Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga hinga noa – ngā raruraru me ngā otinga

1. Ka taka noa tetahi tinana 1-kg mai i te tūnga, mai i te teitei o te 80 m. Ko te tere o te kaha ā-papa he 10 m/s² ^. He aha te pūngao nekeneke ina pā te tinana ki te whenua.

Mōhiotia:

Taumaha (m) = 1 kg

Teitei (h) = 80 m

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: te pūngao nekeneke ina pā te tinana ki te whenua

Rongoā:

Ko te pūngao ā-pūkaha tīmatanga (ME _o ) = te pūngao pūmanawa ā-papa (PE)

M E _o = P E = mgh = (1)(10)(80) = 800 Joule

Ko te pūngao miihini whakamutunga (M E _t ) = te pūngao nekeneke (K E )

Te mātāpono o te tiaki i te pūngao miihini :

ME o = ME _t​

P E = K E

800 = K E

Ko te pūngao nekeneke whakamutunga ko 800 Joules.

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2. Ka taka noa tētahi tinana 4-kg te taumaha mai i te tūnga, mai i te teitei o te 10 m. Ko te tere o te kaha ā-papa he 10 ms ^–2 . He aha te pūngao nekeneke me te tere i te 5 mita i runga ake i te whenua.

Mōhiotia:

Ko te panonitanga o te teitei (h) = 10 – 5 = 5 mita s

Taumaha (m) = 4 kg

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Pūngao nekeneke i te 5 mita i runga ake i te whenua me te tere i te 5 mita i runga ake i te whenua

Rongoā:

(a) Pūngao nekeneke i te 5 mita i runga ake i te whenua

Ko te pūngao miihini tīmatanga (M E _o ) = te pūngao pūmanawa ā-papa (P E )

M E _o = P E = mgh = (4)(10)(5) = 200 Joule

Ko te pūngao miihini whakamutunga (EM _t ) = te pūngao nekeneke (EK)

M E _t = K E

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga.

ME o = ME _t​

200 = K E

Ko te pūngao nekeneke i te 5 mita i runga ake i te whenua he 200 Joules.

(b) te tere i te 5 mita i runga ake i te whenua

Ko te pūngao miihini tīmatanga (M E _o ) = te pūngao miihini whakamutunga (M E _t )

P E = K E

200 = ½ mv ²

2(200) / 4 = v ²

100 = v ²

v = √100

v = 10 m/s

Ko te tere o te tinana i te 5 mita i runga ake i te whenua he 10 m/s.

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3. Ka taka noa te māngo mai i te tūnga, mai i te teitei o te 2 mita. Ko te tere o te kaha ā-papa he 10 ms ^–2 . Tātaihia te tere o te māngo ina pā ki te whenua.

Mōhiotia:

Teitei (h) = 2 mita s

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: te tere o te māngo ina pā ki te whenua.

Rongoā:

Ko te pūngao miihini tīmatanga (M E _o ) = te pūngao pūmanawa ā-papa (P E )

M E = P E = mgh = m (10)(2) = 20 m

Ko te pūngao miihini whakamutunga (M E _t ) = te pūngao nekeneke (K E )

M E _t = K E = ½ mv ²

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga.

ME o = ME _t​

20 m = ½ mv ²

20 = ½ v ²

2(20) = ^v2

40 = v ²

v = √40 = √(4)(10) = 2√10 m/ s

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1. Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
2. Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
3. Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
4. Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
5. Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
6. Ngā raruraru hiko me ngā otinga
7. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
8. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
9. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
10. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
11. Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere