14 Ngā Tauira o Ngā Pātai mō ngā Āhuatanga Matūriki
1. Kei runga i tētahi mata papatahi maeneene te poraka A, he 5 kg te taumaha, kei te whakairihia te poraka B, he 3 kg te taumaha, ki tētahi taura, ā, kei te honoa ki te poraka A mā tētahi pūreirei. Mēnā ko te g = 10 m/s2, whakatauhia te whakaterenga o te poraka!
A. 3,50 m/s2
B. 3,75 m/s 2
C. 4,00 m/s 2
D. 5,00 m/s 2
E. 5,25 m/s 2
Kōrero
E mōhiotia ana:
Mata maeneene papatahi.
Taumaha o te poraka A (m A ) = 5 kg
Taumaha o te poraka B (m B ) = 3 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka B (w B ) = m B g = (3)(10) = 30 Newton
Pātai: Te whakaterenga o te poraka (a)
Whakautu:
He maeneene te mata papatahi, nō reira kāore he kaha waku e aukati ana i te nekehanga o te poraka A. Ko te kaha e neke ana i te pūnaha poraka ko te taumaha o te poraka B.
ΣF = ma
w B = (m A + m B ) a
30 = (5 + 3) he
30 = 8
ā = 30 / 8
a = 3,75 m/s 2
Ko te whakautu tika ko B.
2. E ai ki te pikitia, e mōhiotia ana:
(1) te kore whakaterenga o te mea
(2) ngā mea e neke ana i te rārangi tika i te tere pumau
(3) ngā mea kei roto i te āhua okioki
(4) ka neke te mea mena he iti iho te taumaha o te mea i te kaha kukume
Ko te kōrero tika ko….
A. (1) me (2) anake
B. (1) me (3) anake
C. (1) me (4)
D. (1), (2) me (3) anake
E. (1), (2), (3) me (4)
Kōrero
(1) te kore whakaterenga o te mea
Kore te whakaterenga o tētahi mea mēnā he ōrite te kaha hua ki te kore. Te kaha hua:
∑F = ma 
whakaterenga (a) = 0
∑ F = 0
F 1 + F 2 – F 3 = 12 + 24 – 36 = 36 – 36 = 0 N
(2) ngā mea e neke ana i te rārangi tika i te tere pumau
Ko te kore whakaterenga o tētahi mea, ko te tikanga pea kei te okioki te mea, kei te neke rānei te mea i te rārangi tika i te tere pumau (kei te neke te mea i te tere pumau).
(3) ngā mea kei roto i te āhua okioki
Ko te hua o te kaha o te kore he tohu pea kei te okioki te mea.
(4) ka neke te mea mena he iti iho te taumaha o te mea i te kaha kukume
Ka mahi poutū te taumaha o tētahi mea, ka mahi whakapae te kaha kume. Nā te mea ka neke whakapae te mea, ko ngā kaha whakapae anake ka pā ki te mea.
Ko te whakautu tika ko D.
3. Tirohia te pikitia kei te taha!
Mena ko te tauwehenga o te waku nekeneke i waenga i te poraka A me te tēpu he 0,1, ā, ko te whakaterenga nā te kaha ā-papa he 10 m/s-2 kātahi ka whakamahia te kaha ki a A kia neke ai te pūnaha ki maui me te whakaterenga
n 2 ms-2 ko ….
A. 70 N
B. 90 N
C. 150 N
D. 250 N
E. 330 N
Kōrero
E mōhiotia ana:
Taumaha o te poraka A (m A ) = 30 kg
Taumaha o te poraka A (w A ) = (30 kg)(10 m/s 2 ) = 300 kg m/s 2 , 300 Newton rānei
Taumaha o te poraka B (m B ) = 20 kg
Taumaha o te poraka B (w B ) = (20 kg)(10 m/s 2 ) = 200 kg m/s 2, 200 Newton rānei
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te tauwehenga o te waku nekeneke (
) = 0,1
Te whakaterenga o te pūnaha (a) = 2 m/s 2 (te ahunga whakaterenga ki te taha maui)
Te kaha waku nekeneke (fk) = N= wA = (0,1)(300) = 30 Ngā Newton
Pātai: He aha te rahi o te kaha F?
Whakautu:
Te Ture Tuarua a Newton:
Σ F = ma
Ka neke te pūnaha ki te taha maui
F – f k – w B = (m A + m B ) a
F – 30 – 200 = (30 + 20)(2)
F – 230 = (50)(2)
F – 230 = 100
F = 230 + 100
F = 330 Newton
Ko te whakautu tika ko E.
4. E rua ngā mea A me B, he 2 kg te taumaha, ā, he 6 kg te taumaha, e herea ana ki te taura mā te whakamahi i tētahi pūrei maeneene e whakaaturia ana i te pikitia. Ka puritia te mea tuatahi, arā, ko B, kātahi ka tukuna. Mena ko g = 10 ms -2 , ko te whakaterenga o te mea B ko...
A. 8,0 ms-2
B. 7,5 ms -2
C. 6,0 ms -2
D. 5,0 ms -2
E. 4,0 ms -2
Kōrero
E mōhiotia ana:
m A = 2 kg, m B = 6 kg, g = 10 m/s 2
w A = (m A )(g) = (2)(10) = 20 N
w B = (m B )(g) = (6)(10) = 60 N
Pātai: te whakaterenga o te mea B, te whakaterenga rānei o te pūnaha?
Whakautu:
w B > w A nō reira ka neke te mea B ki raro, ka neke te mea A ki runga (ka neke te pūnaha ki te taha matau).
Σ F = ma
w B – w A = (m A + m B ) a
60 – 20 = (2 + 6) he
40 = (8) he
a = 5 m/s 2
Ko te whakautu tika ko D.
5. Ka honoa tētahi mea he taumaha tōna mā te taura mā roto i tētahi pūrei maeneene e whakaaturia ana i te pikitia. Mena ko m1 = 1 kg, m2 = 2 kg, me g = 10 ms -2 , ko te kukū T ko ….
A. 10,2 N 
B. 13,3 N
C. 15,5 N
D. 18,3 N
E. 20,0 N
Kōrero
E mōhiotia ana:
m1 = 1 kg, m2 = 2 kg, karamu = 10 m/ s2
w1 = m1 karamu = (1 kg)(10 m/s2 ) = 10 kg m/s2 , 10 Newton rānei
w2 = m2 karamu = (2 kg)(10 m/s2 ) = 20 kg m/s2 , 20 Newton rānei
Pātai: He aha te kaha kume o te taura (T)?
Whakautu:
Whakaterenga pūnaha
w 2 > w 1 nō reira ka neke te pūnaha ki te taha matau (ka neke a m 2 ki raro, ka neke a m 1 ki runga).
Te Ture Tuarua a Newton:
Σ F = ma
w 2 – w 1 = (m 1 + m 2 ) a
20 – 10 = (1 + 2) a
10 = (3) he
a = 3,3 m/s 2
Ko te whakaterenga o te pūnaha he 3,3 m/ s².
Te kukū o te aho?
ka neke iho a m2
w 2 – T 2 = m 2 a
20 – T 2 = (2)(3,33)
20 – T 2 = 6,66
T 2 = 20 – 6,66
T 2 = 13,3 Newton
ka neke ake a m 1
T 1 – w 1 = m 1 a
T 1 – 10 = (1)(3,3)
T 1 – 10 = 3,33
T 1 = 10 + 3,33
T 1 = 13,3 Newton
Te kukū aho (T) = 13,3 Newton.
Ko te whakautu tika ko B.
6. Tirohia te pikitia kei te taha! Ko ngā taumaha o ngā poraka ko m1 = 6 kg me m2 = 4 kg, ā, kāore e arohia te taumaha o te pūrakau. Mena he maeneene te mata o te papa, ā, ko g = 10 m/s −2 , ko te whakaterenga o te pūnaha ko….
A. 0,5 ms-2
B. 2,0 ms −2
C. 2,5 ms −2
D. 4,0 ms −2
E. 5,0 ms −2
Kōrero
E mōhiotia ana:
m1 = 6 kg, m2 = 4 kg, karamu = 10 m/ s2
w1 = m1 karamu = (6 kg)(10 m/s2 ) = 60 kg m/s2 , 60 Newton rānei
w2 = m2 karamu = (4 kg)(10 m/s2 ) = 40 kg m/s2 , 40 Newton rānei
I pātaihia: te whakaterenga o te pūnaha (a)?
Whakautu:
Kei runga a m1 i tētahi mata papatahi maeneene, kāore he waku, kia peia ai te pūnaha e te kaha ā-papa o te poraka 2.
Whakamahia te ture tuarua a Newton:
∑ F = ma
w 2 = (m 1 + m 2 ) a
40 N = (6 kg + 4 kg) a
40 N = (10 kg) a
a = 40 N / 10 kg
a = 4 m/s 2
Ko te whakautu tika ko D.
7. E rua ngā poraka, he 2 kg te taumaha o ia poraka, e honoa ana e te taura me te pūrei e whakaaturia ana i te pikitia. He maeneene te mata me te pūrei. Mena ka tōia te poraka B me te kaha whakapae o te 40 N, ko te whakaterenga o te poraka ko… (g = 10 m/s 2 )
A. 5 m/s2
B. 7,5 m/s 2
C. 10 m/s 2
D. 12,5 m/s 2
E. 15 m/s 2
Kōrero:
E mōhiotia ana:
m A = m B = 2 kg, g = 10 m/s 2 , F = 40 N
w A = mg = (2)(10) = 20 N
Pātai: te whakaterenga o te poraka (a)?
Whakautu:
He maeneene te mata o te poraka, nō reira ko ngā kaha e pā ana ki te nekehanga o te poraka ko te kaha F me te taumaha o te poraka A anake.
Whakamahia te ture tuarua a Newton:
∑ F = ma
F – w A = (m A + m B ) a
40 – 20 = (2 + 2) he
20 = (4) he
ā = 20 / 4
a = 5 m/s 2
Ko te whakautu tika ko A.
8. Mai i te pikitia e whai ake nei, ko te taumaha o te poraka A he 2 kg, ā, ko te taumaha o te poraka B he 1 kg. I te tīmatanga, ka tū te poraka B, kātahi ka neke ki raro kia pā ki te papa. Mena ko g = 10 ms -2 , ko te uara o te kume i roto i te aho T ko...
A. 20,0 Newton
B. 10,0 Newton
C. 6,7 Newton
D. 3,3 Newton
E. 1,7 Ngā Newton
Kōrero
E mōhiotia ana :
Taumaha o te poraka A (m A ) = 2 kg
Taumaha o te poraka B (m B ) = 1 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka B (w B ) = m B g = (1)(10) = 10 Newton
Pātai : Te uara o te kume o te taura (T)
Whakautu :
Kāore he kōrero mō te waku i roto i te pātai, nō reira kaua e aro ki te waku.
Te whakaterenga pūnaha (a)
Tuatahi, tatauhia te whakaterenga o te pūnaha mā te whakamahi i te ture tuarua a Newton. Ka whakairihia te Poraka B kia puta he kaha o te kaha ā-papa o te poraka B e neke ana i te poraka B ki raro. Ka honoa te Poraka B me te poraka A e te taura kia kumea ai e te poraka B te poraka A kia neke tahi rāua. Ko te rerekētanga ko te nekehanga o te poraka B ki raro, ā, ko te nekehanga o te poraka A ki te taha matau. Kotahi anake te kaha e whakarara ana ki te nekehanga o ngā poraka e rua, arā, ko te kaha ā-papa o te poraka B (wB). He poutū te kaha ā-papa o te poraka A ki te ahunga o te nekehanga o te poraka A, nō reira kāore i te whakaarohia i roto i te whakaoti rapanga. He rite te kaha kume o te taura i te taha o te taura, engari he rerekē ngā ahunga, nō reira ka whakakorea e rāua tetahi ki tetahi.
∑ F = ma
w B = (m A + m B ) a
10 = (2 + 1) he
10 = 3
ā = 10/3
Te kukū o te taura (T)
Ka tatauhia te kume o te taura mā te whakaaro motuhake ki ia poraka.
Te kumekume o te taura i te poraka A
∑ F = ma
T = m A a = (2)(10/3) = 20/3 = 6,7 Ngā Newton
Te kukū o te taura i te poraka B
∑ F = ma
w B – T = m B a
10 – T = (1)(10/3)
10 – T = 3,3
T = 10 – 3,3 = 6,7 Newton
Te kukū o te taura (T) = 6,7 Newton
Ko te whakautu tika ko C.
9. Mai i te ahua e whai ake nei, ko te taumaha o te poraka A he 2 kg, ā, ko te taumaha o te poraka B he 1 kg. Mēnā ko te kaha waku i waenganui i te mea A me te papa he 2,5 Newton, ā, kāore e arohia te kaha waku i waenganui i te taura me te pūreirei, ko te whakaterenga o ngā mea e rua ko...
A. 20,0 ms-2
B. 10,0 ms -2
C. 6,7 ms -2
D. 3,3 ms -2
E. 2,5 ms -2
Kōrero
E mōhiotia ana :
Taumaha o te poraka A (m A ) = 2 kg
Taumaha o te poraka B (m B ) = 1 kg
Ko te kaha waku i waenganui i te poraka A me te mata papatahi (f ges A ) = 2,5 Newton
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka B (w B ) = m B g = (1)(10) = 10 Newton
Pātai : Te whakaterenga o ngā mea e rua (a)
Whakautu :
Ka tatauhia te whakaterenga o ngā mea e rua mā te whakamahi i te tātai ture tuarua a Newton.
