Matsalolin da aka Magance a fannin Fizik na Asali

1. Ana jujjuya ƙwallon 0.2-kg, wacce aka haɗa a ƙarshen igiyar kwance, a cikin da'irar radius mai mita 1 kuma matsakaicin saurin ƙwallon shine 10 rpm. Menene girman saurin centripetal da girman ƙarfin tashin hankali?

An sani:

Nauyi (m) = 0.2 kg

Radius (r) = 1 m

Gudun kusurwa (ω) = 10 juyawa/min = 10 juyawa/60 s = 0.17 juyawa/s = (0.17)(6.28 rad)/s = 1 rad/s

Gudun (v) = r ω = (1 m)(1 rad/s) = 1 m/s

Ana so: a _s da Σ F

Magani:

(a) Girman hanzarin centripetal

(b) Girman ƙarfin tashin hankali

Σ F = ma

T = ma _s

T = (0.2 kg)(1 m/s ² )

T = 0.2 kg m/s ²

T = 0.2 N

[irp]

2. Kwallo mai nauyin kilogiram 1 a ƙarshen igiya tana juyawa daidai gwargwado a cikin da'irar kwance ta radius mita 1. Igiyar za ta karye lokacin da matsin lamba a cikinta ya wuce N 100. Menene matsakaicin saurin da ƙwallon zai iya samu?

An sani:

Nauyi (m) = 1 kg

Radius (r) = mita 1

Ƙarfin tashin hankali (T) = Ƙarfin tsakiya ( Σ F) = 100 N

Ana so: v mafi girma

Magani:

[irp]

[wpdm_package id='499′]

1. Nauyi da nauyi
2. ƙarfin al'ada
3. Dokar motsi ta biyu ta Newton
4. Ƙarfin gogayya
5. Motsi a kan 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

Karin bayani

1. Mota tana zagaye lanƙwasa mai bandeji. Menene kusurwar hanya wacce take da lanƙwasa mai tsawon mita 60 tare da saurin ƙira na mita 20/s? A ɗauka babu gogayya tsakanin mota da hanya.

Magani

N = ba ƙarfin yau da kullun

N sin θ = sashin kwance na ƙarfin al'ada

N cos θ = bangaren tsaye na ƙarfin al'ada

w = mg = nauyin motar

An tsara hanyar ne don a yi mata bandeji domin kawar da dogaro da gogayya.

Ana buƙatar ƙarfin kwance na raga, ɓangaren kwance na ƙarfin da aka saba amfani da shi ( N sin θ) , don ci gaba da tafiya a cikin da'ira a kusa da lanƙwasa.

Mun zaɓi axis na x a matsayin kwance da axis na y a matsayin tsaye, don haka hanzarta centripetal, a_R, yana kan hanyar kwance. A cikin hanyar kwance, ƙarfin kawai shine ɓangaren kwance na ƙarfin al'ada (N zunubi θ), wanda ake buƙata don samar da hanzarin tsakiya. N sin θ = centripetal karfi.

Yi amfani da dokar motsi ta Newton a tsaye:

[irp]

A yi amfani da dokar motsi ta Newton a kan alkiblar kwance:

Maye gurbin N a cikin lissafi na 1 zuwa N a cikin lissafi na 2 :

[wpdm_package id='497′]

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

Karin bayani

1. Mota mai nauyin kilogiram 2000 tana zagaye lanƙwasa a kan titin da ke da faɗi na radius mita 150. Matsakaicin gogayya mai tsauri shine 0.5. Ƙayyade matsakaicin gudu don motar ta bi lanƙwasa kuma kada ta zame. Saurin gudu saboda nauyi = 10 m/s ².

An sani:

Nauyi (m) = 2000 kg

Radius (r) = mita 150

Ma'aunin gogayya mai tsauri ( μs ₎ = 0.5

Nauyi (w) = mg = (2000 kg)(10 m/s ² ) = 20,000 kg m/s ² = 20,000 N

Ƙarfin juzu'i (F _s ) = μ _s N = μ _s w = (0.7) (20,000 N) = 14,000 N

Ana nema : v

Magani:

[irp]

[wpdm_package id='496′]

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

Karin bayani

1. Tasoshi biyu m ₁ = 2 kg da m ₂ = 5 kg suna kan layi mai karkata kuma an haɗa su tare da igiya kamar yadda aka nuna a cikin hoton. Matsakaicin gogayya tsakanin m ₁ da karkata shine 0.2 kuma ƙimar gogayya tsakanin m ₂ da karkata shine 0.1.

(a) Ƙayyade saurin su

(b) Ƙayyade ƙarfin tashin hankali

An sani:

Nauyi 1 (m ₁ ) = 2 kg

Nauyi 2 (m2 ₎ = 4 kg

Ma'aunin gogayya tsakanin m ₁ da jirgin sama mai karkata (μ _k1 ) = 0.2

Ma'aunin gogayya tsakanin m2 _da jirgin sama mai karkata (μ _k2 ) = 0.1

Saurin gudu saboda nauyi (g) = 9.8 m/s ²

a) Girma da alkiblar saurin gudu

w ₁ = nauyi 1 = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 Newtons

w _1x = w ₁ zunubi 30 ^o = (19.6 N)(0.5) = 9.8 Newtons

w _1y = w ₁ cos 30 ^o = (19.6 N)(0.87) = Newtons 17

N ₁ = Ƙarfin da aka saba da shi akan m ₁ = w _1y = 17 Newtons

F _k1 = Ƙarfin gogayya mai motsi akan m ₁ = μ _k1 N ₁ = (0.2)(17 N) = 3.4 Newtons

---

w ₂ = nauyi 2 = m ₂ g = (kilogiram 4)(9.8 m/s ² ) = 39.2 Newtons

w _2x = w ₂ zunubi 60 ^o = (39.2 N) (0.87) = 34.1 Newtons

w _2y = w ₂ cos 60 ^o = (39.2 N)(0.5) = 19.6 Newtons

N ₂ = Ƙarfin da aka saba da shi akan m ₂ = w _2y = 19.6 Newtons

F _k2 = Ƙarfin gogayya mai motsi akan m ₂ = μ _k2 N ₂ = (0.1)(19.6 N) = 1.96 Newtons

---

Girman hanzarin:

∑ F _x = ma _x

w _2x > w _1x don haka alkiblar hanzarin daidai take da alkiblar w _2x.

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

w_2x - F_k2 - T₂ + T₁ - w_1x - F_k1 = (m₁ +m₂) da kuma_x

w _2x – F _k2 – w _1x – F _k1 = (m ₁ + m ₂ ) a _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 = 3.16 m/s ²

Girman hanzarin = 3.16 m/s ^2. Alkiblar hanzarin = alkiblar T ₁ = alkiblar w _2x

b) Girman ƙarfin tashin hankali

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

w _2x – F _k2 – T ₂ = m ₂ a _x

34.1 N - 1.96 N - T ₂ = (4 kg) (3.16 m/s ² )

32.14 N – T ₂ = 12.64 N

T ₂ = 32.14 N – 12.64 N = 19.5 Newtons

Ƙarfin tashin hankali = T = T ₁ = T ₂ = 19.5 Newtons

[irp]

2. m ₁ = 4 kg, m ₂ = 2 kg. Kayyade (a) girma da alkiblar hanzari (b) Girman ƙarfin tashin hankali wanda ya haɗa m ₁ da m ₂ (c) girman ƙarfin tashin hankali wanda ya haɗa pulley da rufin.

Magani

w ₁ = m ₁ g = (kilogiram 4)(9.8 m/s ² ) = 39.2 Newtons

w ₂ = m ₂ g = (2 kg)(9.8 m/s ² ) = 19.6 Newtons

a) Girma da alkiblar saurin gudu

∑ F _y = may _y

w ₁ > w ₂ don haka alkiblar abu iri ɗaya ce da alkiblar nauyin 1 ( w ₁ ) . Ƙarfin da ke da alkibla iri ɗaya da hanzari suna da kyau kuma ƙarfin da ke da alkibla akasin gudu suna da korau.

w ₁ – T ₁ + T ₂ – w ₂ = (m ₁ + m ₂ ) a _y

w ₁ – w ₂ = (m ₁ + m ₂ ) a _y

39.2 N - 19.6 N = (4 kg + 2 kg) a _y

19.6 N = (kilogiram 6) a _y

a _y = 19.6 N: 6 kg

a _y = 3.26 m/s ²

Girman hanzari = 3.26 m/s ^2. Alkiblar hanzari = alkiblar w ₁.

b) Girman ƙarfin tashin hankali wanda ke haɗa m ₁ da m ₂

Yi amfani da dokar Newton ta biyu akan m ₂ :

∑ F _y = may _y

w ₁ – T ₁ = m ₁ a _y

39.2 N - T ₁ = (4 kg) (3.26 m/s ² )

39.2 N – T ₁ = 13.04 N

T ₁ = 39.2 N – 13.04 N

T ₁ = 26.16 Newton

Girman ƙarfin tashin hankali wanda ke haɗa abubuwa = T = T ₁ = T ₂ = 26.16 Newtons

