E toru ngā ture nekehanga a Newton, arā, ko te ture tuatahi a Newton, ko te ture tuarua a Newton, me te ture tuatoru a Newton.
Te Ture Tuatahi a Newton
E ai ki te Ture Tuatahi a Newton, ko ia mea e okioki ana ka noho okioki tonu, ko ia mea rānei e neke ana i te rārangi tika i te tere pumau ka haere tonu i te neke i te rārangi tika i te tere pumau mena he kore te kaha katoa e pā ana ki te mea.
Whakaarohia tētahi mea e karapoti ana i a koe, hei tauira he tēpu, he toka rānei, he aha atu rānei. Ka noho tonu te tēpu e takoto ana ki te takoto mena kāore e nekehia, e kore rānei e tukuna he kaha o waho pēnei i te kaha pana, tō rānei. Waihoki, ko ētahi atu mea e takoto ana ki te takoto. Kāore he kaha e pā ana ki te tēpu, ki te toka rānei, ki tētahi atu mea rānei e takoto ana ki te takoto? He kaha e pā ana ki te mea, engari ko te tapeke o ngā kaha katoa e pā ana ki te mea, ki te kaha katoa rānei, he ōrite ki te kore. Ko ngā kaha e pā ana ki tētahi mea e takoto ana ki te takoto ki te mata o tētahi aorangi pēnei i a Papatūānuku ko te kaha ā-papa (w) me te kaha noa (N). Ko te ahunga o te kaha ā-papa he poutū ki waenganui o Papatūānuku, ko te ahunga o te kaha noa he poutū ki waenganui o Papatūānuku. He ōrite te rahi o ēnei kaha e rua engari he rerekē te ahunga, nō reira he ōrite te kaha katoa ki te kore.
Ā, me pēhea tētahi mea e neke ana i te rārangi tika me te tere pumau? Hei whakamārama i tēnei take, me kī ka panaia e koe tētahi mea, hei tauira, he wahi whakarewa, puta noa i te mata o te papa. Whai muri i te panaia, ka puhoi te nekehanga o te wahi whakarewa, kātahi ka mutu nā te kaha waku . Kia neke haere ai ngā wahi whakarewa, kia roa ake rānei, me whakangawari te mata o te papa me te mata o ngā wahi whakarewa. Ko te maeneene ake o te mata o te papa me te mata o ngā wahi whakarewa, ko te tawhiti ake o te nekehanga o ngā wahi whakarewa. Mena he tino maeneene te mata o te papa, ā, kāore he waku, ka haere tonu ngā wahi whakarewa ki te neke, ā, kāore e mutu. Kāore he kaha e pā ana ki tētahi wahi whakarewa e neke ana i runga i te mata papa tino maeneene? He kaha kei te mahi ki ngā wahi whakarewa, arā, ko te kaha ā-papa me ngā kaha noa. Ka mahi ēnei kaha e rua i te ahunga poutū, ā, kāore e pā ki te nekehanga o ngā wahi whakarewa i te ahunga whakapae mena he tino maeneene te papa.
Te Ture Tuarua a Newton
E ai ki te Ture Tuarua a Newton, ki te kore te kaha kupenga e pā ana ki tētahi mea i te kore, ka tere ake te mea. He rite te rahi o te whakaterenga ki te rahi o te kaha kupenga, ā, he rite whakamuri ki te papatipu o te mea. He rite te ahunga o te whakaterenga ki te ahunga o te kaha kupenga.
ΣF = ma(1.2)
Whakaahuatanga: ΣF = te kaha katoa (kg m/s 2 ), m = te papatipu (kg), a = te whakaterenga (m/s 2 )
Ko te whārite 1.2 he tauākī pāngarau mō te ture tuarua a Newton.
Mena he ōrite te rahi o te whakaterenga ki te kore (a = 0) ka huri te whārite 1.2 ki te whārite 1.1. Nō reira, ko te ture tuatahi a Newton he take motuhake o te ture tuarua a Newton.
I runga i te whārite 1.2, ka whakatauhia ko te nui ake o te kaha, ko te nui ake o te whakaterenga. I tetahi atu taha, ko te nui ake o te papatipu, ko te iti ake o te whakaterenga. Ka mārama ake te whanaungatanga i waenga i te kaha, te papatipu, me te whakaterenga i muri i te whakahaere i ngā whakamātautau e pā ana ki tēnei. Ko tētahi whakamātautau ka taea te whakahaere ko te whakamātautau hei whakatere i tētahi tereina hihiri i runga i ngā rēri mā te whakamahi i tētahi papatipu e hinga noa ana. Whakamahia he taima tohu hei whakatau i te whakaterenga o te tereina.
