Tsarin ƙwayoyin cuta - matsaloli da mafita

Tsarin ƙwayoyin cuta - matsaloli da mafita

1. Abu A mai nauyin kilogiram 6 da abu B mai nauyin kilogiram 4 da aka haɗa ta hanyar igiya kuma aka ja ta da ƙarfin F = 60 N, kamar yadda aka nuna a cikin hoton da ke ƙasa. Matsakaicin gogayya tsakanin ƙasa da abubuwa biyu shine 0.5 (tan θ = ¾). Hawan nauyi saboda nauyi shine 10 m/s ^2. Menene girman ƙarfin tashin hankali?

An sani:

Nauyin abu A (m)_A) = 6 kg

Nauyin abu B (m _B ) = 4 kg

Ƙarfi (F) = 60 Newton

Ma'aunin gogayya tsakanin abu da bene (μk ₎ = 0.5

Saurin gudu saboda nauyi (g) = 10 m/s²

Tan θ = 3/4

Ana nema: Ƙarfin tashin hankali (T)

Magani:

Sashen kwance na ƙarfi F:

F _x = F cos θ

F _x = (60)(4/5) = (4)(12) = 48 N

Sashen tsaye na ƙarfi F:

F _y = F sin θ

F _y = (60)(3/5) = (3)(12) = 36 N

Ƙarfin da aka saba amfani da shi akan abu A:

N _A = w _A = m _A g = (6)(10) = 60 N

Ƙarfin da aka saba amfani da shi akan abu B:

N _B + F _y – w _B = 0

N _B + F _y = w _B

N _B = w _B – F _y = m _B g – F _y = (4)(10) – 36 = 40 – 36 = 4 N

Ƙarfin gogayya tsakanin abu A da bene:

f _kA = μ _k N _A = (0.5) (60) = 30 N

Ƙarfin gogayya tsakanin abu B da bene:

f _kB = μ _k N _B = (0.5) (4) = 2 N

Lissafa hanzarin abubuwa biyu:

ΣF = ma

F _x – T + T – f _kB – f _kA = (m _A + m _B ) a

F _x – f _kB – f _kA = (m _A + m _B ) a

48 – 2 – 30 = (6 + 4) a

16 = 10 a

a = 16/10

a = 1.6 m/s ²

Lissafa ƙarfin tashin hankali:

Abu A:

ΣF = ma

T _A – f _kA = m _A a

T _A – 30 = (6)(1.6)

T _A – 30 = 9.6

T _A = 9.6 + 30 = 39.6 N

Abu na B:

ΣF = ma

F _x – f _kB – T _B = m _B a

48 – 2 – T _B = (4)(1.6)

46 – T _B = 6.4

46 – 6.4 = T _B

T _B = 39.6 N

2. Idan ma'aunin gogayya tsakanin tubalan da bene shine 0.2, menene hanzarin abubuwa biyu? (cos 37 ^o = 0,8, sin 37 ^o = 0,6)

An sani:

Nauyin abu A (m)_A) = 4 kg

Nauyin abu B (m _B ) = 2 kg

Ƙarfi (F) = 30 Newton

Ma'aunin gogayya tsakanin abu da bene (μk ₎ = 0.2

Saurin gudu saboda nauyi (g) = 10 m/s²

cos 37 ^o = 0.8

zunubi 37 ^o = 0.6

Ana so: Haɓaka abubuwa biyu

Magani:

Bangaren kwance na ƙarfi F:

F _x = F cos θ

F _x = (30)(0.8) = 24 N

Bangaren tsaye na ƙarfi F:

F _y = F sin θ

F _y = (30)(0.6) = 18 N

Ƙarfin da aka saba da shi akan abu A:

N _A = w _A = m _A g = (4)(10) = 40 N

Ƙarfin da aka saba amfani da shi akan abu B:

N _B + F _y – w _B = 0

N _B + F _y = w _B

N _B = w _B – F _y = m _B g – F _y = (2)(10) – 18 = 20 – 18 = 2 N

Ƙarfin gogayya tsakanin abu A da bene:

f _kA = μ _k N _A = (0.2) (40) = 8 N

Ƙarfin gogayya tsakanin abu B da bene:

f _kB = μ _k N _B = (0.2) (2) = 0.4 N

Haɓaka abubuwa biyu:

ΣF = ma

F _x – f _kB – f _kA = (m _A + m _B ) a

24 – 0.4 – 8 = (4 + 2) a

15.6 = 6 a

a = 15.6/6

a = 2.6 m/s ²

3. Abubuwa biyu da aka haɗa ta hanyar igiya a kan wani abin jan ƙarfe kamar yadda aka nuna a cikin hoton da ke ƙasa. Yawan abu A = m _A , taro f abu B = m _B da kuma hanzarta toshe B shine a. Saurin nauyi saboda nauyi shine g. Menene ƙarfin tashin hankali akan toshe B.

Magani:

Saman kwance yana da santsi don haka babu gogayya. Ƙarfin da ke hanzarta tsarin shine nauyin toshe B.

Haɓaka tsarin:

Ƙarfin tashin hankali (T):

Maye gurbin m _A a cikin lissafi na 1 da m _A a cikin lissafi na 2.

1. Menene bambanci tsakanin statics da dynamics a cikin mahallin barbashi?
   • amsa: Statics yana magana ne game da nazarin ƙarfi akan barbashi a cikin daidaito, inda dukkan ƙarfin ke daidaita, kuma babu hanzari. Dynamics, a gefe guda, yana nazarin ƙarfi da motsi da ke faruwa na barbashi lokacin da ƙarfin ba su daidaita ba, wanda ke haifar da hanzari.
2. Ta yaya Dokar Newton ta Biyu ta shafi motsin ƙwayar cuta?
   • amsa: Dokar Newton ta Biyu ta bayyana cewa ƙarfin da ke aiki akan ƙwayar cuta daidai yake da nauyin ƙwayar cuta sau da sauri: $F=ma$Wannan doka ta bayyana yadda ƙarfi zai shafi motsin ƙwayar cuta, ya danganta da nauyinta da kuma saurin da ƙarfin ya samar.
3. Menene ƙa'idar kiyaye ƙarfin layin layi, kuma ta yaya yake aiki ga ƙwayoyin cuta?
   • amsa: Ka'idar kiyaye ƙarfin linzamin kwamfuta ta bayyana cewa jimlar ƙarfin linzamin kwamfuta na tsarin rufewa na barbashi yana nan daram idan babu wani ƙarfin waje da ke aiki akan tsarin. Wannan yana nufin cewa jimlar ƙarfin lantarki kafin da bayan hulɗa tsakanin barbashi a cikin tsarin zai zama iri ɗaya.
4. Ta yaya manufar aikin da aka yi a kan ƙwayar cuta ta shafi ƙarfin da aka yi amfani da shi da kuma yadda ƙwayar cuta ta motsa?
   • amsa: Aikin da aka yi akan barbashi shine samfurin ƙarfin da aka yi amfani da shi ga barbashi, canjin barbashi, da kuma cosine na kusurwar da ke tsakanin ƙarfin da vectors na ƙaura: $W=Fd\cos \theta$.
5. Menene bambanci tsakanin kuzarin motsi da makamashi mai yuwuwa a cikin mahallin ƙwayar cuta?
   • amsa: Makamashin motsi shine makamashin barbashi saboda motsinsa kuma ana bayar da shi da 1/2 ​mv², inda $m$ shine taro kuma $v$ shine saurin. Makamashin da ake iya samu shine makamashin da aka adana a cikin barbashi saboda matsayinsa a filin ƙarfi (kamar filayen nauyi ko wutar lantarki). Takamaiman bayanin makamashin da ake iya samu ya dogara ne akan ƙarfin da ke aiki akan barbashi.
6. Ta yaya motsin da ke kan ƙwayar cuta ke da alaƙa da canjin motsinta?
   • amsa: Tura-ture akan barbashi samfurin ƙarfin da aka yi wa barbashi da kuma tsawon lokacin da aka yi amfani da ƙarfin. Daidai yake da canjin motsin barbashi: $I=F\Delta t=\Delta p$.
7. Menene ma'anar "ƙwayar halitta mai 'yanci," kuma ta yaya take aiki?
   • amsa: Kwayar halitta mai 'yanci ita ce wadda ba ta fuskantar kowace irin ƙarfi. A cewar Dokar Farko ta Newton, ƙwayar halitta mai 'yanci za ta kasance a hutawa idan da farko tana hutawa ko kuma ta yi tafiya da sauri mai ɗorewa idan da farko tana motsi.
8. Wace rawa gogayya ke takawa a cikin yanayin ƙwayoyin cuta?
   • amsa: Fogewa ƙarfi ne da ke adawa da motsin da ke tsakanin saman da ke hulɗa. A cikin mahallin motsin ƙwayoyin cuta, gogayya na iya rage gudu ko dakatar da motsin ƙwayoyin cuta, ya danganta da alkibla da girman ƙarfin gogayya.
9. Ta yaya ƙarfin tsakiya ke tasiri ga hanyar ƙwayar cuta?
   • amsa: Ƙarfin tsakiya shine wanda ke aiki a kan layin da ke haɗa ƙwayar zuwa wani wuri mai tsayayye, wanda ake kira tsakiya. Irin waɗannan ƙarfin suna da yawa a cikin hulɗar nauyi da lantarki kuma zasu sa ƙwayar ta motsa a cikin hanyar da ke riƙe da takamaiman motsi na kusurwa kusa da tsakiya, wanda galibi yakan haifar da zagaye mai siffar elliptical ko zagaye.
10. Menene alaƙar da ke tsakanin ƙarfin waje na waje da ke aiki akan tsarin ƙwayoyin cuta da kuma saurin canjin jimillar motsi na layi na tsarin?

• amsa: A bisa ga Dokar Biyu ta Newton da aka yi amfani da ita ga tsarin ƙwayoyin cuta, ƙarfin waje da ke aiki akan tsarin daidai yake da ƙimar canjin jimlar motsi na layi na tsarin: FEx​=dP/dt​, inda $\mathbf{P}$ shine jimlar motsi na layi.