8 ngā tauira o te pūngao pūmanawa me te pūngao nekeneke
1. Tirohia te pikitia i raro nei!
Ko te taumaha o te Taonga A he 1.500 karamu, ā, kei te tūranga e whakaaturia ana i te pikitia. I muri i tētahi wā, ka taka te taonga ki te whenua. Pūngao pūmanawa te mea nui rawa atu nō te mea A
ko... (e mōhiotia ana ko te g o te whenua = 10 m/s2)
A. 15 Joules
B. 200 Joules
C. 300 Joule
D. 30.000 Joule
Kōrero
E mōhiotia ana:
Whakahuatia ngā waeine katoa o te Pūnaha Ao Whānui
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te mea (m) = 1500 karamu = 1500/1000 kirokaramu = 1,5 kirokaramu
Teitei (h) = 20 mita
Pātai: Pūngao pūmanawa o te mea A
Whakautu:
Kei te Taonga A te pūngao pūmanawa nui rawa atu ina tae ki tōna pūwāhi teitei rawa atu, arā, 20 mita mai i te mata o te whenua, ā, ko te pūngao pūmanawa iti rawa ina noho te taonga ki runga i te mata o te whenua.
Ka tatauhia te pūngao pūmanawa o tētahi mea mā te whakamahi i te tātai pūngao pūmanawa ā-papa:
EP = mgh = (1,5 kg)(10 m/s² ) (20 m) = 300 kg m² / s² = 300 Joule
Ko te whakautu tika ko C.
2. E neke ana tētahi matā he 10 karamu te taumaha i te tere o te 100 m/s. Ko te pūngao nekeneke o te matā ko…..
A. 50 Joules
B. 1.000 Joules
C. 10.000 Joule
D. 50.000 Joule
Kōrero
E mōhiotia ana:
Taumaha o te matā (m) = 10 karamu = 10/1000 kirokaramu = 1/100 kirokaramu = 0,01 kirokaramu
Tere matā (v) = 100 mita/hekona
Pātai: Pūngao nekeneke o te matā
Whakautu:
Ka tatauhia te pūngao nekeneke o te matā mā te whakamahi i te tātai pūngao nekeneke:
EK = 1/2 mv 2
EK = 1/2 (0,01 kg)(100 m/s) 2
EK = 1/2 (0,01 kg)(10.000 m 2 /s 2 )
EK = (0,01 kg)(5000 m 2 /s 2 )
EK = 50 kg m² / s²
EK = 50 Joule
Ko te whakautu tika ko A.
3. He ōrite te taumaha o te motuka A me te motuka B. He rerekē te kaha nekeneke o ngā motuka e rua. Mena ko te kaha nekeneke o te motuka A ki te kaha nekeneke o te motuka B he 4:9, ko te tere o te motuka A ki te tere o te motuka B he….
A. 2 : 3
B. 3 : 2
C. 4 : 9
D. 9 : 4
Kōrero
E mōhiotia ana:
Te pūngao nekeneke o te motuka A (EK)A) = 4
Te pūngao nekeneke o te motuka B (EK)B) = 9
Taumaha o te motuka A (mA) = te taumaha o te motuka B (mB) = m
Pātai: Te tere o te motuka A ki te tere o te motuka B
Whakautu:
Me kī ko te taumaha o te motuka A = te taumaha o te motuka B = m = 1
Pūngao nekeneke o te motuka A:
EK = ½ mv2 —-> Tātai pūngao nekeneke
4 = ½ (1) v2
(2)(4) = v2
vA = √(2)(4)
Pūngao nekeneke o te motuka B:
EK = ½ mv2 —-> Tātai pūngao nekeneke
9 = ½ (1) v2
(2)(9) = v2
vB = √(2)(9)
Te whakataurite i te tere o te motuka A me te motuka B:
vA i roto iB
√(2)(4) : √(2)(9)
2√2 : 3√2
2: 3
Ko te whakautu tika ko A.
4. He ōrite te taumaha o ngā mea e rua, a A rāua ko B. Ko te kaha nekeneke o te mea A he 4 J, ā, ko te kaha nekeneke o te mea B he 16 J. Ko te ōwehenga o te tere o te mea A ki a B ko….
A. 1 : 2
B. 1 : 4
C. 2 : 1
D. 4 : 1
Kōrero
E mōhiotia ana:
Te pūngao nekeneke o te mea A (EK)A) = 4 Joule
Te pūngao nekeneke o te mea B (EKB) = 16 Joule
Papatipu o te mea A (mA) = te papatipu o te mea B (mB) = m
Pātai: Te whakataurite i te tere o te mea A ki te tere o te mea B
Whakautu:
Me kī ko te papatipu o te mea A = te papatipu o te mea B = m = 1
Pūngao nekeneke o te mea A:
EK = ½ mv2 —-> Tātai pūngao nekeneke
4 = ½ (1) v2
(2)(4) = v2
vA = √(2)(4)
Pūngao nekeneke o te mea B:
EK = ½ mv2 —-> Tātai pūngao nekeneke
16 = ½ (1) v2
(2)(16) = v2
vB = √(2)(16)
Te whakataurite i te tere o te motuka A me te motuka B:
vA i roto iB
√(2)(4) : √(2)(16)
2√2 : 4√2
2: 4
1: 2
Ko te whakautu tika ko A.
5. E rua ngā mea he rite te taumaha e neke ana. Ko te ōwehenga o te pūngao nekeneke o ngā mea tuatahi me ngā mea tuarua ko te 1:4. Ko te ōwehenga o te tere o te mea tuatahi ki te mea tuarua ko….
A. 1 : 2
B. 1 : 4
C. 2 : 1
D. 4 : 1
Kōrero
E mōhiotia ana:
Te pūngao nekeneke o te mea tuatahi (EK)1) = 1
Te pūngao nekeneke o te mea tuarua (EK)2) = 4
Te taumaha o te mea tuatahi (m1) = te papatipu o te mea tuarua (m2) = m
Pātai: Te whakataurite i te tere o te mea tuatahi ki te tere o te mea tuarua
Whakautu:
Me kī ko te papatipu o te mea tuatahi = te papatipu o te mea tuarua = m = 1
Pūngao nekeneke o te mea tuatahi:
EK = ½ mv2 —-> Tātai pūngao nekeneke
1 = ½ (1) v2
(2)(1) = v2
2 = v2
vA = √2
Pūngao nekeneke o te mea tuarua:
EK = ½ mv2 —-> Tātai pūngao nekeneke
4 = ½ (1) v2
(2)(4) = v2
vB = √(2)(4)
Te whakataurite i te tere o te motuka A me te motuka B:
v1 i roto i2
√2 : √(2)(4)
√2 : 2√2
1: 2
Ko te whakautu tika ko A.
6. Ka paheke tētahi poraka i runga i tētahi mata piko i te tere pumau. Ko te huringa pūngao e puta ana ko…
A. pūngao pūmanawa → pūngao nekeneke
B. pūngao nekeneke → pūngao pūmanawa
C. pūngao pūmanawa → pūngao wera
D. pūngao nekeneke → pūngao wera
E. pūngao wera → pūngao nekeneke
Kōrero
Ki te paheke tētahi poraka i runga i tētahi mata hihira, mai i runga ki raro, ka hurihia te pūngao pūmanawa ā-papa hei pūngao nekeneke.
Ko te whakautu tika ko A.
Tirohia te ara iahiko i te pikitia.
7. Ka hoatu he nekehanga tīmatanga ki tētahi pendulum pāngarau, kātahi ka wiriwiri i runga i te āhua harmonic e whakaaturia ana i te pikitia. Mena ko te pūwāhi tohutoro mō te ine i te pūngao pūmanawa ko te pūwāhi C, ko tēhea kōrero te mea tika?
(1) He rite tonu te kaha nekeneke o te pendulum i te pūwāhi A' ki te kaha nekeneke o te pendulum i te pūwāhi B'
(2) He rite tonu te kaha pūmanawa o te pendulum i te pūwāhi A' ki te kaha pūmanawa o te pendulum i te pūwāhi B'
(3) He rite tonu te rerekētanga o te pūngao nekeneke o te pendulum i ngā pūwāhi A' me A ki te rerekētanga o te pūngao pūmanawa o te pendulum i ngā pūwāhi B' me B.
(4) He rite tonu te tere o te pendulum i te pūwāhi A' ki te tere o te pendulum i te pūwāhi B.
Kōrero
Ko ngā kōrero tika ko 1, 2 me te 3.
8. Tirohia te pikitia!
Ko te pūngao nekeneke o tētahi mea i te pūwāhi B = 100 J. Mena he 2,5 kg te taumaha o te mea, ko te pūngao nekeneke o te mea ina pā ki te whenua i te pūwāhi C ko…
A. 350 J
B. 250 J
C. 150 J
D. 100 J
Kōrero
Ko te pūngao nekeneke o te mea ina tae ki te pūwāhi B:
EP = mgh = (2,5)(10)(4) = 100 Joule
Ko te pūngao nekeneke o te mea ina tae ki te pūwāhi C:
EP = mgh
EP = (2,5)(10)(4 + 6)
EP = (2,5)(10)(10)
EP = 250 Joule
Ko te whakautu tika ko B.
Pūtake pātai:
Ngā Pātai Whakamātautau Pūtaiao ā-Motu mō te Kura Tuarua/Kura Tuarua Ihirama
Ngā Pātai Ahupūngao SBMPTN
