Physics

Matsalolin da aka Warware a Motsin Layi - Abubuwa masu faɗuwa cikin 'yanci

1. Wani abu ya faɗo daga saman wani dutse. Ana ganin ya faɗi ƙasa a ƙasa bayan daƙiƙa 3. A ƙayyade saurinsa kafin ya faɗi ƙasa. Saurin nauyi shine 10 m/s ^2. A yi watsi da juriyar ruwa.

An sani:

Saurin farko (v _o ) = 0 (an sauke abu)

Tazarar lokaci (t) = daƙiƙa 3

Saurin nauyi (g) = 10 m/s ²

Ana so: Saurin ƙarshe (v _t )

Magani:

Saurin gudu saboda nauyi a saman duniya, girmansa shine 9.8 m/s ^2. Domin sauƙaƙa lissafi, muna amfani da 10 m/s ².

10 m/s ² ko 10 m/s / daƙiƙa 1, yana nufin cewa saurin yana ƙaruwa a layi a cikin lokaci da 10 m/s a cikin kowane daƙiƙa.

Bayan daƙiƙa 1, saurin abu = 10 m/s

Bayan daƙiƙa 2, saurin abu = 20 m/s

Bayan daƙiƙa 3, saurin abu = 30 m/s.

Haka kuma za mu iya amfani da 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

Faɗuwar 'yanci ba ta da saurin farko (v _o = 0), don haka ana iya canza lissafin da ke sama kamar yadda aka nuna a ƙasa:

Daidaito na motsi na faɗuwa kyauta :

v _t = gt ………… 1

h = ½ gt ² ………… 2

v _t ² = 2 gh ………….. 3

v _t = gt

v _t = (10)(3)

v _t = 30 m/s

Gudun ƙarshe shine 30 m/s

[irp]

2. Jiki ya faɗi cikin 'yanci daga hutawa, daga tsayin mita 25. Nemo (a) Saurin da yake yi wa ƙasa. (b) Lokacin da ake ɗauka kafin a isa ƙasa.

Saurin gudu saboda nauyi a saman Duniya shine 10 m/s ².

An sani:

Tsawo (h) = mita 5

Saurin nauyi (g) = 10 m/s ²

Ana so:

(a) Saurin ƙarshe (v _t )

(b) Tazarar lokaci (t)

Magani:

Daidaiton 'Free fall':

v _t = gt

h = ½ gt ²

v _t ² = 2 gh

(a) Saurin ƙarshe (v _t )

v _t ² = 2 gh = 2(10)(5) = 100

v _t = 10 m/s

(b) Tazarar lokaci (t)

h = ½ gt ²

5 = ½ (10) t ²

5 = 5 t ²

t ² = 5/5 = 1

t = daƙiƙa 1

[irp]

3. Ƙwallo ta faɗi daga tsayi. Nemo (a) Hanzari (b) Nisa bayan daƙiƙa 3 (c) Lokacin da ke cikin iska idan saurin ƙarshe ya kai m20/s. Hanzari saboda nauyi = m10/s ²

An sani :

Saurin nauyi (g) = 10 m/s ²

Ana so:

(a) Hanzartawa (a)

(b) Nisa ko tsayi (h) idan lokaci ya wuce (t) = daƙiƙa 3

(c) Tazarar lokaci (t) idan v _t = 20 m/s

Magani:

Daidaiton 'Free fall':

v _t = gt

h = ½ gt ²

v _t ² = 2 gh

(a) Hanzartawa (a)

Hawan sauri = hanzari saboda nauyi = 10 m/s ^2. Yana nufin ƙaruwar gudu da 10 m/s a kowace daƙiƙa.

(b) Nisa ko tsayi (h) bayan t = daƙiƙa 3

h = ½ gt ² = ½ (10)(3) ² = (5)(9) = mita 45

(c) Lokaci ya shude (t) idan v _t = 20 m/s

v _t = gt

20 = (10) t

t = 20/10 = daƙiƙa 2

[irp]

[wpdm_package id='511′]

[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 - Saurin sauri akai-akai

1. Mota tana sauri daga hutawa zuwa 20 m/s cikin daƙiƙa 10. Kayyade saurin motar!

Magani

An sani:

Saurin farko (v _o ) = 0 (hutu)

Tazarar lokaci (t) = daƙiƙa 10

Saurin ƙarshe (v _t ) = 20 m/s

Ana nema : Hanzari (a)

