1. E honoa ana tētahi papatipu 2-kg ki tētahi puna. Mena he 4 cm te roa o te puna, tautuhia te pūngao pūmanawa o te puna rapa . Ko te whakaterenga nā te kaha ā-papatipu he 10 m/ s².
Mōhiotia:
Taumaha (m) = 2 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha (w) = mg = (2)(10) = 20 N
Te toronga (x) = 4 cm = 0.04 m
E hiahiatia ana: Pūngao pūmanawa o te puna rapa
Rongoā:
Te tauira o te ture a Hooke :
F = kx
F = kaha, k = pūmau puna, x = te huringa o te roa o te puna
Pūmau puna:
k = w / x = 20 / 0.04 = 500 N/m
Pūngao pūmanawa o te puna rapa:
PE = ½ kx 2 = ½ (500)(0.04) 2 = (250)(0.0016) = 0.4 Joules
Otinga kē atu:
PE = ½ kx 2 = ½ (w / x) x 2 = ½ wx = ½ mgx
w = taumaha, m = papatipu, x = te huringa o te roa o te puna
PE = ½ (2)(10)(0.04) = (10)(0.04) = 0.4 Joules.
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2. Ko te roa o te puna i totorohia e te kaha F = 50 N he 10 cm. He aha te pūngao pūmanawa o te puna rapa mēnā he 12 cm te roa o te puna.
Mōhiotia:
Te toronga (x) = 10 cm = 0.1 m
Te kaha (F) = 50 N
E hiahiatia ana : Te pūngao pūmanawa o te puna rapa
Rongoā:
Pūmau puna:
k = F / x = 50 / 0.1 = 500 N/m
Ko te pūngao pūmanawa o te puna rapa mēnā he 12 cm te roa o te puna:
PE = ½ kx 2 = ½ (500)(0.12) 2 = (250)(0.0144) = 3.6 Joules.
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3. Ko te kauwhata o F vs x e whakaaturia ana i te pikitia i raro nei. He aha te pūngao pūmanawa o te puna rapa, mēnā ko te roa o te puna he 10 cm.
Mōhiotia:
Te kaha (F) = 5 N
Te roa o te puna (x) = 2 cm = 0.02 m
E hiahiatia ana: Te pūngao pūmanawa o te puna rapa mēnā ko te roanga o te puna he 0.1 m.
Rongoā:
Pūmau puna:
k = F / x = 5 / 0.02 = 250 N/m
Ko te pūngao pūmanawa o te puna rapa mēnā ko te roanga o te puna he 0.1 m:
PE = ½ kx 2 = ½ (250)(0.1) 2 = (125)(0.01) = 1.25 Joules.
4. Ka peke tetahi kaitākaro ki runga i tētahi pūoro puna he 500 N te taumaha, ka whakapotohia te puna kia 4 cm. Tātaihia te nui o te pūngao pūmanawa hei akiaki i te kaitākaro.
A. 20 Joules
B. 10 Joules
C. 5 Joule
D. 2 Joule
Mōhiotia:
Te kaha (F) = 500 N
Ko te panonitanga o te roa o te puna (Δx) = 4 cm = 0.04 m
E hiahiatia ana: Te pūngao pūmanawa o te puna
Rongoā:
Tātaihia te pūmau rapa o tētahi puna mā te whakamahi i te whārite o te ture a Hooke:
k = F / Δx = 500 N / 0.04 m = 12500 N/m
Te pūngao pūmanawa rapa o te puna:
PE = ½ k Δx 2 = ½ (12500)(0.04) 2 = (6250)(0.0016)
PE = 10 Joule
Ko te whakautu tika ko B.
5. Ina whakairihia he puna me te taumaha 500 karamu, ka piki ake tōna roa mā te 5 cm. Tātaihia tōna pūmau me tōna pūngao pūmanawa.
Mōhiotia:
Taumaha o te mea (m) = 500 karamu = (500/1000) kg = 5/10 kg = 0.5 kg
Whakaterenga (g) = 10 m/s 2
Taumaha o te mea (w) = mg = (0.5 kg)(10 m/s² ) = 5 kg m/s² = 5 Newton
Ko te panonitanga o te roa o te puna (Δx) = 5 cm = 0.05 m
E hiahiatia ana: te pūmau o te puna (k) me te pūngao pūmanawa (PE)
Rongoā:
Tuatahi, tatauhia te pūmau o te puna mā te whakamahi i te whārite o te ture a Hooke:
k = w / Δx = 5 N / 0.05 m = 100 N/m
Te pūngao rapa o te puna:
PE = ½ k Δx 2 = ½ (100)(0.05) 2 = (50)(0.0025)
PE = 0.125 Joule
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- Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
- Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
- Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
- Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
- Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
- Ngā raruraru hiko me ngā otinga
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i ngā mata piko
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te papa hianga
- Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere
