Me pēhea te tatau i te pūngao pūmanawa
Ko te pūngao pūmanawa (PE) tētahi o ngā ariā matua o te ahupūngao. E whakaahua ana i te pūngao kei roto i tētahi mea nā tōna tūranga, tōna hanganga, tōna āhua rānei. He maha ngā momo pūngao pūmanawa tae atu ki te pūngao pūmanawa ā-papa, te pūngao pūmanawa ngāwari, me te pūngao pūmanawa matū. He mea nui te mārama ki te tatau i te pūngao pūmanawa hei whakaoti rapanga maha i roto i te ahupūngao, te hangarau, tae noa ki te oranga o ia rā. Ka rukuhia e tēnei tuhinga ngā momo pūngao pūmanawa rerekē, ā, ka whakaaturia ngā tikanga e whakamahia ana hei tatau i ia mea.
### 1. Pūngao Pūmanawa Ā-Toi
E pā ana te pūngao pūmanawa ā-papa ki te teitei o tētahi mea i runga ake i te taumata tohutoro, arā, ko te whenua. Koinei te pūngao kei roto i tētahi mea nā tōna tūranga i roto i te papa ā-papa. Ko te tātai hei tatau i te pūngao pūmanawa ā-papa ko:
\[ PE_g = mgh \]
Kei hea:
– Ko te pūngao pūmanawa ā-papatipu \( PE_g \).
– Ko te papatipu o te mea ko \( m \).
– Ko te whakaterenga nā te kaha ā-papatipu (tata ki te 9.8 m/s^2 i runga i te Ao).
– Ko te teitei o runga ake i te pūwāhi tohutoro ko \( h \).
#### Tauira:
Whakaarohia he pukapuka he 2 kg te taumaha e whakatakotoria ana ki runga i tētahi whata he 3 mita te teitei. Ka tatauhia te pūngao pūmanawa ā-papa penei:
\[ PE_g = mgh \]
PE_g = (2 \, \text{kg})(9.8 \, \text{m/s}^2)(3 \, \text{m}) \]
\[ PE_g = 58.8 \, \text{J} \]
Nō reira, ko te pūngao pūmanawa ā-papa kei roto i te pukapuka he 58.8 joule.
### 2. Pūngao Pūmanawa Ātaahua
Kei roto i ngā mea ka taea te totoro, te pēhi rānei te pūngao pūmanawa ngāwari, pērā i ngā puna, i ngā here rapa rānei, te pūngao pūmanawa. E whakamahia whānuitia ana te Ture a Hooke hei whakaahua i te kaha i roto i aua rauemi ngāwari. Ko te tātai hei tatau i te pūngao pūmanawa ngāwari, mō te puna, ko:
\[ PE_{rauropi} = \frac{1}{2}kx^2 \]
Kei hea:
– Ko te pūngao pūmanawa pūngao te \( PE_{elastic} \).
– Ko te pūmau puna ko te \( k \) (he ine i te pakari o te puna).
– Ko te \( x \) te nekehanga, te huringa rānei o te roa mai i te tūranga taurite.
#### Tauira:
Whakaarohia he puna me te pūmau puna o \( 200 \, \text{N/m} \) kua pēhia e te 0.1 mita. Ka tatauhia te pūngao pūmanawa rapa penei:
\[ PE_{rauropi} = \frac{1}{2}kx^2 \]
\[ PE_{rauropi} = \frac{1}{2}(200 \, \text{N/m})(0.1 \, \text{m})^2 \]
\[ PE_{rauropi} = 1 \, \text{J} \]
Nō reira, ka rongoa e te puna kōpeke te 1 joule o te pūngao pūmanawa rapa.
### 3. Pūngao Pūmanawa Matū
Ko te pūngao pūmanawa matū ko te pūngao e rongoatia ana i roto i ngā hononga o ngā matū matū. Ka taea te tuku, te mimiti rānei i tēnei pūngao i roto i ngā tauhohenga matū. Ahakoa he uaua te tatau tika i te pūngao pūmanawa matū, ā, he maha ngā wā e hiahiatia ana he mātauranga matū matatau, ka taea te matapae i ngā huringa o te pūngao pūmanawa matū mā te whakaaro ki ngā matū tauhohenga me ngā hua o tētahi tauhohenga.
#### Tauira:
I roto i te tahunga o te penehīni, ka hurihia te pūngao pūmanawa matū ki ētahi atu momo pūngao pērā i te wera me te pūngao nekeneke. Ka taea te whakatau tata i te nui o te pūngao o te penehīni mā te uara karori, tata ki te \( 44 \, \text{MJ/kg} \). Hei tatau i te pūngao pūmanawa i roto i tētahi taumaha penehīni kua hoatu:
\[ PE_{matū} = \kuputuhi{papatipu} \whakareatia \kuputuhi{uara karori} \]
Mō te 1 kg o te penehīni:
\[ PE_{matū} = 1 \, \text{kg} \times 44 \, \text{MJ/kg} \]
\[ PE_{matū} = 44 \, \kuputuhi{MJ} \]
Nō reira, kei roto i te 1 kirokaramu o te penehīni tata ki te 44 megajoules o te pūngao pūmanawa matū.
### 4. Pūngao Pūmanawa Hiko
Kei te tūnga o ngā utu i roto i te papa hiko te pūngao pūmanawa hiko. Hei tauira, i roto i tētahi pūnaha e rua ngā utu pūwāhi, ka taea te tatau i te pūngao pūmanawa hiko mā te whakamahi i te Ture a Coulomb:
\[ PE_{hiko} = k_e \frac{q_1 q_2}{r} \]
Kei hea:
– Ko te pūngao pūmanawa hiko te \( PE_{electric} \).
– Ko te pūmau a Coulomb te \( k_e \) (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)).
– Ko \( q_1 \) me \( q_2 \) ngā utu tohu.
– Ko te \( r \) te tawhiti i waenganui i ngā utu.
#### Tauira:
Whakaarohia kia rua ngā utu, \( q_1 = 1 \, \mu\text{C} \) (microcoulomb) me \( q_2 = 2 \, \mu\text{C} \), e 0.05 mita te tawhiti. Ko te pūngao pūmanawa hiko ko:
\[ PE_{hiko} = k_e \frac{q_1 q_2}{r} \]
\[ PE_{hiko} = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \frac{(1 \times 10^{-6} \, \text{C})(2 \times 10^{-6} \, \text{C})}{0.05 \, \text{m}} \]
\[ PE_{hiko} = 0.3596 \, \kuputuhi{J} \]
Nō reira, ko te pūngao pūmanawa hiko o tēnei pūnaha he tata ki te 0.3596 joule.
### Whakamutunga
He ariā nui te pūngao pūmanawa i roto i ngā momo mara o te pūtaiao me te hangarau. Ko ngā pūngao pūmanawa ā-papa, ā-pūngao rapa, ā-matū, ā-hiko, me ā-hiko he torutoru noa iho o ngā momo e whakaatu ana i te āhua o te penapena me te whakaputa ke i te pūngao. Ko te tatau i te pūngao pūmanawa ko te mārama me te whakamahi i ngā tātai motuhake e pā ana ki ia momo pūngao pūmanawa. Mā te matatau ki ēnei tatau ka kitea he māramatanga hohonu ake ki ngā mahi hangarau o te ao tūroa, ā, ka whakarei ake i te kaha o te tangata ki te whakaoti rapanga pūtaiao rerekē. Nō reira, he mea tino nui te hopu i ngā mātāpono o te pūngao pūmanawa me ōna tataunga mō ngā ākonga, ngā tohunga ngaio, me te hunga katoa e hiahia ana ki ngā mea whakamiharo o te ahupūngao.