∑ F = ma
w B – f ges = (m A + m B ) a
10 – 2,5 = (2 + 1) he
7,5 = 3
a = 7,5 / 3 = 2,5 m/s 2
Ko te whakautu tika ko E.
10. Tirohia te pikitia! Ko te poraka A me te taumaha 30 kg e takoto ana i runga i te papa maeneene kua honoa ki te poraka B me te taumaha 10 kg mā te pūrei. Ka puritia tuatahitia te poraka B, kātahi ka tukuna kia neke ki raro. Ko te whakaterenga o te pūnaha ko… (g = 10 ms -2 )
A. 2,5 ms-2
B. 10 ms -2
C. 12 ms -2
D. 15 ms -2
E. 18 ms -2
Kōrero
E mōhiotia ana :
Taumaha o te poraka A (m A ) = 30 kg
Taumaha o te poraka B (m B ) = 10 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka B (w B ) = m B g = (10)(10) = 100 Newton
Pātai : Te whakaterenga o te pūnaha (a)
Whakautu :
∑ F = ma
w B = (m A + m B ) a
100 = (30 + 10) he
100 = 40
ā = 100 / 40
a = 2,5 m/s 2
Ko te whakautu tika ko A.
11. Ka whakatakotoria ngā poraka A me B, he 8 kg te taumaha o ia poraka, me te 12 kg te taumaha, ki runga i tētahi tēpu e whakaaturia ana i te pikitia. Ko te tauwehenga o te waku i waenga i te poraka A me te tēpu he 0,3. Kātahi ka whakatakotoria te poraka C, he 4 kg te taumaha, ki runga i te poraka A. Ko tēhea o ngā kōrero e whai ake nei te mea tika?
A. He nui ake te kukū o te taura i tō mua, he iti iho te whakaterenga i tō mua
B. Kāore te kume o te taura me te whakaterenga o te pūnaha e rerekē.
C. He iti ake te kukū o te taura i tō mua, he nui ake te whakaterenga i tō mua.
D. He nui ake te kukū o te taura i tō mua, he pumau tonu te whakaterenga.
E. Ka mau tonu te kukū o te taura, engari he iti iho te whakaterenga i tō mua.
Kōrero
E mōhiotia ana:
Taumaha o te poraka A (m A ) = 8 kg
Taumaha o te poraka B (m B ) = 12 kg
Taumaha o te poraka C (m C ) = 4 kg
Ko te tauwehenga waku i waenga i te poraka A me te tēpu ( μ k ) = 0,3
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka A (w A ) = m A g = (8 kg)(10 m/s 2 ) = 80 kg m/s 2
Taumaha o te poraka B (w B ) = m B g = (12 kg)(10 m/s 2 ) = 120 kg m/s 2
Ko te kaha waku i waenganui i te poraka A me te tēpu (f k ) = μ k N A = μ k w A = (0,3)(80) = 24 N
Whakautu:
Whakaterenga pūnaha:
Σ F = ma
w B – f k = (m A + m B ) a
120 – 24 = ( 8 + 12 ) a
96 = ( 20 ) he
ā = 96 / 20
a = 4,8 m/s 2
Te kukū o te taura:
Whakaarohia tētahi o ngā mea, hei tauira ko te B.
Σ F = ma
w B – T = (m B ) a
120 – T = ( 12 ) 4,8
120 – T = 57,6
T = 120 – 57,6
T = 62,4 Ngā Niutona
Kātahi ka whakatakotoria he poraka C, he 4 kg te taumaha, ki runga i te poraka A.
Whakaterenga pūnaha:
Σ F = ma
w B – f k = (m A + m B + m C ) a
120 – 24 = ( 8 + 12 + 4 ) a
96 = ( 24 ) he
ā = 96 / 24
a = 4 m/s 2
Te kukū o te taura:
Whakaarohia tētahi o ngā mea, hei tauira ko te B.
Σ F = ma
w B – T = (m B ) a
120 – T = ( 12 ) 4
120 – T = 48
T = 120 – 48
T = 72 Ngā Niutona
Ko te whakautu tika ko A.
12. Mai i te pikitia e whai ake nei, ko te taumaha o te poraka A he 2 kg, ā, ko te taumaha o te poraka B he 1 kg. I te tīmatanga, ka tū te poraka B, kātahi ka neke ki raro kia pā ki te papa. Mena ko g = 10 ms -2 , ko te uara o te kume i roto i te aho T ko...
