Te Tātai Taurite Puna i roto i te Ararewa
Pengantar
He taputapu te pauna puna e whakamahia ana hei ine i te taumaha, i te kaha rānei. E mahi ana i runga i te mātāpono o te Ture a Hooke, e kī ana ko te kaha pīataata e tukuna ana e te puna he rite tonu ki tōna roa. Heoi, ina whakamahia he pauna puna i roto i te ararewa, ka rerekē pea ngā pānui e whakaaturia ana e te pauna i runga i te nekehanga o te ararewa. I roto i tēnei tuhinga, ka tūhuratia e tātou te pānga o te nekehanga ararewa ki ngā pānui pauna puna, ngā tātai e tika ana, me ētahi tauira me ngā tono mahi.
Ngā Mātāpono Taketake o te Taurite o te Koanga
Ka mahi ngā pauna puna i runga i te Ture a Hooke, e kīia ana penei:
\[ F = -kx \]
Kei hea:
– Ko te kaha e pā ana ki te puna (Newton, N) ko \( F \),
– Ko te pūmau puna (Newton ia mita, N/m) te \( k \),
– Ko te \( x \) te toronga, te pēhanga rānei o te puna mai i te tūranga taurite (mita, m).
Ina whakairihia he mea ki runga i te pauna puna i roto i te āhua tūmau, ka taurite te kaha ā-papa e pā ana ki te mea e te kaha pīngore o te puna:
\[ mg = kx \]
Kei hea:
– Ko te taumaha o te mea (kirokaramu, kg) ko te \( m \),
– Ko te whakaterenga nā te kaha ā-papatipu te \( g \) (9.8 mita ia hekona tapawhā, m/s²).
Taurite Puna i roto i te Ararewa Neke
Ina kei roto i tētahi ararewa e neke ana te taurite puna, ka pā te tere o te ararewa ki te kaha e inehia ana e te taurite. He maha ngā āhuatanga o te nekehanga o te ararewa hei whakaaroaro:
1. Kei te tū tonu te ararewa, kei te neke rānei i te tere pumau
Mena kei te tū te ararewa, kei te neke rānei i te tere pumau, ka kore te whakaterenga ararewa (\(a\)). I tēnei āhua, ko te kaha i inehia e te taurite puna ka pāngia anake e te kaha o te taumaha:
\[ F = mg \]
2. Ka neke ake te ararewa me te whakaterenga.
Ki te neke te ararewa ki runga me te whakaterenga (\(a\)), ko te whakaterenga katoa e pā ana ki te mea ko \(g + a\). Ko te kaha i inehia e te taurite puna i raro i ēnei tikanga ko:
\[ F = m(g + a) \]
3. Ka heke te ararewa me te whakaterenga.
Ki te neke te ararewa ki raro me te whakaterenga (\(a\)), ko te whakaterenga katoa e pā ana ki te mea ka \(g – a\). Ko te kaha i inehia e te taurite puna i raro i ēnei tikanga ko:
\[ F = m(g – a) \]
4. Kei te hinga noa te ararewa
Mena kei te taka noa te ararewa (hei tauira, kua whati te taura ararewa), ka ōrite te whakaterenga ararewa (\(a\)) ki te whakaterenga nā te kaha ā-papa (\(g\)). I tēnei āhua, ko te whakaterenga katoa e pā ana ki te mea he kore, nō reira ko te kaha i inehia e te taurite puna ko:
\[ F = m(g – g) = 0 \]
Tauira Tātaitanga
Me titiro tātou ki ētahi tauira tataunga kia pai ake ai te mārama ki te pānga o te nekehanga o te ararewa ki ngā pānui taurite puna.
Tauira 1: Ararewa e okioki ana, e neke ana rānei i te tere pumau
Mehemea kei te whakairihia tētahi mea he 5 kg te taumaha ki runga i tētahi pauna puna i roto i tētahi ararewa e tū ana, e neke ana rānei i te tere pumau.
Ko te kaha i inehia e te taurite puna ko:
\[ F = mg \]
\[ F = 5 \whakareatia ki te 9.8 \]
\[ F = 49 \, \kuputuhi{N} \]
Tauira 2: Te Nekehanga o te Ararewa ki Runga me te Whakaterenga
Inaianei, me kī kei te neke ake te ararewa me te whakaterenga o te 2 m/s². Ko te kaha i inehia e te taurite puna ko:
\[ F = m(g + a) \]
\[ F = 5 (9.8 + 2) \]
\[ F = 5 \whakareatia ki te 11.8 \]
\[ F = 59 \, \kuputuhi{N} \]
Tauira 3: Te Nekehanga o te Ararewa ki raro me te Whakaterenga
Me kī kei te neke te ararewa ki raro me te whakaterenga o te 2 m/s². Ko te kaha i inehia e te taurite puna ko:
\[ F = m(g – a) \]
\[ F = 5 (9.8 – 2) \]
\[ F = 5 \whakareatia ki te 7.8 \]
\[ F = 39 \, \kuputuhi{N} \]
Tauira 4: Ararewa i te Hinga Koreutu
Mena kei te taka noa te ararewa, he ōrite te whakaterenga ararewa (\(a\)) ki te whakaterenga ā-papa (\(g\)). Ko te kaha i inehia e te taurite puna ko:
\[ F = m(g – g) = 0 \]
I tēnei āhua, ka whakaatu te taurite puna i te kore nā te mea kei roto te mea i te āhua kore taumaha.
Ngā Whakamahinga Whai Hua
He maha ngā whakamahinga whai hua o te mārama ki te pānga o te nekehanga ararewa ki ngā pānui taurite puna, tae atu ki:
1. Haumaru Ararewa
Ka whakamahia e ngā kaihangarau ēnei mātāpono hei hoahoa i ngā pūnaha haumaru i roto i ngā ararewa, kia kore ai ngā kaha e pā ana ki ngā wāhanga ararewa i raro i ngā āhuatanga nekehanga rerekē e neke ake i ngā rohe haumaru.
2. Ngā Whakamātautau Ahupūngao
I roto i te taiwhanga ahupūngao, mā te mārama ki te panonitanga o ngā kaha i roto i tētahi pūnaha neke ka āwhina i ngā whakamātautau e pā ana ki ngā hihiri me ngā kinematiki. Hei tauira, ko ngā whakamātautau hei ine i te whakaterenga nā te kaha ā-papa ka whakamahi i te panonitanga o te kaha i inehia e te taurite puna i roto i tētahi pūnaha neke.
3. Hoahoa Taputapu Hākinakina
Ka whakamahia hoki e ngā taputapu whakakori tinana pērā i te mīhini oma he pūnaha teitei ō rātou hei whakarerekē i te kaha ka pā ki te kaiwhakamahi i runga i te pikinga me te tere o te taputapu.
Whakamutunga
He taputapu tino whai hua te pauna puna mō te ine i te kaha, engari ka rerekē pea ngā pānui ka puta mai i runga i ngā āhuatanga nekehanga o te pūnaha e whakamahia ana. I roto i te horopaki o ngā ararewa, ka pā te tere o te ararewa ki te kaha i inehia e te pauna, ā, he mea nui te mārama ki tēnei i roto i ngā momo tono mahi, mai i te haumaru o te ararewa ki ngā whakamātautau ahupūngao.
Mā te mārama ki ngā tātai taketake me te mahi i ngā tātaitanga e tika ana, ka taea e tātou te matapae me pēhea te pānga o te nekehanga ararewa ki ngā pānui taurite puna, ā, ka āwhina i a tātou ki te hoahoa i ngā pūnaha haumaru ake, whai hua ake hoki.