Te Ture Tuatoru a Newton
E ai ki te ture tuatoru a Newton, mēnā ka pā te kaha o te mea 1 ki te mea 2, ka pā te kaha o te mea 2 ki te mea 1 i taua wā anō. He rite tonu te rahi o ngā kaha e rua engari he rerekē te ahunga o ngā kaha e rua. Ka kiia tētahi kaha ko te mahi, ko tētahi atu kaha ko te tauhohenga (kaha mahi-tauhohenga).
Mahi F = – Tauhohenga F (1.3)
Ko te whārite 1.3 he tauākī pāngarau mō te ture tuatoru o Newton. Ko te tohu kino i te whārite 1.3 e tohu ana i te ahunga o te kaha.
Whakahaerehia he whakamātautau kia pai ake ai te mārama ki te ture tuatoru a Newton. Mena he papa reti tāu, pana ki te pakitara i a koe e tū ana i runga. Whai muri i te pana ki te pakitara, ka neke whakamuri te papa reti. Ka pana whakamua tō pana, ka neke whakamuri te papa reti. E whakaatu ana tēnei kei te pana anō hoki te pakitara ki a koe. Ina pana koe ki te pakitara, i taua wā anō, kei te pana anō hoki te pakitara ki a koe. Ka mahi tō kaha pana ki te pakitara, ka mahi te kaha pana o te pakitara ki a koe. He ōrite te rahi o ngā kaha e rua engari he rerekē te ahunga. Ka taea e koe te kī ko tētahi kaha he mahi, ko tētahi he tauhohenga.
Ko tētahi atu whakamātautau ka taea e koe ko te pupuhi i tētahi poihau rapa, kātahi ka tukuna i muri i te pupuhi me te whakakī i te hau. I muri i te tukunga, ka "rere" te poihau. Ko te ahunga o te nekehanga o te poihau he ritenga kē ki te ahunga e puta ana te hau mai i te poihau. Me pēhea te whakamārama i tēnei? Ina tukuna te waha o te poihau, ka panaia e te poihau te hau ki waho. I taua wā anō, ka panaia hoki te poihau e te hau. Mā te pana o te hau ka rere te poihau. Ka pā te pana o te poihau ki te hau, ā, ka pā te pana o te hau ki te poihau. He ōrite te kaha o ngā kaha e rua engari he ritenga kē te ahunga.
Tauira raruraru
1. E whā ngā mea, panana = 4 kg, pukapuka = 0,8 kg, poitūkohu = 3,5 kg, māngo = 1,2 kg. Ka tōia te kete me te kaha o te 30 N i runga i te mata papatahi taratara ( μ = 0,4). Kia tika ai te neke o te kete (kāore e arohia te taumaha o te kete), ko ngā mea me whakauru ki roto i te kete ko...
Kōrero
E mōhiotia ana:
Taumaha o te panana (m1 ) = 4 kg
Taumaha o te pukapuka (m² ) = 0,8 kg
Taumaha o te pōro (m3 ) = 3,5 kg
Taumaha o te māngo (m4 ) = 1,2 kg
Te kaha kume (F) = 30 N
Tauwehenga waku pumau ( μ s ) = 0,4
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Kaua e aro ki te puranga kete
Ka mahi te kaha waku pumau (fs ) ina takoto kau ana te mea, ā, kua tata te neke, ko te kaha waku nekeneke ia ka mahi ina neke.
I pātaihia: Te taumaha o te mea
Whakautu:
Ka neke te kete ina rite te rahi o te kaha kukume (F) ki te rahi o te kaha waku pumau (fs ).
Tātaihia te rahi o te kaha waku pumau (f s ):
f s = μ s N = μ s w = μ s mg = (0,4)(m)(10)
fs = 4 m
Ka neke te kete tuturu:
F = fs
30 = 4 mita
m = 30/4
m = 7,5 kg
Taumaha o te panana 4 kg + taumaha o te pōro 3,5 kg = 7,5 kg
Ko ngā mea me whaowhina ki roto i te kete he panana me he pōro.
2. Pātai Whakamātautau ā-Motu SMA/MA 2014/2015 Nama 5
Kua honoa ngā mea A he 6 kg te taumaha me ngā mea B he 4 kg te taumaha mā te taura, ā, kua kumea mā te kaha F = 60 N e whakaatuhia ana i te pikitia e whai ake nei.
Mena kei te neke te pūnaha, ā, ko te tauwehenga o te waku nekeneke i waenga i te mata o te papa me ngā mea e rua he 0,5 (tg θ = 3/4), me te g = 10 ms -2 , ko te rahi o te kaha kume i roto i te taura T e hono ana i ngā mea e rua ko….
A. 28,8 N
B. 30,0 N
C. 39,6 N
D. 48,0 N
E. 50,0 N
Kōrero
E mōhiotia ana:
Papatipu o te mea A (m A ) = 6 kg
Taumaha o te mea B (m B ) = 4 kg
Te kaha kume (F) = 60 Newton
Ko te tauwehenga o te waku nekeneke i waenga i te mea me te papa (μ k ) = 0,5
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Pānga θ = 3/4
Pātai: E hia te rahi o te kume i roto i te taura T?
Whakautu:
Wāhanga whakapae o te kaha F:
F x = F cos θ
F x = (60)(4/5) = (4)(12) = 48 N
Wāhanga poutū o te kaha F:
F y = F sin θ
F y = (60)(3/5) = (3)(12) = 36 N
Te kaha noa o te mea A:
N A = w A = m A g = (6)(10) = 60 N
Te kaha noa o te mea B:
N B + F y – w B = 0
N B + F y = w B
N B = w B – F y = m B g – F y = (4)(10) – 36 = 40 – 36 = 4 N
Te kaha waku nekeneke i waenga i te mea A me te papa:
f kA = μ k N A = (0,5)(60) = 30 N
Te kaha waku nekeneke i waenga i te mea B me te papa:
f kB = μ k N B = (0,5)(4) = 2 N
Tātaihia te whakaterenga o ngā mea e rua:
ΣF = ma
F x – T + T – f kB – f kA = (m A + m B ) a
He rite tonu te kaha kume i roto i te aho T i te roanga o te aho, ā, he rerekē te ahunga, nō reira kua tangohia atu i te whārite.
F x – f kB – f kA = (m A + m B ) a
48 – 2 – 30 = (6 + 4) he
16 = 10
ā = 16/10
a = 1,6 m/s 2
Tātaihia te kaha kume o te taura T:
Whakaarohia te mea A. Ko ngā kaha e pā ana ki te mea A i te ahunga whakapae (whakapae) ko te kaha kume taura (T) e anga ana ki te taha matau me te kaha waku nekeneke (f kA ) e anga ana ki te taha maui.
ΣF = ma
T A – f kA = m A a
T A – 30 = (6)(1,6)
T A – 30 = 9,6
TA = 9,6 + 30 = 39,6 N
Whakaarohia te mea B. Ko ngā kaha e pā ana ki te mea B i te ahunga whakapae (whakapae) ko te kaha F x e anga ana ki te taha matau, te kaha waku nekeneke (f kB ) me te kaha kume taura (T) e anga ana ki te taha maui.
ΣF = ma
F x – f kB – T B = m B a
48 – 2 – T B = (4)(1,6)
46 – T B = 6,4
46 – 6,4 = T B
T B = 39,6 N
Nō reira, ko te kaha kume i roto i te taura e pā ana ki te mea A (T A ) = ko te kaha kume i roto i te taura e pā ana ki te mea B (T B ) = 39,6 N.
Ko te whakautu tika ko C.
3. Ngā Pātai Whakamātautau ā-Motu mō te Ahupūngao SMA/MA 2014/2015 Nama 5
Tirohia te pikitia e whai ake nei!
Nā te kaha F, ka neke te pūnaha o ngā mea. Mena he taratara te papa, ā, ko te tauwehenga o te waku nekeneke i waenga i ngā poraka e rua me te papa he 0,2, he aha te whakaterenga e pā ana ki ngā mea e rua? (cos 37 o = 0,8 , sin 37 o = 0,6)
A. 2,6 ms-2
B. 4,0 ms -2
C. 5,2 ms -2
D. 7,8 ms -2
E. 10,2 ms -2
Kōrero
E mōhiotia ana:
Papatipu o te mea A (m A ) = 4 kg
Taumaha o te mea B (m B ) = 2 kg
Te kaha kume (F) = 30 Newton
Ko te tauwehenga o te waku nekeneke i waenga i te mea me te papa (μ k ) = 0,2
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
cos 37 o = 0,8
hara 37 o = 0,6
Pātai: He aha te whakaterenga ka pā ki ngā mea e rua?
Whakautu:
Wāhanga whakapae o te kaha F:
F x = F cos θ
F x = (30)(0,8) = 24 N
Wāhanga poutū o te kaha F:
F y = F sin θ
F y = (30)(0,6) = 18 N
Te kaha noa o te mea A:
N A = w A = m A g = (4)(10) = 40 N
Te kaha noa o te mea B:
N B + F y – w B = 0
N B + F y = w B
N B = w B – F y = m B g – F y = (2)(10) – 18 = 20 – 18 = 2 N
Te kaha waku nekeneke i waenga i te mea A me te papa:
f kA = μ k N A = (0,2)(40) = 8 N
Te kaha waku nekeneke i waenga i te mea B me te papa:
f kB = μ k N B = (0,2)(2) = 0,4 N
Tātaihia te whakaterenga o ngā mea e rua:
ΣF = ma
F x – f kB – f kA = (m A + m B ) a
24 – 0,4 – 8 = (4 + 2) he
15,6 = 6
ā = 15,6/6
a = 2,6 m/s 2
Ko te whakautu tika ko A.
