Physics

1. Nauyin abu = 2 kg, hanzari saboda nauyi = 9.8 m/s ² , daidaiton gogayya mai tsauri = 0.2, daidaiton gogayya mai motsi = 0.1. Shin abu yana hutawa ne ko kuma hanzari? Idan abu ya yi sauri, nemo (a) ƙarfin da ke sama (b) girma da alkiblar hanzarin akwatin!

Magani

An sani:

Nauyi (m) = 2 kg

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

Ma'aunin gogayya mai tsauri ( μs ₎ = 0.2

Ma'aunin gogayya ta motsi ( μk ₎ = 0.1

Nauyi (w) = mg = (2)(9.8) = 19.6 Newtons

Sashen kwance na nauyin (w _x ) = w sin 30 ^o = (19.6)(0.5) = 9.8 Newtons

Sashen tsaye na nauyin th (w _y ) = w cos 30 ^o = (19.6)(0.5√3) = 9.8√3 Newtons

Ƙarfin da aka saba (N) = w _y = 9.8√3 Newtons

Ƙarfin gogayya mai motsi (f _s ) = (0.2)(9.8√3) = 1.96√3 Newton = 3.39 Newton

Ƙarfin gogayya mai motsi (f _k ) = (0.1)(9.8√3) = 0.98√3 Newton = 1.69 Newton

Magani:

Abu yana hutawa idan w _x <fs _s , abu yana motsawa ƙasa idan w _x > fs _s.

w _x = 9.8 Newtons da f _s = 3.39 Newtons.

(a) ƙarfin da ba a iya amfani da shi ba

∑ F = w _x – f _k = 9.8 – 1.69 = 8.11 Newtons

(b) girma da alkiblar saurin gudu

∑ F = ma

8.11 = (2) a

a = 4.05 ba

Girman hanzarin = 4.05 m/s ² da kuma alkiblar hanzarin = ƙasa.

[irp]

2. Nauyin abu = 4 kg, hanzari saboda nauyi = 9,8 m/s ^2. Ma'aunin gogayya mai motsi = 0.2 da kuma ma'aunin gogayya mai motsi = 0.4. Girman ƙarfin F = 40 Newtons. Abu yana hutawa ko yana zamewa ƙasa? Idan abu yana zamewa ƙasa, nemo (a) ƙarfin da aka tara (b) girma da alkiblar hanzari!

Magani

An sani:

Nauyi (m) = 4 kg

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

Ma'aunin gogayya mai tsauri ( μs ₎ = 0.4

Ma'aunin gogayya mai motsi ( μk ₎ = 0.2

Nauyi (w) = mg = (4)(9.8) = 39.2 Newtons

Sashen kwance na nauyin (w _x ) = w sin 30 ^o = (39.2)(0.5) = 19.6 Newtons

Sashen tsaye na nauyin (w _y ) = w cos 30 ^o = (392)(0..5√3) = 19.6√3 Newtons

Ƙarfin da aka saba (N) = w _y = 19.6√3 Newtons = 33.95 Newtons

Ƙarfin gogayya mai canzawa (fs ₎ = μs _N = (0,4)(33.95) = 13.58 Newtons

Ƙarfin gogayya na motsi (f _k ) = μ _k N = (0.2)(33.95) = 6.79 Newtons

F = 40 Newton

Magani:

Abu zai zame ƙasa idan F <w _x + fs _s . Abu zai zame sama idan F > w _x + fs _s.

F = Newtons 40, w _x = 19.6 Newtons da f _s = 13.58 Newtons.

_{F ya fi w x} + f _s girma don haka abin ya zame sama.

(a) Ƙarfin da ba a iya amfani da shi ba

∑ F = F – w _x – f _k = 40 – 19.6 – 6.79 = 13.61 Newtons

(b) Girma da alkiblar saurin gudu

∑ F = ma

6.4 = (4) a

a = 1.6 ba

Girman saurin gudu shine 1.6 m/s ² kuma alkiblar saurin gudu tana sama.

[irp]

[wpdm_package id='481′]

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. Nauyin akwatin = 2 kg, hanzari saboda nauyi = 9.8 m/s ^{2. Nemo (a) ƙarfin da ke hanzarta akwatin zuwa ƙasa (b) girman} hanzarin akwatin.

Magani

An sani:

Nauyi (m) = 2 kg

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

Nauyi (w) = mg = (2)(9.8) = 19.6 Newtons

w _x = w zunubi 30 = (19.6)(0.5) = 9.8 Newtons

wy ₌ w cos 30 = (19.6)(0.5√3) = 9.8√3 Newtons

Magani:

(a) Ramin da ke hanzarta akwatin

Jirgin da aka karkata yana da santsi, don haka babu ƙarfin gogayya. Ƙarfin da ke aiki akan abu shine w _x.

∑ F = w _x

∑ F = 9.8 Newton

(b) girman hanzarin

∑ F = ma

9.8 = (2) a

a = 9.8/2

a = 4.9 m/s ²

Girman saurin gudu shine 4.9 m/s ² , alkiblar saurin gudu tana ƙasa.

[irp]

2. Jirgin da aka karkata yana da santsi don haka babu ƙarfin gogayya . Nauyin abu shine kilogiram 3, hanzarin da aka samu saboda nauyi shine 9.8 m/s ^2. Ƙayyade girman ƙarfin F idan (a) abin yana hutawa (b) abin yana motsawa ƙasa tare da hanzarin da aka saba yi na 2 m/s ² (c) abin yana motsawa sama tare da hanzarin da aka saba yi na 2 m/s ².

Magani

An sani:

Nauyi (m) = 3 kg

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

Nauyi (w) = mg = (3)(9.8) = 29.4 Newtons

w _x = w zunubi 30 = (29.4)(0.5) = 14.7 Newtons

wy ₌ w cos 30 = (29.4)(0.5√3) = 14.7√3 Newtons

Magani:

(a) Girman ƙarfin F idan wani abu yana hutawa

Dokar farko ta Newton ta bayyana cewa idan abu yana hutawa, ƙarfin da ke aiki akan abu ba shi da sifili.

∑ F = 0

F – w _x = 0

F = w _x

F = 14.7 Newton

(b) Girman ƙarfin F idan wani abu yana tafiya ƙasa a madaidaicin mita 2/s ²

∑ F = ma

w _x – F = ma

14.7 – F = (3)(2)

14.7 – F = 6

F = 14.7–6

F = 8.7 Newton

(c) Girman ƙarfin F idan wani abu yana tafiya sama a madaidaicin mita 2/s ²

∑ F = ma

F – w _x = ma

F – 14.7 = (3)(2)

F – 14.7 = 6

F = 14.7 + 6

F = 20.7 Newton

[irp]

[wpdm_package id='479′]

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. 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.

[irp]

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.

[irp]

[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 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

Karin bayani

1. Nauyin abu 1 shine 2 kg, nauyin abu 2 shine 4 kg, saurin nauyi shine 10 m/s ² , girman ƙarfin F shine 12 Newtons. Kayyade girma da alkiblar saurin abubuwa.

An sani:

m ₁ = 2 kg, m ₂ = 4 kg, g = 10 m/s ² , F = 12 Newtons

Ana so : a

Magani:

Σ F = ma

F = (m ₁ + m ₂ ) a

12 = (2 + 4) a

12 = 6 a

a = 12/6

a = 2 m/s ²

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

[irp]

2. Nauyin abu 1 shine 2 kg, nauyin abu 2 shine 4 kg, saurin nauyi shine 10 m/s ² , girman ƙarfin F shine 24 N. Kayyade girma da alkiblar saurin.

An sani:

m ₁ = 2 kg, m ₂ = 4 kg, g = 10 m/s ² , F = 24 Newtons

Ana so: hanzari (a)

Magani:

Σ F = ma

F = (m ₁ + m ₂ ) a

24 = (2 + 4) a

24 = 6 a

a = 24/6

a = 4 m/s ²

Alkiblar hanzarin = alkiblar ƙarfin raga = zuwa dama.

[irp]

[wpdm_package id='474′]

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

An warware matsaloli a cikin dokokin motsi na Newton - Ƙarfin rikitar da ke tsakanin motsi da motsi

1. Wani abu yana rataye a kan ƙasa mai kwance. Ma'aunin gogayya mai motsi shine 0.4 kuma saurin nauyi shine 9.8 m/s ^2. Ƙayyade (a) Matsakaicin ƙarfin gogayya mai motsi (b) Mafi ƙarancin ƙarfin F

Magani

An sani:

Nauyi (m) = 1 kg

Ma'aunin gogayya mai tsauri (μs ₎ = 0.4

Saurin nauyi (g) = 9.8 m/s ²

Nauyi (w) = mg = (1 kg)(10 m/s ² ) = 10 kg m/s ² = 10 Newtons

Ƙarfin al'ada (N) = w = Newtons 10

Ana so:

(a) Matsakaicin ƙarfin gogayya mai tsauri (b) Mafi ƙarancin ƙarfin F

Magani:

(a) Matsakaicin ƙarfin gogayya mai motsi

f _s = μ _s N

f _s = (0.4)(9.8 N) = 3.92 Newtons

(b) Mafi ƙarancin ƙarfin F

Idan an yi amfani da ƙarfin F a kan abin amma abin bai motsa ba, to dole ne a sami ƙarfin gogayya mai tsayi da ƙasa ke yi a kan abin. Idan abin zai fara motsawa, kuma an wuce ƙarfin gogayya mai tsayi, dole ne a sami ƙarfin gogayya mai tsayi. Abu zai fara motsawa idan F ya fi ƙarfin gogayya mai tsayi.

Don haka mafi ƙarancin ƙarfin F = matsakaicin ƙarfin gogayya mai tsauri = 3.92 Newtons.

