Te nekehanga porowhita – ngā raruraru me ngā otinga

1. E neke ana tētahi mea 10-kg te taumaha i roto i tētahi porowhita i te tere pumau 4 m/s. Mena he 0.5 mita te pūtoro o te porowhita, kāti:

1) Ko te auau o ngā porowhita he 4/π Hz

2) Ko te whakaterenga ā-pokapū he 32 ms ^-2

3) Ko te kaha pokapū he 320 N

4) Ko te wā ko 4π s.

Ko ēhea ngā kōrero pono?

Mōhiotia:

Papatipu o te mea (m) = 10 kg

Ko te tere rārangi (v) = 4 m/s

Ko te radius o te porowhita (r) = 0.5 mita

Rongoā:

1) Te auau o te porowhita

v = 2 π rf

4 = 2 π (0.5) f

4 = π f

f = 4/π Hertz

2) Te whakaterenga ā-pokapū

a _s = v ² / r = 4 ² / 0,5 = 16 / 0,5 = 32 m/s ²

3) Te kaha pokapū

F = ma _s = (10)(32) = 320 N

4) Wā

T = 1 : f = 1 : 4/π = 1 x π/4 = π/4

2. E neke ana tētahi mea i roto i tētahi porowhita he 6 mita te whānui o te pūtoro. Mēnā ka takahurihia e te mea ngā porowhita 16 i roto i te 2 meneti, he aha te tere rārangi o te mea?

Mōhiotia:

Pūtoro (r) = 6 mita

Ko te tere koki (ω) = 16 hurihanga / 2 meneti = 8 hurihanga / meneti = 8 hurihanga / 60 hēkona = 0.13 hurihanga/hekona.

E hiahiatia ana: Te tere rārangi (v)?

Rongoā:

v = r ω = (6 mita)(0.13 hurihanga/hēkona) = 0.8 mita/hēkona

I roto i ngā rātihana:

1 hurihanga = 2π rātiana = 2(3.14) = 6.28 rātiana

Ko te tere koki = 8 (6.28) ngā rātiana / 60 hēkona = 50.24 ngā rātiana / 60 hēkona = 0.84 ngā rātiana/hēkona

v = r ω = (6 mita)(0.84 rātiana/hēkona) = 5.04 rātiana/hēkona.

3. E 4 ngā wā e huri ana tētahi mea he 20/π cm te whānui o tōna pūtoro i roto i te 1 hēkona. He aha te tere rārangi o te taha o tētahi mea?

Mōhiotia:

Pūtoro (r) = 20/π henimita = 20 / 3.14 henimita = 6.4 henimita = 0.064 mita

Ko te tere koki (ω) = 4 hurihanga / 1 hēkona = 4 hurihanga / hēkona.

1 hurihanga = (2)(3.14) ngā rātiana = 6.28 ngā rātiana

Ko te tere koki (ω) = (4)(6.28) ngā rātiana/hēkona = 25.12 ngā rātiana/hēkona

E hiahiatia ana: Te tere raina o te taha o te mea (v)

Rongoā:

v = r ω = (0.064 mita)(25.12 rātiana/hēkona) = 1.6 mita/hēkona

4. He mea e neke ana i roto i te porowhita i te tere pumau, ko te tere raina o te mea e whakawhirinaki ana ki…

Rongoā:

Ko te whārite o te tere rārangi o te nekehanga porowhita:

v = te tere rārangi

d = 2πr = porowhita

T = wā = te wā e hiahiatia ana mō te hurihanga kotahi.

5. E neke ana tētahi mea i roto i tētahi porowhita he 50 mita te whānui o te pūtoro. Mena he 120 rpm te tere koki o te mea, he aha te wā me te tere rārangi o te mea?

Mōhiotia:

Pūtoro (r) = 50 henimita = 0.5 mita

Ko te tere koki (ω) = 120 rpm = 120 hurihanga / 1 meneti = 120 hurihanga / 60 meneti = 2 hurihanga / 1 hēkona

1 hurihanga = 2π rātiana

Ko te tere koki (ω) = 2 (2π rātiana) / 1 hēkona = 4π rātiana/hēkona

E hiahiatia ana: Te wā (T) me te tere rārangi (v)

Rongoā:

Wā (T):

Ko te wā te wā e hiahiatia ana mō te hurihanga kotahi.

E rua ngā hurihanga o tētahi mea i roto i te 1 hēkona = 1 hurihanga mō ia 0.5 hēkona. Wā = 0.5 hēkona.

Te tere rārangi (v):

v = r ω = (0.5 mita)(4π ngā rātiana/hēkona) = 2π mita/hēkona.

He aha te rerekētanga i waenga i te tere pātata me te tere koki i roto i te nekehanga porowhita?
Whakautu : Ko te tere tāngāwari te tere rārangi o tētahi pūwāhi i runga i tētahi mea e hurihuri ana, ā, e tohu ana i te tere o te neke o te pūwāhi i tōna ara porowhita. Ko te tere koki, i tētahi atu ringa, e pā ana ki te tere o te hurihanga o te koki i te mea e hurihuri ana te mea. Ko te tere tāngāwari ka inehia i roto i ngā mita ia hekona (m/s) ko te tere koki ia ka inehia i roto i ngā rātiana ia hekona (rad/s).
He aha te whakaterenga ā-pokapū, ā, he aha tōna hononga ki te nekehanga porowhita?
Whakautu : Ko te whakaterenga pūrua ko te whakaterenga e pā ana ki tētahi mea e neke ana i te ara porowhita. E tohu tonu ana ki te pokapū o te porowhita, ā, koia te take e pupuri ai te mea i tōna ara porowhita. Ko te tātai mō te whakaterenga pūrua ko $_{c} = v 2 ^{/ r}$ ko $v$ te tere tānga, ā, ko $r$ te pūtoro o te porowhita.
He aha i tere ai te nekeneke o tētahi mea e neke ana i te porowhita ōrite ahakoa he pumau tonu tōna tere?
Whakautu : Ahakoa e mau tonu ana te rahi (te rahi rānei) o te tere i roto i te nekehanga porowhita ōrite, ka rerekē te ahunga o te tere. Nā te mea ko te whakaterenga te huringa o te tere, ā, ko te tere he rahinga whārite me te rahi me te ahunga, ko te huringa o te ahunga he whakaterenga. I tēnei wā, he whakaterenga pokapū.
He aha te pānga o te kaha e hiahiatia ana hei pupuri i te nekehanga porowhita ki te papatipu o te mea me te pūtoro o te porowhita?
Whakautu : Ko te kaha e hiahiatia ana hei pupuri i te nekehanga porowhita ka hoatuhia e te tātai kaha pokapū: $F_{c} = m \times a_{c} = m \times v ^{2 /r}$
He aha koe ka pēhia ai ki waho ina huri koi te motuka (hei tauira, i roto i te porowhita)?
Whakautu : Nā te kaha porotītaha "rūpahu" tēnei, arā, he kaha e kitea ana e mahi ana ki waho i runga i te tinana e neke ana i te ara porowhita. Ehara i te kaha tūturu i roto i te tikanga o te pana, te kume rānei, engari he pānga o te korekore. E hiahia ana tō tinana ki te neke i te rārangi tika (te ture tuatahi a Newton), engari ko ngā pakitara o te motuka, ko te whitiki nohoanga rānei, ka whakamahia he kaha hei pupuri i a koe kia neke i roto i te porowhita. Ka puta te ahua o te panaia ki waho.
He aha te mahi a te waku i roto i te nekehanga porowhita, inā koa ina huri ana te motuka i te rori?
Whakautu : Mā te waku i waenga i ngā potae me te rori ka puta te kaha pokapū e tika ana hei āwhina i te motuka ki te huri. Ki te kore e ranea te waku, ka paheke, ka paheke rānei te motuka, ā, ka kore e whai i tōna ara porowhita e hiahiatia ana.
Me pēhea te hurihanga o te kaha pokapū mēnā ka hauruatia te pūtoro o te ara porowhita engari ka mau tonu te tere?
Whakautu : Ki te hauruatia te pūtoro, ā, ka noho tonu te tere, ka takirua te kaha pūrua, nā te mea he rite whakamuri te kaha pūrua ki te pūtoro.
He aha e kore ai e taea te whakamahi i te kaha porowhita me te kore he kaha porowhita i roto i te nekehanga porowhita?
Whakautu : Ko te kaha pūngao he kaha tauhohe, he kaha "rūpahu" rānei e kitea ana i roto i te anga tohutoro hurihuri. Te āhua nei ka panaia ngā mea ki waho i te pokapū o te hurihanga. Heoi, kia neke ai te mea i roto i te ara porowhita, me whai kaha tūturu e mahi ana ki te pokapū, arā, ko te kaha pūngao. Ki te kore te kaha pūngao, kāore he nekehanga porowhita i te tīmatanga, nō reira, kāore he tirohanga ki te kaha pūngao.
He pēhea te kawenga o te kaha ā-papa i waenganui i a Papatūānuku me te Marama mō te porowhita porowhita o te Marama?
Whakautu : Ko te kaha ā-pū i waenganui i a Papatūānuku me te Marama e mahi ana hei kaha pokapū e pupuri ana i te Marama i roto i tōna porowhita huri noa i a Papatūānuku. Ki te kore tēnei kukume ā-pū, ka neke te Marama i te rārangi tika, kaua i tōna porowhita porowhita (he tika ake rānei, he porowhita).
Ki te whakapotoa te aho e herea ana ki te pōro kia haurua i a ia e hurihuri ana i te pōro i roto i te porowhita i te tere kotahi, ka pēhea te rerekētanga o te kukū o te aho?

Whakautu : Ki te whakawhāititia te roa o te aho (e rite ana ki te pūtoro o te ara porowhita) kia haurua, me te pupuri tonu i te tere kia pumau, ka takirua te kaha pūrua e hiahiatia ana (ā, nō reira, te kume i roto i te aho). Nā te mea he rite whakamuri te kaha pūrua (ā, he rerekē te kume mō tēnei horopaki) ki te pūtoro.