20 Ngā Tauira o ngā Ture a Newton
Te Ture Tuatahi a Newton
1. Mena he ōrite te kaha hua e pā ana ki tētahi mea ki te kore, kāti...
(1) kāore te mea e tere ake
(2) kei te okioki tonu ngā mea
(3) he kore te huringa o te tere o te mea
(4) kāore e taea e te mea te neke i te rārangi tika i te tere pumau
Ko te pono…
A. (1), (2) me (3)
B. (1) me (3) anake
C. (2) me (4) anake
D. (4) anake
E. (1), (2), (3) me (4)
Kōrero
Ko te whakautu tika ko:
(1) Kāore te mea e tere ake
Mā te kaha e puta mai ana ka tere ake te tere o tētahi mea. Mēnā he kore te kaha e puta mai ana, e kore te mea e tere ake.
(2) Kei te takoto kau tonu ngā mea
E ai ki te Ture Tuatahi a Newton, mēnā he kore te kaha hua e pā ana ki tētahi mea, ka noho tonu te mea e okioki ana , ā, ka noho tonu te mea e neke ana i te tere pumau (nekehanga rārangi ōrite) ki te neke i te tere pumau.
(3) Kore te huringa o te tere o te mea
Te huringa o te tere = te whakaterenga. Ko te huringa o te tere o tētahi mea he kore, ko te tikanga he kore te whakaterenga o te mea. Mena he kore te whakaterenga, ko te kaha hua ka pā ki te mea he kore.
Ko te whakautu tika ko A.
Ngā Mea i roto i te Ararewa
2. I a Sandi i roto i tētahi ararewa tūmau, ko tōna taumaha he 500 N. Ko te whakaterenga nā te kaha ā-papatipu = 10 ms –2 . Ina whakaterenga te ararewa, ka eke te kukū o te taura ki te 750 N. Nō reira, ko te whakaterenga o te ararewa ko…
A. 5,0 ms –2
B. 7,5 ms –2
C. 10,0 ms –2
D. 12,5 ms –2
E. 15,0 ms –2
Kōrero
E mōhiotia ana:
Taumaha waehere (w) = 500 Newton = 500 kg ms –2 (ararewa e okioki ana)
Te whakaterenga nā te kaha ā-papa (g) = 10 m s –2
Taumaha Kupuhipa (m) = 500 / 10 = 50 kg
Te kukū o te taura (T) = 750 N (te whakaterenga o te ararewa)
Kāore i te whakaarohia te taumaha o te ararewa.
I pātaihia: Te whakaterenga o te ararewa
Whakautu:
Kei te okioki te ararewa, kāore he whakaterenga (a = 0). He pai te kaha whakarunga, he kino te kaha whakararo.
ΣF = ma
T – w = 0
T = w
T = 500 Ngā Niutona
Ki te tere ake te hiki ki raro, ka iti iho te kaha kume i roto i te taura i te 500 Newton. I tētahi atu ringa, ki te tere ake te hiki ki runga, ka nui ake te kaha kume i roto i te taura i te 500 Newton.
Ka eke te kukū o te taura ki te 750 N, ka tere ake te ararewa ki runga. He pai ngā kaha i te ahunga kotahi me te nekehanga o te ararewa, ā, he kino ngā kaha i te ahunga kē.
T – w = ma
750 – 500 = 50 a
250 = 50
ā = 250 / 50
a = 5,0 ms –2
Ko te whakautu tika ko A.
3. Kei roto i tētahi ararewa tētahi tangata he 60 kg tōna taumaha e neke ana ki raro me te whakaterenga o te 3 ms -2 . Mena ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , ko te rahi o te kaha noa e pā ana ki te papa o te ararewa ki te tangata ko...
A. 180 N
B. 200 N
C. 340 N
D. 420 N
E. 600 N
Kōrero
E mōhiotia ana:
Taumaha (m) = 60 kg
Te whakaterenga o te tangata me te ararewa (a) = 3 m/s 2
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te kaha ā-papatipu (w) = mg = (60)(10) = 600 Newton
I pātaihia: te kaha noa (N)
Whakautu:
E rua ngā kaha e pā ana ki tētahi tangata i roto i tētahi ararewa, arā, te kaha ā-papa (w) me te kaha noa e tukuna ana e te papa ararewa ki te tangata (N). E toru ngā rahinga whārite, arā, te kaha ā-papa, te kaha noa, me te whakaterenga ararewa, ko te wāhi e anga ana te kaha ā-papa ki raro, ko te kaha noa ki runga, ā, ko te whakaterenga ararewa ki raro. Ka whiriwhiria te rahinga whārite e anga ana ki raro kia whai tohu pai, ā, ka whiriwhiria te rahinga whārite e anga ana ki runga kia whai tohu kino.
∑ F = ma
w – N = (60)(3)
600 – N = 180
N = 600 – 180
N = 420 Niutona
Ko te whakautu tika ko D.
4. Kei roto a Reza i tētahi ararewa e neke ake ana, he 40 kg te taumaha. Mena ko te kaha o te papa o te ararewa ki runga i ngā waewae o Reza he 520 N, ā, ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , ko te whakaterenga o te ararewa he...
A. 1,0 ms -2
B. 1,5 ms -2
C. 2,0 ms -2
D. 2,5 ms -2
E. 3,0 ms -2
Kōrero
E mōhiotia ana:
Taumaha (m) = 40 kg
Te kaha noa (N) = 520 N
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te kaha o te taumaha (w) = mg = (40)(10) = 400 N
I pātaihia: Te whakaterenga o te ararewa
Whakautu:
∑ F = ma
400 – 520 = (40)(a)
-120 = (40)(a)
ā = -120/40
a = -3 m/s 2
Ko te whakaterenga o te ararewa he 3 m/s² . Ko te tohu kino e tohu ana kei te neke ake te ararewa.
5. Kei roto i tētahi ararewa te tangata he 60 kg te taumaha e neke ana ki raro me te whakaterenga o te 3 ms -2 . E hia te pēhanga e pā ana ki te papa o te ararewa e ngā waewae o te tangata?
Kōrero
E mōhiotia ana:
Taumaha o te tangata (m) = 60 kg
Taumaha o te tangata (w) = mg = (60 kg)(10 m/s² ) = 600 kg m/s² = 600 Newton
Te whakaterenga o te ararewa (a) = 3 m/s 2 , ki raro.
I pātaihia: E hia te pēhanga e pā ana ki te papa o te ararewa e ngā waewae o te tangata?
Whakautu:
Ka neke te ararewa ki raro me te whakaterenga (a) o te 3 m/s 2. He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino te kaha i te ahunga ke atu i te nekehanga o te ararewa.
w – N = ma
N = w – ma
N = 600 – (60)(3)
N = 600 – 180
N = 420 Niutona
Koinei te kaha noa e pā ana ki te papa o te ararewa ki te tangata. Kei te tū te tangata i runga i te ararewa kia rite te rahi o te kaha noa ki te taumaha kitea o te tangata. He rite te taumaha kitea ki te pēhanga o ngā waewae o te tangata ki te papa.
Pūnaha Utaina Taura Poro
6. E rua ngā mea A me B, he 6 kg te taumaha o ia mea, he 2 kg te taumaha, e herea ana ki te taura i runga i te pōro e whakaaturia ana i te pikitia. Mēnā ka warewarehia te waku i waenganui i te taura me te pōro, ā, ko g = 10 ms -2 , ko te kukū o te taura ko...
A. 20 N
B. 24 N
C. 27 N
D. 30 N
E. 50 N
Kōrero
E mōhiotia ana:
m A = 6 kg, m B = 2 kg, g = 10 m/s 2
w A = m A g = (6 kg)(10 m/s² ) = 60 kg m/ s²
w B = m B karamu = (2 kg)(10 m/s² ) = 20 kg m/ s²
Pātai: He aha te kaha kume o te taura (T)?
Whakautu:
w A > w B nō reira ka neke te pūnaha i te taha maui (ka neke a m A ki raro, ka neke a m B ki runga).
Whakaterenga
ΣF = ma
w A – w B = (m A + m B ) a
60 – 20 = (6 + 2) he
40 = (8) he
a = 40 / 8 = 5 m/s 2
Te kukū o te taura
ka neke iho a m A
w A – T A = m A a
60 – T A = (6)(5)
60 – TA = 30
TA = 60 – 30
T 2 = 30 Newton
ka neke ake a m B
T B – w B = m B a
T B – 20 = (2)(5)
T B – 20 = 10
T B = 10 + 20
T 1 = 30 Newton
Te kukū aho (T) = 30 Newton.
Ko te whakautu tika ko D.
7. Tirohia te pikitia kei te taha! Kāore e arohia te waku o te taura me te pūreirei. Mena ko te papatipu A = 5 kg, ko te g = 10 m s —2 , ā, ka neke iho a A me te whakaterenga o te 2,5 m s —2 , ko te aha te papatipu o B?
