Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita

1. Tasoshi biyu m1 = 2 kg da m2 = 5 kg suna kan wani jirgin sama mai karkata kuma an haɗa su tare da igiya kamar yadda aka nuna a cikin hoton. Ma'aunin gogayya tsakanin m1 kuma karkacewa shine 0.2 kuma ma'aunin gogayya ta motsi tsakanin m2 kuma karkata shine 0.1.

(a) Tabbatar da matsayinsu hanzari

(b) Ƙayyade ƙarfin tashin hankali

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 1

An sani:

Mass 1 (m1) = 2kg

Tashi 2 (m2) = 4kg

Daidaiton gogayya tsakanin m1 da kuma jirgin sama mai karkata (μk1) = 0.2

Daidaiton gogayya tsakanin m2 da kuma jirgin sama mai karkata (μ)k2) = 0.1

Hanzarta saboda nauyi (g) = 9.8 m/s2

a) Girma da alkiblar saurin gudu

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 2

w1 = nauyi 1 = m1 g = (kilogiram 2)(mita 9.8/s2) = 19.6 Newton

w1x = w1 ba 30o = (19.6 N)(0.5) = 9.8 Newtons

w1y = w1 kowa 30o = (19.6 N)(0.87) = 17 Newtons

N1 = Da ƙarfin yau da kullun a kan m1 = w1y = 17 Newton

Fk1 = Ƙarfin gogayya ta motsi akan m1 = μk1 N1 = (0.2)(17 N) = 3.4 Newton

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w2 = nauyi 2 = m2 g = (kilogiram 4)(mita 9.8/s2) = 39.2 Newton

w2x = w2 ba 60o = (39.2 N)(0.87) = 34.1 Newtons

w2y = w2 kowa 60o = (39.2 N)(0.5) = 19.6 Newtons

N2 = Ƙarfin da aka saba da shi akan m2 = w2y = 19.6 Newton

Fk2 = Ƙarfin gogayya ta motsi akan m2 = μk2 N2 = (0.1)(19.6 N) = 1.96 Newton

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Girman hanzarin:

ΣFx = max

w2x > w1x don haka alkiblar hanzarin daidai take da alkiblar w2x.

Ƙarfin da ke nuna guduwa yana da kyau, kuma ƙarfin da ke da akasin alkiblar guduwa yana da korau.

w2x - Fk2 - T2 + T1 - w1x - Fk1 = (m1 +m2) da kumax

w2x - Fk2 - w1x - Fk1 = (m1 +m2 ) da kumax

34.1 N - 1.96 N - 9.8 N - 3.4 N = (2 kg + 4 kg) ax

18.94 N = (6 kg) ax

ax = 18.94 N: 6 kg

ax = 3.16m/s2

Girman hanzarin = 3.16 m/s2 Alkiblar hanzarin = alkiblar T1 = alkiblar w2x

b) Girman ƙarfin tashin hankali

Yi amfani da dokar Newton ta biyu akan abu na 2:

w2x - Fk2 - T2 = m2 ax

34.1 N – 1.96 N – T2 = (kilogiram 4)(mita 3.16/s2)

32.14 N – T2 = 12.64N

T2 = 32.14 N – 12.64 N = 19.5 Newtons

Ƙarfin tashin hankali = T = T1 = T ba2 = 19.5 Newton

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2. m1 = 4 kg, m2 = 2 kg. Kayyade (a) girma da alkiblar hanzarin (b) Girman ƙarfin tashin hankali wanda ke haɗa m1 kuma m2 (c) girman ƙarfin tashin hankali wanda ke haɗa pulley da rufin.

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 3

Magani

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 4

w1 = m1 g = (kilogiram 4)(mita 9.8/s2) = 39.2 Newton

w2 = m2 g = (kilogiram 2)(mita 9.8/s2) = 19.6 Newton

a) Girma da alkiblar saurin gudu

ΣFy = may

w1 > w2 don haka alkiblar abin iri ɗaya ce da alkiblar nauyin 1 (w1)Ƙarfin da ke da alkibla iri ɗaya da hanzari suna da kyau kuma ƙarfin da ke da alkibla akasin gudu suna da korau.

w1 - T1 + T2 - w2 = (m1 +m2) da kumay

w1 - w2 = (m1 +m2) da kumay

39.2 N - 19.6 N = (4 kg + 2 kg) ay

19.6 N = (6 kg) ay

ay = 19.6 N: 6 kg

ay = 3.26m/s2

Girman hanzari = 3.26 m/s2Alkiblar hanzari = alkiblar w1 .

b) Girman ƙarfin tashin hankali wanda ke haɗa m1 kuma m2

Aiwatar Dokar Newton ta biyu a kan m2 :

ΣFy = may

w1 - T1 = m1 ay

39.2 N – T1 = (kilogiram 4)( 3.26 m/s2)

39.2 N – T1 = 13.04N

T1 = 39.2 N – 13.04 N

T1 = 26.16 Newton

Girman ƙarfin tashin hankali wanda ke haɗa abubuwa = T = T1 = T ba2 = 26.16 Newton

c) Girman ƙarfin tashin hankali wanda ke haɗa pulley da rufin.

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 5Pulley yana hutawa:

ΣFy = may —— ay = 0

ΣFy = 0

Ƙarfin sama yana da kyau, ƙarfin ƙasa kuma yana da korau:

T3 - T1 - T2 = 0

T3 = T ba1 + T2

T1 da kuma T2 suna da irin wannan girma, T1 = T ba2 = T = 26.16 N:

T3 = 2T = 2(26.16 N) = 52.32 Newtons

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3. Toshe na 1 (m1 = 10 kg) da kuma toshe 2 (m2 = 15 kg) wanda aka haɗa ta hanyar igiya akan pulley mara gogayya. Ma'aunin gogayya mai tsayawa tsakanin toshe 2 tare da karkacewa = 0.6. Ma'aunin gogayya mai motsi tsakanin toshe 2 tare da karkacewa = 0.42. Ƙayyade (a) Girman ƙaramin ƙarfin F da aka yi akan abubuwan don abubuwan su hanzarta sama (b) Ƙayyade girman ƙarfin tashin hankali.

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 6

Magani

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 7

w1 = Nauyin tubalin 1 = m1 g = (kilogiram 10)(mita 9.8/s2) = 98 Newton

w2 = Nauyin tubalin 2 = m2 g = (kilogiram 15)(mita 9.8/s2) = 147 Newton

w2y = w2 kowa 30o = (147 N)(0.87) = 127.89 Newtons

w2x = w2 ba 30o = (147 N)(0.5) = 73.5 Newtons

N2 = Ƙarfin da aka saba da shi akan toshe 2 = w2y = 127.89 Newton

Fk2 = Ƙarfin gogayya mai motsi akan toshe 2 = μk2 N2 = (0.42)(127.89 N) = 53.7 Newton

Fs2 = Ƙarfin gogayya mai tsauri akan toshe 2 = μs2 N2 = (0.6)(127.89 N) = 76.7 Newton

a) Girman ƙaramin ƙarfin F da aka yi wa abubuwan don haka abubuwan suka yi sauri sama

ΣFx = max —— ax = 0

ΣFx = 0

Sojojin sama da na dama suna da kyau, sojojin ƙasa kuma na hagu suna da kyau.

F – Fk2 - w2x - w1 - T2 + T1 = 0

F – Fk2 - w2x - w1 = 0

F = Fk2 +w2x +w1

F = 53.7 N + 73.5 N + 98 N

F = 225.2 Newton

b) Girman ƙarfin tashin hankali

Yi amfani da dokar motsi ta Newton a kan toshe na 1:

ΣFy = may —— ay = 0

ΣFy = 0

T1 - w1 = 0

T1 = w1 = 98 Newton

Yi amfani da dokar motsi ta Newton a kan toshe na 2:

F – Fk2 - w2x - T2 = 0

T2 = F – Fk2 - w2x

T2 = 225.2 N – 53.7 N – 73.5 N

T2 = 98 Newton

Girman ƙarfin tashin hankali = T1 = T ba2 = T = 98 Newton

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4. Toshe na 1 (m1 = 16 kg) yana kwance a kan saman kwance kuma tubalin 2 (m)2 = 12 kg) yana kwance a kan wani jirgin sama mai santsi, wanda aka haɗa ta da igiya da ke ratsa ƙaramin injin jan ƙarfe mara gogayya. Toshe na 3 (m)3 = 5 kg) yana kan toshe na 2. Matsakaicin gogayya tsakanin toshe na 2 da saman kwance shine 0,4. CoefMa'aunin da ke tsakanin toshe 2 da toshe 3 shine 0,3.

(A) Idan aka saki tsarin daga hutu, toshe na 3 da toshe na 2 har yanzu suna zamewa tare?

(B) Idan akwai toshe na 3, menene hanzarin toshe na 1 da toshe na 2?

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 8

Magani:

a) Idan aka saki tsarin daga hutu, toshe na 3 da toshe na 2 har yanzu suna zamewa tare?

Jikuna biyu masu girman hanzari iri ɗaya - Aiwatar da dokar Newton ta matsalolin motsi da mafita 9

w1 = Da nauyin toshe 1 = m1 g = (kilogiram 16)(mita 9.8/s2) = 156.8 Newton

w1x = w1 ba 60o = (156.8 N)(0.87) = 136.4 Newtons

w1y = w1 kowa 60o = (156.8 N)(0.5) = 78.4 Newtons

N1 = Da ƙarfin da aka saba amfani da shi a kan toshe 1 ta hanyar jirgin sama mai karkata = w1y = 78.4 Newton

w3 = Da nauyin toshe 3 = m3 g = (kilogiram 5)(mita 9.8/s2) = 49 Newton

N23 = Da ƙarfin da aka saba amfani da shi a kan toshe na 3 ta hanyar toshe na 2 = w3 = 49 Newton

N32 = Nƙarfin da aka saba amfani da shi a kan toshe na 2 ta hanyar toshe na 3 = N23 = w3 = 49 Newton

(N23 da kuma N32 su ne nau'i-nau'i biyu na aiki-amsawa)

Fs23 = Da ƙarfin gogayya mai tsauri da aka yi a kan toshe 3 ta toshe 2 = μs N23 = (0.3)(49 N) = 14.7 Newton

Fs32 = Da ƙarfin gogayya mai tsauri da aka yi a kan toshe na 2 ta toshe na 3 = Fs23 = 14.7 Newton

(Fs23 da kuma Fs32 su ne nau'i-nau'i biyu na aiki-amsawa)

w2 = Da nauyin tubalin 2 = m2 g = (kilogiram 12)(mita 9.8/s2) = 117.6 Newton

N2 = Da Ƙarfin da aka saba amfani da shi akan abu 2 ta saman kwance = w2 +N32 = 117.6 Newtons + 49

Newton = 166.6 Newton

Fk2 = Da ƙarfin gogayya mai motsi a kan toshe na 2 = μk N2 = (0.4)(166.6 N) = 66.64 Newton

Yi amfani da dokar motsi ta Newton a kan toshe na 3:

ΣFx = max

Fs23 =m3 ax

—–> Fs23 = μs N23 = μs w3 = μs m3 g

μs m3 g=m3 ax

μs g = ax

ax = (0.3)(9.8 m/s2) = 2.94 m/s2

Matsakaicin hanzarin toshe na 3 don toshe na 3 da toshe na 2 su ci gaba da zamewa tare shine 2.94 m/s2.

Yanzu mun ƙididdige girman saurin tsarin bayan an sake shi daga hutu.

Alkiblar matsar da tubalan = alkiblar hanzarta tubalan = alkiblar T2 = alkiblar w1x.

ΣFx = max

w1x - T1 + T2 - Fk2 - Fs32 +Fs23 = (m1 +m2 +m3) da kumax

w1x - Fk2 = (m1 +m2 +m3 ) da kumax

136.4 N - 66.64 N = (16 kg + 12 kg + 5 kg) ax

69.76 N = (33 kg) ax

ax = 2.11m/s2

ax yana da kyau, yana nufin alkiblar matsar da tubalan ko alkiblar hanzarin daidai yake da alkiblar T2 ko kuma alkiblar w1x.

Girman hanzarin shine 2.11 m / s2 , lfiye da bashin 2.94 m / s2 don haka za mu iya kammala da cewa toshe na 3 da toshe na 2 har yanzu suna zamewa tare bayan an sake su daga hutu.

b) Girman hanzarin toshe 1 da toshe 2

ΣFx = max

w1x - Fk2 = (m1 +m2) da kumax

—–> Fk2 = μk N2 = μk w2 = μk m2 g = (0.4)(kilogiram 12)(mita 9.8/s2) = 47.04 Newton

136.4 N - 47.04 N = (16 kg + 12 kg) ax

89.36 N = (28 kg) ax

ax = 89.36 N: 28 kg = 3.19 m/s2

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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 gawawwaki 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 da ƙarfin gogayya
  9. Motsi a cikin lif
  10. Motsin jikin mutum yana da alaƙa da igiyoyi da kuma 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

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