5 Ngā tauira pātai mō te pūngao pūmanawa rapa o ngā puna
1. Ka tukuna he kawenga ki tētahi puna e 2 kg te taumaha, ā, ka whakairihia poutū ki runga i tētahi tūnga. Mēnā ka roa te puna mā te 4 cm, ko te huringa o pūngao pūmanawa Ko te kaha pīngore o te puna ko… g = 10 m/s2
Kōrero
E mōhiotia ana :
Papatipu o te kawenga (m) = 2 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha kawenga (w) = mg = (2)(10) = 20 Newton
Te pikinga o te roa o te puna (x) = 4 cm = 0,04 mita
I pātaihia Pūngao pūmanawa tere o te puna
Whakautu :
Tātai Te ture a Hooke ko F = kx, ko F = kaha, k = pūmau puna, ā, x = pikinga o te roa o te puna. Mēnā ka urutau ki tēnei raruraru, ka hurihia te tātai ture a Hooke ki w = kx, ko w = kaha ā-papaHei tatau i te pūmau puna, hurihia te tātai ture a Hooke ki k = w / x. Nō reira, ko te pūmau puna ko k = w / x = 20 / 0,04 = 500 Newton/mita.
Ko te panonitanga o te pūngao pūmanawa rapa o te puna ko:
EP = ½ kx2 = ½ (500)(0,04)2 = (250)(0,0016) = 0,4 Joule
Ka taea hoki te tatau i te panonitanga o te pūngao pūmanawa rapa o te puna mā te whakamahi i tētahi tātai kotahi:
EP = ½ kx2 = ½ (w / x) x2 = ½ wx = ½ mgx
Whakaahuatanga: w = te taumaha o te kaha o te kawenga, m = te papatipu o te kawenga, x = te huringa o te roa o te puna.
EP = ½ (2)(10)(0,04) = (10)(0,04) = 0,4 Joule.
2. Hei totoro i tētahi puna 10 cm, me whakamahi he kaha 50 N. Ko te kaha pūmanawa e hiahiatia ana hei totoro i te puna 12 cm ko…
Kōrero
E mōhiotia ana :
Te pikinga o te roa o te puna (x) = 10 cm = 0,1 mita
Te Kaha (F) = 50 Newton
I pātaihia : te pūngao pūmanawa pīngore o te puna hei totoro i te puna tae atu ki te 12 cm, arā, 0,12 mita.
Whakautu :
Ko te pūmau puna ko:
k = F / x = 50 / 0,1 = 500 Newton/mita
He rite tonu te puna i whakamahia, nō reira ko te pūmau puna i whiwhihia i te tātaitanga o mua ka whakamahia hei tātai i te pūngao pūmanawa rapa o te puna hei totoro i te puna mā te 0,12 mita.
EP = ½ kx2 = ½ (500)(0,12)2 = (250)(0,0144) = 3,6 Ngā Joule.
3. E whakaatu ana te kauwhata i raro nei i te whanaungatanga i waenga i te kaha (F) me te pikinga o te roa o te puna (x). Mena ka piko te puna mā te 10 cm, ko te kaha pūmanawa pīngore o te puna ko…
Kōrero
E mōhiotia ana :
Te Kaha (F) = 5 Newton
Te pikinga o te roa o te puna (x) = 2 cm = 0,02 mita
I pātaihia : te pūngao pūmanawa o te puna mēnā ka piko te puna mā te 10 cm, arā, 0,1 mita.
Whakautu :
Pūmau puna:
k = F / x = 5 / 0,02 = 250 Newton/mita
Ko te pūngao pūmanawa o te puna mēnā ka piko te puna mā te 0,1 mita:
EP = ½ kx2 = ½ (250)(0,1)2 = (125)(0,01) = 1,25 Ngā Joule.
Pūngao Pūmanawa Ātaahua
4. Ka hoatu he kawenga ki tētahi puna e 2 kg te taumaha, e ai ki te pikitia e whai ake nei. Mēnā ka piki ake te roa o te puna e 5 cm, ā, te whakaterenga nā te kaha ā-papa whenua 10 ms-2, kātahi ko te pūngao pūmanawa rapa o te puna ko...
A. 4,0 J
B. 3,0 J
C. 2,5 J
D. 1,0 J
E. 0,5 J
Kōrero
E mōhiotia ana :
Te pikinga o te roa (Δx) = 5 cm = 0,05 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Papatipu o te kawenga (m) = 2 kg
Taumaha kawenga (w) = mg = (2)(10) = 20 Newton
I pātaihia Pūngao pūmanawa o te rapa?
Whakautu :
Tuatahi, tatauhia te pūmau rapa o te puna mā te whakamahi i te tātai ture a Hooke:
k = w / Δx = 20 / 0,05 = 400 N/m
Ko te pūngao pūmanawa rapa o te puna ko:
EP = ½ k Δx2 = ½ (400)(0,05)2 = (200)(0,0025)
EP = 0,5 Joule
Ko te whakautu tika ko E.
5. Hei totoro i tētahi puna kia 5 cm, me whakamahi he kaha 20 N. Ko te kaha pūmanawa o te puna ina totoro kia 10 cm ko…
A. 2 Joules
B. 4 Joules
C. 20 Joule
D. 50 Joule
E. 100 Joule
Kōrero
E mōhiotia ana :
Te pikinga o te roa (Δx) = 5 cm = 0,05 mita
Te Kaha (F) = 20 Newton
I pātaihia : EP o te puna ina totoro te puna ki te 10 cm?
Whakautu :
Pūmau puna:
k = F / Δx = 20 / 0,05 = 400 N/m
Ko te pūngao pūmanawa o te puna ina Δx = 10 cm = 0,1 mita:
EP = ½ k Δx2 = ½ (400)(0,1)2 = (200)(0,01)
EP = 2 Joule
Ko te whakautu tika ko A.
