Ngā Raru Whakaoti i roto i te Ahupūngao Taketake

1. Ka pāngia tētahi pito o tētahi kurupae he 2 m te roa e te kaha P. He aha te rahi o te taipana ? Ko te tuaka hurihuri i te pūwāhi A.

Mōhiotia:

Te kaha (F) = 10 N

Te roa o AB (r _AB ) = 2 m

He poutū te kaha F ki te kurupae.

Ko te ringa rīwhi (l ) = r _AB sin 90 ^o = (2 m)(1) = 2 m

E hiahiatia ana: Te taipana huri noa i te tuaka hurihuri

Rongoā:

Te taipana:

τ = F l = (10 N)(2 m) = 20 N m

Ko te tohu tāpiri nā te mea ka huri te hihi i te taha maui.

[irp]

2. Ko te roa o te kurupae AB ​​he 2 m, ā, ko te kaha F he 10 N. He aha te kaha o te taipana? Ko te tuaka hurihuri i te pūwāhi A.

Mōhiotia:

Te kaha (F) = 10 N

Te roa o AB (r _AB ) = 2 m

Ko te ringa rīwhi (l ) = r _AB sin 60 ^o = (2 m)(0.5 √3 ) = √3 m

E hiahiatia ana: Te taipana huri noa i te tuaka hurihuri

Rongoā:

Te taipana:

τ = F l = (10 N)( √3 m) = 10 √3 N m

Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F kia huri i te taha maui.

[irp]

3. Ko te roa o te kurupae he 2 m. Ko te rahi o F1 _he 10 N, ā, ko te rahi o F2 _he 15 N. Tātaihia te taipana kupenga i waenganui o te kurupae.

Te tuaka hurihuri i waenganui o te kurupae.

Mōhiotia:

Kaha 1 (F ₁ ) = 10 N

Ko te tawhiti i waenganui i a F ₁ me te pokapū o te kurupae (r ₁ ) = 1 m

Ko te ringa rīwhi 1 (l ₁ ) = r ₁ sin 90 ^o = (1 m)(1) = 1 m

He poutū te kaha F ₁ ki te kurupae.

Kaha 2 (F ₂ ) = 15 N

Ko te tawhiti i waenganui i a F ₂ me te pokapū o te kurupae (r ₂ ) = 1 m

He poutū te kaha F ₂ ki te kurupae.

Ko te ringa rīwhi 2 (l ₂ ) = r ₁ sin 90 ^o = (1 m)(1) = 1 m

E hiahiatia ana: Te taipana kupenga huri noa i te tuaka hurihuri

Rongoā:

Te taipana 1:

τ ₁ = F ₁ l ₁ = (10 N)( 1 m) = 10 N m

Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha o F ₁ kia huri ki te taha maui.

Te taipana 2:

τ ₂ = F ₂ l ₂ = (15 N)( 1 m) = -15 N

Ko te tohu tango nā te mea ka meinga te hihi e te kaha F _{2 kia} huri ki te taha matau.

Te taipana kupenga:

Σ τ = τ ₁ – τ ₂ = 10 – 15 = – 5 N m

Ko te tohu tango nā te mea ka huri te hihi ki te taha matau.

[irp]

4. Ko te roa o te kurupae AB ​​he 2 m, ko te rahi o F1 _he 10 N, ā, ko te rahi o F2 _he 10 N. Tātaihia te taipana kupenga i waenganui o te kurupae.

Te tuaka hurihuri i waenganui o te kurupae.

Mōhiotia:

Kaha 1 (F ₁ ) = 10 Nn

Ko te tawhiti i waenganui i a F ₁ me te pokapū o te kurupae (r ₁ ) = 1 m

Ko te ringa rīwhi 1 (l ₁ ) = r ₁ sin 60 ^o = (1 m)(0.5 √3 ) = 0.5 √3 m

Kaha 2 (F ₂ ) = 10 N

Ko te tawhiti i waenganui i a F ₂ me te pokapū o te kurupae (r ₂ ) = 1 m

He poutū te kaha F ₂ ki te kurupae.

Ko te ringa rīwhi 2 (l ₂ ) = r ₂ sin 90 ^o = (1 m)(1) = 1 m

E hiahiatia ana: Te taipana kupenga huri noa i te tuaka hurihuri

Rongoā:

Te taipana 1:

τ ₁ = F ₁ l ₁ = (10 N)( 0.5 √3 m) = 5 √3 = 8.7 Nm

Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F _{1 kia} huri ki te taha matau.

Te taipana 2:

τ ₂ = F ₂ l ₂ = (10 N)( 1 m) = -10 N m

Ko te tohu tango nā te mea ka meinga te hihi e te kaha F _{2 kia} huri ki te taha matau.

Te taipana kupenga:

Σ τ = τ ₁ – τ ₂ = 8.7 – 10 = – 1.3 N m

Ko te tohu tango nā te mea ka meinga te hihi kia huri ki te taha matau e te kaha kupenga.

[irp]

5. Ko te roa o te kurupae he 10 m, ko te rahi o F1 _he 10 N, ko te rahi o F2 _he 10 N, ā, ko te rahi o F3 _he 15 N. Ko te tawhiti i waenganui i te pūwāhi A me te pūwāhi C he 7.5 m. Kei waenganui o te kurupae te Kaha F2. Tātaihia te taipana kupenga e pā ana ki te pūwāhi C kei te 2.5 m mai i te pūwāhi _B.

Kei te pūwāhi C te tuaka hurihuri

Mōhiotia:

Kaha 1 (F ₁ ) = 10 N

Ko te tawhiti i waenganui i a F ₁ me te pūwāhi C (r ₁ ) = 2.5 m

He poutū te kaha F ₁ ki te kurupae.

Ko te ringa rīwhi 1 (l ₁ ) = r ₁ sin 90 ^o = ( 2.5 m)( 1 ) = 2.5 m

Kaha 2 (F ₂ ) = 10 N

Ko te tawhiti i waenganui i a F ₂ me te pūwāhi C (r ₂ ) = 2.5 m

He poutū te kaha F ₂ ki te kurupae.

Ko te ringa rīwhi 2 (l ₂ ) = r ₂ sin 90 ^o = ( 2.5 m)(1) = 2.5 m

Kaha 3 (F ₃ ) = 15 N

Ko te tawhiti i waenganui i a F ₃ me te pūwāhi C (r ₃ ) = 7.5 m

He poutū te kaha F ₃ ki te kurupae.

Ko te ringa rīwhi 3 (l ₃ ) = r ₃ sin 90 ^o = (7.5 m)(1) = 7.5 m

E hiahiatia ana: Te taipana kupenga huri noa i te tuaka hurihuri

Rongoā:

Te taipana 1:

τ ₁ = F ₁ l ₁ = (10 N)( 2.5 m) = 25 N m

Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F _{1 kia} huri ki te taha matau.

Te taipana 2:

τ ₂ = F ₂ l ₂ = (10 N)( 2.5 m) = 25 N m

Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F _{2 kia} huri ki te taha matau.

Te taipana 3:

τ ₃ = F ₃ l ₃ = (15 N)( 7.5 m) = -112..5 N m

Ko te tohu tango nā te mea ka meinga te hihi e te kaha F _{3 kia} huri ki te taha matau.

Te taipana kupenga:

Σ τ = τ ₁ + τ ₂ – τ ₃ = 25 + 25 – 112.5 = – 62.5 N m

Ko te tohu tango nā te mea ka meinga te hihi kia huri ki te taha matau e te kaha kupenga.

[irp]

6. Ko te roa o te kurupae he 10 m, ko te rahi o F₁ ko te 10 N, ko te rahi o F₂ he 10 N, ā, ko te rahi o F₃ ko te 10 N. Tātaihia te taipana kupenga mō te pūwāhi A, kei te 5 m mai i te poute whakamahinga o te kaha F₁.

Te tuaka hurihuri i te pūwāhi A.

Mōhiotia:

Kaha 1 (F ₁ ) = 10 N

Ko te tawhiti i waenganui i a F ₁ me te pūwāhi A (r ₁ ) = 5 m

Ko te ringa rīwhi 1 (l ₁ ) = r ₁ sin 60 ^o = (5 m)(0.5 √3 ) = 2.5 √3 m

Kaha 2 (F ₂ ) = 10 N

Ko te tawhiti i waenganui i a F ₂ me te pūwāhi A (r ₂ ) = 0

He poutū te kaha F ₂ ki te kurupae.

Ko te ringa rīwhi 2 (l ₂ ) = r ₂ sin 90 ^o = (0)(1) = 0

Ko te kaha 3 (F ₃ ) = 10 N

Ko te tawhiti i waenganui i a F ₃ me te pūwāhi A (r ₃ ) = 10 m

Ko te ringa rīwhi 3 (l ₃ ) = r ₃ sin 30 ^o = (10 m)(0.5) = 5 m

E hiahiatia ana: te taipana kupenga huri noa i te tuaka hurihuri

Rongoā:

Te taipana 1:

τ ₁ = F ₁ l ₁ = (10 N)( 2.5 √3 m ) = 25√3 = 43.3 N m

Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F _{1 kia} huri ki te taha matau.

Te taipana 2:

τ ₂ = F ₂ l ₂ = (10 N)(0) = 0

Te taipana 3:

τ ₃ = F ₃ l ₃ = (10 N)( 5 m) = -50 N m

Ko te tohu tango nā te mea ka meinga te hihi e te kaha F _{3 kia} huri ki te taha matau.

Te taipana kupenga:

Σ τ = τ ₁ + τ ₂ – τ ₃ = 43.3 + 0 – 50 = – 6.7 N m

Ko te tohu tango nā te mea ka meinga te hihi kia huri ki te taha matau e te kaha kupenga.

Pānuitia atu

1. He mea A, he 500 karamu te taumaha , e neke ana i te 10 m/s me te mea B, he 200 karamu te taumaha, e neke ana i te 12 m/s. Ka whakatata ngā mea tetahi ki tetahi, ka tukinga. Mena ko te tere o te mea A i muri i te tukinga he 6 m/s, he aha te tere o te mea B i muri i te tukinga?

Mōhiotia:

Taumaha o te mea 1 (m1 ₎ = 500 karamu = 0.5 kg

Taumaha o te mea 2 (m² ₎ = 200 karamu = 0.2 kg

Te tere tīmatanga o te mea 1 (v ₁ ) = -10 m/s

Te tere tīmatanga o te mea 2 (v ₂ ) = 12 m/s

Ko te tere whakamutunga o te mea 1 (v ₁ ') = 6 m/s

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te ahunga whakamuri.

E hiahiatia ana : te tere whakamutunga o te mea 2 (v ₂ ')

Rongoā:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(0.5)(-10) + (0.2)(12) = (0.5)(6) + (0.2)(v ₂ ')

-5 + 2.4 = 3 + 0.2 v ₂ '

-2.6 = 3 + 0.2 v ₂ '

-2.6 – 3 = 0.2 v ₂ '

-5.6 = 0.2 v ₂ '

v2 _' = -5.6 / 0.2

v ₂ ' = -28 m/s

Ko te tere o te mea 2 i muri i te tukinga he 28 m/s.

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te taha ke.

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2. E rua ngā mea ōrite te taumaha e whakatata ana tetahi ki tetahi, ā, ka tukinga. Ko te tere o te mea 1 he 6 m/s, ā, ko te tere o te mea 2 he 8 m/s. I muri i te tukinga, ka neke te mea 2 ki maui me te tere o te 5 m/s. He aha te rahi me te ahunga o te tere o te mea 1 i muri i te tukinga?

Mōhio:

Papatipu o te mea 1 ( _m1 ) = m

Papatipu o te mea 2 (m2 ₎ = m

Te tere tīmatanga o te mea 1 (v ₁ ) = -6 m/s

te tere tīmatanga o te mea 2 (v ₂ ) = 8 m/s

Ko te tere whakamutunga o te mea 2 (v ₂ ') = -5 m/s

E hiahiatia ana : te rahi me te ahunga o te mea 1 i muri i te tukinga

Rongoā:

Te tātai mō te tiaki i te nekehanga raina :

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

mv ₁ + m v ₂ = m v ₁ ' + m v ₂ '

m (v ₁ + v ₂ ) = m (v ₁ ' + v ₂ ')

v1 + _v2 = _{v1 '} + _v2 '

-6 + 8 = v ₁ ' – 5

2 = v ₁ ' – 5

2 + 5 = v ₁ '

v ₁ ' = 7 m/s

Ko te tere o te mea 1 i muri i te tukinga (v ₁ ') he 3 m/s.

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te taha ke.

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3. He rite te ahunga o te pōro 1-kg me te pōro 2-kg, ā, he rite tonu te tukinga. I mua i te tukinga, ka neke te pōro 1 me te tere o te 10 m/s, ā, ka neke te pōro 2 me te tere o te 5 m/s. Ko te tere o te pōro 2 i muri i te tukinga he 4 m/s. Tātaihia te tere o te pōro 1 i muri i te tukinga.

Mōhiotia:

Papatipu pōro 1 (m1 ₎ = 1 kg

Papatipu pōro 2 (m2 ₎ = 2 kg

Ko te tere o te pōro 1 (v ₁ ) = 10 m/s

Ko te tere o te pōro 2 (v ₂ ) = 5 m/s

Ko te tere whakamutunga o te pōro 2 (v ₂ ') = 4 m/s

Ko te tohu tāpiri o te tere e tohu ana he ōrite te ahunga o ngā pōro.

E hiahiatia ana : te tere whakamutunga o te pōro 1 (v ₁ ')

Rongoā:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(1)(10) + (2)(5) = (1)(v ₁ ') + (2)(4)

10 + 10 = v ₁ ' + 8

20 – 8 = v ₁ '

v ₁ ' = 12 m/s

Ko te tere o te pōro 1 i muri i te tukinga he 12 m/s.

[wpdm_package id='1190′]

1. Ngā raruraru me ngā otinga o te nekehanga rārangi
2. Ngā raruraru me ngā otinga o te nekehanga me te hihiri
3. Ngā raruraru me ngā otinga o ngā tukinga tino ngāwari i roto i te taha kotahi
4. Ngā raruraru me ngā otinga o ngā tukinga kore-whakapūmau tino tika i roto i te taha kotahi
5. Ngā raruraru me ngā otinga mō ngā tukinga kore-whakapūmau i roto i te taha kotahi

Pānuitia atu

1. Ka tukinga tētahi matā 30-karamu e neke ana i te 30 m/s ki tētahi poraka 1-kg e tū ana. Tātaihia te tere o te poraka mēnā ka mau te matā me te poraka hei hua o te tukinga.

Mōhiotia:

Taumaha o te matā (m1 ₎ = 30 karamu = 0.03 kg

Taumaha o te poraka (m² ₎ = 1 kg

Te tere tīmatanga o te matā ( v ₁ ) = 30 m/s

tere tīmatanga o te poraka (v ₂ ) = 0 ( poraka e okioki ana )

E hiahiatia ana : te tere o te matā me te poraka i muri i te tukinga (v')

Rongoā:

m ₁ v ₁ + m ₂ v ₂ = (m ₁ + m ₂ ) v'

(0.03)(30) + (1)(0) = (0.03 + 1) v'

0.9 + 0 = 1.03 v'

0.9 = 1,03 v'

v' = 0.9 / 1,03

v' = 0.87 m/s

[irp]

2. Ka tukinga te pōro piriata A, he 2 kg te taumaha, e neke ana me te tere v _A = 6 ms ^−1, ki te pōro B he ōrite te taumaha. Mēnā he tino kore-whakapūmau te tukinga, he aha ngā tere o ngā pōro e rua i muri i te tukinga.

Mōhiotia:

Taumaha A (m _A ) = 2 kg

Taumaha B (m _B ) = 2 kg

Te tere tīmatanga o te pōro A (v _A ) = -6 m/s

Te tere tīmatanga o te pōro B (v _B ) = 4 m/s

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te ahunga whakamuri.

E hiahiatia ana : te tere o ngā pōro e rua i muri i te tukinga. (v')

Rongoā:

m _A v _A + m _B v _B = (m _A ' + m _B ) v'

(2)(-6) + (2)(4) = (2 + 2) v'

-12 + 8 = 4 v'

-4 = 4 v'

v' = -4 / 4

v' = -1 m/s

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3. m₁ = 3 kirokaramu a m₂ = 4 kirokaramu whakatata tetahi ki tetahi i te taha rerekē me te tere o v₁ = 10m/s a v₂ = 12 m/s. Mena he tino kore-whakapūmau te tukinga, he aha ngā tere o ngā pōro e rua i muri i te tukinga.

Mōhiotia:

Taumaha o te mea 1 (m² ₎ = 3 kg

Taumaha o te mea 2 (m² ₎ = 4 kg

Ko te tere o te mea 1 (v ₁ ) = -10 m/s

Ko te tere o te mea 2 (v ₂ ) = 12 m/s

E hiahiatia ana : te tere i muri i te tukinga (v')

Rongoā:

m ₁ v ₁ + m ₂ v ₂ = (m ₁ ' + m ₂ ) v'

(3)(-10) + (4)(12) = (3 + 4) v'

-30 + 48 = 7 v'

18 = 7 v'

v' = 18 / 7

v' = 2.6 m/s

[wpdm_package id='1157′]

1. Ngā raruraru me ngā otinga o te nekehanga rārangi
2. Ngā raruraru me ngā otinga o te nekehanga me te hihiri
3. Ngā raruraru me ngā otinga o ngā tukinga tino ngāwari i roto i te taha kotahi
4. Ngā raruraru me ngā otinga o ngā tukinga kore-whakapūmau tino tika i roto i te taha kotahi
5. Ngā raruraru me ngā otinga mō ngā tukinga kore-whakapūmau i roto i te taha kotahi

Pānuitia atu

1. He pōro A, 200-karamu te taumaha, e neke ana i te tere o te 10 m/s, e pā ana ki tētahi pōro B, 200-karamu te taumaha, e takoto kau ana. He aha te tere o te pōro A me te pōro B i muri i te tukinga?

Mōhiotia:

Taumaha o te pōro A (m _A ) = 200 karamu = 0.2 kg

Taumaha o te pōro B (m _B ) = 200 karamu = 0.2 kg

Te tere o te pōro A i mua i te tukinga (v _A ) = 10 m/s

Te tere o te pōro B i mua i te tukinga (v _B ) = 0

E hiahiatia ana: te tere o te pōro A (v _A ') me te tere o te pōro B (v _B ') i muri i te tukinga

Rongoā:

v _A ' = v _B = 0

v _B ' = v _A = 10 m/s

[irp]

2. E rua ngā mea e ōrite ana te taumaha e whakatata ana tetahi ki tetahi, ka tukinga, kātahi ka peke atu. Ko te tere o te taumaha A i mua i te tukinga he 8 m/s, ā, ko te tere o te taumaha B i mua i te tukinga he 12 m/s. He aha te rahi me te ahunga o te tere o te taumaha A me te taumaha B i muri i te tukinga!

Mōhiotia:

Papatipu A (m _A ) = m

Papatipu B (m _B ) = m

Tere o te papatipu A i mua i te tukinga (v _A ) = -8 m/s

Te tere o te papatipu B i mua i te tukinga (v _B ) = 12 m/s

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te taha ke.

E hiahiatia ana: te rahi me te ahunga o te tere o te papatipu A (v _A ') me te papatipu B (v _B ') i muri i te tukinga

Rongoā:

I roto i tētahi tukinga tino rapa, mēnā he ōrite te papatipu o ngā mea, ko te tere o A i muri i te tukinga (v _A ') = te tere o B i mua i te tukinga (v _B ) me te tere o B i muri i te tukinga (v _B ') = te tere o A i mua i te tukinga (v _A ).

Mena i mua i te tukinga, ka neke a A ki matau, ā, ka neke a B ki maui, kātahi, i muri i te tukinga, ka neke a A ki maui, ā, ka neke a B ki matau.

He ōrite te taumaha o ngā mea e rua, ā, he tino pīngore te tukinga, nō reira i whakawhitiwhiti tere ai ngā mea e rua.

v _A ' = -v _B = -12 m/s

v _B ' = v _A = 8 m/s

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te taha ke.

[irp]

3. He mea A, 2-kg te taumaha, e neke ana i te tere o te 10 m/s, ka pā ki tētahi pōro B, 4-kg te taumaha, e neke ana i te tere o te 20 m/s. Mēnā he tino pīngore te tukinga, he aha te tere o te mea A me te mea B i muri i te tukinga?

Mōhiotia:

Taumaha A (m _A ) = 2 kg

Taumaha B (m _B ) = 4 kg

Te tere o te mea A i mua i te tukinga (v _A ) = 10 m/s

Te tere o te mea B i mua i te tukinga (v _B ) = 20 m/s

E hiahiatia ana : te tere o te mea A (v _A ') me te tere o te mea B (v _B ') i muri i te tukinga

Otinga :

I roto i te tukinga tino rapa , mēnā he ōrite te taumaha o ngā mea, ā, ka whakatata tetahi ki tetahi, ka tatauhia te tere o te mea i muri i te tukinga mā te whakamahi i tēnei tātai:

Te tere o te mea A i muri i te tukinga:

[irp]

4. Ka pā te tukinga 100-karamu e neke ana i te 20 m/s ki te pakitara, he tino ngāwari te tūtukitanga. He aha te rahi me te ahunga o te tere o te mea i muri i te tukinga?

Mōhiotia:

Taumaha (mA ₎ = 100 karamu = 0.1 kg

Papatipu o te pakitara (m _B ) = mutunga kore

Ko te tere o te papatipu i mua i te tukinga (v _A ) = 20 m/s

Ko te tere o te papatipu i muri i te tukinga (v _B ) = 0

E hiahiatia ana : te rahi me te ahunga o te tere i muri i te tukinga

Rongoā:

Mena he 0 a v _{B ,} he iti rawa a m _{A , he nui rawa hoki a m 2} , ko v _A ' = -v _{A, ā} , ko v ₂ ' = 0.

