4 ngā tauira pātai mō te whakamahinga o ngā ture a Newton ki te nekehanga tika o te ararewa, o te ararewa rānei
1. Kei roto i tētahi ararewa tētahi tangata he 50 kg te taumaha. Te whakaterenga nā te kaha ā-papatipu = 10 m/s2Whakatauhia te rahi o te kaha noa e pā ana ki te papa o te ararewa ki te tangata mēnā:
(a) ararewa wahangu
(b) ka neke te ararewa ki raro i te tere pumau
(c) ka neke te ararewa ki runga me te whakaterenga o te 5 m/s2
(d) ka neke te ararewa ki raro me te whakaterenga o te 5 m/s2
(e) ararewa hinga kore utu
Kōrero
E mōhiotia ana :
Taumaha o te tangata (m) = 50 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha o te tangata (w) = mg = (50)(10) = 500 Newton
Whakautu :
(a) ararewa wahangu
Kei te okioki te ararewa, kāore he whakaterenga (a = 0)
He pai te kaha e anga ana ki runga, he kino ia te kaha e anga ana ki raro.
(b) ka neke te ararewa ki raro i te tere pumau
Ka neke te ararewa i te tere pumau, kāore he whakaterenga (a = 0)
He pai te kaha e anga ana ki runga, he kino ia te kaha e anga ana ki raro.
(c) ka neke te ararewa ki runga me te whakaterenga o te 5 m/s2
Ka neke te ararewa ki runga me te whakaterenga (a) o te 5 m/s2
He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino ia te kaha i te ahunga ke i te nekehanga o te ararewa.
N – w = ma
N = w + ma
N = 500 + (50)(5)
N = 500 + 250
N = 750 Niutona
Ko te rahi o te kaha noa (N) he ōrite ki te taumaha (w), nō reira, ina neke te ararewa ki runga, ka ahua taumaha ake te tinana o te tangata. Arā, ina neke te ararewa ki runga, ka nui ake te taumaha kitea o te tangata. Mena kei te tū te tangata i runga i te tauine, ina neke te ararewa ki runga, ka whakaatuhia e te tauine he nui ake te papatipu o te tangata.
(d) ka neke te ararewa ki raro me te whakaterenga o te 5 m/s2
Ka neke te ararewa ki raro me te whakaterenga (a) o te 5 m/s2
He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino ia te kaha i te ahunga ke i te nekehanga o te ararewa.
w – N = ma
N = w – ma
N = 500 – (50)(5)
N = 500 – 250
N = 250 Niutona
I te hekenga o te ararewa ki raro, ka māmā ake te tinana o te tangata. Arā, i te hekenga o te ararewa ki raro, ka piki ake te taumaha o te tangata. Mēnā kei runga i te tauine te tangata e tū ana, i te hekenga o te ararewa, ka iti ake te taumaha o te tauine.
(e) ararewa hinga kore utu
Ko te tikanga o te ararewa hinga kore utu ka neke te ararewa ki raro, ko te whakaterenga o te ararewa (a) = te whakaterenga ā-papa (g). Hei tauira, g = 10 m/s2 kātahi ka = 10 m/s2
He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino ia te kaha i te ahunga ke i te nekehanga o te ararewa.
w – N = ma
N = w – ma
N = 500 – (50)(10)
N = 500 – 500
N = 0
Ina taka noa te ararewa, ko te taumaha āhua o te tangata he kore. Arā, ka whakaaro te tangata he kore taumaha ia. Mena kei te tū te tangata i runga i te tauine, i te nekehanga o te ararewa ki raro, ka tohu te tauine he kore tōna papatipu. He rite tēnei āhuatanga ki te noho i roto i te wāhi kāore he kaha ā-papa.
2. Tātaihia te rahi o te kaha kume i runga i te taura tautoko hiki me te taumaha o te 2000 kg, mēnā:
(a) ararewa wahangu
(b) ka neke te ararewa ki raro me te whakaterenga o te 5 m/s2
(c) ka neke te ararewa ki runga me te whakaterenga o te 5 m/s2
(d) ararewa hinga kore utu
Me kī ko te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Kōrero
E mōhiotia ana :
Papatipu hiki (m) = 2000 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Taumaha hiki (w) = mg = (2000)(10) = 20.000 Newton
Whakautu :
(a) ararewa wahangu
Kei te okioki te ararewa, kāore he whakaterenga (a = 0)
He pai te kaha e anga ana ki runga, he kino ia te kaha e anga ana ki raro.
Ina tū te hiki, ko te kaha kume i runga i te taura (T) = te taumaha o te hiki (w) = 20.000 Newton
(b) ka neke te ararewa ki raro me te whakaterenga o te 5 m/s2
Ka neke te ararewa ki raro me te whakaterenga (a) o te 5 m/s2
He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino ia te kaha i te ahunga ke i te nekehanga o te ararewa.
w – T = ma
T = w – ma
T = 20.000 – (2000)(5)
T = 20.000 – 10.000
T = 10.000 Ngā Niutona
Ina heke te ararewa ki raro, ka iti ake te kaha kume i runga i te taura (T) i tērā i te wā e tū ana te ararewa.
(c) ka neke te ararewa ki runga me te whakaterenga o te 5 m/s2
Ka neke te ararewa ki runga me te whakaterenga (a) o te 5 m/s2
He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino ia te kaha i te ahunga ke i te nekehanga o te ararewa.
T – w = ma
T = w + ma
T = 20.000 + (2000)(5)
T = 20.000 + 10.000
T = 30.000 Ngā Niutona
Ina neke te ararewa ki runga, ka nui ake te kaha kume i runga i te taura (T) i tērā i te wā e tū ana te ararewa.
(d) ararewa hinga kore utu
Ko te tikanga o te ararewa hinga kore utu ka neke te ararewa ki raro, ko te whakaterenga o te ararewa (a) = te whakaterenga ā-papa (g). Hei tauira, g = 10 m/s2 kātahi ka = 10 m/s2
He pai te kaha i te ahunga kotahi me te nekehanga o te ararewa, he kino ia te kaha i te ahunga ke i te nekehanga o te ararewa.
w – T = ma
T = w – ma
T = 20.000 – (2000)(10)
T = 20.000 – 20.000
T = 0
Ina taka noa te ararewa, ka kore te taumaha o te taura (T). Nā te mea he ōrite te taumaha o te taura ki te taumaha o te ararewa, ina kore te taumaha o te taura, ka āhua kore hoki te taumaha o te ararewa. He rite tēnei āhuatanga ki te mea kei roto te mea i te korehau, i te wāhi rānei kāore he kaha taumaha.
[Ingarihi: Te whakamahinga o te ture nekehanga a Newton i roto i te ararewa]
3. Kei roto i tētahi ararewa e neke ana ki raro tētahi tangata he 60 kg te taumaha, me te tere whakaterenga o te 3 m/s.-2Mena ko te whakaterenga o te kaha ā-papa i runga i te whenua he 10 m/s-2, kātahi ko te rahi o te kaha noa e pā ana ki te papa o te ararewa ki runga i 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/s2
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
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 m/s-2, kātahi ko te whakaterenga o te ararewa ko….
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/s2
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/s2
Ko te whakaterenga o te ararewa he 3 m/s2Ko te tohu kino e tohu ana kei te neke ake te ararewa.
Ko te whakautu tika ko E.
Pūtake pātai:
Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa
