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? Te tuaka hurihuri i te pūwāhi A.

Mōhiotia:

Te kaha (F) = 10 N

Te roa o AB (r_AB) = 2 mita

He poutū te kaha F ki te kurupae.

Ko te ringa rīwhi (l) =r_AB hara 90^o = (2 mita)(1) = 2 mita

Hiahia: Te taipana huri noa i te tuaka hurihuri

Rongoā:

Te taipana:

τ = Fl = (10 N)(2 m) = 20 N m

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

2. Te roa o te kurupae Ko 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 mita

Ko te ringa rīwhi (l) =r_AB hara 60^o = (2 mita)(0.5√3) = √3 m

Hiahia: Te taipana huri noa i te tuaka hurihuri

Rongoā:

Te taipana:

τ = Fl = (10 N)(√3 m) = 10√3 N m

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

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

Te tuaka hurihuri i waenganui o te kurupae.

Mōhiotia:

Kaha 1 (F₁) = 10 N

te tawhiti i waenganui i te F₁ me te pokapū o te kurupae (r₁) = 1 mita

Ko te ringa rīwhi 1 (l₁) =r₁ hara 90^o = (1 mita)(1) = 1 mita

Te kaha F₁ he poutū ki te kurupae.

Kaha 2 (F₂) = 15 N

Te tawhiti i waenganui i a F₂ me te pokapū o te kurupae (r₂) = 1 mita

Te kaha F₂ he poutū ki te kurupae.

Ko te ringa rīwhi 2 (l₂) =r₁ hara 90^o = (1 mita)(1) = 1 mita

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

Rongoā:

Te taipana 1:

τ₁ =F₁ l₁ = (10 N)(1 m) = 10 N m

Ko te tohu tāpiri nā te kaha o F₁ ka puta te hihi ka huri i te taha maui.

Te taipana 2:

τ₂ =F₂ l₂ = (15 N)(1 m) = -15 N

Ko te tohu tango nā te mea ko te kaha F₂ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana kupenga:

Στ = τ₁ – τ₂ = 10 – 15 = – 5 N m

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

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

Te tuaka hurihuri i waenganui o te kurupae.

Mōhiotia:

Kaha 1 (F₁) = 10 Nn

Te tawhiti i waenganui i a F₁ me te pokapū o te kurupae (r₁) = 1 mita

Ko te ringa rīwhi 1 (l₁) =r₁ hara 60^o = (1 mita)(0.5√3) = 0.5√3 m

Kaha 2 (F₂) = 10 N

Te tawhiti i waenganui i a F₂ me te pokapū o te kurupae (r₂) = 1 mita

Te kaha F₂ he poutū ki te kurupae.

Ko te ringa rīwhi 2 (l₂) = r₂ hara 90^o = (1 mita)(1) = 1 mita

E hiahiatia ana: Te taipana kupenga mō te tuaka hurihuri

Rongoā:

Te taipana 1:

τ₁ =F₁ l₁ = (10 N)(0.5√3 m) = 5√3 = 8.7 Nm

Ko te tohu tāpiri nā te mea ko te kaha F₁ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana 2:

τ₂ =F₂ l₂ = (10 N)(1 m) = -10 N m

Ko te tohu tango nā te mea ko te kaha F₂ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana kupenga:

Στ = τ₁ – τ₂ = 8.7 – 10 = – 1.3 N m

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

5. 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 15 N. Ko te tawhiti i waenganui i te pūwāhi A me te pūwāhi C ko 7.5 m. Ko te Kaha F₂ kei waenganui o te kurupae. Tāutuhia 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 (F₁) = 10 N

Te tawhiti i waenganui i a F₁ me te pūwāhi C (r₁) = 2.5 m

Te kaha F₁ he poutū ki te kurupae.

Ko te ringa rīwhi 1 (l₁) =r₁ hara 90^o = ((2.5 m)(1) = 2.5 m

Kaha 2 (F₂) = 10 N

Te tawhiti i waenganui i a F₂ me te pūwāhi C (r₂) = 2.5 m

Te kaha F₂ he poutū ki te kurupae.

Ko te ringa rīwhi 2 (l₂) = r₂ hara 90^o = ((2.5 m)(1) = 2.5 m

Kaha 3 (F₃) = 15 N

Te tawhiti i waenganui i a F₃ me te tohu C (r₃) = 7.5 mita

Te kaha F₃ he poutū ki te kurupae.

Ko te ringa rīwhi 3 (l₃) = r₃ hara 90^o = (7.5 mita)(1) = 7.5 mita

E hiahiatia ana: Te taipana kupenga mō te tuaka hurihuri

Rongoā:

Te taipana 1:

τ₁ =F₁ l₁ = (10 N)(2.5 m) = 25 N m

Ko te tohu tāpiri nā te mea ko te kaha F₁ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana 2:

τ₂ =F₂ l₂ = (10 N)(2.5 m) = 25 N m

Tte tohu tāpiri nā te mea ko te kaha F₂ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana 3:

τ₃ =F₃ l₃ = (15 N)(7.5 m) = -112..5 N m

Ko te tohu tango nā te mea ko te kaha F₃ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana kupenga:

Στ = τ₁ + τ₂ – τ₃ = 25 + 25 - 112.5 = – 62.5 N m

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

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 (F₁) = 10 N

Te tawhiti i waenganui i a F₁ me te pūwāhi A (r₁) = 5 mita

Ko te ringa rīwhi 1 (l₁) =r₁ hara 60^o = (5 mita)(0.5√3) = 2.5√3 m

Force 2 (W₂) = 10 N

Te tawhiti i waenganui i a F₂ me te pūwāhi A (r₂) = 0

Te kaha F₂ he poutū ki te kurupae.

Ko te ringa rīwhi 2 (l₂) = r₂ hara 90^o = (0)(1) = 0

Ko te kaha 3 (F₃) = 10 N

Te tawhiti i waenganui i a F₃ me te pūwāhi A (r₃) = 10 mita

Ko te ringa rīwhi 3 (l₃) = r₃ hara 30^o = (10 mita)(0.5) = 5 mita

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

Rongoā:

Te taipana 1:

τ₁ =F₁ l₁ = (10 N)(2.5√3 mita) = 25√3 = 43.3 N m

Ko te tohu tāpiri nā te mea ko te kaha F₁ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana 2:

τ₂ =F₂ l₂ = (10 N)(0) = 0

Te taipana 3:

τ₃ =F₃ l₃ = (10 N)(5 m) = -50 N m

Ko te tohu tango nā te mea ko te kaha F₃ ka meinga te hihi kia ka huri ki te taha matau.

Te taipana kupenga:

Στ = τ₁ + τ₂ – τ₃ = 43.3 + 0 - 50 = – 6.7 N m

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

Pānuitia atu

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

Mōhiotia:

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

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

tuatahi tere o te mea 1 (v₁) = -10 m/s

Te tere tīmatanga o te mea 2 (v₂) = 12 m/s

Te tere whakamutunga o te mea 1 (v₁') = 6 m/s

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

hiahia : te tere whakamutunga o te mea 2 (v₂')

Rongoā:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(0.5)(-10) + (0.2)(12) = (0.5)(6) + (0.2)(v₂')

-5 + 2.4 = 3 + 0.2 v₂'

-2.6 = 3 + 0.2 v₂'

-2.6 – 3 = 0.2 v₂'

-5.6 = 0.2 v₂'

v₂' = -5.6 / 0.2

v₂' = -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.

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 whakaeke?

Mōhio:

Mass o te mea 1 (m₁) = m

Mass o te mea 2 (m₂) = m

Te tere tīmatanga o te mea 1 (v₁) = -6 m/s

te tere tīmatanga o te mea 2 (v₂) = 8 m/s

Te tere whakamutunga o te mea 2 (v₂') = -5 m/s

hiahia : te rahi me te ahunga o te mea 1 i muri i te tukinga

Rongoā:

Tātai o te tiakitanga o te nekehanga raina :

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

mv₁ +m v₂ = m v₁' + m v₂'

m (v₁ +v₂) = m (v₁' + v₂')

v₁ +v₂ = v₁' + v₂'

-6 + 8 = v₁' – 5

2 = v₁' – 5

2 + 5 = v₁'

v₁' = 7 m/s

Te tere o te mea 1 i muri i te tukinga (v₁') is 3m/s.

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

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:

Mass pōro 1 (m₁) = 1 kirokaramu

Mass pōro 2 (m₂) = 2 kirokaramu

Te tere o te pōro 1 (i roto i₁) = 10 m/s

Te tere o te pōro 2 (v₂) = 5 m/s

Te tere whakamutunga o te pōro 2 (v₂') = 4 m/s

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

hiahia : te tere whakamutunga o te pōro 1 (v₁')

Rongoā:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(1)(10) + (2)(5) = (1)(v)₁') + (2)(4)

10 + 10 = v₁' + 8

20 – 8 = v₁'

v₁' = 12 m/s

Ko te tere o te pōro 1 i muri i te tukinga ko 12m/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 okioki ana. Tātaihia te tere o te poraka mēnā ka mau te matā me te poraka hei hua o te whakaeke.

Mōhiotia:

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

Mass o te poraka (m₂) = 1 kirokaramu

Te tere tīmatanga o te matā (v₁) = 30 m/s

te tere tīmatanga o te poraka (v₂) = 0 (poraka i te okiokinga)

hiahia : te tere o te matā me te poraka i muri i te tukinga (w')

Rongoā:

m₁ v₁ +m₂ v₂ = (m₁ +m₂) 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

2. Pōro piriata A, he 2 kg te taumaha, e neke ana me te tere v_A = 6 ms^-1 ka tukinga kanohi ki te kanohi 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 kirokaramu

Papatipu B (m_B) = 2 kirokaramu

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.

hiahia: ngā 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

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:

Mass ahanoa 1 (m₁) = 3 kirokaramu

Mass ahanoa 2 (m₂) = 4 kirokaramu

Te tere o te mea 1 (v₁) = -10 m/s

Te tere o te mea 2 (v₂) = 12 m/s

hiahia : te tere i muri i te tukinga (w')

Rongoā:

m₁ v₁ +m₂ v₂ = (m₁' + m₂) 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 200-karamu, A, e neke ana i te tere o te 10 m/s, e pā ana ki tētahi pōro 200-karamu, B, e okioki ana. He aha te tere o te pōro A me te pōro B i muri i te whakaeke?

Mōhiotia:

Mass o te pōro A (m_A) = 200 karamu = 0.2 kg

Te 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

Hiahia: 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 = 10m/s

2. E rua ngā mea ōrite 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 papatipu A me te papatipu B i muri i te tukinga!

Mōhiotia:

Taumaha A (m_A) = m

Papatipu B (m_B) = m

Te 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.

Hiahia: 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, ā, He tino pīngore te tukinga, nō reira i whakawhitiwhiti tere ai ngā mea e rua.

v_A' = -v_B = -12 m/h

v_B' = v_A = 8m/s

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

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 kirokaramu

Papatipu B (m_B) = 4 kirokaramu

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

hiahia : te tere o te mea A (v_A') me te tere o te mea B (v_B') i muri i te tukinga

otinga :

In tukinga tino ngāwari, 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:

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 (m_A) = 100 karamu = 0.1 kg

Papatipu o te pakitara (m_B) = mutunga kore

Te tere o te papatipu i mua i te tukinga (v_A) = 20 m/s

Te tere o te papatipu i muri i te tukinga (v_B) = 0

hiahia : te rahi me te ahunga o te tere i muri i te tukinga

Rongoā:

Mena v_B = 0, m_A tino iti, ā, m₂ tino nui rawa atu i te v_A' = -v_A me te v₂' = 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, A me te papatipu o 2 kirokaramu me te pōro B me te papatipu o 5-kg, Kei te whakaatuhia i te pikitia i raro nei ngā āhuatanga i mua atu, ā, i muri mai i te tukinga. Mēnā he tino ngāwari te tukinga, he aha te tere o te pōro A i mua atu i te tukinga?

Mōhiotia:

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

Te taumaha o te pōro B (m_B) = 5 kirokaramu

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 = 10m/s

6. Ka haere ngā taonga 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 taonga 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

Papatipu o te mea B (m_B) = 2 kirokaramu

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 raina o te pōro?

Mōhiotia:

Mass (m) = 0.2 kg

Tere tīmatanga (v_o) = -10 m/s

Tere whakamutunga (v_t) = 10 m/s

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

hiahia : 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

2. He pōro 10-karamu hinga noa mai i te 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 (v_t) = 10 m/s

E hiahiatia ana: Tuhinga (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

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 pa o te pōro ki te patu he 2 maerolngā lisēkona, ā, ko te tere o te pōro i muri i te wehenga atu i te patu he 12 m/s. Ko te te rahi o kaha whakapau kaha nā te kaiwhiu i te pōro ko…

Mōhiotia:

Taumaha (m) = 200 karamu = 0.2 kg

Te tere tīmatanga (v_o) = 4 m/s

Te tere whakamutunga (v_t) = 12 m/s

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

hiahia : 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 (v_t -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 te nekehanga raina o te mea.

Kua mohiotia :

Mass (m) = 1 kg

tere (v) = 10 m/s

E hiahiatia ana: te nekehanga rārangi (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/s²

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:

Mass o te poraka A (m_A) = 2 kirokaramu

Mass o te poraka B (m_B) = 4 kirokaramu

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 raina 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

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

Mōhiotia:

Mass o te poraka A (m_A) = 2 kirokaramu

Te taumaha o te poraka B (m_B) = 2 kirokaramu

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 rārangi o ngā poraka

Rongoā:

M rārangipūngao 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

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

hiahia : 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.

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. He 50-kg oma te tangata te piki i te arawhata 10 mita te teitei in meneti 2. Awhakaterenga Tuhinga o mua te kaha ā-papatipu (g) ​​he 10 m/s². Whakahuahia te mana.