Magani:

v _t = v _o + a

20 = 0 + (a)(10)

20 = 10 a

a = 20/10

a = 2 m/s ²

[irp]

2. Mota tana raguwa daga mita 30/s zuwa hutawa cikin daƙiƙa 10. Kayyade saurin motar.

Magani

An sani:

Saurin farko (v _o ) = 30 m/s

Saurin ƙarshe (v _t ) = 0

Tazarar lokaci (t) = daƙiƙa 10

Ana so: hanzari (a)

Magani:

v _t = v _o + a

0 = 30 + (a)(10)

– 30 = 10 a

a = – 30/10

a = -3 m/s ²

Alamar mara kyau ta bayyana saboda saurin ƙarshe ya ƙasa da saurin farko.

[irp]

3. Mota tana farawa da sauri a daidai lokacin da take gudu da sauri 4 m/s ² a cikin daƙiƙa 1. Kayyade gudu da nisa bayan daƙiƙa 10.

Magani

(a) Sauri

Saurin gudu 4 m/s ² yana nufin ƙaruwar gudu 4 m/s a kowace daƙiƙa 1. Bayan daƙiƙa 2, saurin motar shine 8 m/s. Bayan daƙiƙa 10, saurin motar shine 40 m/s.

(b) Nisa

An sani:

Saurin farko (v _o ) = 0

Saurin ƙarshe (v _t ) = 40 m/s

Hanzari (a) = 4 m/s ²

Ana nema: Nisa

Magani:

s = v _o t + ½ a ² = 0 + ½ (4)(10 ² ) = (2)(100) = mita 200

[irp]

4. Mota tana tafiya a daidai gudun mita 10/s, sannan ta rage gudu a daidai gudun mita 2/s ^{2 har sai ta huta. A ƙayyade lokacin da ya wuce da kuma} nisan motar kafin ta huta.

An sani:

Saurin farko (v _o ) = 10 m/s

Hanzari (a) = -2 m/s ² (Alamar mara kyau ta bayyana saboda saurin ƙarshe ya ƙasa da saurin farko)

Saurin ƙarshe (v _t ) = 0 (hutu)

Ana so: Tazarar lokaci da nisa

Magani:

(a) Tazarar lokaci (t)

v _t = v _o + a

0 = 10 + (-2)(t)

0 = 10 – 2 t

10 = 2t

t = 10/2 = daƙiƙa 5

(b) Nisa

v _t ² = v _o ² + 2 kamar yadda

0 = 10 ² + 2(-2) s

0 = 100 – 4 s

100 = daƙiƙa 4

s = 100 / 4 = mita 25

[irp]

5. Mota tana tafiya a gudun mita 40/s, tana raguwa a gudun mita 4/s ² har sai ta huta. Kayyade gudu da nisa bayan raguwar gudu cikin daƙiƙa 10!

Magani

An sani:

Saurin farko (v _o ) = 40 m/s

Hanzari (a) = -4 m/s ²

Tazarar lokaci (t) = daƙiƙa 10

Ana so: saurin ƙarshe (v _t ) da nisa (s)

Magani:

(a) Saurin ƙarshe

v _t = v _o + a = 40 + (-4)(10) = 40 – 40 = 0 m/s

0 m/s yana nufin hutawa a mota.

(b) Nisa

s = v _o t + ½ a ² = (40)(10) + ½ (-4)(10 ² ) = 400 + (-2)(100) = 400 – 200 = mita 200

[irp]

6. Kayyade nisa bayan daƙiƙa 10!

Magani

Nisa: s = vt = (10-0)(5-0) = (10)(5) = mita 50

7. Kayyade nisa bayan daƙiƙa 4!

Magani

Nisa = murabba'in yanki + murabba'in yanki

Nisa = (8-0)(8-0) + ½ (16-8)(8-0) = (8)(8) + ½ (8)(8) = 64 + 32 = mita 96

8. Kayyade nisan motar bayan daƙiƙa 4!

Magani

Nisa = yanki mai kusurwa uku = ½ (4-0)(8-0) = ½ (4)(8) = mita 16

9. Wata mota tana tafiya a gudun kilomita 90/h ta wuce motar 'yan sanda da ta tsaya a gefen hanya. Minti daya bayan haka, motar 'yan sanda ta bi ta a ^gudun mita 0.8/s . Har yaushe motar 'yan sanda ta isa motar?

