Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga

1. Ko te Taonga A he 6-kg te taumaha, me te Taonga B he 4-kg te taumaha , e honoa ana e te taura, ā, e tōia ana e te kaha o F = 60 N, e whakaaturia ana i te pikitia i raro nei. Ko te tauwehenga o te waku nekeneke i waenga i te papa me ngā taonga e rua he 0.5 (tan θ = ¾). Ko te whakaterenga nā te kaha ā-papa he 10 m/s ^2. He aha te rahi o te kaha kume?

Mōhiotia:

Papatipu o te mea A (m_A) = 6 kirokaramu Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga 1

Taumaha o te mea B (m _B ) = 4 kg

Te Kaha (F) = 60 Newton

Ko te tauwehenga o te waku nekeneke i waenga i te mea me te papa (μ _k ) = 0.5

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²

Tāne θ = 3/4

E hiahiatia ana: Te kaha kume (T)

Rongoā:

Wāhanga whakapae o te kaha F:

F _x = F cos θ

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

Wāhanga poutū o te kaha F:

F _y = F sin θ

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

Ko te kaha noa i runga i te mea A:

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

Te kaha noa i runga i te mea 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

Te kaha o te waku nekeneke i waenga i te mea A me te papa:

f _kA = μ _k N _A = (0.5)(60) = 30 N

Te kaha o te waku nekeneke i waenga i te mea B me te papa:

f _kB = μ _k N _B = (0.5)(4) = 2 N

Tātaihia te whakaterenga o ngā mea e rua:

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) he

16 = 10

ā = 16/10

a = 1.6 m/s ²

Tātaihia te kaha kume:

Ahanoa 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

Ahanoa 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. Mena ko te tauwehenga o te waku nekeneke i waenga i ngā poraka e rua me te papa he 0.2, he aha te whakaterenga o ngā mea e rua? (cos 37 ^o = 0,8, sin 37 ^o = 0,6)

Mōhiotia:

Papatipu o te mea A (m_A) = 4 kirokaramu Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga 3

Taumaha o te mea B (m _B ) = 2 kg

Te Kaha (F) = 30 Newton

Ko te tauwehenga o te waku nekeneke i waenga i te mea me te papa (μ _k ) = 0.2

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²

cos 37 ^o = 0.8

hara 37 ^o = 0.6

E hiahiatia ana: Te whakaterenga o ngā mea e rua

Rongoā:

Ko te wāhanga whakapae o te kaha F:

F _x = F cos θ

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

Ko te wāhanga poutū o te kaha F:

F _y = F sin θ

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

Ko te kaha noa i runga i te mea A:

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

Te kaha noa i runga i te mea 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

Te kaha o te waku nekeneke i waenga i te mea A me te papa:

f _kA = μ _k N _A = (0.2)(40) = 8 N

Te kaha o te waku nekeneke i waenga i te mea B me te papa:

f _kB = μ _k N _B = (0.2)(2) = 0.4 N

Te whakaterenga o ngā mea e rua:

ΣF = ma

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

24 – 0.4 – 8 = (4 + 2) he

15.6 = 6

ā = 15.6 / 6

a = 2.6 m/s ²

3. E rua ngā mea e honoa ana e te taura i runga i te pūrei e whakaaturia ana i te pikitia i raro nei. Te taumaha o te mea A = m _A , te taumaha f o te mea B = m _B , ā, ko te whakaterenga o te poraka B ko a. Ko te whakaterenga nā te kaha ā-papatipu ko g. He aha te kaha kume i runga i te poraka B.

Rongoā: Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga 5

He maeneene te mata whakapae, nō reira kāore he waku. Ko te taumaha o te poraka B anake te kaha e whakateretere ana i te pūnaha.

Te whakaterenga o te pūnaha:

Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga 6

Te kaha kume (T):

Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga 7

Whakakapia a m _A i te whārite 1 ki a m _A i te whārite 2.

Ngā whanaketanga o ngā matūriki – ngā raruraru me ngā otinga 8

He aha te rerekētanga i waenga i te pūmau me te hihiri i roto i te horopaki o ngā matūriki?
- whakahoki: Ko te Pūtake e pā ana ki te ako i ngā kaha ki runga i ngā matūriki i roto i te taurite, ina taurite ngā kaha katoa, ā, kāore he whakaterenga. Ko te Pūtake ia, e ako ana i ngā kaha me te nekehanga o ngā matūriki ina kore taurite ngā kaha, ka puta ai te whakaterenga.
He pēhea te pānga o te Ture Tuarua a Newton ki te nekehanga o tētahi matūriki?
- whakahoki: E ai ki te Ture Tuarua o Newton, ko te kaha e pā ana ki tētahi matūriki he ōrite ki te papatipu o te matūriki i whakareatia ki tōna whakaterenga: $F = ma$ E whakaahua ana tēnei ture i te pānga o te kaha ki te nekehanga o tētahi matūriki, i runga i tōna papatipu me te whakaterenga i puta mai i te kaha.
He aha te mātāpono o te tiakitanga o te nekehanga rārangi, ā, me pēhea tōna pānga ki ngā matūriki?
- whakahoki: Ko te mātāpono o te tiaki i te nekehanga raina e kī ana ko te nekehanga raina katoa o tētahi pūnaha matūriki kati ka noho pumau tonu mēnā kāore he kaha o waho e pā ana ki te pūnaha. Ko te tikanga o tēnei ko te nekehanga katoa i mua me muri i te taunekeneke i waenga i ngā matūriki i roto i te pūnaha ka rite tonu.
He aha te hononga o te ariā o te mahi i mahia ki tētahi matūriki ki te kaha i whakamahia me te nekehanga o te matūriki?
- whakahoki: Ko te mahi i mahia ki tētahi matūriki ko te hua o te kaha i pā ki te matūriki, te nekehanga o te matūriki, me te kosinī o te koki i waenganui i te kaha me ngā whārite nekehanga: $W = F d cos θ$ .
He aha te rerekētanga i waenga i te pūngao nekeneke me te pūngao pūmanawa i roto i te horopaki o tētahi matūriki?
- whakahoki: Ko te pūngao nekeneke te pūngao o tētahi matūriki nā tōna nekehanga, ā, e homai ana e te 1/2 $m v^{2}$ , i reira $m$ ko te papatipu me $v$ ko te tere. Ko te pūngao pūmanawa ko te pūngao rongoa i roto i tētahi matūriki nā tōna tūranga i roto i tētahi āpure kaha (pērā i ngā āpure kaha ā-papa, ā-hiko rānei). Ko te whakapuakitanga motuhake mō te pūngao pūmanawa e whakawhirinaki ana ki te kaha e pā ana ki te matūriki.
He aha te hononga o te nekehanga i runga i tētahi matūriki ki te huringa o tōna nekehanga?
- whakahoki: Ko te pana i runga i tētahi matūriki ko te hua o te kaha e pā ana ki te matūriki me te roanga o te wā e pā ana te kaha. He rite ki te huringa o te pana o te matūriki: $I = F Δ t = Δ p$ .
He aha te tikanga o te "matūriki kore utu," ā, he pēhea tana whanonga?
- whakahoki: Ko te matūriki kore utu he matūriki kāore e pāngia e tētahi kaha. E ai ki te Ture Tuatahi a Newton, ka noho tonu te matūriki kore utu ki te okioki mēnā ka okioki i te tīmatanga, ka neke rānei me te tere pumau mēnā ka neke i te tīmatanga.
He aha te tūranga o te waku i roto i ngā whanaketanga o ngā matūriki?
- whakahoki: Ko te waku he kaha e ātete ana i te nekehanga whanaunga i waenga i ngā mata e pa ana. I roto i te horopaki o te hihiri matūriki, ka taea e te waku te whakaroa, te aukati rānei i te nekehanga o te matūriki, i runga i te ahunga me te rahi o te kaha waku.
He pēhea te awe o te kaha pokapū ki te ara o te matūriki?
- whakahoki: Ko te kaha pokapū he mea e mahi ana i te rārangi e hono ana i te matūriki ki tētahi pūwāhi pumau, e kiia nei ko te pokapū. He mea noa ēnei kaha i roto i ngā taunekeneke ā-papa me te hiko, ā, ka meinga te matūriki kia neke i roto i tētahi ara e pupuri ana i tētahi nekehanga koki motuhake huri noa i te pokapū, ka hua ake he porowhita porowhita, he porowhita rānei.
He aha te whanaungatanga i waenga i te kaha o waho kupenga e pā ana ki tētahi pūnaha matūriki me te tere o te huringa o te nekehanga rārangi katoa o te pūnaha?

whakahoki: E ai ki te Ture Tuarua a Newton e pā ana ki tētahi pūnaha matūriki, ko te kaha o waho kupenga e pā ana ki te pūnaha he ōrite ki te tere o te huringa o te nekehanga rārangi katoa o te pūnaha: $F_{ext} = d P/ d t$ , i reira $P$ ko te nekehanga rārangi katoa.