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

Pulley yana hutawa:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

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

T ₃ – T ₁ – T ₂ = 0

T3 = _T1 + _T2

T ₁ da T ₂ suna da girma iri ɗaya , T ₁ = T ₂ = T = 26.16 N:

T ₃ = 2T = 2(26.16 N) = 52.32 Newtons

[irp]

3. Toshe na 1 (m ₁ = 10 kg) da toshe na 2 (m ₂ = 15 kg) an haɗa su da igiya akan pulley mara gogayya. Coefficient na gogayya mai tsayayye tsakanin toshe na 2 tare da karkacewa = 0.6. Coefficient na gogayya mai motsi tsakanin toshe na 2 tare da karkacewa = 0.42. Kayyade (a) Girman ƙaramin ƙarfin F da aka yi akan abubuwan don abubuwan su hanzarta sama (b) Kayyade girman ƙarfin tashin hankali.

Magani

w ₁ = Nauyin tubalin 1 = m ₁ g = (10 kg)(9.8 m/s ² ) = Newtons 98

w ₂ = Nauyin tubalin 2 = m ₂ g = (15 kg)(9.8 m/s ² ) = Newtons 147

w _2y = w ₂ cos 30 ^o = (147 N)(0.87) = 127.89 Newtons

w _2x = w ₂ zunubi 30 ^o = (147 N) (0.5) = 73.5 Newtons

N ₂ = Ƙarfin da aka saba da shi akan toshe 2 = w _2y = 127.89 Newtons

F _k2 = Ƙarfin gogayya mai motsi akan toshe 2 = μ _k2 N ₂ = (0.42)(127.89 N) = 53.7 Newtons

F _s2 = Ƙarfin gogayya mai tsauri akan toshe 2 = μ _s2 N ₂ = (0.6)(127.89 N) = 76.7 Newtons

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

∑ F _x = ma _x —— a _x = 0

∑ F _x = 0

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

F – F _k2 – w _2x – w ₁ – T ₂ + T ₁ = 0

F - F _k2 - w _2x - w ₁ = 0

F = F _k2 + w _2x + w ₁

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:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = 98 Newton

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

F – F _k2 – w _2x – T ₂ = 0

T ₂ = F – F _k2 – w _2x

T ₂ = 225.2 N – 53.7 N – 73.5 N

T ₂ = 98 Newton

Girman ƙarfin tashin hankali = T ₁ = T ₂ = T = 98 Newtons

[irp]

4. Toshe na 1 (m ₁ = 16 kg) yana kwance a saman kwance kuma toshe na 2 (m ₂ = 12 kg) yana kwance a kan wani santsi mai karkata, wanda aka haɗa ta da igiya wacce ke ratsa ƙaramin injin da ba shi da gogayya. Toshe na 3 (m ₃ = 5 kg) yana kwance akan toshe na 2. Haɗaɗɗen gogayya tsakanin toshe na 2 da saman kwance shine 0,4. Haɗaɗɗen gogayya tsakanin toshe na 2 da toshe na 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?

Magani:

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

w ₁ = Nauyin tubalin 1 = m ₁ g = (kilogiram 16)(9.8 m/s ² ) = Newtons 156.8

w _1x = w ₁ zunubi 60 ^o = (156.8 N)(0.87) = 136.4 Newtons

w _1y = w ₁ cos 60 ^o = (156.8 N)(0.5) = 78.4 Newtons

N ₁ = Ƙarfin da aka saba amfani da shi a kan toshe 1 ta hanyar jirgin sama mai karkata = w _1y = 78.4 Newtons

w ₃ = Nauyin tubalin 3 = m ₃ g = (kilogiram 5)(9.8 m/s ² ) = Newtons 49

N ₂₃ = Ƙarfin da aka saba amfani da shi a kan toshe 3 ta hanyar toshe 2 = w ₃ = 49 Newtons

N ₃₂ = Ƙarfin da aka saba amfani da shi a kan toshe na 2 ta hanyar toshe na 3 = N ₂₃ = w ₃ = 49 Newtons

(N23 _da N32 nau'i biyu ne _na martanin aiki da martani )

F _s23 = Ƙarfin gogayya mai tsauri da aka yi a kan toshe 3 ta hanyar toshe 2 = μ _s N ₂₃ = (0.3)(49 N) = 14.7 Newtons

F _s32 = Ƙarfin gogayya mai tsauri da aka yi a kan toshe na 2 ta toshe na 3 = F _{s 23} = 14.7 Newtons

