He tauira o te ture a Hooke

9 Ngā Tauira o ngā Pātai Ture a Hooke

1. Kei te whakaatuhia te kauwhata o te whanaungatanga i waenga i te kaha (F) me te pikinga o te roa (x) i te ahua i raro nei. Ko te pūmau puna i runga i te kauwhata ko…
Kōrero
Tātai Te ture a Hooke :
k = F / x
Ngā Mōhiohio:
F = kaha (ko te waeine ā-ao ko Newton, he whakarāpopototanga N)
k = pūmau puna (ko te waeine ā-ao ko Newton/mita, he whakarāpopototanga ko N/m)
x = te pikinga o te roa (ko te waeine ā-ao ko ngā mita, he whakarāpopototanga m)
 
Pūmau puna i runga i te kauwhata i runga ake nei ko:
k = 10 / 0,02 = 20 / 0,04
k = 500 N/m

2. I runga i te whakamātautau hei whakatau i te pūmau o te puna Ko ngā raraunga i whiwhihia koia kei roto i te ripanga i raro nei. Ko te pūmau puna i runga i ngā raraunga kei roto i te ripanga ko…

Kōrero
Pūmau puna i runga i ngā raraunga o te ripanga ko:
k = F / x
k = 5 / 0,01 = 10 / 0,02 = 15 / 0,03 = 20 / 0,04
k = 500 N/m

3. Ko te roa tīmatanga o ngā puna A me B he 60 cm me te 90 cm, ā, he ōrite te kaha e kumea ana. Ko te pūmau puna o A he 100 N/m, ā, ko te pūmau puna o B he 200 N/m. Ko te ōwehenga o te pikinga o te roa o te puna A me te puna B he...
Kōrero
E mōhiotia ana:
Pūmau puna A (k)_A) = 100 N/m
Pūmau puna B (k)_B) = 200 N/m
Ko te kaha e kukume ana i te puna A (F)_A) = F
Ko te kaha e kukume ana i te puna B (F_B) = F
I pātaihia: te ōwehenga o te pikinga o te roa o te puna A me te puna B (x_A x_B)
Whakautu:
Te tātai mō te whakanui ake i te roa o te puna :
x = F / k
Te pikinga o te roa o te puna A:
x_A =F_A /k_A = F / 100
Te pikinga o te roa o te puna B:
x_B =F_B /k_B = F / 200
Te whakataurite i te pikinga o te roa o te puna A me te puna B :
x_A x_B
F/100 : F/200
1 / 100 : 1 / 200
1 / 1 : 1 / 2
2: 1
Kia mōhio: kāore te roa tīmatanga o te puna i roto i te tatau. Ko te x i roto i te tātai ture a Hooke ko te pikinga o te roa, ehara i te roa tīmatanga.

4. Ko te roa tīmatanga o tētahi waea he 20 cm. Ina tōia ki kāhua 10 Newton, ka piki te waea mā te 2 cm te roa. Kia 6 cm te pikinga o te roa, ko te kaha kume ko...
Kōrero
E mōhiotia ana:
Te kaha kume (F) = 10 Newton
Te pikinga o te roa o te waea (x) = 2 cm = 0,02 mita
I pātaihia: te rahi o te kaha kume (F) mēnā ka piki te roa o te waea mā te 6 cm, mā te 0,06 mita rānei.
Whakautu:
Pūmau waea :
k = F / x
k = 10 / 0,02 = 500 N/m
Ko te rahi o te kaha kume F mēnā ka piki ake te roa o te waea mā te 0,06 mita :
F = kx
F = (500)(0,06) = 30 Ngā Niutoni

5. E whakaatu ana te kauwhata i raro nei i te whanaungatanga i waenga i te huringa o te kawenga (ΔF) me te pikinga o te roa (ΔX), te kauwhata e whakaatu ana i te uara iti rawa o te pūmau rapa...
Kōrero

Te tauira ture a Hooke
k = F / Δx
Ngā Mōhiohio:
Δx = te pikinga o te roa, F = te kaha, k = te pūmau rapa
Pūmau te ngāwari
k_A = F / Δx = 1 / 8 = 0,125
k_B = F / Δx = 8 / 3 = 2,7
k_C = F / Δx = 6 / 6 = 1
k_D = F / Δx = 3 / 5 = 0,6
k_E = F / Δx = 2 / 4 = 0,5
Ko te whakautu tika ko A.

6. Tirohia te kauwhata o te whanaungatanga i waenganui i kāhua (F) ki te pikinga o te roa e whai ake nei (ΔX)! Ko tēhea te mea nui rawa te pūmau rapa?
Kōrero
Pūmau te ngāwari
k_A = F / Δx = 50 / 10 = 5
k_B = F / Δx = 50 / 0,1 = 500
k_C = F / Δx = 5 / 0,1 = 50
k_D = F / Δx = 500 / 0,1 = 5000
k_E = F / Δx = 500 / 10 = 50
Ko te whakautu tika ko D.

7. Ina hoatu he kaha ki te 160 karamu, ka piki ake te roa o tētahi puna mā te 4 cm. Ina whakaritea kia toru ngā puna rite e ai ki te whakaaturanga, ko te pikinga katoa o te roa o ngā puna ko...

A. 2 henemita

B. 3 henemita

C. 6 henimita

D. 7 henimita

E. 10 henimita

Kōrero

E mōhiotia ana:

Te pikinga o te roa (Δx) = 4 henimita = 0,04 mita

Taumaha (m) = 160 karamu = 0,16 kg

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

Taumaha (w) = mg = (0,16)(10) = 1,6 Ngā Niutoni

I pātaihia: Te pikinga o te roanga katoa o te puna ((Δx) mēnā kua whakaritea kia rite ki te pikitia

Whakautu:

Tuatahi, tatauhia te pūmau rapa o te puna mā te whakamahi i te tātai ture a Hooke:

k = w / Δx = 1,6 / 0,04 = 40 N/m

He rite tonu ngā puna e toru, nō reira he rite tonu te pūmau (k), arā 40 N/m.

Tātaihia te pūmau whakakapinga:

Koanga 2 (k₂) me te puna 3 (k₃) kua whakaritea kia whakarara. Ko te pūmau puna ōrite ko:

k₂₃ = k₂ +k₃ = 40 + 40 = 80 N/m

Koanga 1 (k₁) me te puna whakakapinga (k₂₃) kua whakaritea kia raupapa. Ko te pūmau puna ōrite ko:

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

k = 80/3

Tātaihia te pikinga o te roa katoa o te puna mā te whakamahi i te tātai ture a Hooke:

Δx = w / k = 1,6 : 80/3 = (1,6)(3/80) = 4,8/80 = 0,06 mita = 6 henimita

Ko te whakautu tika ko C.

8. E toru ngā puna ōriteWhakaritea kia rite ki te pikitia. Mena ko te pūmau puna ko k₁ = k₂ = k₃ = 300 Nm^-1 kātahi ka piki ake te roa o te whakaritenga o te puna ki te... (g = 10 ms^-2).

A. 0,1 mita

B. 0,2 mita

C. 0,4 mita

D. 0,5 mita

E. 0,8 m

Kōrero

E mōhiotia ana:

Pūmau puna k₁ = k₂ = k₃ = 300 Nm^-1

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

Papatipu o te kawenga (m) = 2 kg

Taumaha kawenga (w) = mg = (2)(10) = 20 Newton

I pātaihia: Te pikinga ake o te roa o te huihuinga puna ((Δx)

Whakautu:

Tātaihia te pūmau whakakapinga:

Koanga 1 (k₁) me te puna 2 (k₂) kua whakaritea kia whakarara. Ko te pūmau puna ōrite ko:

k₁₂ = k₁ +k₂ = 300 + 300 = 600 N/m

Koanga 3 (k₃) me te puna whakakapinga (k₁₂) kua whakaritea kia raupapa. Ko te pūmau puna ōrite ko:

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

k = 600/3 = 200 N / m

Tātaihia te pikinga o te roa katoa o te puna mā te whakamahi i te tātai ture a Hooke:

Δx = w / k = 20/200 = 2/20 = 1/10 = 0,1 mita

Ko te whakautu tika ko A.

9. E toru ngā puna kua whakaritea e whakaaturia ana i te pikitia e whai ake nei. Mēnā ko te pūmau puna k = 50 Nm^-1 ā, ka whakairihia he kawenga 400 karamu ki runga i te huihuinga puna, kātahi ka piki ake te roa o te huihuinga puna...

A. 2 henemita

B. 4 henemita

C. 8 henimita

D. 16 henimita

E. 50 henimita

Kōrero

E mōhiotia ana:

Pūmau puna 1 (k)₁) = k = 50 Nm^-1

Pūmau puna 2 (k)₂) = k = 50 Nm^-1

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

Papatipu kawenga (m) = 400 karamu = 0,4 kg

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

Taumaha kawenga (w) = mg = (0,4)(10) = 4 Newton

I pātaihia: Te pikinga ake o te roa o te huihuinga puna ((Δx)

Whakautu:

Tātaihia te pūmau whakakapinga:

Koanga 1 (k₁) me te puna 2 (k₂) kua whakaritea kia whakarara. Ko te pūmau puna ōrite ko:

k₁₂ = k₁ +k₂ = 50 + 50 = 100 N/m

Koanga 3 (k₃) me te puna whakakapinga (k₁₂) kua whakaritea kia raupapa. Ko te pūmau puna ōrite ko:

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

k = 100/2 = 50 N/m

Tātaihia te pikinga o te roa o te huihuinga puna mā te whakamahi i te tātai ture a Hooke:

Δx = w / k = 4 / 50 = = 0,08 mita = 8 cm

Ko te whakautu tika ko C.

Pūtake pātai:

Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa