4 Ngā tauira o te mahi me te pūngao pūmanawa ā-papa
1. He mea he 1 kg te taumaha hinga noa mai i te teitei o te 10 mita ki te mata o te whenua. Whakatauhia:
(a) Te mahi i mahia e te kaha ā-papa i runga i te mea
(b) Ngā Huringa pūngao pūmanawa kaha ā-papa
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Kōrero
E mōhiotia ana :
Papatipu o te mea (m) = 1 kg
Teitei (h) = 10 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Whakautu:
(a) Te mahi i mahia e te kaha o te kaha ā-papa
Ina taka noa tetahi mea, ka heke te ahunga o te nekehanga o te mea, ā, ka heke hoki te ahunga o te kaha ā-papa e pā ana ki te mea (te taumaha o te mea). Nā te mea kei te ahunga kotahi rāua, ka ōrite ngā kaha ā-papa, ka hanga rānei i tētahi koki o te 0.o me te ahunga o te nekehanga o te mea. Ko te Cos 0 = 1, ā, ko ia tau e whakareatia ana ki te 1 he rite tonu ki taua tau, nō reira kāore e hiahiatia kia whakaurua te cos 0 ki te tātai mahi.
Ko te tātai mahi ko W = F s, ko W = mahi, ko F = kaha, ā, ko s = nekehanga. Mēnā ka whakatikatikaina ki tēnei raruraru, ka huri te tātai mahi ki W = wh = mgh, ko W = mahi, w = kaha ā-papatipu, h = huringa teitei o te mea, m = papatipu o te mea, g = whakaterenga nā te kaha ā-papatipu.
Nā, ko te mahi e mahia ana e te kaha ā-papa ko:
W = wh = mgh = (1)(10)(10) = 100 Joule
(B) Te huringa o te pūngao pūmanawa ā-papa
I te teitei o te 10 mita i runga ake i te whenua, ko te kaha pūmanawa ā-papa o te mea he 100 Joule. I a ia e neke ana ki raro, ka heke te teitei o te mea, ā, ka heke tōna kaha pūmanawa ā-papa. Ina tae ki te whenua, ki te kore te teitei o te mea, ka kore tōna kaha pūmanawa ā-papa. Nō reira, ka heke te kaha pūmanawa ā-papa o te mea mā te 100 Joule.
2. Kei runga i tētahi papa whakarara maeneene me te koki whakarara o te 30° tētahi mea, e 10 Newton te taumaha.o. E 2 mita te roa o te taha whakarunga. Ko te mahi i mahia e te kaha ā-papa i runga i te mea i a ia e reti ana i te taha whakarunga ko…
Kōrero
E mōhiotia ana :
Te kaha ā-papatipu (w) = 10 Newton
wx = w hara tit = (10)(hara 30o) = (10)(0,5) = 5 Nētana
Te roa o te taha whakarunga (s) = 2 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
I pātaihia : te mahi e mahia ana e te kaha ā-papa
Whakautu :
E rua ngā huarahi e taea ai te whakatau i tēnei raruraru.
Ko te ara tuatahi :
Ko te tātai mahi ko W = F s. Mēnā ka whakatikatikaina ki tēnei raruraru, ka huri te tātai mahi ki W = wx s. Nō reira, ko te mahi e mahia ana e te kaha ā-papa ko W = wx s = (5)(2) = 10 Joule.
Ara tuarua :
Ko te mahi e mahia ana e te kaha pūmau, pērā i te kaha ā-papa, kāore e whakawhirinaki ki te ara e haerehia ana e te mea engari e whakawhirinaki ana ki te huringa o te teitei. Nō reira, hei tatau i te mahi e mahia ana e te kaha ā-papa, tuatahi tatauhia te teitei o te mea.
Hara 30o = taha poutū / taha whakarara
0,5 = taha poutū / 2
Taha poutū = (0,5)(2)
Taha poutū = 1 mita
Kotahi mita te teitei o te mea.
Ko te mahi e mahia ana e te kaha ā-papa ina neke te mea ki raro ko W = wh = (10)(1) = 10 Joules.
3. E 5000 Joule o te pūngao e whakamahia ana hei hiki i tētahi mea he 50 kg te taumaha. Ka piki te mea ki te teitei o… g = 10 m/s2
A. 5 mita
B. 10 mita
C. 12 mita
D. 15 mita
E. 20 m
Kōrero:
E mōhiotia ana :
Te kaha ā-papa EP = 5000 Joule, m = 50 kg, g = 10 m/s2.
I pātaihia :
h?
Whakautu :
EP = mgh
5000 = (50)(10)(h)
5000 = 500 hāora
h = 5000 / 500 = 10 mita
Ko te whakautu tika ko B.
4. Kei te 5 mita te teitei o tētahi mea he 2 kg te taumaha i runga ake i te whenua. Te whakaterenga nā te kaha ā-papatipu = 10 m/s2Ko te kaha e hiahiatia ana hei hiki i tētahi mea ki te teitei o te 15 mita i runga ake i te mata o te whenua ko…
A. 100 Joules
B. 200 Joules
C. 300 Joule
D. 400 Joule
E. 500 Joule
Kōrero:
E mōhiotia ana :
m = 2 kg, h1 = 5 mita, h2 = 15 mita, karamu = 10 m/s2
I pātaihia :
W?
Whakautu :
Mahi (W) = huringa o te pūngao pūmanawa ā-papa (EP)2 – EP1).
W = EP2 – EP1
W = mgh2 – mgh1
W = mg (h2 – h1)
W = (2)(10)(15-5) = (2)(10)(10) = 200 Joule.
Ko te whakautu tika ko B.