(F _s23 da F _s32 sune haɗin kai-da martani )

w ₂ = Nauyin tubalin 2 = m ₂ g = (12 kg)(9.8 m/s ² ) = 117.6 Newtons

N ₂ = Ƙarfin da aka saba amfani da shi akan abu 2 ta saman kwance = w ₂ + N ₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F _k2 = Ƙarfin gogayya mai motsi akan toshe 2 = μ _k N ₂ = (0.4)(166.6 N) = 66.64 Newtons

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

∑ F _x = ma _x

F _s23 = m ₃ a _x

—–> F_s23 = μ_s N₂₃ = μ_s w₃ = μ_s m₃ g

μ _s m ₃ g = m ₃ a _x

μ _s g = _x

a _x = (0.3)(9.8 m/s ² ) = 2.94 m/s ²

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

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

Alkiblar matsar da tubalan = alkiblar hanzarta tubalan = alkiblar T ₂ = alkiblar w _1x.

∑ F _x = ma _x

w_1x - T₁ + T₂ - F_k2 - F_s32 +F_s23 = (m₁ +m₂ +m₃) da kuma_x

w _1x – F _k2 = (m ₁ + m ₂ + m ₃ ) a _x

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

69.76 N = (33 kg) a _x

a _x = 2.11 m/s ²

x yana da kyau, ma'ana alkiblar matsar da tubalan ko alkiblar hanzarin iri ɗaya ne da alkiblar T _{2 ko} alkiblar w _1x.

Girman saurin gudu shine 2.11 m/s ² , ƙasa da 2.94 m/s ² don haka za mu iya kammala 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

∑ F _x = ma _x

w _1x – F _k2 = (m ₁ + m ₂ ) a _x

—–> F_k2 = μ_k N₂ = μ_k w₂ = μ_k m₂ g = (0.4)(kilogiram 12)(mita 9.8/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/s ²

[wpdm_package id='493′]

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

Karin bayani

1. Toshe mai nauyin kilogiram 2 yana kwance a kan wani jirgin sama mai karkata a kusurwar 37 ^o zuwa kwance. Kayyade girman ƙarfin waje da aka yi amfani da shi a kan toshe, don haka toshe bai zame ƙasa da jirgin ba. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µ _k = 0.2)

An sani:

Nauyi (m) = 2 kg

Saurin gudu saboda nauyi (g) = 10 m/s ²

Nauyin tubalan ( w) = mg = (2)(10) = Newtons 20

Zunubi 37 ^o = 0.6

cos 37 ^o = 0.8

Ma'aunin gogayya mai motsi (µ _k ) = 0.2

y-partment na nauyin (w _y ) = w cos 37 ^o = (20)(0.8) = Newtons 16

Sashen x na nauyin (w _x ) = w sin θ = (20)(sin 37) = (20)(0.6) = Newtons 12

Ƙarfin da aka saba (N) = w _y = 16 Newtons

Ana so : Ƙarfin waje (F)

Mafita :

w_x = 12 Newton

Ƙarfin gogayya mai motsi (f _k ) = µ _k N = (0.1)(16) = 1.6 Newtons

Girman ƙarfin waje F da aka yi a kan toshe :

F + f _k – w _x = 0

F = w _x – f _k

F = 12 – 1.6

F = 10.4 Newton

Ƙarfin waje F ya fi Newtons 10.4 girma.

[irp]

2. Nauyin tubali = 2 kg, ma'aunin gogayya mai tsauri µ _s = 0.4 da θ = 45 ^o . Kayyade girman ƙarfin F don haka tubalin ya fara zamewa sama.

An sani:

Ma'aunin gogayya mai tsauri (µ _s ) = 0.4

Kusurwoyi (θ) = 45 ^o

Saurin gudu saboda nauyi (g) = 10 m/s ²

Nauyin tubalan (m) = kilogiram 2

Nauyin tubalan (w) = mg = (2 kg)(10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Sashen x na nauyin (w _x ) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 Newtons

y-partion na nauyin (w _y ) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newtons

Ana so : Girman ƙarfin F

Magani:

Toshe zai fara zamewa sama, idan F ≥ w_x + f_s.

Sashen x na nauyin:

w _x = 10√2 Newton

bangaren y na nauyin :

w _y = 10√2 Newton

Ƙarfin al'ada :

N = w _y = 10√2 Newton

Ƙarfin gogayya mai motsi :

f _s = µ _s N = (0,4) (10√2) = 4√2

Girman ƙarfin F don toshe ya fara zamewa sama :

F ≥ w _x + f _s

F ≥ 10√2 + 4 √2

F ≥ 14√2 Newton

[wpdm_package id='492′]

1. Ƙwayoyin cuta a cikin ma'auni ɗaya
2. Ƙwayoyin cuta a cikin ma'auni mai girma biyu
3. Daidaiton jikin da aka haɗa ta hanyar igiyoyi da ƙwallo
4. Daidaiton jikin da ke kan jirgin da aka karkata

Karin bayani

1. Akwatin nauyi na kilogiram 5 yana kan jirgin sama mai karkata a kusurwar 30 ^o . Akwatin yana da igiya. Kayyade ƙarfin tashin hankali (T) da ƙarfin da aka saba (N)!

Magani

ΣF_x = 0

T – w sin 30 ^o = 0

T = w daidai da 30 ^o

T = (5 kg)(9.8 m/s ² ) kusan 30 ^o

T = (49)(0.5)

T = 24.5 Newtons

∑ F _y = 0

N – w cos 30 ^o = 0

N = w cos 30 ^o

N = (49)(0.87)

N = 43 Newton

[irp]

2. Abubuwa biyu na nauyi m ₁ = m ₂ = 2 kg, an haɗa su da igiya mara nauyi akan pulley mara gogayya. Nemo ƙarfin tashin hankali T ₁ da T ₂.

Magani

(a) Zane-zanen jiki kyauta don abu na 1 (b) Zane-zanen jiki kyauta don abu na 2

Yi amfani da dokar farko ta Newton ga ƙin yarda ta 1:

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 N

Yi amfani da dokar farko ta Newton ga ƙin yarda ta 2:

∑ F _y = 0

T ₂ – w ₂ = 0

T ₂ = w ₂ = m ₂ g = (2 kg)(9.8 m/s ² ) = 19.6 N

T ₁ = T ₂ = N 19.6.

[irp]

3. An haɗa wani abu mai nauyi w _A = 30 N da abu mai nauyi w _B = 40 N, ta hanyar igiya mai sauƙi wadda ke ratsa wani kurji mara gogayya na nauyin da ba shi da yawa. A ƙayyade ma'aunin matsakaicin gogayya tsakanin w _B da saman da aka karkata, idan tsarin yana hutawa.

Magani

(a) Zane-zanen jiki kyauta don abu w _A (b) Zane-zanen jiki kyauta don abu w _B

Yi amfani da dokar farko ta Newton don nuna rashin jituwa a alkiblar w _A a tsaye (y):

∑ F _y = 0 (babu hanzari a tsaye)

T – w _A = 0

T = w _A = 30 Newton

Yi amfani da dokar farko ta Newton ga ƙin yarda w _B a tsaye (y) alkibla :

∑ F _y = 0

N – w _B cos 45 ^o = 0

N = w _B cos 45 ^o = (40)(0.7) = Newtons 28

Yi amfani da dokar farko ta Newton ga ƙin yarda w _B a cikin alkiblar kwance (x):

∑ F _x = 0

F _k + w _B sin 45 ^o – T = 0

μ _s N + w _B zunubi 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

Matsakaicin matsakaicin gogayya tsakanin w _B da saman da aka karkata = 0.07.

[wpdm_package id='490′]

1. Ƙwayoyin cuta a cikin ma'auni ɗaya
2. Ƙwayoyin cuta a cikin ma'auni mai girma biyu
3. Daidaiton jikin da aka haɗa ta hanyar igiyoyi da ƙwallo
4. Daidaiton jikin da ke kan jirgin sama mai karkata

Karin bayani

1. Nemo ƙarfin tashin hankali T ₁ , T ₂ , da T _{3. Yi watsi da} nauyin igiya.

Magani

(a) Zane-zanen jiki kyauta ga abu (b) Zane-zanen jiki kyauta ga igiya

Yi amfani da dokar farko ta Newton akan abu:

ΣF _y = 0

T ₁ – w = 0

T ₁ = w = mg

T ₁ = (kilogiram 5)(9.8 m/s ² )

T ₁ = 49 kg m/s ²

T ₁ = 49 N

Yi amfani da dokar farko ta Newton a kan igiyar:

∑ F _x = 0

T _3x – T _2x = 0

T ₃ cos 30 ^o – T ₂ cos 40 ^o = 0

0.87 T ₃ – 0.77 T ₂ = 0

0.87 T ₃ = 0.77 T ₂

T ₂ = 0.87 T ₃ / 0.77 = 1.1 T ₃ ———- Daidaito 1

[irp]

-

∑ F _y = 0

T _3y + T _2y – T _1y = 0

T ₃ zunubi 30 ^o + T ₂ zunubi 40 ^o – T ₁ = 0

0.5 T ₃ + 0.64 T ₂ – 49 N = 0 ———- Daidaito na 2

Sauya T ₂ a cikin lissafin 2 zuwa lissafin 2:

0.5 T ₃ + 0.64 (1.1 T ₃ ) – 49 N = 0

0.5 T ₃ + 0.70 T ₃ – 49 = 0

1.2 T ₃ – 49 = 0

1.2 T ₃ = 49

T ₃ = 49 / 1.2

T ₃ = 41 N

---

T ₂ = 1.1 T ₃

T ₂ = (1.1)(40.8 N)

T ₂ = 45 N

[wpdm_package id='488′]

1. Ƙwayoyin cuta a cikin ma'auni ɗaya
2. Ƙwayoyin cuta a cikin ma'auni mai girma biyu
3. Daidaiton jikin da aka haɗa ta hanyar igiyoyi da ƙwallo
4. Daidaiton jikin da ke kan jirgin sama mai karkata

Karin bayani

^{1. Nauyin abu, m = 10 kg, wanda igiya ke tallafawa. Nemo matsin lamba a cikin igiyar!} g = 10 m/s ²

An sani:

Nauyi (m) = 10 kg

Saurin gudu saboda nauyi (g) = 10 m/s ²

Ana nema: Ƙarfin tashin hankali (T)

Magani:

ΣF _y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s ² ) = 100 kg m/s ²

T = 100 Newtons

[irp]

2. Nauyin abu shine kilogiram 10. Nemo matsin lamba a cikin igiyar….. Saurin nauyi saboda nauyi = 10 m/s ².

Magani

An sani:

Nauyi (m) = 10 kg

Saurin gudu saboda nauyi (g) = 10 m/s ².

Ana nema: Ƙarfin tashin hankali (T)

Magani:

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

T ₁ = ƙarfin tashin hankali 1

_{T 1x} = sashin x na ƙarfin tashin hankali 1 = T ₁ cos 45 ^o = 0.7 T ₁

_{T 1y} = sashin y na ƙarfin tashin hankali 2 = T ₁ zunubi 45 ^o = 0.7 T ₁

T ₂ = ƙarfin tashin hankali 2

_{T 2x} = sashin x na ƙarfin tashin hankali 2 = T ₂ cos 45 ^o = 0.7 T ₂

_{T 2y} = sashin y na ƙarfin tashin hankali 2 = T ₂ zunubi 45 ^o = 0.7 T ₂

Yanayin daidaito ΣF = 0.

y axis:

ΣF _y = 0

T _1y + T _2y – w = 0

0.7T ₁ + 0.7T ₂ – 100 = 0

0.7T ₁ + 0.7T ₂ = 100 —– daidaito 1

x axis:

ΣF _x = 0

T _2x – T _1x = 0

0.7T ₂ – 0.7T ₁ = 0

0.7T ₂ = 0.7T ₁

T ₂ = T ₁ —– lissafi na 2

Ƙayyade girman _T1 :

0.7T ₁ + 0.7T ₁ = 100

1.4T ₁ = 100

T ₁ = 100 / 1.4

T ₁ = 71.4 Newton

T ₁ = T ₂ don haka T ₂ = 71.4 Newtons

[wpdm_package id='486′]

1. Ƙwayoyin cuta a cikin ma'auni ɗaya
2. Ƙwayoyin cuta a cikin ma'auni mai girma biyu
3. Daidaiton jikin da aka haɗa ta hanyar igiyoyi da ƙwallo
4. Daidaiton jikin da ke kan jirgin sama mai karkata

Karin bayani

1. Akwatuna biyu suna haɗuwa da igiya da ke gudana a kan kura. Yi watsi da nauyin igiyar da kura da duk wani gogayya a cikin kura. Nauyin akwatin 1 = 2 kg, nauyin akwatin 2 = 3 kg, hanzari saboda nauyi = 10 m/s ^2. Nemo (a) Hanzarta tsarin (b) Jinkirin da ke cikin igiyar!

Magani

An sani:

Nauyin akwatin 1 (m1 ₎ = 2 kg

Nauyin akwatin 2 (m2 ₎ = 3 kg

Saurin gudu saboda nauyi (g) = 10 m/s ²

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

Nauyin akwatin 2 (w ₂ ) = m ₂ g = (3)(10) = 30 Newtons

Magani:

(a) girma da alkiblar saurin gudu

w ₂ > w ₁ don haka akwatin 2 yana sauri ƙasa kuma akwatin 1 yana sauri sama.

Ƙarfin da ke da alkibla iri ɗaya tare da hanzari (w ₂ da T ₁ ), alamarsu tana da kyau. Ƙarfin da ke da alkiblar da ke da sabani da hanzari (T ₂ da w ₁ ), alamarsu tana da korau.

∑ F = ma

w₂ - T₂ + T₁ - w₁ = (m₁ +m₂) a ——-> T₁ = T ba₂ = T ba

w ₂ – T + T – w ₁ = (m ₁ + m ₂ ) a

w ₂ – w ₁ = (m ₁ + m ₂ ) a

30 – 20 = (2 + 3) a

10 = 5 a

a = 10/5

a = 2 m/s ²

Girman saurin gudu shine 2 m/s ².

(b) Ƙarfin tashin hankali

Akwati na 2:

Akwai ƙarfi guda biyu a cikin akwatin 2: na farko, nauyin akwatin 2 (w ₂ ), yana nuna ƙasa don haka yana da kyau. Na biyu, ƙarfin tashin hankali da aka yi a kan akwatin 2 (T ₂ ), yana nuna sama don haka yana da korau. Yi amfani da dokar motsi ta biyu ta Newton .

∑ F = ma

w ₂ – T ₂ = m ₂ a

30 – T ₂ = (3)(2)

30 – T ₂ = 6

T ₂ = 30 – 6

T ₂ = 24 Newton

Akwati na 1:

Akwai ƙarfi guda biyu a akwatin 1. Na farko , nauyin akwatin 1 (w ₁ ), yana nuna ƙasa don haka yana da korau. Na biyu , ƙarfin tashin hankali da aka yi a akwatin 1 (T ₁ ) yana nuna sama don haka yana da tabbatacce. Yi amfani da dokar motsi ta biyu ta Newton:

∑ F = ma

T ₁ – w ₁ = m ₁ a

T ₁ – 20 = (2)(2)

T ₁ – 20 = 4

T ₁ = 20 + 4

T ₁ = 24 Newton

Girman ƙarfin tashin hankali = T ₁ = T ₂ = T = 24 Newtons

[irp]

2. Abu a kan wani abu mai kauri a kwance. Nauyin abu 1 = 2 kg, nauyin abu 2 = 4 kg, hanzari saboda nauyi = 10 m/s ² , daidaiton gogayya mai tsauri = 0.4, daidaiton gogayya mai motsi = 0.3. Tsarin yana hutawa ko yana hanzarta? Idan tsarin ya hanzarta, nemo girma da alkiblar hanzarin tsarin!

Magani

An sani:

Nauyin abu 1 (m1 ₎ = 2 kg

Nauyin abu 2 (m2 ₎ = 4 kg

Saurin gudu saboda nauyi (g) = 10 m/s ²

Ma'aunin gogayya mai tsauri ( μs ₎ = 0.4

Ma'aunin gogayya mai motsi ( μk ₎ = 0.3

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

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

Ƙarfin da aka yi amfani da shi a kan abu 1 (N) = w ₁ = 20 Newtons

Ƙarfin gogayya mai motsi da aka yi wa abu 1 (f _s ) = μ _s N = (0.4)(20) = 8 Newtons

Ƙarfin gogayya mai motsi da aka yi akan abu 1 (f _k ) = μ _k N = (0.3)(20) = 6 Newtons

Ana so: hanzari (a)

Magani:

w ₂ > f _s (40 Newton > 8 Newton) don haka ana hanzarta abu na 2 a tsaye zuwa ƙasa kuma ana hanzarta abu na 1 a kwance zuwa dama. Ƙarfin gogayya da ke aiki akan abubuwa na 1 shine ƙarfin gogayya mai motsi (f _k ). Yi amfani da dokar motsi ta biyu ta Newton:

∑ F = ma

w ₂ – da = (m ₁ + m ₂ ) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s ²

Girman hanzarin = 5.7 m/s ²

[wpdm_package id='484′]

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

Karin bayani

1. Mutum mai nauyin kilogiram 50 a cikin lif. Saurin nauyi saboda nauyi = 10 m/s ^2. Kayyade ƙarfin da lif ke amfani da shi akan abu, idan:

(a) lif ɗin yana hutawa

(b) lif ɗin yana tafiya ƙasa a kan gudu mai ɗorewa

(c) lif yana hanzarta hawa sama a cikin hanzari akai-akai 5 / s ²

(d) lif yana hanzarta sauka ƙasa a daidai lokacin da mita 5/s ke juyawa ²

(e) lif a cikin faɗuwar 'yanci

Magani

An sani:

Nauyin mutum (m) = 50 kg

Saurin gudu saboda nauyi (g) = 10 m/s ²

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

Ana so: Ƙarfin da aka saba (N)

Magani:

(a) lif ɗin yana hutawa

Lif ɗin yana hutawa don haka babu hanzari (a = 0)

Mu kan zaɓi alkiblar sama a alkiblar kyau, yayin da muke zaɓar alkiblar ƙasa a alkiblar mara kyau.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(b) lif ɗin yana tafiya ƙasa a kan gudu mai ɗorewa

Saurin gudu mai ɗorewa don haka babu hanzari (a = 0)

Mu kan zaɓi alkiblar sama a alkiblar kyau, yayin da muke zaɓar alkiblar ƙasa a alkiblar mara kyau.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(c) lif yana hanzarta hawa sama a daidai lokacin da yake gudun mita 5/s ²

Alkiblar hanzarin tana sama, don haka muka zaɓi alkiblar da ta dace kamar sama.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Mutumin yana jin ƙasan yana matsawa sama da ƙarfi fiye da lokacin da lif ɗin yake tsaye ko kuma yana motsi da gudu mai ɗorewa.

Idan mutum ya tsaya a kan sikelin, sikelin yana nuna girman ƙarfin ƙasa da mutumin da ke kan sikelin ke yi. Ta hanyar dokar Newton ta uku, wannan yana daidai da girman ƙarfin sama na yau da kullun da sikelin ke yi a kan mutum.

(d) lif yana hanzarta sauka ƙasa a daidai lokacin da mita 5/s ke juyawa ²

Alkiblar hanzarin tana ƙasa, don haka muka zaɓi alkibla mai kyau kamar ƙasa.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 – 250

N = 250 Newton

Nauyin mutum shine N250, ƙasa da ainihin nauyin w = N500.

(e) lif a cikin faɗuwar 'yanci

Faɗuwa daga kan hanya yana nufin saurin lif ɗin yayi daidai da saurin da aka samu saboda nauyi. Girman saurin da aka samu sakamakon nauyi shine 9,8 m/s ² , alkiblarsa tana ƙasa zuwa tsakiyar Duniya. Saurin yana ƙaruwa a layi a cikin lokaci da 9,8 m/s a kowane daƙiƙa.

Alkiblar hanzarin tana ƙasa, don haka muka zaɓi alkibla mai kyau kamar ƙasa.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 – 500

N = 0

[irp]

2. Ƙayyade matsin lamba a cikin kebul na lif. Nauyin lif = 2000 kg.

(a) lif ɗin yana hutawa

(b) lif yana hanzarta sauka ƙasa a daidai lokacin da mita 5/s ke juyawa ²

(c) lif yana hanzarta hawa sama a daidai lokacin da yake gudun mita 5/s ²

(d) lif a lokacin faɗuwar rana

Saurin gudu saboda nauyi (g) = 10 m/s ²

Magani

An sani:

Nauyin lif (m) = 2000 kg

Saurin nauyi (g) = 10 m/s ²

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

Ana nema: Ƙarfin tashin hankali (T)

Magani:

(a) lif ɗin yana hutawa

lif yana hutawa don haka babu hanzari (a = 0)

Mu kan zaɓi alkiblar sama a matsayin alkibla mai kyau, yayin da muke zaɓar alkiblar ƙasa a matsayin alkibla mara kyau.

Σ F = ma

T – w = 0

T = w

T = 20,000 Newtons

Tashin hankali a cikin kebul (T) = nauyin lif (w) = 20,000 Newtons

(b) lif yana hanzarta sauka ƙasa a daidai lokacin da mita 5/s ke juyawa ²

Alkiblar hanzarin tana ƙasa, don haka muka zaɓi alkibla mai kyau kamar ƙasa.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 – 10,000

T = 10,000 Newtons

c) lif yana hanzarta hawa sama a daidai lokacin da yake gudun mita 5/s ²

Alkiblar hanzarin tana ƙasa, don haka muka zaɓi alkibla mai kyau kamar sama.

T – w = ma

T = w + ma

T = 20,000 + (2000)(5)

T = 20,000 + 10,000

T = 30,000 Newtons

(d) lif a lokacin faɗuwar rana

Alkiblar hanzarin tana ƙasa, don haka muka zaɓi alkibla mai kyau kamar ƙasa.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 – 20,000

T = 0

[wpdm_package id='482′]

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 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

Karin bayani