Ngā Tātai me ngā Tauira Raru mō te Ture a Hooke
Mā te tūhura i ngā mātāpono o te ahupūngao ka tūtaki tātou ki tētahi ture matua e mōhiotia ana ko te Ture a Hooke. I tapaina i muri i te tohunga ahupūngao Piritana o te rautau 17, a Robert Hooke, e whakaahua ana tēnei ture i te whanonga o ngā puna me ngā rauemi rapa i raro i te awe o tētahi kaha o waho. He mea nui te mārama ki te Ture a Hooke i roto i ngā mara maha, tae atu ki te miihini, te pūtaiao rauemi, me te tātari hanganga. Ka rukuhia e tēnei tuhinga ngā tātai e pā ana ki te Ture a Hooke, ā, ka whakaratohia he tauira tauira hei whakau i tō tātou māramatanga.
Te Whakamāramatanga o te Ture a Hooke
E ai ki te Ture a Hooke, ko te kaha (F) e hiahiatia ana hei whakaroa, hei pēhi rānei i tētahi puna mā te tawhiti (x) he rite tonu ki taua tawhiti. Mā te pāngarau, ka whakaaturia penei:
\[ F = -kx \]
Kei hea:
– Ko te kaha whakaora e tukuna ana e te puna ko \( F \) (i roto i ngā Newton, N)
– Ko te pūmau puna, te pakari rānei o te puna (i roto i ngā Newton ia mita, N/m) \( k \)
– Ko te nekehanga mai i te tūnga taurite (i roto i ngā mita, m) ko te \( x \)
– Ko te tohu kino e tohu ana kei te taha kē te kaha e pā ana ki te puna i te nekehanga.
Te Mārama ki te Pūmau Puna (k)
Ko te pūmau puna \( k \) he ine i te pakari o te puna. Ko te uara \( k \) nui ake e tohu ana i te puna pakari ake, e hiahia ana ki te kaha nui ake hei whakaputa i te nekehanga ōrite ki te whakaritea ki te puna he iti ake te uara \( k \). Ka whakatauhia te pūmau puna i runga i te rauemi me te hanganga o te puna.
Ngā Here o te Ture a Hooke
Ka whai mana te Ture a Hooke i roto i te rohe pūmau o tētahi rauemi anake. I tua atu i tēnei rohe, kāore ngā rauemi e hoki ki tō rātou āhua taketake ina tangohia te kaha, ka puta he rerekētanga pumau. He mea nui kia mārama ki tēnei whanonga, inā koa i roto i ngā tono hangarau e tino hira ana te pono o ngā rauemi.
Ngā Tauira Raru mō te Ture a Hooke
Tauira Raru 1: Te Tatau i te Nekehanga
Ka pēhia he puna me te pūmau puna \( k \) o te 200 N/m mā te whakamahi i te kaha o te 50 N. Tātaihia te nekehanga \( x \) i puta i te puna.
Rongoā:
Kua whakawhiwhia:
\( F = 50 \) N
\( k = 200 \) N/m
Mā te whakamahi i te tātai \( F = kx \), ka whakatauhia e mātou mō \( x \):
\[ x = \frac{F}{k} = \frac{50 \, \text{N}}{200 \, \text{N/m}} = 0.25 \, \text{m} \]
Nō reira, ko te nekehanga \( x \) he 0.25 mita.
Tauira Raru 2: Te Whakatau i te Pūmau Puna
E hiahiatia ana he kaha 100 N hei totoro i tētahi puna mā te 0.2 mita. Kimihia te pūmau puna \( k \).
Rongoā:
Kua whakawhiwhia:
\( F = 100 \) N
\( x = 0.2 \) mita
Mā te whakamahi i te tātai \( F = kx \), ka whakatauhia e mātou mō \( k \):
\[ k = \frac{F}{x} = \frac{100 \, \text{N}}{0.2 \, \text{m}} = 500 \, \text{N/m} \]
Nō reira, ko te pūmau puna \( k \) he 500 N/m.
Tauira Raru 3: Te Tatau i te Kaha mai i te Nekehanga
Kua nekehia tētahi puna me te pūmau puna \( k \) o te 150 N/m mā te 0.1 mita mai i tōna tūranga taurite. Tātaihia te kaha e pā ana ki te puna.
Rongoā:
Kua whakawhiwhia:
\( k = 150 \) N/m
\( x = 0.1 \) mita
Mā te whakamahi i te tātai \( F = kx \):
\[ F = kx = 150 \times 0.1 = 15 \, \text{N} \]
Ko te kaha e pā ana ki te puna he 15 N.
Tauira Raru 4: Te Mārama ki te Pūngao e Penapenahia ana i roto i te Puna
Ko te pūngao pūmanawa (U) e rongoatia ana i roto i te puna kōpeke, totoro rānei, ka hoatuhia e te tātai:
\[ U = \frac{1}{2} kx^2 \]
Me whakaaro tātou ki tētahi puna me te pūmau puna \( k \) o te 300 N/m, e pēhia ana e te 0.05 mita. Tātaihia te pūngao e rongoatia ana i roto i te puna.
Rongoā:
Kua whakawhiwhia:
\( k = 300 \) N/m
\( x = 0.05 \) mita
Mā te whakamahi i te tātai \( U = \frac{1}{2} kx^2 \):
\[ U = \frac{1}{2} \times 300 \times (0.05)^2 \]
\[ U = 150 \whakareatia ki te 0.0025 \]
\[ U = 0.375 \, \kuputuhi{J} \]
Ko te pūngao e rongoa ana i roto i te puna he 0.375 Joules.
Ngā Whakamahinga o te Ture a Hooke
He mea nui te Ture a Hooke hei mārama me te hoahoa i ngā pūnaha maha:
1. Hangarau: He mea tino nui tēnei i te hoahoa i ngā pūnaha whakatārewatanga, me te whakarite kia noho tonu ngā rauemi i roto i ō rātou rohe ngāwari kia kore ai e huri āhua tuturu.
2. Hanganga: I roto i te hoahoanga, ka āwhina i te tātari i ngā ahotea me ngā taumahatanga i roto i ngā rauemi hanga, kia mau ai te pumau o te hanganga.
3. Rongoā: E whakamahia ana ngā mātāpono o te Ture a Hooke i roto i te hoahoa i ngā prosthetics me ngā orthotics, e hiahia ana ki ngā rauemi e whai ana i te ngāwari o ngā wāhanga tinana tūturu.
4. Ngā Hua Kaihoko: Ko ngā taonga o ia rā pēnei i ngā moenga, ngā nohoanga motuka, me ngā taputapu hākinakina, he mea hanga i runga i te whakaaro ki ngā āhuatanga pīngore e whakaarohia ana e te Ture a Hooke.
Opaniraa
Mā te Ture a Hooke ka kitea he māramatanga māmā engari he hohonu ki te whanonga o ngā rauemi pīngore i raro i te kaha. Mā te mārama ki te whanaungatanga i waenga i te kaha, te nekehanga, me te pūmau puna, ka taea e ngā kaipūtaiao me ngā miihini te matapae me te whakahaere i te whanonga o ngā pūnaha rerekē. Ko ngā tauira raruraru e whakaatuhia ana i roto i tēnei tuhinga e whai ana ki te whakamārama i te whakamahinga mahi o te ture, me te whakaatu me pēhea e whakahaere ai i te pīngore o ngā rauemi i roto i ngā horopaki o te ao tūturu. Mā roto i ēnei mātāpono, ka haere tonu ngā mara o te ahupūngao, te miihini, me te pūtaiao rauemi ki te auaha me te hiranga.