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te taha ke.

5. E rua ngā pōro, ko A he 2-kg te taumaha , me te pōro B he 5-kg te taumaha, i mua me muri i te tukinga, e whakaaturia ana i te pikitia i raro nei. Mena he tino ngāwari te tukinga, he aha te tere o te pōro A i mua i te tukinga?

Mōhiotia:

Te taumaha o te pōro A (m_A) = 2 kirokaramu

Taumaha o te pōro B (m _B ) = 5 kg

Te tere o te pōro B i mua i te tukinga (v _B ) = 2 m/s

Te tere o te pōro A i muri i te tukinga (v _A ') = 5 m/s

Te tere o te pōro B i muri i te tukinga (v _B ') = 4 m/s

Kei te neke ngā pōro e rua ki te taha matau, nō reira ko te tere kua hainatia he pai.

E hiahiatia ana: Te tere o te pōro A i mua i te tukinga (v _A )

Rongoā:

m_A v_A +m_B v_B = m_A v_A' + m_B v_B'

2(v _A ) + (5)(2) = (2)(5) + (5)(4)

2(v _A ) + 10 = 10 + 20

2(v _A ) + 10 = 30

2(v _A ) = 30 – 10

2(v _A ) = 20

v _A = 20/2

v _A = 10 m/s

[irp]

6. Ka haere ngā mea A me B i te papa whakapae, e whakaaturia ana i te pikitia i raro nei. Mēnā he tino ngāwari te tukinga, ā, ko te tere o te mea B i muri i te tukinga he 15 m/s1 ^, he aha te tere o te mea A i muri i te tukinga?

Mōhiotia:

Papatipu o te mea A (m_A) = 5 kirokaramu

Taumaha o te mea B (m _B ) = 2 kg

Te tere o te mea A i mua i te tukinga (v _A ) = 12 m/s

Te tere o te mea B i mua i te tukinga (v _B ) = 10 m/s

Te tere o te mea B i muri i te tukinga (v _B ') = 15 m/s

Ka neke ngā mea e rua ki te taha matau, i mua me i muri i te tukinga, nō reira he pai te tere.

E hiahiatia ana: Te tere o te mea A i muri i te tukinga (v _A ')

Rongoā:

m_A v_A +m_B v_B = m_A v_A' + m_B v_B'

(5)(12) + (2)(10) = (5)v _A ' + (2)(15)

60 + 20 = (5)v _A ' + 30

80 = (5)v _A ' + 30

80 – 30 = (5)v _A '

50 = (5)v _A '

v _A ' = 50/5

v _A ' = 10 m/s

[wpdm_package id='1156′]

1. Ngā raruraru me ngā otinga o te nekehanga rārangi
2. Ngā raruraru me ngā otinga o te nekehanga me te hihiri
3. Ngā raruraru me ngā otinga o ngā tukinga tino ngāwari i roto i te taha kotahi
4. Ngā raruraru me ngā otinga o ngā tukinga kore-whakapūmau tino tika i roto i te taha kotahi
5. Ngā raruraru me ngā otinga mō ngā tukinga kore-whakapūmau i roto i te taha kotahi

Pānuitia atu

1. Ka whiua whakararatia tētahi pōro iti me te tere pumau o te 10 m/s. Ka pā te pōro ki te pakitara, ā, ka whakaatahia me te tere ōrite. He aha te panoni o te nekehanga rārangi o te pōro?

Mōhiotia:

Taumaha (m) = 0.2 kg

Tere tīmatanga (v _o ) = -10 m/s

Tere whakamutunga (vt ₎ = 10 m/s

Ko ngā tohu tāpiri me ngā tohu tango e tohu ana kei te neke ngā mea i te ahunga whakamuri.

E hiahiatia ana : te huringa o te nekehanga raina (Δp)

Rongoā:

Te tātai o te huringa o te nekehanga raina :

Δp = mv _t – mv _o = m (v _t – v _o )

Te huringa o te nekehanga raina:

Δp = 0.2 (10 – (-10)) = 0.2 (10 + 10)

Δp = 0.2 (20)

Δp = 4 kg m/s

[irp]

2. Ka taka noa tētahi pōro 10-karamu mai i tētahi teitei, ka pā ki te papa i te 15 m/s, kātahi ka whakaata ake i te 10 m/s. Tātaihia te iri!

Mōhiotia:

Taumaha (m) = 10 karamu = 0.01 kg

Te tere tīmatanga (v _o ) = -15 m/s

Te tere whakamutunga (vt ₎ = 10 m/s

E hiahiatia ana: Te hihiri (I)

Rongoā:

Ko te nekehanga (I) he ōrite ki te huringa o te nekehanga (Δp)

I = mv _t – mv _o = m (v _t – v _o )

Hihiri:

I = 0.01 (10 – (-15)) = 0.01 (10 + 15)

I = 0.01 (25)

I = 0.25 kg m/s

[irp]

3. I whiua whakararatia tētahi pōro 200-karamu me te tere o te 4 m/s, kātahi ka whiua te pōro ki te ahunga kotahi. Ko te roa o te pānga o te pōro ki te patu he 2 maero hēkona , ā, ko te tere o te pōro i muri i te wehenga atu i te patu he 12 m/s. Ko te kaha i tukuna e te patu ki te pōro he …

Mōhiotia:

Taumaha (m) = 200 karamu = 0.2 kg

Te tere tīmatanga (v _o ) = 4 m/s

Te tere whakamutunga (vt ₎ = 12 m/s

Wā wā (t) = 2 mirihekona = (2/1000) hēkona = 0.002 hēkona

E hiahiatia ana : Te rahi o te kaha (F)

Rongoā:

Te tauira o te hihiri:

I = Ft

Te tātai o te huringa o te nekehanga:

mv _t – mv _o = m (v _t – v _o )

Ko te nekehanga (I) he ōrite ki te huringa o te nekehanga (Δp)

I = Δp

Ft = m (vt _– v _o )

F (0.002) = (0.2)(12 – 4)

F (0.002) = (0.2)(8)

F (0.002) = 1.6

F = 1.6 / 0.002

F = 800 Newton

[wpdm_package id='1155′]

1. Ngā raruraru me ngā otinga o te nekehanga rārangi
2. Ngā raruraru me ngā otinga o te nekehanga me te hihiri
3. Ngā raruraru me ngā otinga o ngā tukinga tino ngāwari i roto i te taha kotahi
4. Ngā raruraru me ngā otinga o ngā tukinga kore-whakapūmau tino tika i roto i te taha kotahi
5. Ngā raruraru me ngā otinga mō ngā tukinga kore-whakapūmau i roto i te taha kotahi

Pānuitia atu

1. Ka tere te haere o tētahi mea i te tere pumau 10 m/s. Tātaihia te nekehanga rārangi o te mea.

Mōhiotia :

Taumaha (m) = 1 kg

Tere (v) = 10 m/s

E hiahiatia ana: te nekehanga raina (p)

Rongoā:

Te tātai o te nekehanga rārangi:

p = mv

p = te nekehanga rārangi, m = te papatipu, v = te tere

Te nekehanga raina:

p = mv = (1)(10) = 10 kg m/s ²

[irp]

2. E neke ana tētahi poraka 2-kg me tētahi poraka 4-kg i te tere pumau 20 m/s. He aha te nekehanga rārangi o ngā poraka?

Mōhiotia:

Taumaha o te poraka A (m _A ) = 2 kg

Taumaha o te poraka B (m _B ) = 4 kg

Te tere o te poraka A (v _A ) = 20 m/s

Te tere o te poraka B (v _B ) = 20 m/s

E hiahiatia ana: Te nekehanga rārangi o te poraka A (p _A ) me te nekehanga rārangi o te poraka B (p _B )

Rongoā:

Te nekehanga rārangi o te poraka A :

p _A = m _A v _A = (2)(20) = 40 kg m/s

Te nekehanga rārangi o te poraka B :

p _B = m _B v _B = (4)(20) = 80 kg m/s

[irp]

3. E neke ana tētahi poraka 2-kg i te tere pumau 2 m/s, ā, e neke ana tētahi poraka 2-kg i te tere pumau 4 m/s. Tātaihia te nekehanga rārangi o ngā poraka.

Mōhiotia:

Taumaha o te poraka A (m _A ) = 2 kg

Taumaha o te poraka B (m _B ) = 2 kg

Te tere o te poraka A (v _A ) = 2 m/s

Te tere o te poraka B (v _B ) = 4 m/s

E hiahiatia ana: te nekehanga raina o ngā poraka

Rongoā:

Te nekehanga rārangi o te poraka A :

p _A = m _A v _A = (2)(2) = 4 kg m/s

Te nekehanga rārangi o te poraka B:

p _B = m _B v _B = (2)(4) = 8 kg m/s

[irp]

4. He mea 5-kg te taumaha e okioki ana. He aha te nekehanga rārangi o te nekehanga?

Mōhiotia:

Taumaha (m) = 5 kg

Te tere o te mea (v) = 0

E hiahiatia ana : te nekehanga raina (p)

Rongoā:

p = mv = (5)(0) = 0

[wpdm_package id='1155′]

1. Ngā raruraru me ngā otinga o te nekehanga rārangi
2. Ngā raruraru me ngā otinga o te nekehanga me te hihiri
3. Ngā raruraru me ngā otinga o ngā tukinga tino ngāwari i roto i te taha kotahi
4. Ngā raruraru me ngā otinga o ngā tukinga kore-whakapūmau tino tika i roto i te taha kotahi
5. Ngā raruraru me ngā otinga mō ngā tukinga kore-whakapūmau i roto i te taha kotahi

Pānuitia atu

Ko te mana te tere o te mahi i roto i tētahi wā kua whakaritea. I roto i te pāngarau, ko te mana te ōwehenga mahi/wā.

P = W/t

Whakaahuatanga: P = mana (Joule/hēkona = Watt), W = mahi (Joule), t = wā (hēkona)

I runga i tēnei whārite, ka taea te whakatau ko te nui ake o te tere mahi, ko te nui ake o te mana. I tētahi atu taha, ko te iti ake o te tere mahi, ko te iti ake o te mana. Ko te tere mahi e pā ana ki te tere o te mahi.

[irp]

He tauine tauine te mana. Ko te waeine SI mō te mana ko te Joule/hēkona. Ko te Joule/hēkona = Watt (i whakarapopototia ko W), i tapaina pērā hei whakanui i a James Watt. Ko te waeine emepaea o Peretānia mō te mana ko te foot-pauna ia hekona.

He iti rawa tēnei waeine mō ngā mahi whaihua, nō reira ka whakamahia te waeine nui ake, arā, te hōihopa (arā, te hp). Kotahi hōihopa = 550 putu-pauna ia hekona = 764 Watts = ¾ kilowatt.

Ka taea hoki te whakaatu i te nui o te mahi i roto i ngā waeine mana x wā, hei tauira, kilowatt-hāora, kWh rānei. Ko te kotahi kWh e pā ana ki te mahi i mahia i te tere pumau o te 1 kiloWatt mō te haora kotahi.

1. E oma ana tētahi tangata 50-kg i ngā arawhata, 10 mita te teitei ⁱ roto i te 2 meneti. Ko te tere o te kaha ā -papa (g) he 10 m/ s2 . Tātaihia te mana.

Mōhiotia:

Taumaha (m) = 50 kg

Teitei (h) = 10 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Wā poto (t) = 2 meneti = 2 (60) = 120 hēkona s

E hiahiatia ana : Mana (P)

Rongoā:

Tātai o te mana:

P = W / t

P = mana , W = mahi , t = wā

Tātai Mahi:

W = F s = wh = mgh

W = mahi , F = kaha , w = taumaha , d = nekehanga , h = teitei , m = papatipu, g = whakaterenga nā te kaha ā-papatipu

W = mgh = (50)(10)(10) = 5000 Joule.

P = W / t = 5000 / 120 = 41.7 Joules/se c i runga i te d.

[irp]

2. Tātaihia te mana e hiahiatia ana mō tētahi tangata 60-kg te taumaha e piki ana i tētahi rākau e 5 mita te teitei i roto i te 10 hēkona. Ko te whakaterenga nā te kaha ā-papa he 10 m/ ^s².

Mōhiotia:

Taumaha (m) = 60 kg

Teitei (h) = 5 mita s

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Wā wā (t) = 10 hēkona

E hiahiatia ana : Mana

Rongoā:

Mahi:

W = mgh = (60)(10)(5) = 3000 Joule

Mana:

P = W / t = 3000 / 10 = 300 Joules/se te āhua.

3. He kōmeke hurihuri, he 300 watts te kaha, ā, e 5 meneti te roa o te wā e hurihuri ana i ngā rauna e 5. Ko te kaha e whakamahia ana e ia ko….

A. 15 kJ

B. 75 kJ

C. 90 kJ

D. 450 kJ

Mōhiotia:

Mana (P) = 300 Watts = 300 Joules/hēkona

Wā (T) = 5 meneti = 5 (60 hēkona) = 300 hēkona

Te maha o ngā hurihanga = 5

E hiahiatia ana: Pūngao i whakamahia e te pukuhohe hurihuri

Rongoā:

Ko te whakautu tika ko D.

[wpdm_package id='1190′]

1. I mahia te mahi mā te kaha, ngā raruraru me ngā otinga
2. Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
3. Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
4. Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
5. Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
6. Ngā raruraru hiko me ngā otinga
7. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
8. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
9. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
10. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
11. Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere

Pānuitia atu

1. Ka paheke iho tētahi poraka i runga i tētahi papa whakarara maeneene, kāore he waku . He aha te tere o te poraka ina pā ki te whenua? Ko te whakaterenga nā te kaha ā-papa he 10 m/ ^s²

Mōhiotia:

Teitei (h) = 8 m

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana : tere (v)

Otinga :

Pūngao ā-pūkaha tīmatanga (ME _o ) = pūngao pūmanawa ā-papa (PE)

ME _o = PE = mgh = m (10)(8) = 80 m

Pūngao miihini whakamutunga (MEt ₎ = pūngao nekeneke (KE)

ME _t = KE = ½ mv ²

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga:

ME _o = ME _t

80 m = ½ mv ²

80 = ½ v ²

160 = v ²

v = √160 = √(16)(10) = 4√10 m/s

[irp]

2. Ka paheke te mea 1-kg i raro i te 8 mita. Tātaihia te pūngao nekeneke i muri i te neke o te mea i runga i te 5 mita… Te whakaterenga nā te kaha ā-papatipu g = 10 m/s ²

Mōhiotia:

Taumaha (m) = 0.2 kg

d = 5 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana : pūngao nekeneke (KE)

Rongoā:

sin 30 ^o = h / d

0.5 = hāora / 5

h = (0.5)(5) = 2.5 mita

Ko te rerekētanga o te teitei o te mea he 2.5 mita.

Ko te pūngao ā-pūkaha tīmatanga (ME _o ) = te pūngao pūmanawa ā-papa (PE)

ME _o = PE = mgh = (1)(10)(2.5) = 25 Joule

Ko te pūngao miihini whakamutunga (ME _t ) = te pūngao nekeneke (KE)

ME _t = KE

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga:

ME _o = ME _t

25 = KE

Pūngao nekeneke = 25 Joule.

[wpdm_package id='1170′]

1. Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
2. Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
3. Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
4. Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
5. Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
6. Ngā raruraru hiko me ngā otinga
7. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
8. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
9. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
10. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
11. Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere

Pānuitia atu

1. Ka paheke iho tētahi poraka 1-kg te taumaha i runga i te mata kōpiko maeneene. Tātaihia te pūngao nekeneke me te tere o te poraka i te mata o raro rawa. Ko te whakaterenga nā te kaha ā-papatipu he 10 m/s ².

Mōhiotia:

Taumaha (m) = 1 kg

Ko te panonitanga o te teitei (h) = 5 m

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te pūngao nekeneke (KE) me te tere o te poraka.

Rongoā:

(a) Pūngao nekeneke

Ko te pūngao ā-pūkaha tīmatanga = te pūngao pūmanawa ā-papa

ME _o = PE = mgh = (1)(10)(5) = 50 Joule

Ko te pūngao miihini whakamutunga = te pūngao nekeneke

ME _t = KE = ½ mv _t ²

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga:

ME _o = ME _t

PE = KE

50 = KE

Pūngao nekeneke (KE) = 50 Joule.