A. 20,0 Newton
B. 10,0 Newton
C. 6,7 Newton
D. 3,3 Newton
E. 1,7 Ngā Newton
Kōrero
E mōhiotia ana :
Te taumaha o te poraka A (mA) = 2 kirokaramu
Te taumaha o te poraka B (mB) = 1 kirokaramu
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha o te poraka B (wB) = mB g = (1)(10) = 10 Newton
I pātaihia : Uara kume taura (T)
Whakautu :
Kāore he kōrero mō te waku i roto i te pātai, nō reira kaua e aro ki te waku.
Te whakaterenga pūnaha (a)
Te tatau tuatahi whakaterenga pūnaha mā te whakamahi i te tātai Te ture tuarua a Newton. Ka whakairihia te Poraka B kia puta he kaha o te kaha ā-papatipu o te poraka B hei neke i te poraka B ki raro. Ka honoa te Poraka B me te poraka A e te taura kia kumea ai e te poraka B te poraka A kia neke tahi rā anō rāua. Ko te rerekētanga ko te nekehanga o te poraka B ki raro, ā, ko te nekehanga o te poraka A ki te taha matau. Kotahi anake te kaha e whakarara ana ki te nekehanga o ngā poraka e rua, arā, ko te kaha o te kaha ā-papatipu o te poraka B (wB). Te kaha ā-papatipu He poutū te poraka A ki te ahunga nekehanga o te poraka A, nō reira kāore e whakaarohia ana i te whakaoti rapanga. He rite tonu te kaha o ngā kaha kume i roto i te taura i te roanga o te taura, ā, i ngā ahunga rerekē, nō reira ka whakakorea tetahi i tetahi.
∑F = ma
wB = (mA +mB) a
10 = (2 + 1) he
10 = 3
ā = 10/3
Te kukū o te taura (T)
Ka tatauhia te kume o te taura mā te whakaaro motuhake ki ia poraka.
Te kumekume o te taura i te poraka A
∑F = ma
T = mA a = (2)(10/3) = 20/3 = 6,7 Ngā Newton
Te kukū o te taura i te poraka B
∑F = ma
wB – T = mB a
10 – T = (1)(10/3)
10 – T = 3,3
T = 10 – 3,3 = 6,7 Newton
Te kukū o te taura (T) = 6,7 Newton
Ko te whakautu tika ko C.
13. Mai i te pikitia e whai ake nei, ko te taumaha o te poraka A he 2 kg, ā, ko te taumaha o te poraka B he 1 kg. Ina te kaha o te waku i waenganui i te mea A me te papa 2,5 Newton, i te mea kāore e arohia te kaha waku o te taura me te pūreirei, ko te whakaterenga o ngā mea e rua ko...
A. 20,0 ms-2
B. 10,0 ms-2
C. 6,7 ms-2
D. 3,3 ms-2
E. 2,5 ms-2
Kōrero
E mōhiotia ana :
Te taumaha o te poraka A (mA) = 2 kirokaramu
Te taumaha o te poraka B (mB) = 1 kirokaramu
Ko te kaha waku i waenganui i te poraka A me te mata papatahi (fngā tau A) = 2,5 Niutona
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha o te poraka B (wB) = mB g = (1)(10) = 10 Newton
I pātaihia Te whakaterenga o ngā mea e rua (a)
Whakautu :
Ka tatauhia te whakaterenga o ngā mea e rua mā te whakamahi i te tātai ture tuarua a Newton.
∑F = ma
wB - fTuhinga o mua = (mA +mB) a
10 – 2,5 = (2 + 1) he
7,5 = 3
a = 7,5 / 3 = 2,5 m/s2
Ko te whakautu tika ko E.
14. 
Tirohia te pikitia! Ko te poraka A me te taumaha 30 kg e takoto ana i runga i te papa maeneene kua honoa ki te poraka B me te taumaha 10 kg mā te pūreirei. Ka puritia tuatahitia te poraka B, kātahi ka tukuna kia neke ki raro. Ko te whakaterenga o te pūnaha ko… (g = 10 m/s-2)
A. 2,5 ms-2
B. 10 ms-2
C. 12 ms-2
D. 15 ms-2
E. 18 ms-2
Kōrero
E mōhiotia ana :
Te taumaha o te poraka A (mA) = 30 kirokaramu
Te taumaha o te poraka B (mB) = 10 kirokaramu
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha o te poraka B (wB) = mB g = (10)(10) = 100 Newton
I pātaihia Te whakaterenga pūnaha (a)
Whakautu :
∑F = ma
wB = (mA +mB) a
100 = (30 + 10) he
100 = 40
ā = 100 / 40
a = 2,5 m/s2
Ko te whakautu tika ko A.
Pūtake pātai:
Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa
