Te Hua o te Kaha Hiko
Pengantar
He āhuatanga ā-tinana te hiko kua kukume i te tangata, kua whakahihiri hoki i a ia mai anō i ngā wā onamata. Nā tēnei āhuatanga i whakarerekē te ao me ōna whakamahinga maha i roto i te hangarau hou. I roto i te ahupūngao, ko te kaha hiko tētahi o ngā kaha matua e pā ana ki ngā matūriki utu. Ka matapakihia e tēnei tuhinga te kaha hiko hua, arā, te tapeke o ngā kaha hiko katoa e mahi ana i tētahi pūwāhi.
Ariā Taketake o te Kaha Hiko
I whakamāramahia tuatahitia te kaha hiko e Coulomb mā te ture a Coulomb. E kī ana tēnei ture ko te kaha i waenganui i ngā utu pūwāhi e rua he rite ki te hua o ngā utu, ā, he rite whakamuri ki te tapawhā o te tawhiti i waenganui i a rāua. Mā te pāngarau, ko te ture a Coulomb te kī:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
ko \( F \) te rahi o te kaha i waenganui i ngā utu e rua, ko \( q_1 \) me \( q_2 \) ngā rahi o ngā utu, ko \( r \) te tawhiti i waenganui i ngā utu e rua, ā, ko \( k_e \) te pūmau Coulomb e tata ana ki te \( 8.99 \times 10^9 \) N m²/C². He kaha kukume tēnei mēnā he rerekē ngā tohu o ngā utu e rua, ā, he kaha whakahē mēnā he rite te tohu o ngā utu e rua.
Te Hua o te Kaha Hiko
Ko te kaha hiko e puta mai ana ko te tapeke o ngā kaha katoa e pā ana ki tētahi utu nā ētahi atu utu. Hei whakatau i tēnei kaha e puta mai ana, me whakaaro tātou ki te rahi me te ahunga o ia kaha hiko e pā ana ki te utu.
Te Mātāpono o te Whakatairanga
Ko te mātāpono o te taupatupatu he mātāpono taketake mō te whakatau i te kaha hiko e puta mai ana. E kī ana tēnei mātāpono ko te kaha katoa e pā ana ki tētahi utu nā ētahi atu utu ko te tapeke whārite o ngā kaha takitahi katoa i puta mai i ia utu motuhake. Mā te pāngarau, mēnā he \( n \) utu e pā ana ki tētahi pūwāhi, ka taea te tuhi i te kaha hiko e puta mai ana \( \vec{F}_{\text{total}} \) penei:
\[ \vec{F}_{\text{tapeke}} = \tapeke_{i=1}^{n} \vec{F}_i \]
ko \( \vec{F}_i \) te kaha hiko nā te utu \( q_i \).
Tauira o te Tātaitanga o te Kaha Hiko i Hua
Hei mārama ake i tēnei ariā, me titiro tātou ki tētahi tauira māmā kei reira ngā utu e toru \( q_1 \), \( q_2 \), me \( q_3 \) kei ngā tūranga pumau i roto i te papa.
Hei tauira:
– \( q_1 = +2 \ \mu C \)
– \( q_2 = +3 \ \mu C \)
– \( q_3 = -1 \ \mu C \)
ā, ko te tawhiti i waenganui i a \( q_1 \) me \( q_2 \) he 4 cm, ko te tawhiti i waenganui i a \( q_2 \) me \( q_3 \) he 3 cm, ā, ko te tawhiti i waenganui i a \( q_1 \) me \( q_3 \) he 5 cm. E hiahia ana mātou ki te tatau i te kaha hua i runga i a \( q_1 \).
1. Te kaha i waenganui i a \( q_1 \) me \( q_2 \) (\( F_{12} \)):
\[ F_{12} = k_e \frac{|q_1 \cdot q_2|}{r_{12}^2} \]
\[ F_{12} = 8.99 \times 10^9 \frac{|2 \times 10^{-6} \cdot 3 \times 10^{-6}|}{(0.04)^2} \]
\[ F_{12} = 8.99 \times 10^9 \frac{6 \times 10^{-12}}{0.0016} \]
\[ F_{12} = 3.37 \times 10^{-2} \, \text{N} \]
He kaha whakakino tēnei (e anga atu ana i \( q_2 \)).
2. Te kaha i waenganui i a \( q_1 \) me \( q_3 \) (\( F_{13} \)):
\[ F_{13} = k_e \frac{|q_1 \cdot q_3|}{r_{13}^2} \]
\[ F_{13} = 8.99 \times 10^9 \frac{|2 \times 10^{-6} \cdot (-1) \times 10^{-6}|}{(0.05)^2} \]
\[ F_{13} = 8.99 \times 10^9 \frac{2 \times 10^{-12}}{0.0025} \]
\[ F_{13} = 7.19 \times 10^{-3} \, \text{N} \]
He kaha kukume tēnei (te ahunga e whakatata atu ana \( q_3 \)).
3. Hua o te Āhua Whakakaha:
Hei whiwhi i te kaha hua i runga i te \( q_1 \), me tāpirihia ngā whārite \( \vec{F}_{12} \) me te \( \vec{F}_{13} \). Me kī kei runga i te tuaka-x pai a \( \vec{F}_{12} \) ā, kei roto a \( F_{13} \) i tētahi ahunga matapōkere i te papa. Hei whakangawari, me kī ina tirohia i roto i ngā taunga Cartesian, kei runga a \( q_2 \) i te tuaka-x pai mai i \( q_1 \) ā, kei tētahi ahunga a \( q_3 \) i tētahi koki mai i \( q_1 \). Ka whai wāhanga \( \vec{F}_{12} \) me \( \vec{F}_{13} \) mō ia ahunga.
Heoi, hei māmā ake, ka nui ake tā tātou aro ki te rahi o ēnei kaha mēnā he hara māmā te koki.
Te Tāpiri Hangarau i ngā Wekita:
Ki te whakaurua ngā koki, me tatau e tātou \( \vec{F}_{13} \cdot \sin(\theta) \) me \( \vec{F}_{13} \cdot \cos(\theta) \), ko \( \theta \) te koki i waenganui i \( q_1 \) me \( q_3 \) e pā ana ki \( q_1 \) me \( q_2 \).
I muri i te mahi i ngā tātaitanga tika hei kimi i te hua, ka whiwhi tātou i te kaha hua \( \vec{F}_{\text{total}} \).
Koinei te huarahi ki te whiwhi i te kaha hiko e puta mai ana mā te whakamahi i te kaupapa o te taupatupatu. Ka taea tēnei te whakamahi ki ngā kaha neke atu i te rua, ki ngā āhua neke atu rānei i te rua mā te whakamahi i tētahi tikanga ōrite engari he uaua ake pea, i runga i te whirihoranga.
Te Whakamahinga o te Kaha Hiko Hua
He maha ngā whakamahinga o te kaha hiko e puta mai ana i roto i te pūtaiao me te hangarau. Ko ētahi o ēnei ko:
1. Hoahoa Hiko:
He mea nui te mārama ki te tohatoha o ngā kaha hiko i roto i te hoahoa i ngā ara iahiko hiko me ngā ara iahiko moroiti, e pā ana ki te horapa o ngā mara hiko puta noa i ngā wāhanga tino iti.
2. Te Rongoā me te Hangarau Koiora:
Kei roto i te whakaora ko te whakamahi i ngā mara hiko hei whakaoho i ngā pūtau, mā te whakaora hiko rānei.
3. Kaiwhakahaere Matūriki Utu Hiko:
He mea nui anō hoki i roto i te ahupūngao matūriki te whakahaere me te raweke i ngā matūriki kua utua i roto i ngā whakateretere, i ngā tātaritanga whānuitanga rānei.
4. Hoahoa Pūnga:
Whakapaipai i te hoahoa pūnga hiko mā te tatau tika i te papa hiko me ngā kaha ka puta mai i runga i ngā pereti.
Whakamutunga
Ko te kaha hiko e puta mai ana he ariā matua i roto i te ahupūngao e āhei ai tātou ki te mārama me te matapae i ngā taunekeneke i waenga i ngā utu. Mā te whakamahi i te ture a Coulomb me te mātāpono o te taupatupatu, ka taea e tātou te whakatau i te kaha katoa e pāngia ana e te utu i roto i tētahi mara hiko matatini. Ehara i te mea he mea nui tēnei ariā i roto i te ariā anake engari he tono mahi anō hoki i roto i te whānuitanga o ngā mara. Mā te mārama ki te kaha hiko e puta mai ana ka āwhina i a tātou ki te maioha ki ngā whanaketanga uaua o te ao moroiti e whai pānga tonu ana ki te hangarau me ngā kitenga hou.
