Ki te pana koe i tētahi pukapuka ki runga i tētahi tēpu kia neke rā anō, kei te mahi koe i runga i te pukapuka. Ki te taka tētahi mea ki te mata o te whenua nā te mea e tōia ana e te kaha o te kaha ā-papa, ka mahi te kaha o te kaha ā-papa ki runga i te mea. I tua atu, ki te pana koe i tētahi mea ki tō kaha katoa kia mākū rawa koe i te werawera engari kāore te mea e neke, kāti kāore koe i mahi i runga i te mea. I roto i te oranga o ia rā, e kī ana ētahi atu kua mahi koe, kua kaha rānei te mahi ki te pana i te mea, engari e ai ki te ahupūngao , kāore koe i mahi i runga i te mea nā te mea kāore te mea e pāngia e te nekehanga.
Ka taea te mahi i runga i tētahi mea mā te kaha pumau (ka noho tonu te rahi me te ahunga o te kaha) mā te kaha taurangi rānei (ka rerekē tonu te rahi me te ahunga o te kaha). Ko tētahi tauira o tētahi kaha pumau te rahi me te ahunga ko te kaha ā-pūmau e pā ana ki tētahi mea ina tata te mea ki te mata o te Ao. Ina taka noa te mea i te taha o te mata o te Ao, ka pumau te rahi me te ahunga o te whakaterenga taka noa o te mea nā te mea he pumau te rahi me te ahunga o te kaha ā-pūmau e whakatere ana i te mea. Ko tētahi tauira o tētahi kaha kāore i te pumau te rahi (he pumau te ahunga o te kaha) ko te kaha o tētahi puna . Ki te totoro koe i tētahi puna, ka nui ake te pikinga o te roa o te puna, ka kaha ake tō kukume. Kāore te rahi o te kaha e pā ana ki te puna i te pumau i te totorotanga o te puna. Ko tētahi atu tauira ko te neke o tētahi rōkete ki te wāhi, te hoki rānei ki te mata o te Ao. Ina neke te rōkete, ka huri te rahi o te kaha ā-pūmau e pā ana ki te rōkete i runga i te āhua whakahurihuri ki te tapawhā o te tawhiti mai i te pokapū o te Ao.
I roto i te pāngarau, ko te mahi i mahia e te kaha pumau ki runga i tētahi mea ka tautuhia hei hua o te nekehanga whakareatia ki te kaha, ki te wāhanga rānei o te kaha i te ahunga o te nekehanga o te mea.
Kāore e taea te tatau i te mahi e mahia ana e te kaha kore-pūmau pērā i te puna mā te whakamahi i te tātai mō te mahi e te kaha pūmau. Mēnā ka totorohia te puna, i te mea ka totoro haere te puna, ka nui ake hoki te kaha kume e hiahiatia ana hei totoro i te puna. Waihoki, ki te pēhia te puna, ina piri ake te puna, ka nui ake hoki te kaha pana e hiahiatia ana. Mēnā ka pēhia, ka totorohia rānei te puna, ka huri te kaha puna mai i te 0 (x = 0) ki te mōrahi (F = kx) nō reira ka tatauhia te kaha puna mā te whakamahi i te toharite.
Tauira raruraru
1. Ngā Pātai Whakamātautau ā-Motu 2018
Kei runga i tētahi mata papatahi maeneene tētahi poraka he taumaha m. Kei te okioki te poraka i tōna tūranga (1) ā, ka tōia e te kaha F ki tōna tūranga (2) i roto i tētahi wā t e whakaaturia ana i te pikitia.
Mā te whakarerekē i te papatipu me te kaha, ka puta ngā raraunga e whai ake nei:
Mai i te ripanga i runga ake nei, ko te mahi i mahia e ngā mea mai i te mea nui ki te mea iti ko…
Kōrero
E mōhiotia ana:
Te tere tīmatanga (v o ) = 0
I pātaihia:
Whakautu:
Tātai mahi:
W = Fs ………. Tātai 1
Tātai GLBB:
s = v o t + 1/2 i te 2
s = 1/2 i te 2
Whakakapia ki te tātai 1
W = F ( 1/2 i te 2 ) ………. Tātai 2
Tātai kaha:
F = ma
a = F / m
Whakakapia ki te tātai 2
W = 0,5 F (F/m) t 2
W = 0,5 (F 2 /m) t 2 ………. Tātai 3
Whakamahia te tātai 3 hei tatau i te kaha.
1) W = 0,5 (F 2 /m) t 2 = 0,5 (3 2 /12)(4 2 ) = (0,5)(9/12)(16) = (9/12) 8 = 6
2) W = 0,5 (F 2 /m) t 2 = 0,5 (4 2 /16)(3 2 ) = (0,5)(16/16)(9) = (1) 4,5 = 4,5
3) W = 0,5 (F 2 /m) t 2 = 0,5 (5 2 /20)(2 2 ) = (0,5)(25/20)(4) = (1,25) 2 = 2,5
4) W = 0,5 (F 2 /m) t 2 = 0,5 (6 2 /24)(1 2 ) = (0,5)(36/24)(1) = (1,5) 0,5 = 0,75
Ko te mahi i mahia e ngā mea mai i te mea nui rawa ki te mea iti rawa ko 1, 2, 3, 4.
2. Ngā Pātai Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa mō te tau 2017
Kei te paheke tētahi pouaka 6 kg te taumaha i te tere o te 8 m/s -1 i runga i tētahi papa whakarara taratara me te koki whakarara α ki te papa whakapae. Mena ko te kaha waku e pā ana ki te pouaka he 5 N, ā, ko te tan α = 3/4, ko te kaha F me whakamahi hei aukati i te pouaka i raro i te papa whakarara ko…
A. 15 N
B. 25 N
C. 45 N
D. 55 N
E. 69,4 N
Kōrero
E mōhiotia ana:
Taumaha o te pouaka (m) = 6 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te tere tīmatanga o te pouaka (v o ) = 8 m/s
Te tere whakamutunga o te pouaka (vt ) = 0 m/s (me tū te pouaka i mua i te taenga ki te pito o te papa whakarara)
Te kaha waku (F waku ) = 5 N
Pānga α = taha mua / taha raro = 3/4
Te piko = 5 mita
I pātaihia: F
Whakautu:
Te ariā mahi-pūngao ā-mīhini:
Te mahi i mahia e te kaha kore-pūmau = te huringa o te pūngao miihini
Ko te mahi i mahia e te kaha kore-pūmau = te huringa o te pūngao nekeneke me te pūngao pūmanawa.
E rua ngā kaha kore-pūmau, arā, te waku nekeneke me te kaha F.
Ko te mahi i mahia e te kaha waku nekeneke i runga i te pouaka:
W = -(F ges )(s) = -(5)(5) = -25
Kāore i te pai nā te mea he rerekē te ahunga o te kaha waku ki te ahunga nekehanga o te pouaka.
Te mahi i mahia e te kaha F:
W = (F)(s) = (F)(5) = -5F
Tōraro nā te mea he rerekē te ahunga o te kaha F i te ahunga nekehanga o te pouaka.
Te huringa o te pūngao nekeneke:
Δ EK = 1/2 m (v t 2 – v o 2 ) = 1/2 (6)(0 2 – 8 2 ) = (3)(0-64) = (3)(-64) = -192
Te huringa o te pūngao pūmanawa ā-papa:
Δ EP = mgh = (6)(10)(-3) = -180
He kino a h nā te mea kei raro iho te tūranga whakamutunga i te tūranga tīmatanga
Te ariā mahi-pūngao ā-mīhini:
W nc = Δ EM
W ges + W F = Δ EP + Δ EK
-25 – 5F = -180 -192
-25 – 5F = -372
-5F = -372 + 25
-5F = – 347
F = -347 / -5
F = 69,4 Newton
Ko te whakautu tika ko E.
3. Ngā Pātai Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa mō te tau 2017
Ka paheke iho tētahi poraka 10 kg te taumaha mai i te pūwāhi A puta noa i te pūwāhi B, ā, ka tū ki te pūwāhi C e whakaaturia ana i te pikitia. Ko te tauwehenga o te waku nekeneke i waenga i te poraka me te mata taratara he 0,2, nō reira ko te roa o te ara ABC he…
A. 250 henemita
B. 200 henemita
C. 150 henimita
D. 100 henimita
E. 80 henimita
Kōrero
E mōhiotia ana:
Taumaha o te poraka (m) = 10 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka (w) = mg = (10 kg)(10 m/s 2 ) = 100 Newton
Teitei o te papa whakarara (h) = 30 cm = 0,3 mita
Te roa o te papa piko (s) = 50 cm = 0,5 mita
Tauwehenga o te waku nekeneke ( μ k ) = 0,2
Te kaha waku nekeneke (f k ) = μ k N = μ k w = (0,2)(100 N) = 20 N
Pātai: Te roa o te ara ABC
Whakautu:
Whakaarohia te nekehanga o te mea mai i te pūwāhi AB.
Pūngao ā-pūkaha tīmatanga i te pūwāhi A = pūngao pūmanawa ā-papa = mgh = (10)(10)(0,3) = (10)(3) = 30 Joule
Pūngao miihini whakamutunga i te pūwāhi B = pūngao nekeneke
Te ture tiaki i te pūngao ā-pūkaha:
Pūngao miihini tīmatanga = pūngao miihini whakamutunga
30 Joules = Pūngao nekeneke
Nō reira, ko te pūngao nekeneke i te pūwāhi B = 30 Joule.
Whakaarohia te nekehanga o te mea mai i te pūwāhi BC.
E ai ki te ariā mahi-pūngao mīhini, ko te mahi i mahia e te kaha kore-pūmau he rite ki te huringa o te pūngao mīhini o te mea. Ko te huringa o te pūngao mīhini = te pūngao mīhini whakamutunga – te pūngao mīhini tīmatanga. Mā te pāngarau:
W NC = Δ EM
W NC = EM 2 – EM 1
Kei runga i te mata papatahi te mea e tū ana, ā, kāore he kaha pūmanawa ā-papa. Pūngao miihini (EM) = pūngao nekeneke (EK).
Pūngao nekeneke tīmatanga (EK 1 ) = pūngao nekeneke i te pūwāhi B = 30 Joules
Pūngao nekeneke whakamutunga (EK 2 ) = pūngao nekeneke i te pūwāhi C = 0 (ka mutu te poraka).
Ko te mahi i mahia e te kaha kore-pūmau o BC ko te mahi i mahia e te kaha waku nekeneke.
W NC = – f k s = – 20 s
Jadi
W NC = EK 2 – EK 1
– 20 hēkona = 0 – 30
– 20 hēkona = – 30
20 hēkona = 30
s = 30/20 = 3/2 = 1,5 mita = 1,5 x 100 henimita = 150 henimita.
Te roa o te ara ABC = 50 cm + 150 cm = 200 cm.
Ko te whakautu tika ko B.
4. Pātai Whakamātautau ā-Motu SMA/MA 2014/2015 Nama 8
Tirohia te pikitia e whai ake nei! Ka paheke tētahi poraka i runga i tētahi papa piko taratara, ā, ko te tauwehenga waku he 0,4. Mena ko te g = 10 ms -2 , ko te tere o te poraka ina pā ki te raro o te papa piko ko...
A. 2√5 ms-1
B. 2 √7 ms -1
C. 2 √14 ms -1
D. 2 √19 ms -1
E. 2 √23 ms -1
Kōrero
I a koe e titiro ana ki te pikitia i raro nei
E mōhiotia ana:
Teitei tīmatanga (h o ) = 6 m
Teitei whakamutunga ( t ) = 0 m
Te tere tīmatanga (v o ) = 0 (i te tīmatanga kei te noho pūmau te poraka)
Tauwehenga waku nekeneke ( μ k ) = 0,4 ( ka paheke te poraka, nō reira ko te tauwehenga waku nekeneke, ehara i te tauwehenga waku pumau )
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
cos θ = raro/tītaha = 8/10
Ko te wāhanga taumaha i te ahunga poutū = w y = w cos θ = mg cos θ = m (10) (8/10) = m (10)(4/5) = m (40/5) = 8 m
Te kaha noa = N = w y = 8 m
Te kaha waku nekeneke = f k = μ k N = μ k w y = (0,4)(8 m) = 3,2 m
Pātai: Te tere whakamutunga ( vt )
Whakautu:
E ai ki te ariā mahi-pūngao, ko te mahi i mahia e te kaha kore-pūmau ki runga i tētahi mea he rite ki te huringa o te kaha ā-pūkaha o te mea. Ko tētahi tauira o te kaha kore-pūmau ko te waku nekeneke.
Wnc = ΔEM
W nc = Δ EK + Δ EP
Ngā Mōhiohio:
W nc = Mahi i mahia e te kaha kore-pūmau, Δ EM = Huringa o te pūngao miihini, Δ EK = Huringa o te pūngao nekeneke, Δ EP = Huringa o te pūngao pūmanawa.
Te huringa o te pūngao nekeneke:
ΔEK = 1/2 m (vt2 -vo2) = 1/2 m (vt2 - 0) = 1/2 mvt2
Te huringa o te pūngao pūmanawa:
Δ EP = mg (h t – h o ) = m (10)(0-6) = m (10)(-6) = – 60 m
Te mahi i mahia e te waku nekeneke:
Wnc = – f k s = – ( 3,2 m)(10) = – 32 m
He kino nā te mea he mahi kino tā te kaha waku nekeneke, ina he rerekē te ahunga o te kaha waku nekeneke (ki runga) ki te ahunga o te nekehanga o te mea (ki raro).
Tātaihia te tere whakamutunga (vt ) :
Wnc = Δ EK + Δ EP
– 32 m = 1/2 mv t 2 – 60 m
– 32 m = m (1/2 v t 2 – 60)
– 32 = 1/2 v t 2 – 60
– 32 + 60 = 1/2 v t 2
28 = 1/2 v t 2
2 (28) = v t 2
56 = v t 2
vt = √4.14
v t = 2 √14 ms -1
Ko te whakautu tika ko C.
5. Ngā Pātai Whakamātautau ā-Motu mō te Ahupūngao SMA/MA 2014/2015 Nama 8
Tirohia te pikitia kei te taha!
Ka paheke tetahi poraka i raro i tētahi papa piko taratara, ka tae ki te take o te papa piko i te tere o te 10 ms -1 . Mena ko te kaha waku e mahi ana ko 2 N, ā, ko g = 10 ms -2 , ko te uara o h ko ….
A. 10 mita
B. 8 mita
C. 6 mita
D. 4 mita
E. 2 m
Kōrero
E mōhiotia ana:
Taumaha o te poraka (m) = 1 kg
Te tere tīmatanga (v o ) = 0 (i te tīmatanga kei te noho pūmau te poraka)
Te tere whakamutunga (vt ) = 10 ms -1
Teitei tīmatanga (h o ) = h
Teitei whakamutunga ( t ) = 0
Te kaha waku nekeneke (f k ) = 2 N
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
I pātaihia: Teitei (h)
Whakautu:
Te mahi i mahia e te waku nekeneke:
Wnc = – f k s = – (2 )(15) = – 30
He kino nā te mea he mahi kino tā te kaha waku nekeneke, ina he rerekē te ahunga o te kaha waku nekeneke (ki runga) ki te ahunga o te nekehanga o te mea (ki raro).
Te huringa o te pūngao nekeneke:
ΔEK = 1/2 m (vt2 -vo2) = 1/2 (1)(102 - 0) = 1/2 (102) = 1/2 (100) = 50
Te huringa o te pūngao pūmanawa:
Δ EP = mg (h t – h o ) = (1)(10)(0-h) = (10)(-h) = -10 h
Ko te tātai mō te ariā mahi-pūngao ā-pūngao:
Wnc = Δ EK + Δ EP
– 30 = 50 – 10 hāora
10 hāora = 50 + 30
10 hāora = 80
h = 80/10
h = 8 mita
Ko te whakautu tika ko B.