[irp]

2. Ana jan akwatin kilogiram 1 a saman kwance ta hanyar ƙarfin F, don haka akwatin yana motsawa a cikin saurin da ba ya canzawa. Idan ma'aunin gogayya na motsi shine 0.1, ƙayyade girman ƙarfin F! (g = 9.8 m/s ² )

An sani:

_{Ma'aunin gogayya na motsi} ( μk ) = 0.1

Nauyin akwati (m) = 1 kg

Saurin nauyi (g) = 9.8 m/s ²

Nauyi (w) = mg = (1 kg)(9.8 m/s ² ) = 9.8 kg m/s ² = 9.8 Newtons

Ƙarfin al'ada (N) = w = 9.8 Newtons

Ana nema : F

Magani:

Dokar farko ta Newton ta bayyana cewa idan babu wani ƙarfi da ke aiki a kan wani abu, kowane abu yana ci gaba da kasancewa a cikin yanayin hutawarsa, ko kuma saurinsa na yau da kullun a cikin layi madaidaiciya.

Don haka idan abin yana motsawa a daidai gudun , dole ne babu ƙarfin da ya wuce kima ( Σ F = 0) . Ana amfani da ƙarfi F akan abu a daidai hanyar da za ta sa ƙarfin gogayya mai motsi ya yi aiki akan abu zuwa hagu.

∑ F = 0

F – f _k = 0

F = f _k

Ƙarfin gogayya ta motsi:

f _k = μ _k N = (0.1) (9.8 N) = 0.98 Newtons

abu yana motsawa da saurin da ba ya canzawa, F = f _k = 0.98 Newtons

[irp]

3. Wani abu yana zamewa ƙasa da wani jirgin sama mai karkata tare da saurin da ba ya canzawa. Ƙayyade ma'aunin gogayya na motsi ( _μk ) . g = 9.8 m/s ²

Magani

w = nauyi, w _x = ɓangaren nauyi a kwance, maki tare da karkata, w _y = ɓangaren nauyi a tsaye, a tsaye zuwa ga matakin da aka karkata, N = ƙarfin al'ada, f _k = ƙarfin gogayya ta motsi.

An sani:

Nauyi (m) = 1 kg

Saurin nauyi (g) = 9.8 m/s ²

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

w _x = w sin 30 ^o = (9.8 N)(0.5) = 4.9 Newtons

wy ₌ w cos 30 ^o = (9.8 N)(0.5) √ 3 = 4.9 √ Newtons 3

Ƙarfin al'ada (N) = w _y = 4.9 √ Newtons 3

Ana so : ma'aunin gogayya na motsi ( μk ₎

Magani:

Abu yana zamewa ƙasa da jirgin sama mai karkata tare da saurin da ya dace don ƙarfin raga = 0.

∑ F = 0

w _x – f _k = 0

w _x = f _k

w _x = μ _k N

5 = μ _k ( 5 √ 3 )

μ _k = 5/5 √ 3

μ _k = 1 / √ 3

μ _k = 0.58

[irp]

[wpdm_package id='472′]

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

Karin bayani

An warware matsaloli a cikin dokokin motsi na Newton - dokar motsi ta biyu ta Newton 

1. Abu mai nauyin kilogiram 1 yana sauri a daidai mita 5/s ^2. Kimanta ƙarfin da ake buƙata don hanzarta abin.

An sani:

Nauyi (m) = 1 kg

Hanzari (a) = 5 m/s ²

Ana so : ƙarfin da aka nema (∑F)

Magani:

Muna amfani da dokar Newton ta biyu don samun ƙarfin da ya dace.

∑ F = ma

∑ F = (1 kg)(5 m/s ² ) = 5 kg m/s ² = 5 Newtons

[irp]

2. Nauyin abu = 1 kg, ƙarfin da aka tara ∑F = 2 Newtons. Kayyade girma da alkiblar saurin abin….

An sani:

Nauyi (m) = 1 kg

Ƙarfin da aka samu (∑F) = 2 Newton

Ana so : Girma da alkiblar hanzarin (a)

Magani:

a = ∑F / m

a = 2/1

a = 2 m/s ²

Alkiblar hanzarin = alkiblar ƙarfin raga (∑F)

[irp]

3. Nauyin abu = 2 kg, F ₁ = 5 Newtons, F ₂ = 3 Newton. Girma da alkiblar hanzarin shine…

An sani:

Nauyi (m) = 2 kg

F ₁ = 5 Newton

F ₂ = 3 Newton

Ana so: Girma da alkiblar hanzarin (a)

Magani:

ƙarfi mai ƙarfi:

∑ F = F ₁ – F ₂ = 5 – 3 = Newtons 2

Girman hanzarin:

a = ∑F / m

a = 2/2

a = 1 m/s ²

Alkiblar hanzarin = alkiblar ƙarfin raga = alkiblar F ₁

[irp]

4. Nauyin abu = 2 kg, F ₁ = 10 Newtons, F ₂ = 1 Newton. Girma da alkiblar hanzarin shine…

An sani:

Nauyi (m) = 2 kg

F ₂ = 1 Newton

F ₁ = 10 Newton

F _1x = F ₁ cos 60 ^o = (10)(0.5) = 5 Newtons

Ana so : Girma da alkiblar hanzarin (a)

Magani:

Ƙarfin da aka samu:

∑ F = F _1x – F ₂ = 5 – 1 = Newtons 4

Girman hanzarin:

a = ∑F / m

a = 4/2

a = 2 m/s ²

Alkiblar hanzari = alkiblar ƙarfin raga = alkiblar F _1x

[irp]

