A da jirgin kwance = 2.5 Newtons. Yi watsi da gogayya akan pulley da igiya. Menene hanzarin tubalan biyu.
An sani:
Nauyin toshe A (m)A) = 2 kg
Nauyin tubalin B (m B ) = 1 kg
Ƙarfin gogayya tsakanin kulle a da jirgin kwance (f kA ) = 2.5 Newtons
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin tubalan (w B ) = m B g = (1)(10) = Newtons 10
Ana so: Haɓaka tubalan biyu (a)
Magani:
Yi amfani da dokar Newton ta biyu:
∑ F = ma
w B – f k = (m A + m B ) a
10 – 2.5 = (2 + 1) a
7.5 = 3 a
a = 7.5/3
a = 2.5 m/s 2
10. Nauyin tubalin a = 30 kg, a tsaya a kan jirgin kwance wanda aka haɗa da tubalin B tare da nauyin kilogiram 10 a kan kura. Menene saurin tsarin. Saurin nauyi saboda nauyi shine 10 ms -2.
An sani:
Nauyin toshe A (m)A) = 30 kg
Nauyin tubalin B (m B ) = 10 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin toshe B (w B ) = m B g = (10)(10) = 100 Newtons
Ana so: Haɓaka tsarin (a)
Magani:
∑ F = ma
w B = (m A + m B ) a
100 = (30 + 10) a
100 = 40 a
a = 100/40
a = 2.5 m/s 2
