6 Ngā Tauira o Ngā Pātai Pūngao Mīhini
Te ariā mahi-pūngao miihini
1. Kia aro ki te pikitia nekehanga poraka penei! Me kī ko g = 10 m/s2. Mēnā ko te tauwehenga o te waku nekeneke i waenga i te poraka me te papa μk = 0,5, kāti ko te uara o te nekehanga (s) o te mea ko ….
A. 5,00 mita
B. 4,25 mita
C. 3,00 mita
D. 2,50 mita
E. 2,00 m
Kōrero
E mōhiotia ana :
Te tauwehenga o te waku nekeneke (μk) = 0,5
Taumaha o te poraka (m) = 4 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha o te poraka (w) = mg = (4)(10) = 40 Newton
Mena kei runga te poraka i tētahi mata papatahi, ko te kaha noa (N) = taumaha (w) = 40 Newton.
Te tere tīmatanga (v1) = 5 m/s
Te tere whakamutunga (v2) = 0 m/s
I pātaihia : te nekehanga o te (ngā) mea?
Whakautu :
E ai ki te ariā mahi-pūngao mīhini, ko te mahi (W) i mahia e te kaha kore-pūmau he rite ki te huringa o te pūngao mīhini o te mea, ki te pūngao mīhini whakamutunga rānei (EM).2) – te pūngao miihini tuatahi (EM)1He kaha kore-pūmau te waku nekeneke, ā, ko te kaha kore-pūmau anake e pā ana ki te poraka ko te waku nekeneke.
W= ΔEM
fk s = EM2 – EM1
Te mahi i mahia e te waku nekeneke:
W = fk s = (μk)(N)(s) = (0,5)(40)(s) = 20 hēkona
Ngā panonitanga o te pūngao miihini:
ΔEM = EM2 – EM1 = (EK + EP)2 – (EK + EP)1
Ka neke ngā mea i runga i te mata papatahi, ā, kāore e rerekē te teitei (Δh = 0) nō reira kāore he huringa o te pūngao pūmanawa ā-papa (ΔEP = EP2 – EP1 = 0). Nō reira, ko te huringa o te pūngao miihini e pā ana ki te huringa o te pūngao nekeneke anake.
ΔEM = EK2 – EK1 = ½ mv22 – ½ mv12 = ½ m (v22 -v12)
ΔEM = ½ (4)(02 - 52) = (2)(25) = 50
Ko te nekehanga o te poraka ko:
W= ΔEM
20 hēkona = 50
s = 50 / 20 = 2,5 mita
Ko te whakautu tika ko D.
Te ture tiaki i te pūngao miihini
2. He ōrite te taumaha o ngā taonga A me B. Ka taka te taonga A mai i te teitei o te h mita, ka taka hoki a B mai i te 2h mita. Ki te pā a A ki te whenua me te tere o te vm/s, ka pā te taonga B ki te whenua me te kaha nekeneke o….
A. 2 mv2
B. mv2
C. 3/4 mv2
D. 1/2 mv2
E. 1/4 mv2
Kōrero
Ko te tere whakamutunga o te mea B e taka noa ana mai i te teitei o te 2h ko:
v2 = 2 karamu (2 hāora) = 4 hāora
Ko te pūngao nekeneke o te mea B ko:
EKB = ½ mv2 = ½ m (4 gh) = 2 mgh —– Whārite 1
Ko te pūngao ā-pūkaha tīmatanga o te mea B ko te pūngao pūmanawa ā-papa = mg h. Ko te pūngao ā-pūkaha whakamutunga o te mea B ko te pūngao nekeneke = ½ mv2.
Te ture tiaki i te pūngao miihini :
mgh = ½ mv2.
Na te mea mgh = ½ mv2 kātahi ka taea e tātou te whakakapi i te mgh i te whārite 1 ki te ½ mv2.
Pūngao nekeneke o te mea B = 2 mgh = 2(½ mv2) = mv2
Ko te whakautu tika ko B.
3. Tirohia te pikitia i raro nei! Ka taka noa tetahi mea mai i te teitei o te 20 m. Mena ko te whakaterenga nā te kaha ā-papa he 10 m/s, ko te tere o te mea ina 15 m i runga ake i te whenua ko….
A. 2 m/s
B. 5 m/s
C. 10 m/s
D. 15 m/s
E. 20 m/s
Kōrero
Pūngao miihini whakamutunga = pūngao miihini tīmatanga
Ko te pūngao nekeneke o te mea i te pūwāhi 2 = te whakahekenga o te pūngao pūmanawa ā-papa mā te 5 mita
½ mv2 = mgh
½ v2 = (10)(20-15)
½ v2 = (10)(5)
½ v2 = 50
v2 = (2)(50)
v2 = 100
v = 10 m/s
Ko te whakautu tika ko C.
4. Kei te tihi o te papa whakarara te pupuri i tētahi poraka e whakaaturia ana i te pikitia. Ina tukuna, ka paheke te poraka i te taha o te pari, kāore he waku. Ko te tere o te poraka ina tae ki raro o te pari ko…
B. 8 ms-1
C. 10 ms-1
D. 12 ms-1
E. 16 ms-1
Kōrero
Pūngao miihini tīmatanga = pūngao pūmanawa ā-papa = mgh = m (10)(5) = 50 m
Pūngao miihini whakamutunga = pūngao nekeneke = 1/2 mv2
E ai ki te ture tiaki i te pūngao ā-pūkaha, ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga.
EMo = EMt
50 m = 1/2 mv2
50 = 1/2 v2
100 = v2
v = 10 m/s
Ko te whakautu tika ko C.
5. Ka tukuna he poraka he m kg te taumaha mai i te teitei o h mita i runga ake i te whenua e whakaaturia ana i te pikitia. Ko te ōwehenga o te pūngao pūmanawa (EP) me te pūngao nekeneke (EK) ina tae ki te pūwāhi M ko….
A. 1 : 3 
B. 1 : 2
C. 2 : 1
D. 2 : 5
E. 3 : 7
Kōrero
Pūngao pūmanawa ā-papa i te pūwāhi M:
EPM = mg (0,3 hāora)
Pūngao nekeneke i te pūwāhi M = te whakaiti i te pūngao pūmanawa ā-papa mā te h-0,3h = 0,7 h
EKM = EP = mg (0,7 hāora)
Ko te ōwehenga o te pūngao pūmanawa ā-papa me te pūngao nekeneke i te pūwāhi M ko:
EPM : EKM
mg (0,3 hāora) : mg (0,7 hāora)
0,3: 0,7
3: 7
Ko te whakautu tika ko E.
6. Tirohia te pikitia o te mea A e taka noa ana mai i te pūwāhi P i raro nei!
Mena ko EPQ me EKQ ko ia te pūngao pūmanawa me te pūngao nekeneke i te pūwāhi Q (g = 10 m/s2), kātahi ko EPQ : EKQ ko….
A. 16 : 9
B. 9 : 16
C. 3 : 2
D. 2 : 3
E. 2 : 1
Kōrero
Pūngao pūmanawa ā-papa i te pūwāhi Q:
EPQ = mgh = (m)(10)(1,8) = 18 m
Pūngao nekeneke i te pūwāhi Q = te whakahekenga o te pūngao pūmanawa ā-papa mā te 5-1,8 = 3,2 mita
EKQ = EP = mgh = m (10)(3,2) = 32 m
Ko te ōwehenga o te pūngao pūmanawa ā-papa me te pūngao nekeneke i te pūwāhi Q ko:
EPQ : EKQ
18 mita: 32 mita
18: 32
9: 16
Pūtake pātai:
Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa
