Tātai Pakihi
I roto i te ahupūngao, he kaupapa matua te ariā o te mahi, e whakaahua ana i te whakawhiti pūngao e puta ana ina nekehia ana tētahi mea e te kaha. He mea nui te mahi i roto i ngā āhuatanga taiao me ngā tono hangarau. Ka whakamāramahia e tēnei tuhinga te tauira mō te mahi, ngā tauira, ōna tono i roto i te oranga o ia rā, me tōna whanaungatanga ki te pūngao.
Te Whakamāramatanga o te Pakihi
Ko te mahi he rahinga tauine e puta ana ina nekehia tētahi mea e te kaha e pā ana ki te mea. Ka mahia te mahi e te kaha e puta ai he nekehanga whakarara ki te ahunga o te kaha. I roto i ngā waeine SI, ka inehia te mahi i roto i ngā joule (J), arā, ko te 1 joule he ōrite ki te 1 mita newton (N·m).
Ko te tātai taketake mō te tatau i te mahi (\(W \)) ko:
\[ W = F \cdot d \cdot \cos(\theta) \]
kāore i te mana:
– Ko te mahi te \( W \),
– Ko te rahi o te kaha e pā ana ki te mea ko \( F \),
– Ko te nekehanga o te mea ko te \( d \),
– Ko te \( \theta \) te koki i waenganui i te ahunga o te kaha me te ahunga o te nekehanga.
Te Kaha Tonu
Mō te kaha pumau e mahi whakarara ana ki te ahunga o te nekehanga (\( \theta = 0 \) kia \( \cos(0) = 1 \)), ka whakangawaritia te tātai mahi kia:
\[ W = F \cdot d \]
Hei tauira, ki te panaia tētahi pouaka me te kaha pumau o te 10 newtons mō te 5 mita, ko te mahi i mahia koia tēnei:
\[ W = 10 \, \text{N} \times 5 \, \text{m} = 50 \, \text{J} \]
Nō reira, ko te mahi i mahia he 50 joules.
Pakihi e Hurihuri Ana i te Kāhua
Mena ka rerekē te kaha e pā ana ki tētahi mea i te ara o te nekehanga, ka tatauhia te mahi mā te whakamahi i te tauwehenga:
\[ W = \int_{x_1}^{x_2} F(x) \, dx \]
Ka tāpirihia e tēnei taupū te mahi i mahia e ngā kaha rerekē i ia pūwāhi nekehanga mai i \( x_1 \) ki \( x_2 \).
Tauira o te Tātaitanga o te Mahi me te Kaha Hurihuri
Mehemea ka rerekē te kaha e pā ana ki tētahi mea me te \( F(x) = 2x \) ā, ka neke te mea mai i te \( x = 0 \) ki te \( x = 3 \) mita. Ka taea te tatau i te mahi i mahia penei:
\[ W = \int_{0}^{3} 2x \, dx \]
\[ W = 2 \int_{0}^{3} x \, dx \]
\[ W = 2 \left[ \frac{x^2}{2} \right]_{0}^{3} \]
\[ W = \left[ x^2 \right]_{0}^{3} \]
\[ W = 3^2 – 0^2 \]
\[ W = 9 \, \kuputuhi{J} \]
Nō reira, ko te mahi i mahia he 9 joules.
Ngā Mahi Kino
Ka taea te kī he kino te mahi mēnā he rerekē te ahunga o te nekehanga o te kaha. Hei tauira, mēnā ka pēhia e tātou he motuka e neke ana, ka mahi kino te kaha waku i waenga i ngā potae me te rori nā te mea he rerekē te ahunga o te nekehanga o te motuka i te kaha waku.
Te Kaha me te Pūngao
He hononga tata te mahi ki te pūngao. E kī ana te mātāpono mahi-pūngao ko te mahi i mahia e ngā kaha katoa e pā ana ki tētahi mea he rite ki te huringa o te pūngao nekeneke o te mea. Mā te pāngarau:
\[ W = \Delta KE \]
\[ W = \frac{1}{2} m v_f^2 – \frac{1}{2} m v_i^2 \]
kāore i te mana:
– Ko te huringa o te pūngao nekeneke ko \( \Delta KE \)
– Ko te papatipu o te mea ko \( m \),
– Ko te tere whakamutunga o te mea ko \( v_f \),
– Ko te tere tīmatanga o te mea ko \( v_i \).
Tauira o te Tātaitanga o te Mahi me te Pūngao Kinetic
Mehemea kei te neke tuatahi tētahi waka he 1000 kg te taumaha i te tere o te 10 m/s. I muri i te pānga o te kaha aukati, ka tū te waka (tere whakamutunga = 0 m/s). Ko te mahi i mahia e te kaha aukati ko:
\[ \Delta KE = \frac{1}{2} m v_f^2 – \frac{1}{2} m v_i^2 \]
\[ \Delta KE = \frac{1}{2} \times 1000 \, \text{kg} \times (0 \, \text{m/s})^2 – \frac{1}{2} \times 1000 \, \text{kg} \times (10 \, \text{m/s})^2 \]
\[ \Delta KE = 0 – 5000 \, \text{J} \]
\[ \Delta KE = -5000 \, \text{J} \]
Nō reira, ko te mahi i mahia e te kaha aukati he -5000 joule, e tohu ana kua whakaitihia te pūngao nekeneke o te motuka mā te 5000 joule.
Te Mahi me te Pūngao Pūmanawa
Ka taea hoki e te mahi te whakaputa i ngā huringa o te pūngao pūmanawa, inā koa i roto i ngā āpure kaha pūmau pērā i ngā āpure kaha, ngā āpure hiko rānei. I roto i te āpure kaha, ko te mahi e mahia ana hei hiki i tētahi mea i te teitei \( h \) ki te kaha o te kaha:
\[ W = mgh \]
kāore i te mana:
– Ko te papatipu o te mea ko \( m \),
– Ko te \( g \) te whakaterenga nā te kaha ā-papa (9,8 m/s² i runga i te mata o te Ao),
– Ko te teitei o te mea ko \( h \).
Tauira o te Tātaitanga o te Mahi i roto i te Papa Ā-Toi
Mehemea ka hikitia tētahi mea he 5 kg te taumaha ki te teitei o te 2 mita. Ko te mahi i mahia hei hiki i te mea koia tēnei:
\[ W = mgh \]
\[ W = 5 \, \kuputuhi{kg} \times 9,8 \, \kuputuhi{m/s}^2 \times 2 \, \kuputuhi{m} \]
\[ W = 98 \, \kuputuhi{J} \]
Nō reira, ko te mahi i mahia hei hapai i te mea he 98 joule.
Ngā Taupānga Pakihi i roto i te Oranga o Ia Rā
1. Te Kawe: Ka mahia te mahi e te miihini o te waka hei neke i te waka mai i tētahi wāhi ki tētahi wāhi. Mā te mārama ki te mahi me te pūngao ka āwhina i te hoahoa i ngā miihini whai hua.
2. Ngā Hākinakina: Ka whakapau kaha ngā kaitākaro i te whiunga pōro, i te pekepeke, i te oma rānei. Ka whakamahia e ngā kaiako te ariā o te whakapau kaha hei whakapai ake i te mahi a te kaitākaro.
3. Hanganga: Ka whakamahia e ngā miihini te ariā o te whakapau kaha ki te hoahoa i ngā pūnaha hiki me ngā taputapu taumaha e whakamahia ana i roto i te hanganga o ngā whare me ngā hanganga.
4. Pūngao Whakahou: I roto i ngā hangarau pūngao whakahou, pērā i ngā tāpoi hau me ngā panera rā, ka whakamahia ngā ariā o te mahi me te pūngao hei huri i te pūngao taiao hei pūngao hiko.
Whakamutunga
He ariā taketake te mahi i roto i te ahupūngao e whakaahua ana i te whakawhiti pūngao mā roto i tētahi kaha e puta ai te nekehanga. Mā te whakamahi i te tātai taketake \( W = F \cdot d \cdot \cos(\theta) \), ka taea e tātou te tatau i te mahi i mahia e tētahi kaha pumau, e tētahi kaha hurihuri rānei. He hononga tata te mahi ki te pūngao nekeneke me te pūngao pūmanawa, ā, he maha ngā whakamahinga nui i roto i te oranga o ia rā me te hangarau. Mā te mārama pai ki te mahi ka taea e tātou te hoahoa i ngā pūnaha whai hua me te mārama ki ngā āhuatanga ā-tinana rerekē e puta ana i tō tātou taha.
