Ngā puna raupapa me ngā puna whakarara – ngā raruraru me ngā otinga

1. E piri ana tētahi mea 160-karamu te taumaha ki tētahi pito o tētahi puna, ā, ko te huringa o te roa o te puna he 4 cm. He aha te huringa o te roa o ngā mea e toru? ngā puna e hono ana i roto i te raupapa me te whakarara, e whakaaturia ana i te pikitia i raro nei?

Mōhiotia:

Te panonitanga o te roa o te puna (Δx) = 4 cm = 0.04 m Ngā puna raupapa me ngā puna whakarara – ngā raruraru me ngā otinga 1

Mass (m) = 160 karamu = 0.16 kg

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

Taumaha (w) = mg = (0.16)(10) = 1.6 Ngā Newton

E hiahiatia ana: Te panonitanga o te roa o ngā puna e toru (Δx)

Rongoā:

Ko te whārite o Te ture a Hooke :

k = w / Δx = 1.6 / 0.04 = 40 N/m

He rite tonu te pūmau o ngā puna e toru, k = 40 N/m.

Whakatauhia te pūmau ōrite:

Koanga 2 (k₂) me te puna 3 (k₃) taura hono whakarara. Ko te pūmau ōrite:

k₂₃ = k₂ +k₃ = 40 + 40 = 80 N/m

Koanga 1 (k₁) me te puna 23 (k₂₃) e honoa ana i roto i te raupapa. Ko te pūmau ōrite:

1/k = 1/k₁ + 1/k₂₃ = 1/40 + 1/80 = 2/80 + 1/80 = 3/80

k = 80/3

Tātaihia te huringa o te roa o ngā puna e toru:

Δx = w / k = 1.6 : 80/3 = (1.6)(3/80) = 4.8 / 80 = 0.06 m = 6 cm

2. E toru ngā puna me te pūmau ōrite e hono ana i roto i te raupapa me te whakarara, me tētahi mea 2-kg e piri ana ki tētahi pito o tētahi puna, e whakaaturia ana i te pikitia i raro nei. Ko te pūmau puna ko k₁= k₂ = k₃= 300 N/m. He aha te panonitanga o te roa o ngā puna e toru? Ko te whakaterenga nā te kaha ā-papatipu ko g = 10 ms^-2.

Mōhiotia:

Pūmau puna k₁= k₂ = k₃= 300 Nm^-1

Te whakaterenga nā te kaha ā-papa (g) = 10 ms^-2

Papatipu o te mea (m) = 2 kg

Taumaha o te mea (w) = mg = (2)(10) = 20 Newton

A hi'o atoa Te ture Kirchhoff – ngā raruraru me ngā otinga

E hiahiatia ana: Te huringa o te roa o ngā puna e toru (Δx)

Rongoā:

Whakatauhia te pūmau ōrite:

Koanga 1 (k₁) me te puna 2 (k₂) e honoa ana i te taha whakarara. Ko te pūmau ōrite:

k₁₂ = k₁ +k₂ = 300 + 300 = 600 N/m

Koanga 3 (k₃) me te puna 12 (k₁₂) e honoa ana i roto i te raupapa. Ko te pūmau ōrite:

1/k = 1/k₃ + 1/k₁₂ = 1/300 + 1/600 = 2/600 + 1/600 = 3/600

k = 600/3 = 200 N/m

Tātaihia te huringa o te roa o ngā puna e toru:

Δx = w / k = 20/200 = 2/20 = 1/10 = 0.1 m

3. E toru ngā puna e honoa ana i roto i te raupapa me te whakarara, e whakaaturia ana i te pikitia i raro nei. Mena ko te pūmau puna k = 50 Nm^-1 me te taumaha o te 400 karamu e piri ana ki tētahi pito o te puna. He aha te panonitanga o te roa o ngā puna e toru.

Mōhiotia:

Pūmau puna 1 (k₁) = k = 50 Nm^-1

Pūmau puna 2 (k₂) = k = 50 Nm^-1

Pūmau puna 3 (k₃) = 2k = 2 (50 Nm^-1) = 100 Nm^-1

Papatipu o te mea (m) = 400 karamu = 0.4 kg

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

Taumaha o te mea (w) = mg = (0.4)(10) = 4 Newton

E hiahiatia ana: Te huringa o te roa (Δx)

Rongoā:

Whakatauhia te pūmau ōrite:

Koanga 1 (k₁) me te puna 2 (k₂) e honoa ana i te taha whakarara. Ko te pūmau ōrite:

k₁₂ = k₁ +k₂ = 50 + 50 = 100 N/m

Koanga 3 (k₃) me te puna 12 (k₁₂) e honoa ana i roto i te raupapa. Ko te pūmau ōrite:

1/k = 1/k₃ + 1/k₁₂ = 1/100 + 1/100 = 2/100

k = 100/2 = 50 N/m

Tātaihia te huringa o te roa o ngā puna e toru:

Δx = w / k = 4 / 50 = = 0.08 m = 8 cm

He pēhea te pānga o te whakakotahitanga o ngā puna raupapa ki te pūmau puna whānui?
- whakahoki: Ina whakakotahihia ngā puna i roto i te raupapa, ka whakaitihia te pūmau puna whānui. Ko te tauutuutu o te pūmau puna ōrite ko te tapeke o ngā tauutuutu o ngā pūmau puna takitahi: 1/k $=1/ k ^{1} + 1/ k ^{2}$ .
Ka pēhea te rerekētanga o te pūmau puna whānui ina honoa ngā puna ki te taha whakarara?
- whakahoki: Mā te whakakotahi i ngā puna i te taha whakarara ka puta he pūmau puna whānui, ko te tapeke o ngā pūmau puna takitahi: k $= k_{1} + k_{2}$ .

Mena e rua ngā puna ōrite e whakaritea ana i roto i ngā raupapa, ka pēhea te whakataurite o te pūmau puna whakakotahi ki te pūmau puna o tētahi puna takitahi?
- whakahoki: Ko te pūmau puna whakakotahi ka rite ki te haurua o te pūmau puna o tētahi o ngā puna takitahi.

He aha te mea ka pā ki te toronga, ki te pēhanga rānei o ngā puna i roto i te raupapatanga ina pāngia he kaha?
- whakahoki: Mō ngā puna i roto i te raupapa, mā te kaha kotahi ka toro, ka pēhi rānei ia puna, engari ko te toronga katoa (te pēhitanga rānei) ko te tapeke o ngā toronga (ngā pēhitanga rānei) o ia puna.

Mena ka pāngia ngā puna e te kaha whakarara, me pēhea te tohatoha o taua kaha?
- whakahoki: Mō ngā puna e whakarara ana, ka tohatohahia te kaha ki waenga i ngā puna i runga i ō rātou pūmau puna. Ko ngā puna he pūmau puna teitei ake ka mau i te wāhanga nui ake o te kaha i ērā he iti ake te pūmau puna.
He aha ngā puna i roto i te raupapa e taea ai te whakaaro he puna kotahi he roa ake te roa?
- whakahoki: He rite te pānga whakakotahi o ngā puna raupapa ki te totoro i tētahi puna roa kotahi. Ka tāpirihia ngā toronga, ngā pēhanga rānei o ia puna, pērā i te puna kotahi roa ake.

He pēhea te whakataurite i te pūngao pūmanawa e rongoa ana i roto i ngā puna raupapa ki tērā i roto i ngā puna whakarara mō te kaha ōrite e pā ana?
- whakahoki: He nui ake te pūngao pūmanawa e rongoa ana e ngā puna raupapa i ngā puna whakarara mō te kaha ōrite nā te mea he nui ake te toronga, te pēhanga rānei e pāngia ana e te whakakotahitanga.
Ki te whati, ki te kore rānei e whai hua tētahi o ngā puna i roto i te whirihoranga whakarara, ka pēhea te whanonga whānui o te pūnaha?
- whakahoki: Ki te whati tetahi puna i roto i te whirihoranga whakarara, ka mahi tonu ngā puna e toe ana. Heoi anō, ka heke te pūmau puna whānui o te pūnaha, ā, kāore e taea e te pūnaha te whakamahi i te kaha whakaora rite tonu ki mua.

He aha ngā puna raupapa e ngāwari ake ai te pāngia e ngā whakarerekētanga nui atu i ērā e whakarara ana mō te kaha ōrite?
- whakahoki: Mō ngā puna e raupapa ana, ka pā te kaha kotahi ki ia puna, ka toro atu, ka pēhi rānei ia puna. Ko te huringa katoa ko te tapeke o ngā huringa takitahi. I te wā e whakarara ana, ka tohatohahia te kaha ki waenga i ngā puna, nō reira ka pāngia ia puna e te kaha whai hua kua whakaitihia, ka hua ake he huringa takitahi iti iho.
I roto i ngā mahi whaihua, he aha i whiriwhiri ai ngā kaihangarau ki te whakamahi i ngā puna whakarara kaua i te whakamahi raupapa?

whakahoki: Tērā pea ka whiriwhiria e ngā kaihangarau ngā puna i te taha whakarara hei whakatutuki i tētahi pūmau puna whānui teitei ake, ka hua ake he whanonga pakari ake. Ka taea hoki e tēnei tatūnga te whakarato i te tauutuutu; ki te kore tetahi puna e mahi, ka haere tonu te pūnaha, ahakoa he iti iho te pūmau puna whānui.