Motsin gawawwaki biyu masu hanzari iri ɗaya a saman kwance mai tsauri tare da ƙarfin gogayya - matsaloli da mafita

1. Nauyin akwatin 1 shine 2 kg, nauyin akwatin 2 shine 4 kg, saurin nauyi shine 10 m/s ² , girman ƙarfin F shine 40 Newtons. Ma'aunin gogayya tsakanin akwatin 1 da bene shine 0.2 kuma ma'aunin gogayya tsakanin akwatin 2 da bene shine 0.3. Nemo (a) Girma da alkiblar hanzarin akwatin (b) Girman ƙarfin da akwatin 1 ke yi akan akwatin 2 (F ₁₂ ) da girman ƙarfin da akwatin 2 ke yi akan akwatin 1 (F ₂₁ ).

Magani

An sani:

Nauyin akwatin 1 (m1 ₎ = 2 kg

Nauyin akwatin 2 (m2 ₎ = 4 kg

Saurin nauyi (g) = 10 m/s ² ,

Ƙarfin F = 40 Newton,

Ma'aunin gogayya tsakanin akwatin 1 da bene ( μ _k1 ) = 0.2

Daidaiton gogayya tsakanin akwatin 2 da bene ( μ _k2 ) = 0.3

Nauyin akwatin 1 (w ₁ ) = m ₁ g = (2)(10) = Newtons 20

Nauyin akwatin 2 (w ₂ ) = m ₂ g = (4)(10) = Newtons 40

Ƙarfin da aka saba amfani da shi a kan akwatin 1 (N ₁ ) = w ₁ = Newtons 20

Ƙarfin da aka saba amfani da shi a kan akwatin 2 (N2 ₎ = w ₂ = Newtons 40

Ƙarfin gogayya mai motsi da aka yi a kan akwatin 1 (f _k1 ) = ( μ _k1 )(N ₁ ) = (0.2)(20) = 4 Newtons

Ƙarfin gogayya mai motsi da aka yi a kan akwatin 2 (f _k2 ) = ( μ _k1 )(N ₂ ) = (0.3)(40) = 12 Newtons

Magani:

(a) Girma da alkiblar saurin akwatin

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

Alkiblar hanzari = alkiblar ƙarfin raga = zuwa dama.

(b) Girman ƙarfin da akwatin 1 ke yi a akwatin 2 (F ₁₂ ) da girman ƙarfin da akwatin 2 ke yi a akwatin 1 (F ₂₁ ).

Lissafa girman F ₁₂ :

ΣF = ma

F ₁₂ – f _k2 = (m ₂ ) a

F ₁₂ – 12 = (4)(4)

F ₁₂ – 12 = 16

F ₁₂ = 16 + 12

F ₁₂ = 28 Newton

F ₁₂ da F ₂₁ ƙarfin aiki ne da amsawa waɗanda ke aiki akan abubuwa daban-daban. F ₁₂ da F ₂₁ suna da girma iri ɗaya da alkiblar da ta saba.

F ₁₂ = 28 Newtons = F ₂₁ = 28 Newtons.

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2. Nauyin akwatin 1 shine 2 kg, nauyin akwatin 2 shine 4 kg, saurin nauyi shine 10 m/s ² , ƙarfin F shine 40 N. Ma'aunin gogayya tsakanin akwatin 1 da bene shine 0.2 kuma ma'aunin gogayya tsakanin akwatin 2 da bene shine 0.3. Ƙayyade (a) Girma da alkiblar hanzari (b) Jinkirin da ke cikin igiyar da ke haɗa akwatunan. Yi watsi da nauyin igiya.

An sani:

Nauyin akwatin 1 (m1 ₎ = 2 kg

Nauyin akwatin 2 (m2 ₎ = 4 kg

Saurin nauyi (g) = 10 m/s ² ,

Ƙarfin F = 40 Newton,

Ma'aunin gogayya tsakanin akwatin 1 da bene shine 0.2 ( μ _k1 ) = 0.2

Ma'aunin gogayya tsakanin akwatin 2 da bene shine 0.2 ( μ _k2 ) = 0.3

Nauyin akwatin 1 (w ₁ ) = m ₁ g = (2)(10) = Newtons 20

Nauyin akwatin 2 (w ₂ ) = m ₂ g = (4)(10) = Newtons 40

Ƙarfin da aka saba amfani da shi a kan akwatin 1 (N1 ₎ = w ₁ = Newtons 20

Ƙarfin da aka saba amfani da shi a kan akwatin 2 (N2 ₎ = w ₂ = Newtons 40

Ƙarfin gogayya mai motsi da aka yi a kan akwatin 1 (f _k1 ) = ( μ _k1 )(N ₁ ) = (0.2)(20) = 4 Newtons

Ƙarfin gogayya mai motsi da aka yi a kan akwatin 2 (f _k2 ) = ( μ _k1 )(N ₂ ) = (0.3)(40) = 12 Newtons

Magani:

(a) girma da alkiblar saurin gudu

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

Girman hanzarin shine 4 m/s ² , alkiblar hanzarin = alkiblar ƙarfin raga = zuwa dama.

(b) Tashin hankali a cikin igiyar

Ƙarfin da ke aiki a kan akwatin 1 a cikin alkiblar kwance sune tashin hankali 1 (T ₁ ) zuwa dama da ƙarfin gogayya mai motsi 1 (f _k1 ) zuwa hagu. Aiwatar da dokar Newton ta biyu:

ΣF = ma

T ₁ – f _k1 = m ₁ a

T ₁ – 4 = (2)(4)

T ₁ – 4 = 8

T ₁ = 8 + 4 = 12 Newton

Ƙarfin da ke aiki a kan akwatin 2 a cikin alkiblar kwance sune tashin hankali 2 (T ₂ ) zuwa hagu da kuma ƙarfin gogayya mai motsi 2 (f _k2 ) zuwa dama. Aiwatar da dokar Newton ta biyu :

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

Tashin hankali a cikin igiyar da ke haɗa akwatunan = T ₁ = T ₂ = T = Newtons 12.

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1. Nauyi da nauyi
2. ƙarfin al'ada
3. Dokar motsi ta biyu ta Newton
4. Ƙarfin gogayya
5. Motsi a saman kwance ba tare da ƙarfin gogayya ba
6. Motsin jiki guda biyu tare da hanzari iri ɗaya a kan saman kwance mai tsauri tare da ƙarfin gogayya
7. Motsi a kan jirgin sama mai karkata ba tare da ƙarfin gogayya ba
8. Motsi a kan jirgin sama mai karkata mai ƙarfi tare da ƙarfin gogayya
9. Motsi a cikin lif
10. Motsin gawawwaki da aka haɗa ta hanyar igiyoyi da ƙwallo
11. Jikuna biyu masu girman gudu iri ɗaya
12. Zagaye lanƙwasa mai faɗi - yanayin motsi na zagaye
13. Zagaye lanƙwasa mai banked - yanayin motsi na zagaye
14. Motsi iri ɗaya a cikin da'irar kwance
15. Ƙarfin tsakiya a cikin motsi na zagaye iri ɗaya