An sani:

Saurin mota (v) = 90 km/awa = mita 90,000 / daƙiƙa 3600 = mita 25/daƙiƙa

Tazarar lokaci (t) = minti 1 = daƙiƙa 60

Saurin motar 'yan sanda (a) = 0.8 m/s ²

Saurin farko na motar 'yan sanda (v _o ) = 0 m/s

Ana nema: Nisan da motar 'yan sanda ta yi tafiya

Magani:

Motar tana tafiya a daidai lokacin gudu. Nisa da mota ke tafiya:

Nisa ta farko:

s = vt = (25)(60) = mita 1500

Nisa ta ƙarshe:

s = vt = (25)(t)

Jimlar nisa = 1500 + 25 t

Motar 'yan sanda tana tafiya cikin sauri akai-akai. Nisa da motar 'yan sanda ta yi:

s = v _o t + ½ a ² = (0)(t) + ½ (0.8)(t ² ) = 0 + 0.4 t ² = 0.4 t ²

Idan motar 'yan sanda ta isa motar, nisan da motar 'yan sanda ta yi daidai yake da nisan da motar ta yi.

Nisa da mota ta yi = nisan da motar 'yan sanda ta yi

1500 + 25 t = 0.4 t ²

0.4 t ² – 25 t – 1500 = 0

Yi amfani da dabarar quadratic:

Nisan da motar 'yan sanda ta yi tafiya:

s = 0.4 t ² = (0.4)(100 ² ) = (0.4)(10,000) = mita 4000 s = 4 km

10. Mota tana motsawa a birki mai gudun mita 24/s akai-akai don ta sami raguwar gudu na mita 0.952/s akai - akai . ^2. Kayyade gudun motar bayan nisan mita 250.

An sani:

Saurin farko (v _o ) = 24 m/s

Hanzari (a) = – 0.952 m/s ² ( an sanya alama ta korau saboda raguwar gudu )

Nisa ( d ) = mita 250 a sakan daya

Ana Neman: Saurin mota bayan mita 250 a sakan daya

Magani:

Sananne: saurin farko (v_o), hanzari (a), distance (d), ana so: gudun ƙarshe (v_t) don haka yi amfani da lissafin v_t² = v_o² +2 ba d

v _t = saurin ƙarshe , v _o = saurin farko , a = hanzari , d = nisa

v _t ² = (24) ² + (2)(-0.952)(250)

v _t ² = 576 – 476

v _t ² = 100

v _t = √100

v _t = 10 m/s

[irp]

[wpdm_package id='507′]

[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 - Saurin da ba a Taɓa Yi Ba

1. Mota tana tafiya a daidai lokacin da take tafiya da mita 10/s. Kayyade nisa bayan daƙiƙa 10 da daƙiƙa 60.

Magani

Gudun da ba ya canzawa mita 10/daƙiƙa yana nufin mota tana tafiya mita 10 a kowace daƙiƙa 1.

Bayan daƙiƙa 2, motar ta yi tafiyar mita 20,

Bayan daƙiƙa 5, motar ta yi tafiyar mita 50,

Bayan daƙiƙa 10, motar ta yi tafiyar mita 100 ,

Bayan daƙiƙa 60, motar ta yi tafiyar mita 600.

[irp]

2. Mota tana tafiya a kan hanya madaidaiciya a gudun kilomita 72/h. Kayyade nisan motar bayan mintuna 2 da mintuna 5.

Magani

72 km/h = (72)(mita 1000) / daƙiƙa 3600 = 72,000 / daƙiƙa 3600 = mita 20/daƙiƙa.

Gudun da ake samu a mita 20/daƙiƙa yana nufin motar tana tafiya mita 20 a kowace daƙiƙa 1.

Bayan daƙiƙa 120 ko mintuna 2, mota tana tafiya mita 20 x 120 = mita 2400 ,

Bayan daƙiƙa 300 ko mintuna 5, motar tana tafiya mita 20 x 300 = mita 6000.

[irp]

3. Jiki yana tafiya a kan hanya madaidaiciya na tsawon mita 100 cikin daƙiƙa 50. Kayyade saurin jiki.

Magani

Mita 100 / daƙiƙa 50 = mita 10 / daƙiƙa 5 = mita 2/daƙiƙa.

4. Kayyade gudu bisa ga zane da ke ƙasa….

Magani

Sauri = Nisa / lokaci ya wuce

Gudu = mita 2 / daƙiƙa 1 = mita 4 / daƙiƙa 2 = mita 6 / daƙiƙa 3 = mita 8 / daƙiƙa 4 = mita 2/daƙiƙa.

5. Motoci A da B suna kusantar juna a kan layukan layi daya. Idan nisan da ke tsakanin motocin biyu ya kai mita 100, mota A tana tafiya da sauri na mita 10/s, mota B tana tafiya da sauri na mita 40/s. Kayyade (a) nisan mota A kafin ta wuce mota B (b) tazara ta lokaci kafin motar B ta wuce mota A.

Magani

Mota A tana tafiya da gudu mai tsayi a mita 10/daƙiƙa, ma'ana motar A tana tafiya har zuwa mita 10 a kowace daƙiƙa 1. Bayan daƙiƙa 2, mota tana tafiya har zuwa mita 20.

Motar B tana tafiya da gudu mai tsayi a mita 40/daƙiƙa, ma'ana motar B tana tafiya har zuwa mita 40 a kowace daƙiƙa 1. Bayan daƙiƙa 2, motar B tana tafiya har zuwa mita 80.

Mita 20 + mita 80 = mita 100.

(a) Nisa tsakanin mota A da mota B shine mita 20. Nisa tsakanin mota B da mota A shine mita 80.

(b) Tazarar lokacin da mota B ke yi kafin wucewar mota A shine daƙiƙa 2. Tazarar lokacin da mota A ke yi kafin wucewar mota B shine daƙiƙa 2

5. Idan ma'aunin gudu na mota ya nuna kilomita 108/h, a ƙayyade nisan da mota ta yi a cikin minti ɗaya.

Magani:

Na'urar auna gudu kayan aiki ne don auna gudu. Gudun mota shine kilomita 108/awa.
108 km / h = (108) (mita 1000) / daƙiƙa 3600 = mita 30/daƙiƙa.

Minti 1 = daƙiƙa 60

Gudun motar mita 30/daƙiƙa yana nufin motar tana tafiya har zuwa mita 30 cikin daƙiƙa 1.

Bayan daƙiƙa 1, motar ta yi tafiya har zuwa mita 1 x 30 = mita 30.

Bayan daƙiƙa 2, motar ta yi tafiya har zuwa mita 2 x 30 = mita 60.

Bayan daƙiƙa 60, motar ta yi tafiya har zuwa mita 60 x 30 = mita 1800.

6. Tom ya jefa kwallo kai tsaye ga Andrew . Tom da Andrew sun rabu har zuwa mita 10.08 . An jefa kwallon a kwance kuma tana motsawa a mita 20/ s (yi watsi da nauyi). Andrew ya buga kwallon da dakika 4.00 x 10 ^-3 bayan an jefa kwallon. Idan mai bugawa ya motsa a gudun mita 5.00/s, mai bugawa zai buga kwallon bayan mai bugawa ya motsa har zuwa…

An sani:

Nisa tsakanin Tom da Andrew = mita 10.08

Saurin ƙwallon (v) = 20 m/s

Tazarar lokaci (t) = daƙiƙa 4 x 10 ^-3 = daƙiƙa 0.004

Gudun mai bugawa (v) = 5 m / s

SE busca: Mai bugun ya buge ƙwallon bayan ƙwallon ta yi nisa har zuwa…

Magani:

Nisa tsakanin ƙwallon:

s ₁ = vt = (20) (0.004) = mita 0.08

Nisa tsakanin mai bugawa:

s ₂ = vt = 5 t

Nisan Ball + nisan mai bugawa = nisan da ke tsakanin Tom da Andrew.

0.08 + 5 t = 10.08

5 t = 10.08 – 0.08

5 t = 10

t = 10 / 5

t = daƙiƙa 2

Nisa tsakanin mai bugawa:

s ₂ = vt = 5 t = (5) (2) = mita 10

7. Wani mafarauci da motarsa ​​yana bin barewa. Motar tana tafiya a gudun kilomita 72 a sa'a guda, barewa kuma tana gudu a gudun kilomita 64.8 a sa'a guda. Idan nisan da ke tsakanin motar da barewa ya kai mita 2012, mafarauci ya harba bindigarsa. Harsasai daga bindigar a gudun mita 200 a sa'a guda. A tantance tazarar lokacin da barewa za ta harba.

