Ko te Ture Tuarua o Newton tētahi o ngā ariā matua o te ahupūngao e whakahaere ana i te whanaungatanga i waenga i te kaha, te papatipu, me te whakaterenga. E kī ana tēnei ture ko te whakaterenga o tētahi mea he rite ki te kaha kupenga e pā ana ki a ia, ā, he rite whakamuri ki tōna papatipu. I roto i te pāngarau, ko te Ture Tuarua o Newton te kī:
\[ F = mā \]
Kei hea:
– Ko te kaha kupenga e pā ana ki te mea (i roto i ngā Newton, N) ko \( F \).
– Ko te \( m \) te papatipu o te mea (i roto i ngā kirokaramu, kg).
– Ko te whakaterenga o te mea ko \( a \) (i roto i ngā mita ia hekona tapawhā, \( m/s^2 \)).
I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira o te Ture Tuarua a Newton kia mārama ai koe ki tōna whakamahinga i roto i ngā āhuatanga rerekē.
Tauira Pātai 1: Te Āheinga ki runga i tētahi Waka e Whakateretere Ana
Pātai:
Ka tere ake tētahi motuka he 1000 kg te taumaha mai i te tū ki te tere o te 20 m/s i roto i te 5 hēkona. Tātaihia te kaha e hiahiatia ana hei whakatutuki i tēnei whakaterenga.
Otinga:
Tuatahi, me tatau tātou i te whakaterenga o te motuka. Ka taea te tatau i te whakaterenga (\( a \)) mā te whakamahi i te tātai:
\[ a = \frac{\Delta v}{\Delta t} \]
Kei hea:
– Ko te \(\Delta v\) te huringa o te tere.
– Ko te \(\Delta t\) te huringa o te wā.
Whakakapia ngā uara e mōhiotia ana:
\[ a = \frac{20 \, \text{m/s} – 0 \, \text{m/s}}{5 \, \text{hēkona}} \]
\[ a = \frac{20 \, \text{m/s}}{5 \, \text{hēkona}} \]
\[ a = 4 \, \text{m/s}^2 \]
Nā, ka taea e tātou te tatau i te kaha e hiahiatia ana mā te whakamahi i te Ture Tuarua a Newton:
\[ F = mā \]
\[ F = (1000 \, \kuputuhi{kg})(4 \, \kuputuhi{m/s}^2) \]
\[ F = 4000 \, \kuputuhi{N} \]
Nō reira, ko te kaha e hiahiatia ana hei whakatere i te motuka he 4000 N.
Tauira Pātai 2: Te Kaha Waku i runga i te Pouaka
Pātai:
Ka panaia tētahi pouaka he 50 kg te taumaha ki runga i tētahi mata taratara me te kaha o te 300 N. Mena he 100 N te kaha waku i waenganui i te pouaka me te mata, tatauhia te whakaterenga o te pouaka.
Otinga:
Tuatahi, ka tatauhia e tātou te kaha kupenga e pā ana ki te pouaka. Ko te kaha kupenga (\( F_{\text{net}} \)) ko te kaha katoa e pā ana ki tētahi mea i muri i te whakaaro ki ngā kaha katoa e pā ana ki taua mea, tae atu ki te waku.
\[ F_{\text{net}} = F_{\text{push}} – F_{\text{waru}} \]
\[ F_{\kuputuhi{kupenga}} = 300 \, \kuputuhi{N} – 100 \, \kuputuhi{N} \]
\[ F_{\text{kupenga}} = 200 \, \text{N} \]
Nā, ka taea e tātou te tatau i te whakaterenga o te pouaka mā te whakamahi i te Ture Tuarua a Newton:
\[ F_{\text{net}} = ma \]
\[ 200 \, \text{N} = (50 \, \text{kg})a \]
\[ a = \frac{200 \, \text{N}}{50 \, \text{kg}} \]
\[ a = 4 \, \text{m/s}^2 \]
Nō reira, ko te whakaterenga o te pouaka he 4 m/s².
Tauira Pātai 3: Te Tātai i te Kaha e Hiahiatia ana hei Hiki i te Utaina
Pātai:
E hiki ana tētahi kerēni i tētahi kawenga he 200 kg te taumaha ki runga me te whakaterenga o te 1,5 m/s². Tātaihia te kaha e hiahiatia ana e te kerēni hei hiki i te kawenga.
Otinga:
Tuatahi, me tatau tātou i te kaha ā-papa e pā ana ki te kawenga. Ka taea te tatau i te kaha ā-papa (\( F_g \)) mā te whakamahi i te tātai:
\[ F_g = mg \]
Kei hea:
– Ko te whakaterenga nā te kaha ā-papatipu te \( g \) (\( 9,8 \, \text{m/s}^2 \)).
Whakakapia ngā uara e mōhiotia ana:
\[ F_g = (200 \, \text{kg})(9,8 \, \text{m/s}^2) \]
\[ F_g = 1960 \, \text{N} \]
Nā, ka tatauhia e mātou te kaha katoa (\( F \)) e hiahiatia ana e te kerēne hei hiki i te kawenga me te whakaaro ki te whakaterenga tāpiri:
\[ F = ma + F_g \]
\[ F = (200 \, \kwht{kg})(1,5 \, \kwht{m/s}^2) + 1960 \, \kwht{N} \]
\[ F = 300 \, \kuputuhi{N} + 1960 \, \kuputuhi{N} \]
\[ F = 2260 \, \kuputuhi{N} \]
Nō reira, ko te kaha e hiahiatia ana e te kereni hei hiki i te kawenga he 2260 N.
Tauira Raru 4: Te Kaha i roto i tētahi Pūnaha o ngā Mea e Rua e Honoa ana e te Taura
Pātai:
E rua ngā mea, he 10 kg te taumaha, 20 kg te taumaha, e honoa ana e tētahi taura māmā, ā, e iri ana i tētahi pūreirei. Tātaihia te whakaterenga o te pūnaha me te kumenga o te taura ina tukuna te pūnaha mai i te okiokinga.
Otinga:
Tuatahi, me tautuhi tātou i ngā kaha e pā ana ki ngā mea e rua. Me kī ko ngā papatipu he \( m_1 = 10 \, \text{kg} \) me ngā papatipu he \( m_2 = 20 \, \text{kg} \). Ko te kaha ā-papatipu e pā ana ki ngā mea e rua ko:
\[ F_{g1} = m_1 g = (10 \, \text{kg})(9,8 \, \text{m/s}^2) = 98 \, \text{N} \]
\[ F_{g2} = m_2 g = (20 \, \text{kg})(9,8 \, \text{m/s}^2) = 196 \, \text{N} \]
Nā te mea ka tukuna te pūnaha mai i te okiokinga, ka taea te tatau i te whakaterenga o te pūnaha mā te whakamahi i te Ture Tuarua a Newton. Ko te whakaterenga katoa (\( a \)) o te pūnaha ko:
\[ (m_1 + m_2)a = F_{g2} – F_{g1} \]
\[ (10 \, \text{kg} + 20 \, \text{kg})a = 196 \, \text{N} – 98 \, \text{N} \]
\[ 30 \, \text{kg} \cdot a = 98 \, \text{N} \]
\[ a = \frac{98 \, \text{N}}{30 \, \text{kg}} \]
\[ a = 3,27 \, \text{m/s}^2 \]
Nā, ka tatauhia e tātou te taumahatanga o te aho (\( T \)). Ka taea te tatau i te taumahatanga o te aho mā te whakamahi i te Ture Tuarua a Newton i runga i tētahi o ngā papatipu, hei tauira \( m_1 \):
\[ T – m_1 karamu = m_1 a \]
\[ T – 98 \, \kākau{N} = (10 \, \kākau{kg})(3,27 \, \kākau{m/s}^2) \]
\[ T – 98 \, \kuputuhi{N} = 32,7 \, \kuputuhi{N} \]
\[ T = 32,7 \, \kuputuhi{N} + 98 \, \kuputuhi{N} \]
\[ T = 130,7 \, \kuputuhi{N} \]
Nō reira, ko te whakaterenga o te pūnaha he 3,27 m/s², ā, ko te kukū i roto i te taura he 130,7 N.
Whakamutunga
Mā roto i ngā tauira maha o te Ture Tuarua o Newton, kua ako tātou me pēhea te whakamahi i tēnei mātāpono hei tatau i te kaha, te whakaterenga, me te ahotea i roto i ngā āhuatanga rerekē. Ehara i te mea he mea nui te Ture Tuarua o Newton i roto i te ahupūngao ariā anake, engari he maha hoki ngā whakamahinga mahi i roto i te oranga o ia rā me te hangarau. Mā te mārama me te mahi i te Ture Tuarua o Newton, ka taea e tātou te whakaoti rapanga miihini maha me te whai hua me te tika.