5. F ₁ = 10 Newtons, F ₂ = 1 Newton, m ₁ = 1 kg, m ₂ = 2 kg. Girma da alkiblar hanzarin shine…

An sani:

Nauyi 1 (m1 ₎ = 1 kg

Nauyi 2 (m2 ₎ = 2 kg

F ₁ = 10 Newton

F ₂ = 1 Newton

Ana so : Girma da alkiblar hanzarin (a)

Magani:

Ƙarfin da ke cikinsa:

∑ F = F ₁ – F ₂ = 10 – 1 = Newtons 9

Girman hanzarin:

a = ∑F / (m ₁ + m ₂ )

a = 9 / (1 + 2)

a = 9/3

a = 3 m/s ²

Alkiblar hanzarin = alkiblar ƙarfin raga = alkiblar F ₁

[irp]

6.

Toshe mai nauyin kilogiram 40 da ƙarfin N200 ke ƙaruwa. Hawan toshewar shine 3 m/ s ^2. Kayyade girman ƙarfin gogayya da toshewar ta fuskanta.

A. 15 N

B. 40 N

C. 43 N

D. 80 N

An sani:

Nauyi (m) = 40 kg

Ƙarfi (F) = 200 N

Hanzari (a) = 3 m/s ²

Ana nema: Ƙarfin gogayya (F _g )

Magani:

Daidaiton dokar motsi ta biyu ta Newton

∑ F = ma

∑ F = ƙarfin da aka tara, m = taro, a = hanzari

Alkiblar ƙarfin F zuwa dama, alkiblar ƙarfin gogayya zuwa hagu (alkiblar ƙarfin gogayya yana akasin alkiblar motsin abu).

Zaɓi gefen dama a matsayin mai kyau da kuma gefen hagu a matsayin mara kyau.

∑ F = ma

F – F _g = ma

200 – F _g = (40)(3)

200 – F _g = 120

F _g = 200 – 120

F _g = 80 Newton

Amsar da ta dace ita ce D.

7. Toshe A da nauyin gram 100 a sama da toshe B tare da nauyin gram 300, sannan a tura toshe B da ƙarfin 5 N a tsaye sama. A tantance ƙarfin da toshe B ke yi a kan toshe A.

A. 1 N

B. 1.25 N

C. 2 N

D. 3 N

An sani:

Ƙarfi (F) = 5 Newton

Nauyin tubalin A (mA ₎ = gram 100 = 0.1 kg

Nauyin tubalin B (m _B ) = gram 300 = 0.3 kg

Saurin nauyi (g) = 10 m/s ²

Nauyin tubalin A (w _A ) = (0.1 kg)(10 m/s ² ) = 1 kg m/s ² = 1 Newton

Nauyin tubalin B (w _B ) = (0.3 kg)(10 m/s ² ) = 3 kg m/s ² = 3 Newtons

Ana so: Ƙarfin da aka saba amfani da shi ta hanyar toshe B don toshe A

Magani:

Akwai ƙarfi da dama da ke aiki a kan tubalan biyu, kamar yadda aka nuna a hoto.

F = ƙarfin turawa (aiki akan toshe B)

w _A = nauyin toshe A (aiki akan toshe A)

w _B = nauyin toshe B (aiki akan toshe B)

N _A = ƙarfin da toshe B ke yi akan toshe A (Yi aiki akan toshe A)

N _A ' = ƙarfin da toshe A ke amfani da shi akan toshe B (Yi aiki akan toshe B)

Yi amfani da dokar motsi ta biyu ta Newton a kan dukkan tubalan:

∑ F = ma

F – w _A – w _B + N _A – N _A ' = (m _A + m _B ) a

N _A da N _A ' ƙarfin amsawar aiki ne waɗanda suke da girma iri ɗaya amma akasin haka a alkibla don haka an cire su daga lissafin.

F – w _A – w _B = (m _A + m _B ) a

5 – 1 – 3 = (0.1 + 0.3) a

5 – 4 = (0.4) a

1 = (0.4) a

a = 1/0.4

a = 2.5 m/s ²

Yi amfani da dokar motsi ta biyu ta Newton a kan toshe A:

∑ F = ma

N _A – w _A = m _A a

N _A – 1 = (0.1)(2.5)

NA – ₁ = 0.25

NA = 1 + _0.25

NA = 1.25 _Newtons

Amsar da ta dace ita ce B.

8. Abu mai nauyin N 4 wanda igiya da pulley ke tallafawa. Ƙarfin N 2 yana aiki akan toshe da kuma ƙarshen igiyar da ƙarfin N 9 ke ja. Tantance ƙarfin da ke aiki akan abu X.

A. 3 N sama

B. 4 N ƙasa

C. 9 N sama

D. 9 N ƙasa

An sani:

Nauyin X (w _X ) = 4 Newton

Ƙarfin ja (F _x ) = 2 Newton

Ƙarfin tashin hankali (F _T ) = 9 Newtons

Ana nema: Ƙarfin da ke aiki a kan abu

Magani:

Ƙarfin da ke aiki a tsaye sama wanda ke aiki akan abu

Ƙarfin tashin hankali yana da girma iri ɗaya a dukkan sassan igiyar. Don haka ƙarfin tashin hankali shine 9 N.

Ƙarfin da ke aiki a tsaye a ƙasa wanda ke aiki akan abu

Akwai ƙarfi biyu da ke aiki akan abu X kuma duka ƙarfin suna tsaye a ƙasa, ɓangaren kwance na nauyi w _x da kuma ɓangaren kwance na ƙarfi F _x.

Aikin ƙarfi na net akan abu

F _T – w _X – F _x = 9 – 4 – 2 = 9 – 6 = 3

Ƙarfin da ke aiki akan abu X shine Newtons 3, a tsaye sama.

Amsar da ta dace ita ce A.

9. Abu da farko yana hutawa a saman kwance mai santsi. Ƙarfin N 16 yana aiki akan abu don haka abu yana hanzarta a 2 m/s ^2. Idan abu ɗaya da ke hutawa a kan saman kwance mai tsauri don haka ƙarfin gogayya yana aiki akan abu shine 2 N, to a tantance hanzarin abu idan ƙarfin N 16 iri ɗaya yana aiki akan abu.

A. 1.75 m/s ²

B. 1.50 m/s ²

C. 1.00 m/s ²

D. 0.88 m/s ²

An sani:

Ƙarfi (F) = 16 Newtons = 16 kg m/s ²

Hanzari (a) = 2 m/s ²

Ƙarfin gogayya (F _fric ) = 2 Newtons = 2 kg m/s ²

Ana so: Haɓaka abu?

Magani:

Sufuri mai santsi a kwance (babu ƙarfin gogayya):

ΣF = ma

F = ma

16 = (m) 2

m = 16/2

m = 8 kg

Nauyin abu shine kilo 8.

saman kwance mai kauri (akwai ƙarfin gogayya):

ΣF = ma

F – F _fric = ma

16 – 2 = 8 a

14 = 8 a

a = 14/8

a = 1.75 m/s ²

Saurin gudu na abu shine 1.75 m/s ².

Amsar da ta dace ita ce A.

10. Tom da Andrew suna tura abu a ƙasa mai santsi. Tom suna tura abu da ƙarfin N5.70. Idan nauyin abu ya kai kilogiram 2.00 kuma saurin da abu ya samu ya kai 2.00 ms ^-2 , to sai a tantance girma da alkiblar aikin ƙarfi da Tom ya fuskanta.

A. 1.70 N kuma alkiblarsa akasin ƙarfin da Andre.w ya yi ne.

B. 1.70 N kuma alkiblarsa iri ɗaya ce da ƙarfin da Andrew ya yi

C. 2.30 N kuma alkiblarta akasin ƙarfin da Andrew ya yi ne.

D. 2.30 N kuma alkiblarsa iri ɗaya ce da ƙarfin da Andrew ya yi.

An sani:

Ƙarfin turawa da Andrew ya yi (F ₁ ) = 5.70 Newton

Nauyin abu (m) = 2.00 kg

Hanzari (a) = 2.00 m/s ²

Ana so: Girma da alkiblar ƙarfin da Tom (F ₂ ) ya yi?

Magani:

Yi amfani da dokar motsi ta biyu ta Newton:

∑ F = ma

F ₁ + F ₂ = ma

5.70 + F ₂ = (2)(2)

5.70 + F ₂ = 4

F ₂ = 4 – 5.70

F ₂ = – 1.7 Newton

Alamar da aka rage ta nuna cewa (F ₂ ) akasin ƙarfin turawa ne na Andrew (F ₁ ).

Amsar da ta dace ita ce A.

11. Idan nauyin tonon ya yi daidai, wanne adadi ne ke nuna ƙaramin saurin gudu?

Magani

Ƙarfin da aka samu daga A:

ΣF = 4 N + 2 N - 3 N = 6 N - 3 N = 3 Newtons, hagu

Ƙarfin da aka samu daga net B:

ΣF = 2 N + 3 N - 4 N = 5 N - 4 N = 1 Newtons, dama

Ƙarfin C:

ΣF = 4 N + 3 N - 2 N = 7 N - 2 N = 5 Newtons, dama

Ƙarfin da aka samu D:

ΣF = 3 N + 4 N + 2 N = 9 Newtons, dama

Daidaiton dokar Newton ta biyu:

ΣF = ma

a = ΣF / m

a = hanzari, ΣF = ƙarfin net, m = taro

Bisa ga dabarar da ke sama, hanzarin (a) yana daidai gwargwado kai tsaye da ƙarfin net (ΣF) kuma yana daidai gwargwado da taro (m). Idan nauyin abu iri ɗaya ne, girman ƙarfin da aka samu, girman hanzarin ko ƙaramin ƙarfin da aka samu, ƙaramin hanzarin.
Dangane da lissafin da ke sama, mafi ƙarancin ƙarfin net shine 1 Newton don haka hanzarin shine mafi ƙanƙanta.

Amsar da ta dace ita ce B.

[irp]

12. Wasu ƙarfi suna aiki akan wani abu mai nauyin kilogiram 20, kamar yadda aka nuna a cikin hoton da ke ƙasa.

Kayyade hanzarin abin.

An sani:

Nauyin abu (m) = 20 kg

Ƙarfin net (ΣF) = 25 N + 30 N - 15 N = 40 N

Ana so: Haɓaka abu

Magani:

An ƙididdige hanzarin abu ta amfani da lissafin dokar Newton ta biyu:

ΣF = ma

a = ΣF / m = 40 N / 20 kg = 2 N/kg = 2 m/s ²

[irp]

13. Wace magana a ƙasa ta bayyana dokar Newton ta uku?

(1) Fasinjoji sun matsa gaba lokacin da bas ɗin ya yi birki ba zato ba tsammani

(2) Littattafai a kan takarda ba sa faɗuwa idan aka ja takardar da sauri

(3) Idan ana buga skateboard idan ƙafa ta tura ƙasa baya to skateboard ɗin zai zame gaba

(4) O ars an tura su baya, jiragen ruwa suna ci gaba

Magani:

(1) Dokar farko ta Newton

(2) Dokar farko ta Newton

(3) Dokar Newton ta uku

(4) Dokar Newton ta uku

[wpdm_package id='470′]

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

An warware matsaloli a cikin dokokin motsi na Newton - Ƙarfin al'ada 

1. Wani abu da ke kan teburi, wanda aka nuna a cikin hoton da ke ƙasa. Nauyin abin shine kg 1. Saurin nauyi shine 9.8 m/s ^2. Kayyade ƙarfin da aka saba amfani da shi akan abu ta hanyar teburin.

An sani:

Nauyi (m) = 1 kg

Saurin nauyi (g) = 9.8 m/s ²

Nauyi (w) = mg = (1 kg)(9.8 m/s ² ) = 9.8 kg m/s ² = 9.8 Newtons

Ana so: ƙarfin yau da kullun (N)

Magani:

Abu yana tsaye a kan tebur, don haka ƙarfin da ke kan abu sifili ne (dokar farko ko ta biyu ta Newton). Nauyin abu yana aiki a tsaye zuwa ƙasa, zuwa tsakiyar Duniya. Dole ne a sami wani ƙarfi a kan abu don daidaita ƙarfin nauyi . Abu da ke kwance a kan tebur, don haka teburin yana yin wannan ƙarfin sama. Ƙarfin da teburin ke yi galibi ana kiransa ƙarfi na yau da kullun (N). Na al'ada yana nufin perpendicular.

Zaɓi alkiblar sama a matsayin alkiblar y mai kyau. Ƙarfin da ke kan abu shine:

∑ Fy = 0

N – w = 0

N = w

N = mg

N = 9.8 Newton

Ƙarfin da aka saba da shi a kan abin, wanda teburin ke amfani da shi shine N 9.8 sama.

[irp]

2. Abubuwa biyu da ke kan teburi. Nauyin abu 1 (m ₁ ) = 1 kg, nauyin abu 2 (m ₂ ) = 2 kg, hanzari saboda nauyi (g) = 9.8 m/s ^2. Ƙayyade girma da alkiblar ƙarfin da m ₂ ke bayarwa akan m ₁ da ƙarfin da teburin ke bayarwa akan m ₂.

Magani

An sani:

Nauyin abu 1 (m1 ₎ = 1 kg

Nauyin abu 2 (m2 ₎ = 2 kg

Saurin nauyi (g) = 9.8 m/s ²

Nauyin abu 1 (w ₁ ) = m ₁ g = (1)(9.8 m/s ² ) = 9.8 kg m/s ² = 9.8 Newtons

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

Ana nema: N ₁ da N ₂

Magani:

(a) Ƙarfin da aka saba amfani da shi ta hanyar _m2 zuwa _m1 ( _N1 )

N ₁ = w ₁ = 9.8 Newton

Alkiblar N1 _tana sama.

(b) Ƙarfin da teburin ke amfani da shi a kan _m2 ( _N2 )

N ₂ = w ₁ + w ₂ = 9.8 Newtons + 19.6 Newtons = 29.4 Newtons

Alkiblar N2 _tana sama.

[irp]

3. Abu da ke kan teburi. Nauyin abu shine kilogiram 2, hanzarin da aka samu saboda nauyi shine 9.8 m/s ^2. Girman ƙarfin F shine Newtons 10. Nemo girma da alkiblar ƙarfin da teburin ke amfani da shi akan abu.

Magani

An sani:

Nauyin abu (m) = 2 kg

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

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

Ƙarfin F (F) = 10 Newton

Ana so : girma da alkiblar ƙarfin al'ada (N)

Magani:

alkiblar ƙarfin al'ada tana sama.

Girman ƙarfin da aka saba da shi:

∑ F = 0

N – F – w = 0

N = F + w

N = 10 Newtons + 20 Newtons

N = 30 Newton

[irp]

4. Abu da ke kan teburi. Nauyin abu shine kilogiram 1, hanzarin da aka samu saboda nauyi shine 9,8 m/s ² , ƙarfin F ₁ shine 10 N kuma ƙarfin F ₂ shine 20 N. Kayyade girma da alkiblar ƙarfin da teburin ke amfani da shi akan abu. g = 9.8 m/s ²

Magani

An sani:

Nauyi (m) = 1 kg

Saurin nauyi (g) = 9.8 m/s ²

Nauyi (w) = mg = (1 kg)(9.8 m/s ² ) = 9.8 kg m/s ² = 9.8 Newtons

F ₁ = 10 Newton

F ₂ = 20 Newton

Ana so: girma da alkiblar ƙarfin al'ada (N)

Magani:

Alkiblar ƙarfin al'ada tana sama.

Girman ƙarfin da aka saba da shi:

∑ F = 0

N – F ₂ – w + F ₁ = 0

N = F ₂ + w – F ₁

N = 20 Newtons + 9.8 Newtons – 10 Newtons

N = 19.8 Newton

[irp]

5. Nauyin abu (m) = 2 kg, saurin nauyi (g) = 9.8 m/s ² , kusurwa = 30 ^o . Nemo girma da alkiblar ƙarfin da aka saba amfani da shi akan abu.

Magani:

w shine nauyi, w _x shine ɓangaren kwance na nauyin, w _y shine ɓangaren tsaye na nauyin, N shine ƙarfin al'ada.

An sani:

nauyi (m) = 2 kg

hanzarta nauyi (g) = 9.8 m/s ²

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

w _x = w sin 60 ^o = (19.6 N)(0.5) √ 3 = 9.8 √ Newtons 3

w _y = w cos 60 = (19.6 N)(0.5) = 9.8 Newtons

Ana so: ƙarfin yau da kullun (N)

Magani:

∑ F = 0

N – w _y = 0

N = w _y

N = 9.8 Newton

[irp]

[wpdm_package id='467′]

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

An warware matsaloli a cikin dokokin motsi na Newton - Matsakaici, da nauyi

1. Nauyin nauyin kilogiram 1 a saman Duniya shine… g = 9.8 m/s ²

An sani:

Nauyi (m) = 1 kg

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

Ana so: nauyi (w)

Magani:

w = mg

m = nauyi (Nau'in SI na nauyi shine kilogram, kg)

g = hanzari saboda nauyi (Raka'ar SI ta g shine m/s ² )

w = nauyi (Raka'ar SI ta w shine kg m/s ² ko Newton)

Nauyin:

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

[irp]

2.

(a) Zana ƙarfin nauyi (nauyi) da ke aiki akan abu lokacin da abu ya tsaya akan teburi, kamar yadda aka nuna a hoto (a).

(b) Zana ƙarfin nauyi (nauyi) da sassansa waɗanda ke aiki akan wani abu da ke zamewa ƙasa da jirgin sama mai karkata , kamar yadda aka nuna a hoto (b)

Magani

Alkiblar nauyin tana ƙasa zuwa tsakiyar Duniya.

w _x = ɓangaren kwance na nauyin da w _y = ɓangaren tsaye na nauyin da w y

[irp]

3. Nauyin akwati shine 1 kg kuma hanzarin da aka samu saboda nauyi shine 9.8 m/s ^2. Nemo (a) nauyi (b) ɓangaren kwance da ɓangaren tsaye na nauyin.

Magani

Nauyi: w = mg = (1 kg)(9.8 m/s ² ) = 9.8 kg m/s ² = 9.8 Newtons

Sashen kwance na nauyin:

w _x = w sin 30 ^o = (9,8 N)(0,5) = 4.9 Newtons

A tsaye bangaren nauyin:

w _y = w cos 30 ^o = (9.8 N)(0.5√3) = 4.9√3 Newtons

[irp]

[wpdm_package id='458′]

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

Matsalolin da aka Warware a Motsin Layi - Motsin Sama da Ƙasa a lokacin faɗuwar 'yanci

1. Mutum yana jefa ƙwallo sama zuwa sama da saurin farko na 20 m/s. Lissafa yadda yake tafiya. Yi watsi da juriyar ruwa. Saurin gudu saboda nauyi (g) = 10 m/s ².

Magani

Muna amfani da ɗaya daga cikin waɗannan lissafin kinematic don motsi a cikin hanzari akai-akai , kamar yadda aka nuna a ƙasa.

v _t = v _o + a

s = v _o t + ½ a ²

v _t ² = v _o ² + 2 kamar yadda

An sani:

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

Saurin farko (v _o ) = 20 m/s (sama mai kyau)

Saurin nauyi (g) = – 10 m/s ² (ƙasa ta ƙasa).

Saurin ƙarshe (v _t ) = 0 (gudun sa sifili ne a cikin ɗan lokaci a mafi girman matsayi)

Ana so: Matsakaicin tsayi (h)

Magani:

v _t ² = v _o ² + 2 gh

0 = (20 ² ) + 2(-10) h

0 = 400 – 20 hours

400 = awanni 20

h = 400 / 20 = 40 / 2 = mita 20

[irp]

2. Mutum yana jefa dutse sama a gudun mita 20/s yayin da yake tsaye a gefen wani dutse, ta yadda dutsen zai iya faɗuwa zuwa gindin dutsen mita 100 a ƙasa.

(a) Tsawon lokacin da ƙwallon zai ɗauka kafin ya isa gindin dutsen (b) Saurin ƙarshe kafin dutsen ya bugi ƙasa. Saurin nauyi saboda nauyi (g) = 10 m/s ^2. Yi watsi da juriyar ruwa.

