Ngā ture nekehanga a Newton – ngā raruraru me ngā otinga
Te ture tuatahi o te nekehanga a Newton
1. Ki te kore he kaha kupenga e pā ki tētahi mea, kāti:
(1) kāore te mea i whakaterea
(2) te mea e okioki ana
(3) te huringa o te tere o tētahi mea = 0
(4) kāore e taea e te mea te haere i te tere pumau
Ko tēhea kōrero te mea tika?
otinga
Ko te kōrero tika:
(1) Kāore te mea i whakaterea
Mā te kaha kupenga ka whakatereteretia te mea. Nō reira, ki te kore he kaha kupenga, kāore ngā mea e whakatereteretia ana.
(2) Te mea e okioki ana
E ai ki te ture nekehanga tuatahi a Newton, ki te kore he kaha kupenga e pā ki tētahi mea, ka noho okioki tonu te mea, ka haere tonu rānei te mea i te tere pumau.
(3) Te huringa o te tere o tētahi mea = 0
Huringa o te tere = whakaterenga. Ko te kore huringa o te tere kāore he whakaterenga. Mēnā kāore he whakaterenga, kāore he kaha kupenga e pā ki tētahi mea.
2. Ko te taumaha o te tangata i roto i te ararewa e okioki ana = 500 N. Ko te whakaterenga nā te kaha ā-papa he 10 m/s 2. Ina whakaterenga te ararewa, ko te kaha kume he 750 N. He aha te whakaterenga o te ararewa?
Mōhiotia:
Taumaha o te tangata (w) = 500 Newton = 500 kg ms –2 (hikinga i te okiokinga)
Te whakaterenga o te kaha ā-papa (g) = 10 ms –2
Papatipu o te tangata (m) = 500 / 10 = 50 kg
Te kaha kume (T) = 750 N (te tere o te hiki)
Kāore i arohia te papatipu o te ararewa.
E hiahiatia ana: Te whakaterenga o ngā ararewa
Rongoā:
He ararewa e okioki ana, kāore he whakaterenga (a = 0). He tohu tāpiri kei te kaha e mahi ana ki runga, ā, he tohu tango kei te kaha e mahi ana ki raro.
ΣF = ma
T – w = 0
T = w
T = 500 Ngā Niutona
Ki te tere te ararewa ki raro, ko te kaha kume iti rawa i raro i te 500 N. Ki te kore, ki te tere te ararewa ki runga, ko te kaha kume nui ake i te 500 N.
Ko te kaha kume = 750 N nā te mea ka tere ake te ararewa ki runga. He tohu tāpiri tō te kaha e mahi ana ki runga, ā, he tohu tango tō te kaha e mahi ana ki raro.
T – w = ma
750 – 500 = 50 a
250 = 50
ā = 250 / 50
a = 5.0 ms –2
3. I tere ake te heke o tētahi tangata 60-kg i roto i tētahi ararewa i te 3 m/s² . Mena ko te tere o te kaha ā-papa he 10 m/s² , he aha te kaha noa e pā ana ki te papa o te ararewa ki runga i te tangata?
Mōhiotia:
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
Taumaha (w) = mg = (60)(10) = 600 Ngā Newton
E hiahiatia ana: Te kaha noa (N)
Rongoā:
E rua ngā kaha e pā ana ki te tangata i roto i te ararewa, arā, ko te taumaha (w) o te tangata me te kaha noa (N) e pā ana ki te papa. E toru ngā rahinga whārite, arā, ko te taumaha (w), te kaha noa (N) me te whakaterenga o te ararewa. Ina heke te taumaha, ka piki te kaha noa, ka heke te whakaterenga o te ararewa. He tohu tāpiri kei ngā rahinga whārite e heke ana, ā, he tohu tango kei ngā rahinga whārite e piki ana.
∑F = ma
w – N = (60)(3)
600 – N = 180
N = 600 – 180
N = 420 Niutona
4. I tere ake te piki o tētahi mea 40-kg i roto i tētahi ararewa. Mēnā he 520 N te taumaha o te papa o te ararewa ki runga i te mea, ā, ko te tere o te kaha ā-papa he 10 m/s² . He aha te tere o te ararewa?
Mōhiotia:
Taumaha (m) = 40 kg
Te kaha noa (N) = 520 N
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
taumaha (w) = mg = (40)(10) = 400 N
E hiahiatia ana: Te whakaterenga o te ararewa
Rongoā:
∑F = ma
400 – 520 = (40)(a)
-120 = (40)(a)
ā = -120/40
a = -3 m/s 2
Ko te tere o te ararewa he 3 m/s² . Ko te tohu tango e tohu ana kei te haere te ararewa ki runga.
5. I tere ake te heke o tētahi mea 60-kg i roto i tētahi ararewa i te 3 m/s 2. He aha te kaha i pā ki ngā mea i runga i te papa o te ararewa?
Mōhiotia:
Taumaha (m) = 60 kg
Taumaha (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
E hiahiatia ana: Te kaha i pā ki te papa o te ararewa e te mea i mahia e ia.
Rongoā:
I tere ake te ararewa ki raro i te 3 m/s . He tohu tāpiri kei te kaha e mahi ana ki raro, ā, he tohu tango kei te kaha e mahi ana ki runga.
w – N = ma
N = w – ma
N = 600 – (60)(3)
N = 600 – 180
N = 420 Niutona
Ko te kaha i pā ki te papa o te ararewa = 420 N.
6. E rua ngā poraka e honoa ana e te taura e rere ana i runga i te pūreirei. Kaua e aro ki te taumaha o te taura me te pūreirei me te waku i roto i te pūreirei. Ko te taumaha o te poraka A he 6 kg, ā, ko te taumaha o te poraka B he 2 kg. Ko te tere o te kaha ā-papa he 10 m/s² . He aha te kaha kume?
Mōhiotia:
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
E hiahiatia ana: te kaha kume (T)?
Rongoā:
Ka neke a w A > w B kia heke a m A , ka neke a m B ki runga.
Te ture tuarua a Newton:
Σ F = 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 kaha o te kume:
Ka neke a m A ki raro:
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 kaha kume (T) = 30 Newton.
7. Papatipu o te mea A = 5 kg, whakaterenga nā te kaha ā-papatipu (g) = 10 ms -2 . Ka neke whakararo te mea A i te 2.5 ms -2 . He aha te papatipu o B?
Mōhiotia:
Taumaha A (m A ) = 5 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te whakaterenga o te mea A (a) = 2.5 m/s 2
Taumaha A (w A ) = (m A )(g) = (5)(10) = 50 Ngā Niutona
E hiahiatia ana: Taumaha o te mea B (m B )
Rongoā:
Ka neke te Poraka A ki raro, nō reira he nui ake te taumaha o te mea A (w A ) i te taumaha o te mea B (w B ).
Whakamahia te ture tuarua a Newton:
Σ F = 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
8. Ko te whakaterenga nā te kaha ā-papa he 10 m/s 2. He aha te kaha kume.
Mōhiotia:
Papatipu o te mea 1 (m1) = 2 kirokaramu
Taumaha o te mea 2 (m² ) = 2 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha 1 (w 1 ) = (m 1 )(g) = (2 kg)(10 m/s 2 ) = 20 kg m/s 2
Taumaha 2 (w 2 ) = (m 2 )(g) = (3 kg)(10 m/s 2 ) = 30 kg m/s 2
E hiahiatia ana: te kaha kume (T)
Rongoā:
Ka neke a w 2 ki raro , ka neke a m 1 ki runga.
Te ture tuarua o te nekehanga a Newton:
Σ F = 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 kaha o te taumahatanga?
ka neke whakararo 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 kaha kume (T) = 24 Newton.
- pātai: He aha te ture nekehanga tuatahi a Newton e whakanui ai i te hiranga o ngā kaha o waho ki te whakarerekē i te āhua nekehanga o tētahi mea? whakahoki: Ko te ture nekehanga tuatahi a Newton, e kiia ana ko te ture o te korekore, e kī ana ka noho tonu te mea i te okiokinga, i te nekehanga ōrite rānei i roto i te rārangi tika ki te kore e pāngia e te kaha o waho. E whakaatu ana tēnei ture ko ngā kaha o waho, ehara i te mea ko ngā āhuatanga o roto o te mea tonu, ka taea te whakarerekē i tōna āhua nekehanga.
- pātai: He aha te hononga e pā ana ki te kaha, te papatipu, me te whakaterenga e ai ki te ture tuarua a Newton? whakahoki: E ai ki te ture nekehanga tuarua a Newton, ko te kaha e pā ana ki tētahi mea he ōrite ki te papatipu o taua mea kua whakareatia ki tōna whakaterenga (). Mā tēnei ka whakatūria he ōwehenga tika i waenga i te kaha me te whakaterenga, me te ōwehenga whakamuri i waenga i te papatipu me te whakaterenga, mēnā he kaha pumau.
- pātai: He aha koe te rongo ai i te nekehanga o te Ao ahakoa e nekeneke tonu ana? whakahoki: He tauira tēnei o te ture tuatahi a Newton. Ko tātou, me te Ao me ngā mea katoa i runga, e neke tahi ana i runga i te ōrite. Ki te kore he kaha o waho hei whakarerekē i tēnei āhua nekehanga, kāore he kare ā-roto o te whakaterenga, o te huringa rānei, e āhua tū tonu ana tātou.
- pātai: He pēhea te whakamārama a te ture tuatoru a Newton i te mahi a te rōkete i te wāhi? whakahoki: E ai ki te ture tuatoru a Newton, mō ia mahi, he tauhohenga ōrite, he tauhohenga rerekē. Ka panaia e te rōkete i te wāhi mā te pupuhi i ngā hau putanga ki muri. Ko te mahi ko te hau e neke whakamuri ana, ā, ko te tauhohenga ko te rōkete e neke whakamua ana.
- pātai: He aha koe ka neke whakamua ai i roto i te motuka ina tū whakarere? whakahoki: E ai ki te ture tuatahi a Newton, ka haere tonu tō tinana i tōna āhua nekehanga (whakamua) ina tū te motuka. Ki te kore he kaha (pēnei i te whitiki nohoanga) e pā ki a koe, ka haere tonu koe i mua nā te kore e taea te neke.
- pātai: Ki te makahia he huruhuru manu me te hama ki roto i te korehau, he aha te mea ka taea e ngā ture a Newton te matapae mō tā rāua nekehanga? whakahoki: I roto i te korehau, kāore he ātete hau. E ai ki ngā ture tuatahi me te tuarua a Newton, me taka te huruhuru me te hama i te tere kotahi, ā, me pā tahi ki te whenua nā te mea ko te kaha ā-papa anake te kaha e pā ana ki a rāua.
- pātai: Me pēhea te whakaiti a te pēke hau i te tūponotanga o te whara i te wā o te tukinga motuka? whakahoki: E tohu ana te ture tuatahi a Newton ka noho tonu te mea e neke ana i te nekehanga. I roto i te tukinga, ka haere tonu te nekehanga whakamua o te tangata. Ka whakaratohia e te pēke hau he mata ngohengohe e whakanui ana i te wā o te whakahekenga, ā, ka whakaitihia te kaha e pā ana ki te tangata e ai ki .
- pātai: He aha i māmā ake ai te pana i tētahi kete hokohoko kau i tētahi kete hokohoko kī tonu? whakahoki: Te ture tuarua a Newton () e kī ana, mō te nui o te kaha e pā ana, ka nui ake te whakaterenga o tētahi mea he iti ake te papatipu (kāreti kau) i tētahi mea he nui ake te papatipu (kāreti utaina).
- pātai: He aha te take e pana ai te wai e te kauhoe ki muri kia neke whakamua ai? whakahoki: He whakaaturanga tēnei o te ture tuatoru a Newton. Ina panaia te wai e te kaihoe ki muri (te mahi), ka puta he tauhohenga ōrite, he tauhohenga ritenga kē hoki e pana ana i te kaihoe ki mua.
- pātai: He aha te hononga o te waku ki te ture tuatahi a Newton? whakahoki: Ko te waku he kaha o waho ka taea te mahi ki ngā mea hei whakaroa, hei aukati rānei i tā rātou nekehanga. Ki te kore he waku (he kaha o waho rānei), ka haere tonu te āhua o te nekehanga o te mea mō ake tonu atu, e ai ki te ture tuatahi a Newton.