Mōhiotia:

Mass (m) = 50 kg

teitei (h) = 10 mitaetera

Whakaterenga na te kaha o te kaha (g) = 10 m/s²

wā wā (t) = 2 meneti = 2 (60) = 120 tuaruas

hiahia : Power (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 = taimaha, d = Tuhinga, h = teitei, m = papatipu, g = te whakaterenga nā te kaha ā-papa

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

P = W / t = 5000 / 120 = 41.7 Joules/second.

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 tere o te kaha ā-papa he 10 m/s².

Mōhiotia:

Taumaha (m) = 60 kg

teitei (h) = 5 mitas

Whakaterenga na te kaha o te kaha (g) = 10 m/s²

wā wā (t) = 10 hēkona

hiahia : Power

Rongoā:

Mahi:

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

Mana:

P = W / t = 3000 / 10 = 300 Joules/setikanga

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

Hiahia: 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 te maeneene papa whakarara kahore wakuHe aha te poraka tere ina pā ki te whenua. Ko te tere o te kaha ā-papa he 10 m/s²

Mōhiotia:

Teitei (h) = 8 m

Whakaterenga na te kaha o te kaha (g) = 10 m/s²

hiahia : tere (v)

otinga :

Pūngao miihini tuatahi (ME)_o) = pūngao pūmanawa ā-papa (WAEWAE)

ME_o = PE = mgh = m (10)(8) = 80 m

Pūngao miihini whakamutunga (ME_t) = te kaha kinetic (KI)

ME_t = KE = ½ mv²

Ko te mātāpono o te tiaki i te pūngao miihini e kī ana ko te tīmatanga pūngao miihini = te pūngao miihini whakamutunga:

ME_o = AU_t

80 m = ½ mv²

80 = ½ v²

160 = v²

v = √160 = √(16)(10) = 4√10 m/s

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/s²

Mōhiotia:

Taumaha (m) = 0.2 kg

d = 5 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²

hiahia : pūngao nekeneke (KE)

Rongoā:

hara 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 miihini tuatahi (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) = pūngao nekeneke (KE)

ME_t = KI

Te parau tumu o te tiaki i te pūngao miihini e kī ana ko te pūngao miihini tīmatanga = te pūngao miihini whakamutunga:

ME_o = AU_t

25 = KE

Te kaha Kinetic = 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 te kaha kinetic me te tere o te poraka i te mata o raro rawa. Whakaterenga na te kaha o te kaha he 10 m/s².

Mōhiotia:

Mass (m) = 1 kg

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

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²

Hiahia: Pūngao nekeneke (KE) me te tere o te poraka.

Rongoā:

(a) Pūngao nekeneke

Ko te tuatahi pūngao miihini = 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_t²

Kaupapa o te tiaki i te pūngao miihini e kī ana ko te pūngao miihini tīmatanga = te pūngao miihini whakamutunga:

ME_o = AU_t

PE = KE

50 = KE

Te kaha Kinetic (KE) = 50 Joule.

(b) Te tere o te poraka

Te mātāpono o te tiaki i te pūngao miihini:

Ko te pūngao miihini tuatahi (ME_o) = te pūngao miihini whakamutunga (ME_t)

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

50 = ½ mv²

2(50) / m = v²

100 / 1 = v²

100 = v²

v = √100

v = 10 m/s

2. Ka paheke iho tētahi mea 2-kg te taumaha, 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/s²

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/s²

hiahia : 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_t²

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 = AU_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 tuatahi (ME_o) = te pūngao miihini whakamutunga (EM_t)

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

160 = ½ mv²

160 = ½ (2) v²

160 = v²

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 te whutupōro i te whenua i te koki θ = 30^o me te tere tīmatanga o te 10 m/s. Ko te pōro papatipu = 0.1 kg. Whakaterenga na te kaha o te kaha he 10 m / s². Whakatauhia (a) Te pūngao pūmanawa ā-papa 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/s²

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 tuatahi pūngao miihini (AU_o) = te kaha kinetic (KI)

ME_o = KE = ½ mv_o² = ½ (0.1)(10)² = ½ (0.1)(100) = ½ (10) = 5 Joule

Te pūngao miihini whakamutunga

Pūngao nekeneke i te pūwāhi teitei rawa:

KE = ½ mv_ox² = ½ (0.1)(5√3)² = ½ (0.1)((25)(3)) = ½ (0.1)(75) = 3.75 Joule

Te mātāpono o te tiaki i te pūngao miihini

Ko te pūngao miihini tuatahi (ME_o) = te pūngao miihini whakamutunga (ME_t)

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.

2. He pōro 0.1-kg te taumaha e tukuna whakapaetia ana me te tere tīmatanga v_o = 10 m/s mai i tētahi whare he 10 mita te teitei. Ko te whakaterenga nā te kaha ā-papa he 10 m/s²Tātaihia 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/s²

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

Hiahia: 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_o² = 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

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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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