An sani:

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

Babba (h) = mita -100 (mara kyau saboda matsayin ƙarshe a ƙasa da matsayin farko)

Saurin farko (v _o ) = 20 m/s (sama mai kyau)

Saurin nauyi (g) = -10 m/s ² (ƙasa ta ƙasa)

Ana so:

(a) Lokacin iska ko tazara ta lokaci (t)

(b) Saurin ƙarshe (v _t )

Magani:

(a) Tazarar lokaci (t)

An sani:

Babba (h) = mita -100 (mara kyau saboda matsayin ƙarshe a ƙasa da matsayin farko)

Saurin farko (v _o ) = 20 m/s (mai kyau zuwa sama), Saurin nauyi (g) = -10 m/s ² (mara kyau zuwa ƙasa).

h = v _o t + ½ gt ²

-100 = (20) t + ½ (-10) t ²

-100 = 20 t – 5 t ²

-5 t ² + 20 t + 100 = 0

Muna amfani da dabarar quadratic:

(b) Saurin ƙarshe

v _t ² = v _o ² + 2 gh

v _t ² = (20 ² ) + 2 (-10)(-100)

v _t ² = 400 + 2000

v _t ² = 2400

v _t = 49 m/s

[irp]

[wpdm_package id='515′]

[wpdm_package id='517′]

1. Nisa da ƙaura
2. Matsakaicin gudu da matsakaicin gudu
3. Gudun da ba ya canzawa
4. Ci gaba da hanzari akai-akai
5. Motsin faɗuwa kyauta
6. Motsin ƙasa a cikin faɗuwar 'free fall'
7. Motsin sama da ƙasa a cikin faɗuwar 'yanci

Karin bayani

Matsalolin da aka Warware a Motsin Layi - Motsin Ƙasa a lokacin faɗuwar 'yanci

1. Ana jefa ƙwallon a tsaye ƙasa da saurin farko na 10 m/s kuma ta isa ƙasa cikin daƙiƙa 2. Nemo saurin ƙarshe kafin ƙwallon ta faɗi ƙasa. Saurin nauyi (g) = 10 m/s ^2. Yi watsi da juriyar ruwa.

An sani:

Saurin farko (v _o ) = 10 m/s

Lokacin da ya shude (t) = daƙiƙa 2

Saurin nauyi (g) = 10 m/s ²

Ana so: Saurin ƙarshe (v _t )

Magani:

Hanzari 10 m/s ² yana nufin ƙaruwar gudu da m/s 10 a kowace daƙiƙa. Bayan daƙiƙa 3, gudu = m/s 30.

Saurin ƙarshe = 10 m/s + 20 m/s = 30 m/s.

Lissafin kinematic don motsi a cikin hanzari akai-akai , kamar yadda aka nuna a ƙasa:

v _t = v _o + a ………. 1

h = v _o t + ½ a ² ………. 2

v _t ² = v _o ² + 2 ah………. 3

v _t = v _o + g t

v _t = 10 + (10)(2)

v _t = 10 + 20 = 30 m/s

Saurin ƙarshe = v _t = 30 m/s

[irp]

2. Ana jefa dutse a tsaye daga gada mai saurin farko na m 5/s kuma ya isa ruwan cikin daƙiƙa 2. A ƙididdige tsayin gadar.

An sani:

Saurin farko (v _o ) = 5 m/s

Lokacin da ya shude (t) = daƙiƙa 2

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

Ana so: tsayin gadar (h)

Magani:

h = v _o t + ½ gt ²

h = (5)(2) + ½ (10)(2) ²

h = 10 + (5)(4)

h = 10 + 20

h = mita 30

[irp]

3. Ana jefa ƙwallon a tsaye ƙasa da saurin farko na mita 10/s daga tsayin mita 80. Nemo (a) Lokacin da ake cikin iska (b) Saurin ƙarshe kafin ƙwallon ta faɗi ƙasa.

An sani:

tsayi (h) = mita 80

Saurin farko (v _o ) = 10 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so:

(a) Tazarar lokaci (t)

(b) Saurin ƙarshe (v _t )

Magani:

(a) Tazarar lokaci (t)

Saurin ƙarshe:

v _t ² = v _o ² + 2 gh

v _t ² = (10) ² + 2(10)(80) = 100 + 1600 = 1700

v _t = 41 m/s

Tazarar lokaci (t):

v _t = v _o + g t

41 = 10 + (10)(t)

41 – 10 = 10 t

31 = 10t

t = 31/10 = daƙiƙa 3,1

(b) Saurin ƙarshe (v _{t )}?

v _t = 41 m/s

[irp]

[wpdm_package id='513′]

[wpdm_package id='517′]

1. Nisa da ƙaura
2. Matsakaicin gudu da matsakaicin gudu
3. Gudun da ba ya canzawa
4. Ci gaba da hanzari akai-akai
5. Motsin faɗuwa kyauta
6. Motsin ƙasa a cikin faɗuwar 'free fall'
7. Motsin sama da ƙasa a cikin faɗuwar 'yanci

Karin bayani