Nekehanga hinga noa

He tuhinga mō te nekehanga hinga noa

I roto i te oranga o ia rā, he maha ngā wā ka kite tātou i ngā mea e pāngia ana e te nekehanga hinganga kore utu, hei tauira, te nekehanga o te hua e taka ana mai i te rākau, te nekehanga o ngā mea e taka ana, e taka ana rānei mai i tētahi teitei. He aha ngā mea e pāngia ana e te nekehanga hinganga kore utu? Ki te tirohia i te tirohanga kotahi, ka pāngia te mea e te hinganga kore utu me te mea he tere pumau tōna, arā, kāore te mea e tere haere. Ko te mea pono, ko ia mea e taka noa ana ka pāngia e te tere haere tonu. Nā tēnei take ka puta te nekehanga hinganga kore utu, tae atu ki te tauira o te nekehanga raina kore-taurite. Me pēhea te whakamatau he pāngia ngā mea e pāngia ana e te hinganga kore utu e te tere haere tonu , e te piki haere rānei o tōna tere?

Monoa kia rua ngā whao ki te whenua, ka maturuturu he kōhatu mai i tētahi teitei rerekē ki ia whao. Ka kite koe ko ngā whao e pāngia ana e ngā kōhatu i tētahi taumata teitei ake, he hohonu ake te mau i ngā whao kē atu. Ko te teitei ake o te tūnga o te kōhatu mai i te mata o te whenua, ko te tere ake o te kōhatu ina pā ki te whenua, kia hohonu ake ai te pēhi i te whao.

I ngā wā o mua, he kaupapa tino whakamere te nekehanga o ngā mea e taka ana ki te whenua i roto i te rapunga whakaaro taiao. I kī a Aristotle, he tohunga whakaaro, he tere ake te taka o tētahi mea he nui ake te papatipu i ngā mea mama ake. Nā te whakaaro o Aristotle i awe ngā tirohanga a te hunga i noho i mua i te wā o Galileo, i whakaaro ko ngā mea he nui ake te papatipu ka tere ake te taka i ngā mea mama ake, ā, ko te tere o te taka o ngā mea he rite ki te papatipu o te mea. Tērā pea i mua i te ako i tēnei kaupapa, kei te whakaaro anō koe pērā. Hei tauira, ka taka e tātou tētahi pepa me tētahi toka mai i te teitei kotahi. Ko ngā hua i kitea e tātou i whakaatu ko te kohatu i pa tuatahi ki te whenua, ki te mata o te papa rānei i te pepa. Inaianei, me taka e tātou ētahi kohatu e rua mai i te teitei kotahi, he nui ake tētahi kohatu i tētahi atu. I pa ngā kohatu e rua ki te mata o te whenua i te wā kotahi, ki te whakataurite ki te kohatu me te pepa i taka e tātou i mua. Ka taea hoki e tātou te whakamātautau ki te taka i ngā kohatu me te pepa hei puranga.

He aha te mea e pā ana ki te nekehanga o ngā toka, o ngā pepa rānei e hinga ana? Te kaha o te waku hau! He nui te pānga o te ātete hau, te waku rānei ki te nekehanga hinga kore utu. I whakapae a Galileo ka hinga ngā mea katoa me te tere ōrite mena kāore he hau, he arai rānei. I kī a Galileo ka hinga ngā mea katoa, ahakoa taumaha, ahakoa māmā, me te tere ōrite, mena kāore he hau. I whakapono a Galileo he arai te hau ki ngā mea tino māmā he mata nui. Engari i roto i te maha o ngā āhuatanga, ka taea te wareware i tēnei ātete hau. I roto i tētahi rūma kua mimitihia te hau (korehau), ka hinga ngā mea māmā pēnei i tētahi pepa e puritia ana i runga i te whakapae me te tere ōrite ki ētahi atu mea. Ka taea te whakarāpopoto i te takoha a Galileo ki tō tātou māramatanga ki te nekehanga o ngā mea e hinga ana penei:

I tētahi wāhi motuhake o te whenua, ā, kāore he ātete hau, ka hinga ngā mea katoa me te tere pumau ōrite. Ka kiia tēnei he tere nā te kaha ā-papatipu, ā, ka hoatu he tohu g. Ko te rahi o g he tata ki te 9.8 m/s² ^. I roto i ngā waeine Pūnaha Ingarihi, ko te rahi o g he tata ki te 32 ft/s² ^. Ko te ahunga o te tere o te kaha ā-papatipu e anga atu ana ki waenganui o te whenua.

Te whakamāramatanga o te nekehanga hinga noa

Ka kiia he taka noa te mea mēnā ka neke poutū te mea ki waenganui o te whenua, ā, i a ia e neke ana, ka pāngia te mea e te tere o te kaha ā-papatipu. Mēnā ka tata te taka noa ki te mata o te whenua, ka pāngia te mea e te tere o te kaha ā-papatipu o te 9.8 m/s²^.

me te ahunga o te whakaterenga o te kaha ā-papa ki te pokapū o te whenua (e tū tika ana ki te mata o te whenua). Hei whakangawari i ngā tātaitanga, ko te g he 10 m/s ².

E toru ngā āhuatanga rerekē:

1. Ka neke poutū ngā mea ki raro, kāore he tere tīmatanga (kāore he v _o ). Hei tauira, ka taka te hua mai i te rākau i muri i te tukunga mai i te kakau. Kei raro tonu te ahunga nekehanga, ā, ka tere te mea, nō reira he pai tonu te g. I roto i ētahi pukapuka ahupūngao e kīia ana ko te nekehanga taka-kore.

2. Ka neke poutū te mea ki raro me te tere tīmatanga (ko te v o te nekehanga tēnei ₎ . Hei tauira, he kōhatu i whiua poutū ki raro. Ka heke tonu te ahunga o te nekehanga, ā, ka tere ake te mea, nō reira he pai tonu te g. I roto i ētahi pukapuka ahupūngao, ka kiia ko te nekehanga poutū ki raro.

3. Ka neke poutū te mea ki runga i te tere tīmatanga, ā, i muri i te taenga ki te teitei rawa, ka hoki whakamuri te mea ki raro. Me kī ka whiua e koe ngā māpere poutū ki runga, ka hopukina anō ina heke ngā māpere. Ina neke whakarunga, ka pāngia ngā mea e te whakahekenga tere (g kino), ā, ina heke poutū ki raro, ka tere ake te mea (g pai). I roto i ētahi pukapuka ahupūngao, ka kiia ko te nekehanga poutū ki runga. Me mōhio mēnā ka pāngia tētahi mea e tētahi o ngā āhuatanga e toru i runga ake nei, ka kiia te mea e mahi ana i te nekehanga hinga-kore.

Te whārite o te nekehanga hinga noa

Ko te nekehanga hinga-kore he tauira o te nekehanga rārangi kore-taurite, nō reira he rite tonu te whārite o te nekehanga hinga-kore ki te whārite o te nekehanga rārangi kore-taurite, ā, kua whakatikatikaina ki ngā āhuatanga o te nekehanga hinga-kore.

h = teitei (mita), v ₌ tere tīmatanga (mita/hēkona), v ₌ tere whakamutunga (mita/hēkona), t = wā (hēkona), g = whakaterenga o te kaha ā-papa (mita/hēkona) = 9.8 m/s2 ^, 10 m/s2 ^rānei.

He pumau te whakaterenga o te kaha ā-papa i te 10 m/s ² (he pai te karamu, ka neke te mea ki raro) ko te tikanga ka piki te tere o te mea mā te 10 m/s ia 1 hēkona. I muri i te 2 hēkona, ka piki te tere o te mea mā te 20 m/s. I muri i te 3 hēkona, ka piki te tere o te mea mā te 30 m/s. Ko te whakahekenga pumau o te kaha ā-papa he 10 m/s ² (he kino te karamu, ka neke te mea ki runga) ko te tikanga ka heke te tere o te mea mā te 10 m/s ia 1 hēkona. I muri i te 2 hēkona, ka heke te tere o te mea mā te 20 m/s. I muri i te 3 hēkona, ka heke te tere o te mea mā te 30 m/s. Ko te whakaterenga pumau, te whakahekenga pumau rānei ka puta noa i te mata o te whenua.

Tauira raruraru 1:

Ka tukuna te māngo ka taka ki te whenua. Mena kei te 10 mita te tūnga tīmatanga mai i te mata o te whenua, ā, ko te taumaha o te māngo he 5 karamu, tautuhia:

(a) te tere o te māngo ina tae ki te whenua

(b) te wā e tau ai te māngo ki te whenua.

karamu = 9.8 m/s ²

Rongoā:

E mōhiotia ana: h = 10 m, g = 9.8 m/ ^s2

a) Te tere o te manga ina tae ki te whenua

Ka tatauhia te papatipu i roto i te whārite o te nekehanga hinga-kore

b) Te wā i te rangi

Tauira raruraru 2:

Ka taka tetahi mea mai i tētahi teitei. Whakatauhia:

(a) te rahi o te whakaterenga o te mea

(b) te tawhiti i haerea e te mea mō ngā hēkona tuatahi e 2

(c) te tere o te mea i muri i te hinganga o te 50 mita

(d) te roa o te wā e hiahiatia ana kia eke te mea ki te tere o te 20 m/s,

(e) te roa o te wā e hiahiatia ana kia taka te mea ki te tawhiti o te 100 mita

Rongoā:

E mōhiotia ana: g = 9.8 m/s ²

a) Te rahi o te whakaterenga o te mea

Te whakaterenga o te mea = te whakaterenga o te kaha ā-papatipu = g = 9.8 m/s ²

b) Te tawhiti i haerea e te mea mō ngā hēkona tuatahi e 2

E mōhiotia ana: g = 9.8 m/s² ^, t = 2 s

E hiahiatia ana: h

h = 1⁄2 gt ² = 1⁄2 (9.8)(2) ² = (4.9)(4) = 19.6 mita

c) Te tere o te mea i muri i te hinganga tae atu ki te 50 mita

E mōhiotia ana: h = 50 m, g = 9,8 m/ ^s2

E hiahiatia ana: v _t

d) E hia te wā e hiahiatia ana kia eke ai ngā mea ki te tere o te 20 m/s

E mōhiotia ana: v _t = 20 m/s, g = 9,8 m/s ²

E hiahiatia ana: t

e) Te wā e hiahiatia ana kia taka ai ngā mea ki te tawhiti o te 100 mita

E hiahiatia ana: h = 100 m, g = 9,8 m/s ²

Otinga: t

Tauira raruraru 3:

Ka whiua he kōhatu ki roto i tētahi puna me te tere tīmatanga o te 5 m/s. Mēnā ka taka te kōhatu ki roto i te wai i muri i te 4 hēkona, tautuhia:

(a) te tere o te kōhatu ina tae ki te wai

(b) te hohonutanga o te puna

Rongoā:

a) Te tere o te kōhatu ina uru ki te wai

Mōhiotia:

v _o = 5 m/s, t = 4 s, g = 9.8 m/s ²

E hiahiatia ana: v _t

vt = v _{o +} g t

v _t = 5 m/s + (9.8 m/s ² )(4 s) = 5 m/s + 39.2 m/s

v _t = 44.2 m/s

b) Te hohonu o te puna

Mōhiotia:

v _o = 5 m/s, t = 4 s, g = 9.8 m/s ²

E hiahiatia ana: h

h = v _o t + ½ gt ²

h = (5)(4) + ½ (9.8)(4) ²

h = 20 + (4.9)(16)

h = 20 + 78.4

h = 98.4 mita

Tauira raruraru 4:

Mai i te tihi o te whare e 50 mita te teitei, ka whiua poutū ki raro tētahi mōkihi i te tere o te 10 m/s. Whakatauhia:

(a) Te wā i te rangi

(b) Te tere o te mōkihi ina pā ki te whenua

Rongoā:

a) Te wā i te rangi

Mōhiotia:

h = 50 m, g = 9.8 m/s² ^, v ₌ 10 m/s

E hiahiatia ana: t

h = v _o t + ½ gt ²

50 = 10 t + ½ (9.8) t ²

50 = 10 t + 4.9 t ²

4.9 t ² + 10 t – 50 = 0

Whakamahia te tātai tapawhā:

Te wā i te rangi = 2.3 hēkona

b) Te tere o te mōkihi ina pā ki te whenua

Mōhiotia:

h = 50 m, g = 9.8 m/s² ^, v ₌ 10 m/s

E hiahiatia ana: v _t

Tauira raruraru 5:

Ka whiua poutū ake tētahi pōro i te tere tīmatanga o te 20 m/s. Tātaihia te teitei mōrahi i taea e te pōro.

Rongoā:

He pai ngā rahinga o te whārite e ahu whakarunga ana, he kino ngā rahinga o te whārite e ahu whakararo ana. Ko te tūranga tīmatanga o te pōro te mea i whiriwhiria hei pūwāhi tohutoro.

Mōhiotia:

v _o = 20 m/s (ko te ahunga o te tere tīmatanga kei runga, ka whiua te pōro ki runga, nō reira he pai te v _{o )}

v _t = 0 m/s (ko te tere o te pōro i te teitei mōrahi ko 0 m/s)

g = – 9.8 m/s ² (kei raro te ahunga o te whakaterenga o te kaha ā-papa, nō reira he kino a g)

E hiahiatia ana: h

Tauira raruraru 6:

Ka whiua poutū ake tētahi māpere mai i te tihi o tētahi whare, 100 mita te teitei ake i te whenua, i te tere tīmatanga o te 20 m/s. Whakatauhia:

(a) Te wā i te rangi

(b) te tere o te māpere ina pā ki te whenua

Rongoā:

Te tūnga e whiua ana te māpere hei pūwāhi tohutoro; ko te tihi o te whare he pūwāhi tohutoro. He pai te rahi o te whārite e ahu whakarunga ana, he kino te rahi o te whārite e ahu whakararo ana.

a) Te wā i te rangi

Mōhiotia:

h = – 100 m (he kino a h nā te mea kei raro iho te mata o te whenua i te tūranga tīmatanga, i te pūwāhi tohutoro rānei)

v _o = 20 m/s (kei runga te ahunga o te tere tīmatanga, nō reira he pai te v _{o )}

g = – 9.8 m/s ² (kei raro te ahunga o te whakaterenga o te kaha ā-papa, nō reira he kino a g)

E hiahiatia ana: t

Whakamahia te tātai tapawhā:

Te wā e hiahiatia ana hei tae atu ki te whenua mai i taua wā

ka whiua te pōro = 7 hēkona.

b) Te tere o te māpere ina pā ki te mata o te whenua

Mōhiotia:

h = -100 m (kino nā te mea kei raro iho te mata o te whenua i te pūwāhi tohutoro, i te tūranga tīmatanga rānei)

v _o = 20 m/s (kei runga te ahunga o te tere tīmatanga, nō reira he pai te v _{o )}

g = -9.8 m/s ² (kei raro te ahunga o te whakaterenga o te kaha ā-papa, nō reira he kino a g).

E hiahiatia ana: v _t

Ngā pātai ariā me ngā whakautu mō te nekehanga hinga noa

1. He aha te nekehanga taka noa?

   Ko te nekehanga hinga noa ko te nekehanga o tētahi mea i raro i te awe o te kaha ā-papa anake, kāore he kaha kē atu e pā ana ki taua mea, pērā i te ātete hau.

2. He aha te whakaterenga nā te kaha ā-papa?

   Ko te whakaterenga nā te kaha ā-papa ko te whakaterenga ka pā ki tētahi mea ina taka noa ki te mata o te Ao. Ko te tikanga he 'g', ā, ko te uara tata ki te 9.8 m/s².

3. He aha te tātai mō te nekehanga i roto i te nekehanga hinga noa, i runga i te tere me te wā tīmatanga?

   Ko te tātai ko h = ut + ½gt², ko h te nekehanga (teitei), ko u te tere tīmatanga, ko g te whakaterenga nā te kaha ā-papatipu, ā, ko t te wā.

4. He pēhea te rerekētanga o te tere o tētahi mea i te wā e hinga noa ana?

   I te wā e hinga noa ana, ka piki haere te tere o te mea i roto i te wā nā te whakaterenga pumau o te kaha ā-papa.

5. He aha te tātai mō te tere whakamutunga i roto i te nekehanga hinga noa, i runga i te tere tīmatanga me te wā?

   Ko te tātai ko v = u + gt, ko v te tere whakamutunga, ko u te tere tīmatanga, ā, ko g te whakaterenga nā te kaha ā-papatipu.

6. He aha te mea ka pā ki te tere o tētahi mea i te tihi o tōna ara i roto i te nekehanga taka noa?

   I te tihi o tōna ara, ka kore te tere o te mea mō tētahi wā poto.

7. He aha te tohu kino e tohu ana i roto i te horopaki o te nekehanga hinga noa?

   Ko te tohu kino e tohu ana i tētahi ahunga e rerekē ana i te ahunga pai kua whiriwhiria. I runga anō i te horopaki, ka tohu pea i te hinganga ki raro (mēnā he pai te pikinga) i te maka rānei ki raro (mēnā he kino te pikinga).

8. He aha te mea ka pā ki te whakaterenga o tētahi mea e taka noa ana ina tae ki tōna teitei mōrahi?

   Ko te whakaterenga o tētahi mea i tōna teitei rawa i te hinganga kore utu e rite tonu ana ki te karamu (tata ki te -9.8 m/s² e tata ana ki te mata o te Ao), e anga ana ki raro.

9. He pēhea te pānga o te ātete hau ki te nekehanga taka noa?

   Ko te mea pono, ka taea e te ātete hau te whakaroa i te hekenga o te mea, ā, kāore te nekehanga e taka noa. Heoi, i roto i te maha o ngā raruraru ahupūngao, kāore e arohia te ātete hau mō te māmā noa iho.

10. He aha te wā rere i roto i te nekehanga hinga noa?

Ko te wā rere ko te katoa o te wā e noho ana te mea i te rangi. Mō tētahi mea i whakarewaina, ā, i tau ki te teitei kotahi, ka kitea te wā rere mā te tātai t = 2u/g.

Ngā raruraru me ngā otinga mō te nekehanga hinga noa

1. He raruraru: Ka taka tetahi toka mai i te pari he 78.4 mita te teitei. Kia pēhea te roa ka tae te toka ki te whenua? Rongoā: Ka whakamahia e mātou te whārite h = ½gt². Mā te whakaoti i te wā, t = √(2h/g) = √(2×78.4/9.8) = 4 s.
2. He raruraru: Ka whiua te pōro ki runga me te tere tīmatanga o te 19.6 m/s. E hia te teitei o te pōro? Rongoā: Mā te whakamahi i te whārite h = v₀t – ½gt² i te teitei mōrahi (ko te tere whakamutunga he 0), ko te teitei h = v₀² / (2g) = (19.6)² / (2×9.8) = 20 m.
3. He raruraru: Ka whiua te kōhatu ki runga me te tere tīmatanga o te 10 m/s. He aha tōna tere i muri i te 2 hēkona? Rongoā: Mā te whārite v = v₀ – gt ka puta te tere v = 10 – 9.8×2 = -9.6 m/s.
4. He raruraru: Ka makahia he moni ki raro i te puna, ā, ka tau ki te wai i muri i te 3 hēkona. He aha te hohonu o te puna? Rongoā: Mā te whakamahi i te h = ½gt², ko te hohonutanga h = ½x9.8×3² = 44.1 m.
5. He raruraru: Ka taka tētahi pukapuka i te tēpu, ā, i muri i te 0.5 hēkona ka tau ki te whenua. E hia te teitei o te tēpu? Rongoā: Mā te whakamahi i te h = ½gt², ko te teitei h = ½x9.8x(0.5)² = 1.225 m.
6. He raruraru: Ka whiua te pōro ki runga me te tere tīmatanga o te 20 m/s. Āhea ka eke ki tōna teitei mōrahi? Rongoā: I te teitei rawa, v = 0. Mā te whakaoti i te t = (v – v₀) / -g, ko te wā t = (0 – 20) / -9.8 = 2.04 s.
7. He raruraru: E ono hēkona te roa o te takanga o tētahi mea. He aha tōna tere whakamutunga? Rongoā: Mā te whakamahi i a v = v₀ + gt me te tere tīmatanga v₀ = 0, ko te tere whakamutunga v = 0 + 9.8×6 = 58.8 m/s.
8. He raruraru: Ka taka tetahi aporo mai i tētahi rākau, ā, e 1.5 hēkona te roa ka pā ki te whenua. He aha te teitei o te rākau? Rongoā: Mā te whakamahi i te h = ½gt², ko te teitei h = ½x9.8x(1.5)² = 11 m.
9. He raruraru: Ka whanahia poutū ake tētahi pōro whutupaoro me te tere tīmatanga o te 25 m/s. Kia pēhea te roa ka pā ki te whenua? Rongoā: Te wā ki te teitei mōrahi t = v₀ / g = 25 / 9.8 = 2.55 s. Ko te tapeke o te wā ki te pā ki te whenua e rua ngā wā, nō reira t = 2×2.55 = 5.1 s.
10. He raruraru: Ka taka te kōhatu i te piriti, ā, ka tau ki te wai i muri i te 4 hēkona. E hia te teitei o te piriti? Rongoā: Mā te whakamahi i te h = ½gt², ko te teitei h = ½x9.8×4² = 78.4 m.
11. He raruraru: Ka whakarewaina tika atu tētahi rōkete i te tere 50 m/s. E hia te teitei o tōna rere? Rongoā: Mā te whakamahi i te h = v₀² / (2g), ko te teitei h = (50)² / (2×9.8) = 127.55 m.
12. He raruraru: Ka whiua he pōro ki raro me te tere tīmatanga o te 10 m/s. He aha tōna tere i muri i te 2 hēkona? Rongoā: Mā te whakamahi i a v = v₀ + gt, ko te tere v = 10 + 9.8×2 = 29.6 m/s.
13. He raruraru: Ka whiua poutū ake tētahi pōro, ā, ka hoki ki te whenua i roto i te 6 hēkona. He aha tōna tere tīmatanga? Rongoā: Mā te whakamahi i te v₀ = gt / 2 (nā te mea e rua te roa o te wā katoa i te wā e eke ai ki te teitei mōrahi), ko te tere tīmatanga v₀ = 9.8×6 / 2 = 29.4 m/s.
14. He raruraru: Ka taka tetahi mea mō te 10 hēkona. Kia pēhea te tawhiti o tōna takanga? Rongoā: Mā te whakamahi i te h = ½gt², ko te tawhiti h = ½x9.8×10² = 490 m.
15. He raruraru: Ka taka he māpere mai i tētahi pourewa, ā, e 5 hēkona te roa ka pā ki te whenua. E hia te teitei o te pourewa? Rongoā: Mā te whakamahi i te h = ½gt², ko te teitei h = ½x9.8×5² = 122.5 m.
16. He raruraru: Ka whiua poutū ake tētahi pōro pēhipōro me te tere tīmatanga o te 15 m/s. Āhea ka eke ki tōna teitei mōrahi? Rongoā: I te teitei rawa, v = 0. Mā te whakaoti i te t = (v – v₀) / -g, ko te wā t = (0 – 15) / -9.8 = 1.53 s.
17. He raruraru: Ka taka tetahi mea, ā, ka hinga mō te 7 hēkona. He aha tōna tere whakamutunga? Rongoā: Mā te whakamahi i a v = v₀ + gt me te tere tīmatanga v₀ = 0, ko te tere whakamutunga v = 0 + 9.8×7 = 68.6 m/s.
18. He raruraru: Ka whiua te toka ki runga me te tere tīmatanga o te 30 m/s. He aha tōna tere i muri i te 3 hēkona? Rongoā: Mā te whakamahi i te v = v₀ – gt, ko te tere v = 30 – 9.8×3 = 0.6 m/s.
19. He raruraru: Ka taka te kōhatu i te pari, ā, ka tau ki te whenua i muri i te 8 hēkona. E hia te teitei o te pari? Rongoā: Mā te whakamahi i te h = ½gt², ko te teitei h = ½x9.8×8² = 313.6 m.

20. Raru: Ka koperea tika te pere ki runga i te tere 60 m/s. Kia pēhea te roa ka pā ki te whenua? Otinga: Te wā ki te teitei mōrahi t = v₀ / g = 60 / 9.8 = 6.12 s. Ko te tapeke o te wā ki te pā ki te whenua e rua ngā wā, nō reira t = 2×6.12 = 12.24 s.