Te kaupapa o te mahi-pūngao Te kaha kore-pūmau Te nekehanga i runga i te papa whakarara me te waku – Ngā Raru me ngā Otinga

2 Te kaupapa mahi-pūngao Te kaha kore-pūmau Te nekehanga i runga i te papa whakarara me te waku – Ngā Raru me ngā Otinga

1. Ka paheke tetahi poraka i raro i te papa whakarara me te waku. He aha te tere o te poraka ina pa te poraka ki te whenua? Ko te tauwehenga waku nekeneke ko 0.4. Ko te whakaterenga nā te kaha ā-papatipu ko 10 m/s ².

Mōhiotia:

Teitei tīmatanga (h_o) = 6 mita

Teitei whakamutunga ( _t ) = 0 m

Tere tīmatanga (v _o ) = 0 (poraka i te tīmatanga i te okiokinga)

Tauwehenga o te waku nekeneke (μ _k ) = 0.4

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

cos θ = adj/hyp = 8/10

Ko te wāhanga poutū o te taumaha = w _y = w cos θ = mg cos θ = m (10)(8/10) = m (10)(4/5) = m (40/5) = 8 m

Te kaha noa = N = w _y = 8 m

Te kaha o te waku nekeneke = f _k = μ _k N = μ _k w _y = (0.4)(8 m) = 3.2 m

E hiahiatia ana: Tere whakamutunga ( _vt )

Rongoā:

Ko te mātāpono o te pūngao mahi-mīhini e kī ana ko te mahi i mahia e ngā kaha kore-pūmau e pā ana ki tētahi mea he rite ki te huringa katoa o ngā pūngao nekeneke me ngā pūngao pūmanawa.

W_nc = ΔEM

W _nc = ΔEK + ΔEP

W _nc = Te mahi i mahia e te kaha kore-pūmau, Δ EM = Te huringa o te pūngao miihini , Δ EK = Te huringa o te pūngao nekeneke, Δ EP = Te huringa o te pūngao pūmanawa.

Te huringa o te pūngao nekeneke :

ΔEK = 1/2 m (v _t ² – v _o ² ) = 1/2 m (v _t ² – 0) = 1/2 mv _t ²

Te huringa o te pūngao pūmanawa :

ΔEP = mg (h _t – h _o ) = m (10)(0-6) = m (10)(-6) = – 60 m

Te mahi i mahia e te kaha o te waku nekeneke:

W _nc = – f _k s = – (3.2 m)(10) = – 32 m

Ko te tohu tango e tohu ana he kino te mahi i mahia e te kaha o te waku nekeneke i runga i te poraka.

Whakatauhia te tere whakamutunga (vt ₎ :

W _nc = ΔEK + ΔEP

– 32 m = 1/2 mv _t ² – 60 m

– 32 m = m (1/2 v _t ² – 60)

– 32 = 1/2 v _t ² – 60

– 32 + 60 = 1/2 v _t ²

28 = 1/2 v _t ²

2 (28) = v _t ²

56 = v _t ²

vt ₌ √4.14

vt = _2√14 ms ^-1

2.

Ka paheke iho tētahi poraka i runga i tētahi papa whakarara me te waku. Ko te tere whakamutunga o te poraka ina pā ki te whenua ko 10 m/s² ^. Mena ko te kaha waku ko 2 N, ā, ko te whakaterenga nā te kaha ā-papa ko 10 m/s² ^. He aha te teitei o te h?

Mōhiotia:

Taumaha o te poraka (m) = 1 kg

Tere tīmatanga (v _o ) = 0 (poraka i te tīmatanga i te okiokinga)

Tere whakamutunga (vt ₎ = 10 ms ^-1

Teitei tīmatanga (h _o ) = h

Teitei whakamutunga ( _t ) = 0

Te kaha o te waku nekeneke (f _k ) = 2 N

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

Teitei e hiahiatia ana: Teitei (h)

Rongoā:

Ka mahia te mahi e te kaha o te waku nekeneke:

W _nc = – f _k d = – (2)(15) = – 30

Ko te tohu tango e tohu ana he kino te mahi i mahia e te kaha o te waku nekeneke i runga i te poraka.

Te huringa o te pūngao nekeneke:

ΔEK = 1/2 m (v _t ² – v _o ² ) = 1/2 (1)(10 ² – 0) = 1/2 (10 ² ) = 1/2 (100) = 50

Te huringa o te pūngao pūmanawa:

ΔEP = mg (h _t – h _o ) = (1)(10)(0-h) = (10)(-h) = -10 h

Ko te whārite o te mātāpono mahi-pūngao mīhini:

W _nc = ΔEK + ΔEP

– 30 = 50 – 10 hāora

10 hāora = 50 + 30

10 hāora = 80

h = 80/10

h = 8 mita

1. He aha te mātāpono o te mahi-pūngao?
   • whakahoki: E ai ki te mātāpono o te pūngao mahi, he rite te mahi i mahia ki tētahi mea ki te huringa o tōna pūngao nekeneke. Mā te pāngarau, $W=\Delta KE$, i reira $W$ kua oti te mahi, ā, $\Delta KE$ ko te huringa o te pūngao nekeneke.
2. He aha te rerekētanga o tētahi kaha kore-pūmau i tētahi kaha pūmau?
   • whakahoki: Ko te kaha kore-pūmau, pērā i te waku, ka hua ake te ngaronga o te pūngao miihini mai i tētahi pūnaha, ko te nuinga he wera. He rerekē, ko ngā kaha pūmau, pērā i te kaha ā-papa, i te kaha puna rānei, kāore e tohatoha i te pūngao miihini engari ka taea te huri i waenganui i te pūngao pūmanawa me te pūngao nekeneke i roto i te pūnaha.
3. He aha te pānga o te waku ki te mahi e mahia ana ki tētahi mea e neke ana i runga i te papa hianga?
   • whakahoki: Ka mahi te waku i te ahunga e rerekē ana ki te nekehanga o te mea. Ko te tikanga o tēnei ka mahi kino te waku ki te mea, ka whakaiti i tōna pūngao nekeneke, ka whakanui rānei i te nui o te mahi o waho e hiahiatia ana hei neke ake i te pari.
4. He aha te take kāore e rerekē ai te pūngao pūmanawa o tētahi mea nā ngā kaha kore-pūmau?
   • whakahoki: E pā ana te pūngao pūmanawa ki ngā kaha pūmau, ā, ko tōna huringa e whakawhirinaki ana ki ngā tūranga tīmatanga me ngā tūranga whakamutunga anake, kaua ki te ara i tangohia. Ka taea e ngā kaha kore-pūmau te whakarerekē i te pūngao nekeneke o tētahi mea engari kāore he pūngao pūmanawa e pā ana.
5. He pēhea te awe o te koki piko ki te nekehanga o tētahi mea i runga i te papa piko me te waku?
   • whakahoki: Ka nui ake te koki o te piko, ka nui ake te wāhanga o te kaha ā-papa e mahi whakarara ana ki te papa. Mā tēnei ka uaua ake te pupuri i te mea kia okioki, kia neke ake rānei i te papa, ā, ka māmā ake te whakatere iho i te papa. Ka ātete te waku ki tēnei nekehanga, engari ka iti ake te pānga ina piki haere te koki.
6. He aha ngā mea kāore e tere tonu i runga i te papa pīnaki me te waku?
   • whakahoki: Nā te waku, i te nekehanga o te mea, ka hurihia ētahi o te pūngao pūmanawa ā-papa hei wera. Ā tōna wā, ka taurite te kaha ā-papa e pā ana ki te papa e te kaha waku, ā, ka neke te mea me te tere pumau, ka tū rānei.
7. Ka taea te whakahoki mai i te mahi i mahia e te ope taua kore-mātāpono?
   • whakahoki: Ko te mahi a ngā kaha kore-pūmau ka hurihia hei momo pūngao pērā i te wera, he uaua ake te huri hei pūngao miihini whai hua. I te nuinga o ngā wā, ka kiia tēnei pūngao he "ngaro" ki te pūnaha.
8. He aha te mea e whakatau ana i te rahi o te kaha waku i runga i te papa hianga?
   • whakahoki: Ko te kaha waku i runga i te papa piko ka whakatauhia e te kaha noa (poutū) me te tauwehenga waku i waenga i ngā mata. Ka hoatu e ffriction​=μ×fnormal​, i reira $\mu$ ko te tauwehenga o te waku.
9. He aha i tautuhia ai te pūngao pūmanawa hei kore i ētahi pūwāhi tohutoro?
   • whakahoki: He inenga whanaunga te pūngao pūmanawa. Mā te tautuhi i tētahi pūwāhi tohutoro kei reira te pūngao pūmanawa he kore, ka whakaratohia he pūtake pumau mō te tatau i ngā huringa o te pūngao pūmanawa mō ngā tūranga rerekē e pā ana ki taua tohutoro.
10. Me pēhea te rerekētanga o te nekehanga o tētahi mea i runga i te papa hianga mēnā kāore he waku?

• whakahoki: Ki te kore he waku, ko te kaha anake e pā ana ki te mea i te taha o te papa ko te wāhanga o te kaha ā-papa e whakarara ana ki te piko. Nō reira, ka tere ake te mea i te papa nā tēnei kaha anake, ā, e kore e eke ki te tere pumau ki te kore e pāngia e tētahi atu kaha o waho.