(b) Te tere o te poraka

Te mātāpono o te tiaki i te pūngao miihini:

Ko te pūngao miihini tīmatanga (ME₂o ₎ = te pūngao miihini whakamutunga ( _ME₂t )

Ko te pūngao pūmanawa ā-papa (PE) = te pūngao nekeneke (KE)

50 = ½ mv ²

2(50) / m = v ²

100 / 1 = v ²

100 = v ²

v = √100

v = 10 m/s

[irp]

2. Ka paheke te mea 2-kg ki raro, kāore he waku. He aha te pūngao nekeneke me te tere o te mea i te 2 mita i runga ake i te whenua? Ko te whakaterenga nā te kaha ā-papa he 10 m/s ²

Mōhiotia:

Taumaha (m) = 2 kg

Ko te panonitanga o te teitei (h) = 10 – 2 = 8 m

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana : te pūngao nekeneke (KE) me te tere (v) i te 2 mita i runga ake i te whenua.

Rongoā:

(a) Pūngao nekeneke i te 2 mita i runga ake i te whenua

Ko te pūngao ā-pūkaha tīmatanga = te pūngao pūmanawa ā-papa

ME _o = PE = mgh = (2)(10)(8) = 160 Joule

Ko te pūngao miihini whakamutunga = te pūngao nekeneke

ME _t = KE = ½ mv _t ²

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga:

ME _o = ME _t

PE = KE

160 = KE

Ko te pūngao nekeneke (KE) i te 2 mita i runga ake i te whenua he 160 Joules.

(b) Te tere o te mea i te mata o raro rawa

Te mātāpono o te tiaki i te pūngao ā-pūkaha:

Ko te pūngao miihini tīmatanga (ME₂o ₎ = te pūngao miihini whakamutunga ( _EM₂t )

Ko te pūngao pūmanawa ā-papa (PE) = te pūngao nekeneke (KE)

160 = ½ mv ²

160 = ½ (2) v ²

160 = v ²

v = √160 = √(16)(10) = 4√10 m/s

[wpdm_package id='1167′]

1. Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
2. Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
3. Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
4. Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
5. Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
6. Ngā raruraru hiko me ngā otinga
7. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
8. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
9. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
10. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te papa whakarara
11. Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere

Pānuitia atu

1. Ka wehe atu tētahi whutupōro i te whenua i te koki θ = 30 ^o me te tere tīmatanga o te 10 m/s. Ko te papatipu o te pōro = 0.1 kg. Ko te whakaterenga nā te kaha ā-papatipu he 10 m/s2 ^. Whakatauhia (a) Te kaha pūmanawa ā-papatipu i te pūwāhi teitei rawa (b) Te pūwāhi teitei rawa, te teitei mōrahi rānei

Mōhiotia:

Taumaha (m) = 0.1 kg

Ko te tere tīmatanga (v _o ) = 10 m/s

Koki = 30 ^o

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Rongoā:

(a) Te pūngao pūmanawa ā-papa

Tātaihia te wāhanga whakapae (v _ox ) me te wāhanga poutū (v _oy ) o te tere tīmatanga.

v_ox = v_o cos θ = (10)(cos 30^o) = (10)(0.5√3) = 5√3 m/s

v _oy = v _o hara θ = (10)(hara 30 ^o ) = (10)( 0.5) = 5 m/s

Te pūngao miihini tuatahi

Ko te pūngao miihini tīmatanga (ME _o ) = te pūngao nekeneke (KE)

ME _o = KE = ½ mv _o ² = ½ (0.1)(10) ² = ½ (0.1)(100) = ½ (10) = 5 Joules

Te pūngao miihini whakamutunga

Pūngao nekeneke i te pūwāhi teitei rawa:

KE = ½ mv _ox ² = ½ (0.1)(5√3) ² = ½ (0.1)((25)(3)) = ½ (0.1)(75) = 3.75 Joules

Te mātāpono o te tiaki i te pūngao miihini

Ko te pūngao miihini tīmatanga (ME₂o ₎ = te pūngao miihini whakamutunga ( _ME₂t )

KE = PE + KE

5 = EP + 3.75

PE = 5 – 3.75 = 1.25 Joule

Ko te pūngao pūmanawa ā-papa i te pūwāhi teitei rawa ko 1.25 Joules.

(b) Te pūwāhi teitei rawa, te teitei mōrahi rānei

PE = mgh

1.25 = (0.1)(10) hāora

1.25 = hāora

Ko te teitei mōrahi he 1.25 mita.

[irp]

2. Ka tukuna whakapaetia tētahi pōro 0.1-kg te taumaha, ko te tere tīmatanga v _o = 10 m/s mai i tētahi whare e 10 mita te teitei. Ko te whakaterenga nā te kaha ā-papatipu he 10 m/s2 ^. Tātaihia te pūngao nekeneke o te pōro ina pā ki te whenua.

Mōhiotia:

Taumaha (m) = 0.1 kg

Te tere tīmatanga (v _o ) = 10 m/s

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Ko te panonitanga o te teitei (h) = 10 – 2 = 8 m

E hiahiatia ana: te pūngao nekeneke i te 2 mita i runga ake i te whenua

Rongoā:

Ko te pūngao pūmanawa ā-papa (PE) = mgh = (0.1)(10)(10) = 10 Joule

Ko te pūngao nekeneke tīmatanga (KE)= ½ mv _o ² = ½ (0.1)(10) ² = ½ (0.1)(100) = ½ (10) = 5 Joule

Ko te pūngao nekeneke whakamutunga = te pūngao pūmanawa ā-papa tuatahi + te pūngao nekeneke tuatahi = 10 + 5 = 15 Joule

[wpdm_package id='1173′]

1. Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
2. Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
3. Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
4. Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
5. Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
6. Ngā raruraru hiko me ngā otinga
7. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
8. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
9. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
10. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
11. Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere

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