Tauira o te whakaritenga raupapa-whakarara o ngā puna

4 ngā tauira o ngā whakaritenga puna raupapa-whakarara

1. E toru ngā puna ōrite, he 200 N/m te pūmau rapa o ia puna, kua whakaritea kia raupapa, kia whakarara hoki e ai ki te pikitia i raro nei. Kei te whakairihia he taumaha w mai i te pito o raro o te huihuinga puna, ka whakanuia te roa o te huihuinga puna mā te 1 cm. Ko te taumaha o te taumaha w ko…
Kōrero
E mōhiotia ana:
Ko te pūmau o ia puna (k₁ = k₂ = k₃) = 200 N/m
Ko te pikinga o te roa o te pūnaha puna (x) = 1 cm = 0,01 mita
I pātaihia: te taumaha o te kawenga (w)
Whakautu:
Te tatau tuatahi pūmau puna whakakotahitanga
Kei te whakarite whakarara te puna 1 me te puna 2. Ko te pūmau puna ōrite ko:
k_p = k₁ +k₂ = 200 + 200 = 400 Ngā Newton/mita

Ngā puna whakakapinga whakaritenga whakarara (k)_p) me te puna 3 (k₃) kua whakaritea kia raupapa. Ko te pūmau puna whakakapinga ko:
1/k = 1/k_p + 1/k₃ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400
k = 400/3 Newton/mita
Tātaihia te taumaha o te kawenga mā te whakamahi i te tātai Te ture a Hooke.
F = w = kx
w = (400/3)(0,01) = 4/3 Ngā Niutoni
Ko te taumaha o te kawenga he 4/3 Newtons

2. E whā ngā puna rite tonu, he 500 N/m te pūmau o ia puna, he raupapa, he whakarara hoki. Tātaihia te pikinga o te roa o te pūnaha puna ina hoatu he kawenga o te 20 Newton.
Kōrero
E mōhiotia ana:
Ko te pūmau o ia puna (k₁ = k₂ = k₃ = k₄) = 500 N/m
Te kaha taumaha (w) = 20 Newton
Pātai: te pikinga o te roa o te pūnaha puna (x)
Whakautu:
Tuatahi, tatauhia te pūmau puna whakakotahi.
Kei te whakarite whakarara te puna 1, te puna 2 me te puna 3. Ko te pūmau puna ōrite ko:
k_p = k₁ +k₂ +k₃ = 500 + 500 + 500 = 1500 Ngā Newton/mita

Ngā puna whakakapinga whakaritenga whakarara (k)_p) me te puna 4 (k₄) kua whakaritea kia raupapa. Ko te pūmau puna whakakapinga ko:
1/k = 1/k_p + 1/k₃ = 1/1500 + 1/500 = 1/1500 + 3/1500 = 4/1500
k = 1500/4 = 375 Newton/mita
Whakamahia te ture a Hooke hei whakatau i te pikinga o te roa o te pūnaha puna. Ko te pikinga o te roa o te pūnaha puna ko:
x = F / k = w / k
x = 20 / 375
x = 0,05 mita
x = 5 henemita

3. E whā ngā puna ōrite kua whakaritea kia raupapa, kia whakarara hoki, e ai ki te pikitia i raro nei. Ina hoatu he kawenga o te 20 Newton, ka piki ake te roa o te pūnaha puna mā te 4 cm. Whakatauhia (a) te pūmau whakakotahi o te pūnaha. ngā puna raupapa-whakarara (b) te pūmau o ia puna.
Kōrero
E mōhiotia ana:
Te kaha taumaha (w) = 20 Newton
Ko te pikinga o te roa o te pūnaha puna (x) = 4 cm = 0,04 mita
Whakautu:
(a) pūmau whakakotahi o te pūnaha puna
k = F / x = w / x
k = 20 / 0,04 = 500 Newton/mita
(B) te pumau o ia puna
He ōrite ngā puna e whā, ā, he ōrite te pūmau o ngā puna e whā. Mēnā ka whakakapia ngā puna 1, 2, me te 3 ki tētahi puna kotahi, ka rua ngā puna, arā, ko ngā puna whakakapinga whakarara (k_p) me te puna 4 (k₄). Kua whakaritea ēnei puna e rua kia raupapa. Ko te tātai mō te whakatau i te pūmau raupapa ko:
1/k = 1/k_p + 1/k₄  
1/500 = 1/k_p + 1/k₄  —- whārite 1
k_p ko te pūmau puna whakakapinga mō ngā puna 1, 2, me te 3 kua whakaritea kia whakarara. Nā te mea he ōrite ngā puna e toru, he rite te rahi o te pūmau puna o ia puna, ā, ka taea te whakaatu mā te reta k.
k_p = k₁ +k₂ +k₃
k_p = k + k + k
k_p = 3k —- whārite 2
Whakakapia k_p i roto i te whārite 1 me k_p i te whārite 2. Tāpirihia hoki ki te k₄ me k
1/500 = 1/3k + 1/k
1/500 = 1/3k + 3/3k
1/500 = 4/3k
3k = (4)(500)
3k = 2000
k = 2000 / 3
k = 667 N/m (hua porowhita)
Nō reira, ko te pūmau o ia puna ko k₁ = k₂ = k₃ = k₄ = 667 Ngā Newtoni/mita.

4. E toru ngā puna kua whakaritea e ai ki te pikitia i raro nei. Ko te pūmau o ia puna ko k.₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m. Kei te iri te papatipu ki raro i te puna kia piki ake te roa o te huihuinga puna ki te 10 cm. Mena ko te whakaterenga nā te kaha ā-papatipu he 10 m/s² kātahi ko te taumaha o te kawenga he…
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg

Kōrero:
E mōhiotia ana :
k₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m
x = 10 henimita = 0,1 mita
karamu = 10 m/s²
I pātaihia :
Te taumaha o te kawenga (m) ?
Whakautu :
Te Tātai Ture a Hooke :
F = kx
w = kx
mg = kx
Whakaahuatanga: F = te kaha, w = te taumaha ā-papatipu, m = te papatipu o te kawenga, g = te whakaterenga nā te taumaha ā-papatipu, k = te pūmau puna, x = te pikinga o te roa o te huihuinga puna
Tātaihia te pūmau puna whakakotahi :
Kei te whakarite whakarara te puna 1 me te puna 2. Ko te pūmau puna ōrite ko:
k_p = k₁ +k₂ = 100 + 100 = 200 N/m
Kua whakaritea te puna whakakapinga me te puna 3 kia raupapa. Ko te pūmau puna whakakapinga ko:
1/k = 1/k_p + 1/k₃ = 1/200 + 1/200 = 2/200
k = 200/2 = 100 N/m
Tātaihia te papatipu o te kawenga :
mg = kx
m (10) = (100)(0,1)
m (10) = 10
m = 10 / 10
m = 1 kg
Ko te whakautu tika ko A.