A. 0,5 kg
B. 1 kg
C. 1,5 kg
D. 2 kg
E. 3 kg
Kōrero
E mōhiotia ana:
Taumaha A (m A ) = 5 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Whakaterenga A, whakaterenga pūnaha rānei (a) = 2,5 m/s 2
Taumaha A (w A ) = (m A )(g) = (5)(10) = 50 Ngā Niutona
I pātaihia: he aha te papatipu o B (m B )?
Whakautu:
Ka neke te Poraka A ki raro, nō reira he nui ake te taumaha o A (w A ) i te taumaha o B (w B ).
Whakamahia te ture tuarua a Newton:
ΣF = ma
w A – w B = (m A + m B ) a
50 – (m B )(10) = (5 + m B ) (2,5)
50 – 10 m B = 12,5 + 2,5 m B
50 – 12,5 = 2,5 m B + 10 m B
37,5 = 12,5 m B
m B = 3 kg
Ko te whakautu tika ko E.
8. E rua ngā mea, he 2 kg me te 3 kg te taumaha, kua herea ki te taura, kātahi ka herea ki tētahi pūrei, kāore e arohia tōna taumaha e whakaaturia ana i te pikitia.
Mena ko te rahi o te whakaterenga ā-papatipu = 10 ms -2 , ko te kaha kume o te taura e pāngia ana e te pūnaha ko...
A. 20 N
B. 24 N
C. 27 N
D. 30 N
E. 50 N
Kōrero
E mōhiotia ana:
m1 = 2 kg, m2 = 3 kg, karamu = 10 m/ s2
w1 = (m1 ) (g) = (2 kg)(10 m/s2 ) = 20 kg m/s2 , 20 Newton rānei
w2 = (m2 ) (g) = (3 kg)(10 m/s2 ) = 30 kg m/s2 , 30 Newton rānei
Pātai: He aha te kaha kume o te taura (T)?
Whakautu:
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).
Whakaterenga
ΣF = ma
w 2 – w 1 = (m 1 + m 2 ) a
30 – 20 = (2 + 3) a
10 = (5) he
a = 10 / 5 = 2 m/ s2.
Te kukū o te taura
ka neke iho a m2
w 2 – T 2 = m 2 a
30 – T 2 = (3)(2)
30 – T 2 = 6
T 2 = 30 – 6
T 2 = 24 Newton
ka neke ake a m 1
T 1 – w 1 = m 1 a
T 1 – 20 = (2)(2)
T 1 – 20 = 4
T 1 = 20 + 4
T 1 = 24 Newton
Te kukū aho (T) = 24 Newton.
Ko te whakautu tika ko B.
9. E rua ngā poraka e honoa ana e tētahi pūreirei maeneene, ā, kāore e arohia te papatipu o te pūreirei e whakaaturia ana i te pikitia. Papatipu A = m A , papatipu B = m B , ā, ka hinga te poraka B me te whakaterenga a. Mena ko te whakaterenga nā te kaha ā-papatipu ko g, ko te rahi o te kume taura e puta ana i te poraka B ko…
A. T = mB.a
B. T = m A (a – g)
C. T = m A (g – a)
D. T = m B (a – g)
E. T = m B (g – a)
Kōrero
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.
Tātaihia te whakaterenga o te pūnaha:

Tātaihia te kaha kume o te taura (T):
Whakaarohia te nekehanga o tētahi o ngā mea, hei tauira ko A. Ka neke a A ki te taha matau.

Whakakapia a m A i te whārite 1 ki a m A i te whārite 2.

Ko te whakautu tika ko E.
10. Ka whakatakotoria he poraka he 10 kg te taumaha ki runga i te papa taratara, kātahi ka tōia e te kaha whakapae F. Mena ko μ te tauwehenga o te waku pumaus = 0,5 me te tauwehenga o te waku nekeneke μk = 0,3. Tātaihia te rahi o te kaha waku ina tata te poraka te neke. (g = 10 m/s2)
Kōrero
Ka neke tika te poraka mēnā ko te rahi o te kaha kukume = te rahi o te kaha waku pūmau mōrahi. Ka pā te waku pūmau ki tētahi mea (ka ārai i te nekehanga o te mea) i te wā e tōia ana te mea engari kāore anō kia neke te mea. He uara mōrahi te waku pūmau ina tata te neke o te mea (kāore anō kia neke te mea, kua tata neke te mea). I tetahi atu taha, ka pā te waku nekeneke ki tētahi mea (ka ārai i te nekehanga o te mea) i te wā e neke ana te mea.
E mōhiotia ana:
Pātai: Te kaha waku pūmau mōrahi (fs)?
Whakautu:
Mena kei runga te mea i tētahi papa papatahi pērā i te pikitia, ko te rahi o te kaha noa = te taumaha o te mea.
Te kaha noa (N) = te kaha ā-papatipu (w) = 100 Newton
Te tātai kaha waku pūmau mōrahi:
Kāore te tauwehenga o te waku nekeneke e whakamahia ana i roto i ngā tataunga.
11. E rua ngā poraka e honoa ana e tētahi taura māmā e tōia ana e te kaha whakapae F = 20 N (tirohia te pikitia). Mena ko g = 10 ms-2 ā, ko te tauwehenga o te waku nekeneke i waenganui i te poraka me te mata he 0,1, whakatauhia te rahi o te whakaterenga o te poraka...
Kōrero
E mōhiotia ana:
I pātaihia: te whakaterenga (a) o te poraka?
Whakautu:
12. Kua whakaritea te poraka A he 2 kg te taumaha me te poraka B he 4 kg te taumaha e whakaaturia ana i te pikitia. Mena he 3 ngā wā o te tauwehenga waku o te papa i te tauwehenga waku o te poraka B, ka neke te poraka A me te whakaterenga o te 5 m/s.-2Nō reira, ko te ōwehenga o te kaha waku i waenga i te poraka A me te papa ki ngā poraka A me B ko… g = 10 m/s2
Kōrero
E mōhiotia ana:
I pātaihia:
Te whakataurite i te kaha waku o te poraka A me te papa (fs A) me te kaha waku o ngā poraka A me B (fs B)?
Whakautu:

13. Tirohia te pikitia kei te taha! Ko te taumaha o ia poraka he m.1 = 2 kg me te m2 = 3 kg, ā, kāore te taumaha o te pūreirei e arohia. Mena he maeneene te mata o te papa, ā, ko te g = 10 ms-2, kātahi 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. 6,0 ms-2
Kōrero
E mōhiotia ana:
m1 = 2 kg, mita2 = 3 kg, karamu = 10 ms-2
w2 = m2 karamu = (3)(10) = 30 kg m/s2 30 Newton rānei
Pātai: Te whakaterenga o te pūnaha (a)?
Whakautu:
14. Ka honoa tētahi mea he taumaha tōna mā te taura e tika ana mā roto i tētahi pūrei maeneene e whakaaturia ana i te pikitia. Mena m1 = 2 kg, mita2 = 3 kg me te karamu = 10 ms-2, kātahi ko te rahi o te kaha kume o te taura T ko…
A. 10,2 N
B. 13,3 N
C. 15,5 N
D. 18,3 N
E. 24,0 N
Kōrero
E mōhiotia ana:
m1 = 2 kg, mita2 = 3 kg, karamu = 10 ms-2
w1 = (2)(10) = 20 Ngā Newton
w2 = (3)(10) = 30 Ngā Newton
Pātai: He aha te rahi o te kaha kume i runga i te taura (T)?
Whakautu:
w2 = 30 He nui ake ngā Newton i te w1 = 20 Ngā Newton nō reira m2 neke ki raro, m1 neke ake.
Te tātai ture tuarua a Newton:
Te kaha kume o te taura?
E ai ki te ahunga o te nekehanga o te pūnaha, ki te ahunga rānei o te whakaterenga o te pūnaha, ko te ahunga o te kaha ā-papa m2 ki raro, ko te ahunga o te kaha kume taura i runga i te m2 ki te tihi:
w2 - T2 = m2 a
30 – T2 = (3)(2)
30 – T2 = 6
T2 = 30 - 6
T2 = 24 Niutona
Te ahunga o te kaha ā-papa m1 ki raro, ko te ahunga o te kaha kume taura i runga i te m1 ki te tihi:
T1 - w1 = (m1) (a)
T1 – 20 = (2)(2)
T1 - 20 = 4
T1 = 4 + 20
T1 = 24 Niutona
Te kaha kume taura (T) = T1 =T2 = 24 Ngā Newtoni.
15. E rua ngā poraka, he 4 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 50 N, ko te whakaterenga o te poraka ko… (g = 10 m/s2)
A. 1,25 m/s2
B. 7,5 m/s2
C. 10 m/s2
D. 12,5 m/s2
E. 15 m/s2
Kōrero
E mōhiotia ana:
mA = 4 kg, mitaB = 4 kg, karamu = 10 m/s2
wA = (mA)(g) = 4)(10) = 40 Newton
F = 50 Newton
I pātaihia: te whakaterenga o te pūnaha?
Whakautu:
Te tātai ture tuarua a Newton:
Ko te whakaterenga o ngā poraka e rua he 1,25 m/s2Ko te ahunga o te nekehanga o ngā poraka e rua = te ahunga o te kaha kume F.
16. 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 ms −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, mita2 = 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:
m1kei runga i te mata maeneene, papatahi, kāore he waku, kia peia ai te pūnaha e kaha ā-papa poraka 2.
Terapkan Te ture tuarua a Newton :
∑F = ma
w2 = (m1 +m2) a
40 N = (6 kg + 4 kg) a
40 N = (10 kg) a
a = 40 N / 10 kg
a = 4 m/s2
Ko te whakautu tika ko D.
17. 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/s2
C. 10 m/s2
D. 12,5 m/s2
E. 15 m/s2
Kōrero:
E mōhiotia ana:
mA = mB = 2 kg, karamu = 10 m/s2, F = 40 N
wA = mg = (2)(10) = 20 N
Pātai: te whakaterenga o te poraka (a)?
Whakautu:
He maeneene te mata o te poraka, nō reira ko te kaha e pā ana ki te nekehanga o te poraka he kaha F me te taumaha o te poraka A.
Whakamahia te ture tuarua a Newton:
∑F = ma
F – wA = (mA +mB) a
40 – 20 = (2 + 2) he
20 = (4) he
ā = 20 / 4
a = 5 m/s2
Ko te whakautu tika ko A.
Papa piko
18. Kei runga i tētahi papa angiangi maeneene tētahi poraka he 2 kg te taumaha, ā, ko te koki angiangi = 30o, kia neke ai te poraka me te whakaterenga pumau. Mena ko g = 10 ms-2, kātahi ko te rahi o te kaha e neke ana i te poraka ko...
A. 5 N
B. 6 N
C. 7 N
D. 8 N
E. 10 N
Kōrero
E mōhiotia ana:
m = 2 kg, karamu = 10 m/s2, teta = 30o
w = mg = (2)(10) = 20 kg m/s2 = 20 N
Pātai: He aha te kaha e neke ana i te poraka?
Whakautu:

Ko te kaha e neke ana i te poraka he wx.
wx = w sin teta
wx = (20 N)(sin 30o)
wx = (20 N)(0,5)
wx = 10 N.
Ko te kaha e neke ana i te poraka he 10 Newton.
Ko te whakautu tika ko E.
19. E rua ngā poraka e honoa ana e te taura māmā e tōia ana e te kaha whakapae F = 24 N. g = 10 ms-2 ā, he pahekeheke te mata o te papa. Ko te rahi o te whakaterenga o te poraka mā te whakamahi i te ture tuarua a Newton mō ia mea ko...
Kōrero
E mōhiotia ana:
m1 = 2 kg, mita2 = 4 kg, F = 24 N
Pātai: He aha te whakaterenga o te poraka (a)?
Whakautu:
Ko te rahi o te whakaterenga o te poraka he 4 m/s2.
20. I roto i tētahi ararewa tūmau, ko te taumaha o Sandi he 500 N. Te whakaterenga nā te kaha ā-papatipu = 10 ms-2. Ina tere te ararewa, ka eke te kukū o te taura ki te 750 N. Nō reira, ko te tere o te ararewa ko...
A. 5,0 ms-2
B. 7,5 ms-2
C. 10,0 ms-2
D. 12,5 ms-2
E. 15,0 ms-2
Kōrero
E mōhiotia ana:
w = 500 N, g = 10 m/s2, T = 750 N
Pātai: te whakaterenga o te ararewa (a)?
Whakautu:
Te papatipu kupuhipa:
w = mg
500 = mita (10)
m = 500 / 10
m = 50 kg
Kāore i te mōhiotia te taumaha o te ararewa, nō reira ko te taumaha katoa o te ararewa me ōna mea o roto = te taumaha o te waehere.
E ai ki te ture tuatahi a Newton, ki te mea kei te tū tonu te ararewa, ko te kaha hua = 0.
Ko te kaha kume o te taura (T) ina tū te hiki = 500 N.
Ina tere ake te ararewa, ka eke te kaha kume taura (T) ki te 750 N, ka piki rānei mā te 250 N.
Ko te whakaterenga o te ararewa he 5 m/s2 ā, ko te ahunga o te whakaterenga = ko te ahunga o te nekehanga o te ararewa kei runga.
Pūtake pātai:
Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa