Te ariā a Torricelli – ngā raruraru me ngā otinga

Te ariā a Torricelli – ngā raruraru me ngā otinga

1. He ngongo he 100 cm te teitei kua whakakīia ki te wai. Kei te 10 cm te teitei o te kōhao Q i runga ake i te whenua. He aha te tawhiti whakapae (x)?

Mōhiotia:

Te tawhiti i waenganui i te poka me te mata o te wai (h) = 100 cm – 10 cm = 90 cm = 0.9 m

Whakaterenga na te kaha o te kaha (g) = 10 m/s²

Hiahia: Te tawhiti o x

Rongoā:

Te tere o te rere o te wai i te poka

v= tere, g = te whakaterenga nā te kaha ā-papa, h = te tawhiti i waenganui i te kōhao me te mata o te wai

Te tere o te rere o te wai i te poka:

Te wā i te rangi

Ko te nekehanga o te wai mai i te poka ki te whenua nekehanga kaupapaKa taea te mārama ki te nekehanga o te pere mā te tātari motuhake i ngā wāhanga whakapae me ngā wāhanga poutū o te nekehanga. Ka puta te nekehanga x i te tere pumau, ā, ka puta te nekehanga y i te whakaterenga pumau o te kaha ā-papa.

I roto i tēnei raruraru, nekehanga poutū i tātaritatia hei nekehanga hinga noa.

Tātaihia te wā i te rangi mā te whakamahi i te whārite o te nekehanga hinga noa.

Mōhiotia:

Te teitei o te kōhao (y) = 10 cm = 0.1 m

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

E hiahiatia ana: Wā wā (t)

Rongoā:

y = 1/2 gt²

0.1 = 1/2 (10) t²

0.1 = 5 tāra²

t² = 0.1/5

t² = 0.02

t = √0.02 hēkona

Te tawhiti whakapae (x):

Mōhiotia:

Ko te tere tīmatanga (v_o = v_ox) = 3√2 m/s

Te wā i te rangi (t)= √0.02 hēkona

E hiahiatia ana: Te tawhiti whakapae (x)

Rongoā:

v = x / t

x = vt = (3√2)(√0.02) = (3)(1.41)(0.14) = 0.59 = 0.6 mita

2. He tāke wai kei roto, he 1 mita te teitei. Kei te pūwāhi P, he kōhao. He aha te tere o te rere o te wai i te kōhao? Ko te tere o te kaha ā-papa he 10 m/s².

Mōhiotia:

Te tawhiti i waenganui i te poka me te mata o te wai (h) = 100 cm – 80 cm = 20 cm = 0.2 m

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

Hiahia: Te tere o te rere o te wai i te poka (v)

Rongoā:

Te tere o te rere o te wai i te poka:

3. He nuikaukau e kei roto he wai, ā, he pūwero anō hoki e whakaaturia ana i te pikitia i raro nei. Mēnā ko te g = 10 ms^-2, kātahi ko te tere o te wai e puta ana i te pūwero he…

Mōhiotia:

Teitei (h) = 85 henimita – 40 henimita = 45 henimita = 0.45 mita

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

Hiahia: Tere o te wai (v)

Rongoā:

TE ai ki te ariā a Orricelli, ko te tere o te wai i roto i tētahi kōhao e tawhiti ana i a h mai i te mata o te wai he rite ki te tere o taka-koreTuhinga wai mai i te teitei o te h

Ka tatauhia te tere o te wai mā te whakamahi i te tātai nekehanga hinga noaa v_t² = 2 gh

v_t² = 2 gh = 2(10)(0.45) = 9

v_t = √9 = 3 m/s

4. A pupuhi kī tonu i te wai, ā, kei runga i te pakitara he kōhao (tirohia te ahua i raro neiKo te tere o te wai e puta mai ana i te poka ko… (g = 10 ms^-2)

Mōhiotia:

Teitei (h) = 1.5 m – 0.25 m = 1.25 mita

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

E hiahiatia ana: Ste tere o te wai (V)

Rongoā:

v_t² = 2 gh = 2(10)(1.25) = 25

v_t = √25 = 5 m/s

5. He tāke kei roto te wai tae atu ki te 1 mita te teitei (g = 10 ms)^-2) ā, kei te pakitara he kōhao turuturu (tirohia te ahua i raro neiKo te tere o te wai e puta mai ana i te poka ko...

Mōhiotia:

Teitei (h) = 1 m – 0.20 m = 0.8 mita

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

E hiahiatia ana: Ste tere o te wai (V)

Rongoā:

v_t² = 2 gh = 2(10)(0.8) = 16

v_t = √16 = 4 m/s

1. He aha te whakaahuatanga o te ariā a Torricelli?
   • whakahoki: E hono ana te ariā a Torricelli i te tere o te wai e rere ana i waho o te kōhao ki te teitei o te pou wai i runga ake i te kōhao, me te whakaaro he pumau, he koretake (kāore he matotoru), he rere kore e taea te pēhi.
2. He pēhea te whakapuakitanga o te ariā a Torricelli mā te pāngarau?
   • whakahoki: Ka whakaatuhia te ariā penei v=√2gh​, i reira $v$ ko te tere o te putanga mai, $g$ ko te whakaterenga nā te kaha ā-papa, me $h$ ko te teitei o te pou wai i runga ake i te kōhao.
3. I raro i ēhea ngā whakapae i ahu mai ai te ariā a Torricelli?
   • whakahoki: E whakaarohia ana e te ariā he kore e taea te pēhi i te wai, kāore hoki e mātotoru, he pumau te rere, ā, kāore he pūngao tāpiri e tāpirihia ana, e tangohia ana rānei i te wai.
4. Mena he rerekē te hohonutanga o ngā kōhao e rua o tētahi ipu, ka pēhea te whakataurite i te tere o ngā wai e puta mai ana i ngā kōhao?
   • whakahoki: Ko te wai e puta mai ana i te kōhao e tata atu ana ki te pūtake ka tere ake i te wai mai i te kōhao teitei ake. Nā te mea he nui ake te pēhanga (ā, nō reira, te pūngao pūmanawa) i ngā hohonutanga hohonu.
5. He aha te tere o te rerenga kāore e whakawhirinaki ki te āhua, ki te horahanga whakawhiti rānei o te ipu?
   • whakahoki: Ko te ariā a Torricelli e whai whakaaro ana ki te pūngao pūmanawa nā te teitei o te pou wai i runga ake i te kōhao. Kāore te āhua o te ipu e whakarerekē i tēnei teitei, nō reira ka noho tonu te tere o te putanga.
6. He aha te rerekētanga o te tere tuturu o te wai e rere ana i waho o tētahi kōhao i te matapae i mahia e te ariā a Torricelli i ngā āhuatanga o te ao tūturu?
   • whakahoki: I ngā āhuatanga o te ao tūturu, ka pāngia te tere tuturu e ngā āhuatanga pēnei i te matotoru o te wai, te aueue, me te āhua o te kōhao, ā, he maha ngā wā ka iti iho i te tere e matapaetia ana e te ariā a Torricelli.
7. He aha te whanaungatanga i waenga i te ariā a Torricelli me te tiakitanga o te pūngao?
   • whakahoki: I ahu mai te ariā a Torricelli i te tiakitanga o te pūngao ā-ringa. E whakataurite ana i te pūngao pūmanawa i te mata o te wai ki te pūngao nekeneke i te kōhao.
8. Mena he kōhao kei te tihi rawa o tētahi ipu kī tonu i te wai, me pēhea te whakaahuatanga a te ariā a Torricelli i te tere o te putanga wai?
   • whakahoki: Te teitei $h$ i runga ake i te kōhao ka kore, nō reira e ai ki te ariā a Torricelli, ka kore te tere putanga.
9. He pēhea te pānga o te pēhanga o te hau ki ngā matapae o te ariā a Torricelli?
   • whakahoki: E whakaaro ana te ariā a Torricelli kei te tuwhera te ipu ki te āhuarangi, nō reira, he ōrite te mahi a te pēhanga āhuarangi puta noa i te mata o te wai. Ka whakakorehia tēnei pēhanga ina whakaarohia te rerekētanga pēhanga puta noa i te teitei o te wai, nō reira ka mau tonu te ariā.
10. Ka ahatia te tere o te maringi ina heke te wai i roto i te ipu?

• whakahoki: I te hekenga o te taumata wai, ka heke te teitei $h$ ka heke iho i runga ake i te kōhao. E ai ki te ariā a Torricelli, ka heke te tere o te putanga mai i te mea v=√2gh​.

Mā ēnei pātai me ngā whakautu ka tūhuratia ngā pūtake, ngā pānga, me ngā tono o te ariā a Torricelli i roto i ngā whanaketanga wai.