A. 0.5 s

B. 1 s

C. 1.25 s

D. 1.5 s

An sani:

Gudun mota (v _b ) = 72 km/h = (72)(1000 m) / 3600 s = 20 m/s

Gudun barewa (v _r ) = 64.8 km/h = (64.8)(m 1000) / 3600 s = 64800 m / 3600 s = 18 m/s

Idan aka harba harsashin, nisan da ke tsakanin motar da barewa = mita 202

Gudun wuta (v _p ) = 20 m/s + 200 m/s = 220 m/s

Makamai da mafarauta ke riƙewa waɗanda ke cikin mota mai gudun mita 20/s don haka saurin motar ma ya ƙara da saurin harsashin.

Ana so: A ƙayyade tazarar lokacin da barewa za ta yi harbi

Magani:

Ka yi tunanin motoci da barewa suna tafiya a hankali.

Daidaito: v = s / t ko s = vt

v = gudu, s = nisa, t = tazara lokaci

Nisa = 202 + X _r = 202 + v _r t = 202 + 18 t

Nisa = Y _p = v _p t = 220 t

Nisa da barewa ta yi = nisan da harsashi ya yi

202 + 18 t = 220 t

202 = 220 t – 18 t

202 = 202t

t = 202 / 202

t = daƙiƙa 1

Amsar da ta dace ita ce B.

[irp]

[wpdm_package id='507′]

[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 - Matsakaicin gudu da matsakaicin gudu

1. Mota tana tafiya a kan hanya madaidaiciya zuwa gabas na tsawon mita 100 cikin daƙiƙa 4, sannan ta nufi yamma na tsawon mita 50 cikin daƙiƙa 1. Ka ƙayyade matsakaicin gudu da matsakaicin gudu.

Magani

Nisa = mita 100 + mita 50 = mita 150

Gudun hijira = mita 100 – mita 50 = mita 50, zuwa gabas.

Lokacin da ya wuce = daƙiƙa 4 + daƙiƙa 1 = daƙiƙa 5.

Matsakaicin gudu = Nisa / lokacin da ya wuce = mita 150 / daƙiƙa 5 = mita 30/daƙiƙa.

Matsakaicin gudu = Gudun tafiya / lokacin da ya wuce = mita 50 / daƙiƙa 5 = mita 10/daƙiƙa.

[irp]

2. Mutum yana tafiya mita 4 gabas cikin daƙiƙa 1, sannan ya yi tafiya mita 3 arewa cikin daƙiƙa 1. A ƙayyade matsakaicin gudu da matsakaicin gudu.

Magani

Nisa = mita 4 + mita 3 = mita 7

Gudun Hijira = = mita, zuwa arewa maso gabas.

Lokaci ya shude = daƙiƙa 1 + daƙiƙa 1 = daƙiƙa 2.

Matsakaicin gudu = nisa / lokacin da ya wuce = mita 7 / daƙiƙa 2 = mita 3.5/daƙiƙa

Matsakaicin gudu = ƙaura / lokacin da ya wuce = mita 5 / daƙiƙa 2 = mita 2.5/daƙiƙa

[irp]

3. Mai gudu yana tafiya a kusa da hanyar murabba'i mai tsawon mita 50 da faɗi = mita 20. Bayan ya yi tafiya a kusa da hanyar murabba'i sau biyu, mai gudu yana komawa wurin farawa. Idan lokaci ya wuce = daƙiƙa 100, a ƙayyade matsakaicin gudu da matsakaicin gudu.

Magani

Da'irar murabba'i mai kusurwa huɗu = mita 2(50) + mita 2(20) = mita 100 + mita 40 = mita 140.

Tafiya a kusa da murabba'i sau 2 = mita 2 (mita 140) = mita 280.

Nisa = mita 280.

Matsarwa = mita 0. ( mai gudu zuwa wurin farawa)

Matsakaicin gudu = nisa / lokacin da ya wuce = mita 280 / daƙiƙa 100 = mita 2.8/daƙiƙa.

Matsakaicin gudu = ƙaura / lokacin da ya shuɗe = 0 / 100 daƙiƙa = 0.

[irp]

[wpdm_package id='505′]

[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

An warware matsalolin vectors - ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vector

1. F ₁ = 6 N, F ₂ = 10 N. Kayyade vector mai sakamakon.

Magani

F _1x = F ₁ cos 60 ^o = (6)(0.5) = 3 N ( tabbatacce saboda yana da alkibla iri ɗaya da x axis )

F _2x = F ₂ cos 30 ^o = (10)(0.5 √ 3) = 5 √ 3 = (5)(1.372) = -8.66 N (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F _1y = F ₁ zunubi 60 ^o = (6)(0.5 √ 3) = 3 √ 3 ​​= (3)(1.372) = 4.116 N ( tabbatacce saboda yana da alkibla iri ɗaya da axis y )

F _2y = F ₂ sin 30 ^o = (10)(0.5 ) = -5 N (mara kyau saboda yana da alkibla iri ɗaya da axis -y)

F _x = F _1x – F _2x = 3 – 8.66 = -5.66 N

F _y = F _1y - F _2y = 4.116 - 5 = -0.884 N

 

Sakamakon waɗannan ƙarfin guda biyu shine N5.7.

[irp]

2. F ₁ = 4 N, F ₂ = 4 N, F ₃ = 8 N. Kayyade vector mai sakamakon.

Magani

F_1x = F₁ kowa 60^o = (4)(0.5) = 2 N (tabbatacce saboda yana da alkibla iri ɗaya da x axis)

F _2x = -4 N (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F _3x = F ₃ cos 60 ^o = (8)(0.5) = 4 N ( tabbatacce saboda yana da alkibla iri ɗaya da x axis )

F_1y = F₁ ba 60^o = (4)(0.5)√3) = 2√3 N (tabbatacce saboda yana da alkibla iri ɗaya da axis na y)

F _2y = 0

F_3y = F₃ ba 60^o = (8)(0.5)√3) = -4√3 N (mara kyau) domin yana da alkibla iri ɗaya da -y axis)

F _x = F _1x – F _2x + F _3x = 2 – 4 + 4 = 2 N

F_y = F_1y +F_2y - F_3y = 2√3 + 0-4√3 = -2√3 N

Sakamakon waɗannan ƙarfin guda uku shine N5.7.

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Ƙayyade sakamakon a cikin vector na layi
2. Ƙayyade abubuwan da aka haɗa na vector
3. Ta hanyar amfani da ka'idar Pythagorean, ƙayyade sakamakon vectors guda biyu.
4. Ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines
5. Ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vectors

Karin bayani

An warware matsalolin vectors - ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines

1. F ₁ = 10 N da F ₂ = 20 N. Kayyade vector mai sakamakon.

[irp]

2. A ₁ = 15 da A ₂ = 9. Kusurwar da ke tsakanin vectors guda biyu ita ce 60 ^o . Kayyade vector da aka samu.

Magani

[irp]

3. v ₁ = 5 da v ₂ = 12. Kusurwar da ke tsakanin vectors guda biyu ita ce 90 ^o . Kayyade vector da aka samu.

Magani

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Ƙayyade sakamakon a cikin vector na layi
2. Ƙayyade abubuwan da aka haɗa na vector
3. Ta hanyar amfani da ka'idar Pythagorean, ƙayyade sakamakon vectors guda biyu.
4. Ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines
5. Ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vectors

Karin bayani

An warware matsalolin vectors - ƙayyade sakamakon vectors guda biyu ta amfani da ka'idar Pythagorean

1. Ka tantance sakamakon vectors guda biyu na ƙaura kamar yadda aka nuna a cikin hoton da ke ƙasa.

[irp]

2. Nemo sakamakon ƙarfi biyu , 12 N da 5 N.

[irp]

3. Ɗalibi yana tafiya mita 4 zuwa yamma, sannan mita 6 zuwa arewa da mita 4 zuwa yamma. Nemo wurin da ɗaliban ke ƙaura.

Magani

Gudun hijirar tana da nisan mita 10 , zuwa arewa maso yamma.

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Ƙayyade sakamakon a cikin vector na layi
2. Ƙayyade abubuwan da aka haɗa na vector
3. Ta hanyar amfani da ka'idar Pythagorean, ƙayyade sakamakon vectors guda biyu.
4. Ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines
5. Ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vectors

Karin bayani

An warware matsalolin vectors - ƙayyade abubuwan vector

1. Ƙarfin Newton mai lamba 20 yana yin kusurwar 30 ^o tare da axis ɗin x. Nemo ɓangarorin x da y na ƙarfin.

Magani

F _x = F cos 30 ^o = (20)(cos 30 ^o ) = (20)(0.5 √ 3 ) = 10 √ Newtons 3

F _y = F zunubi 30 ^o = (20) (zunubi 30 ^o ) = (20) (0.5) = 10 Newtons

[irp]

2. F ₁ = 20 Newton yana yin kusurwar 30 ^o tare da axis y kuma F ₂ = 30 Newton yana yin kusurwar 60 ^o tare da axis -x. Nemo sassan x da y na F ₁ da F ₂.

Magani

F _1x = F ₁ cos 60 ^o = (20)(cos 60 ^o ) = (20)(0.5) = -10 Newtons (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F _2x = F ₂ cos 60 ^o = (30)(cos 60 ^o ) = (30)(0.5) = -15 Newtons (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F_1y = F₁ zunubi 60^o = (20)(zunubi 60^o) = (20)(0.5)√3) = 10√3 Newton (alama ce mai kyau saboda tana da alkibla iri ɗaya da axis ɗin y)

F_2y = F₂ zunubi 60^o = (30)(zunubi 60^o) = (30)(0.5)√3) = -15√3 Newton (mara kyau saboda yana da alkibla iri ɗaya da axis -y)

[irp]

3. F ₁ = 2 N, F ₂ = 4 N, F ₃ = 6 N. Nemo sassan x da y na F ₁ , F ₂ da F ₃!

Magani

F _1x = F ₁ cos 60 ^o = (2)(cos 60 ^o ) = (2)(0.5) = Newtons 1 (tabbatacce saboda yana da alkibla iri ɗaya da axis x)

F_2x = F₂ cos 30^o = (4)(kwas 30)^o) = (4)(0.5)√3) = -2√3 Newton (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F _3x = F ₃ cos 60 ^o = (6)(cos 60 ^o ) = (6)(0.5) = Newtons 3 (tabbatacce saboda yana da alkibla iri ɗaya da axis x)

F_1y = F₁ zunubi 60^o = (2)(zunubi 60^o) = (2)(0.5)√3) = √3 Newton (alama ce mai kyau saboda tana da alkibla iri ɗaya da axis ɗin y)

F _{2 y} = F ₂ zunubi 3 0 ^o = (4)(zunubi 30 ^o ) = (4)(0.5) = 2 Newtons (tabbatacce saboda yana da alkibla iri ɗaya da axis y)

F_3y = F₃ zunubi 60^o = (6)(zunubi 60^o) = (6)(0.5)√3) = -3√3 Newton (mara kyau saboda yana da alkibla iri ɗaya da axis -y)

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Ƙayyade sakamakon a cikin vector na layi
2. Ƙayyade abubuwan da aka haɗa na vector
3. Ta hanyar amfani da ka'idar Pythagorean, ƙayyade sakamakon vectors guda biyu.
4. Ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines
5. Ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vectors

Karin bayani

An warware matsalolin vectors - ƙayyade sakamakon vectors na layi

1. Ɗalibi yana tafiya arewa har zuwa mita 10 sannan ya nufi kudu har zuwa mita 4. Korar ɗalibin yana…

Magani

R = 10 m – 4 m = 6 mita

Girman gudun hijirar mita 6 ne, alkiblar gudun hijirar kuma tana arewa.

2. F ₁ = 10 N, F ₂ = 15 N. Kayyade vector mai sakamakon…

Magani

R = 10 N + 15 N = 25 Newton

Girman vector da aka samu shine Newtons 25, alkiblar vector da aka samu shine gabas ko dama.

[irp]

3. F ₁ = 4 N, F ₂ = 8 N. Kayyade vector mai sakamakon…

Magani

R = 8 N – 4 N = 4 Newton

Girman vector da aka samu shine Newtons 4, alkiblar vector da aka samu shine gabas ko dama.

4. F ₁ = 10, F ₂ = 15 N, F ₃ = 5 N. Kayyade vector mai sakamakon…

Magani

R = 10 N + 5 N – 15 N = 0

Girman vector ɗin da aka samu shine 0.

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Ƙayyade sakamakon a cikin vector na layi
2. Ƙayyade abubuwan da aka haɗa na vector
3. Ta hanyar amfani da ka'idar Pythagorean, ƙayyade sakamakon vectors guda biyu.
4. Ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines
5. Ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vectors

Karin bayani