Te ture a Hooke me tōna ngāwari – ngā raruraru me ngā otinga

Te ture a Hooke me tōna ngāwari – ngā raruraru me ngā otinga

Te huringa o te roa

1. Ko te roa o te tokotoko he L, e tōia ana e te kaha o F. Ko te nui o te whakaroa ko ∆L. He aha te rahi o te kaha mēnā ko te huringa o te roa he 4∆L.

Mōhiotia:

Kaha 1 (F ₁ ) = F

Ko te huringa o te roa 1 (∆L ₁ ) = ∆L

Ko te huringa o te roa 2 (∆L ₂ ) = 4 ∆L

E hiahiatia ana: Kaha 2 (F ₂ )

Rongoā:

Te whārite o te ture a Hooke

k = F / ΔL

k = te pūmau o te ngāwari, F = te kaha o F, ΔL = te huringa o te roa

k1 = _k2​

F ₁ / ∆L ₁ = F ₂ / ∆L ₂

F / ΔL = F ₂ / 4ΔL

Wh / 1 = Wh ₂ / 4

F = F ₂ / 4

F ₂ = 4F

2. He hononga raupapa-whakarara ngā puna, e whakaaturia ana i te pikitia i raro nei. He pūmau te puna 1, he pūmau te puna 2, ā, he pūmau te puna 3, he 200 N/m. Ko te taumaha o te mea he 100 karamu, ā, te whakaterenga nā te kaha ā-papa he 10 m/s². He aha te panonitanga o te roa o te ōrite puna.

Mōhiotia:

Papatipu o te mea (m) = 100 karamu = 0.1 kg

k1 = k2 ₌ k3 _{= 200} N/m

w = mg = (0.1 kg)(10 m/s² ⁾ = 1 kg m/s² ⁼ 1 Newton

E hiahiatia ana: Te huringa o te roa o te puna ōrite.

Rongoā:

Whakatauhia te ōrite pūmau puna:

Kei te hono whakarara te puna 2 (k ₂ ) me te puna 3 (k _{3 ). Ko te} pūmau puna ōrite:

kp ₌ k2 + k3 ₌ 200 + 200 = 400 _Nm ⁻¹

Kei te honoa raupapa te puna 1 (k1 ₎ me te puna p (kP _{) . Ko te pūmau puna ōrite:}

1/k _s = 1/k _p + 1/k ₁ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400

k _s = 400/3 Nm ⁻¹

Ko te pūmau puna ōrite ko 400/3 Nm ^-1

Tātaihia te huringa o te roa o te puna ōrite :

Te whārite o te ture a Hooke:

∆x = F / k = w / k

Te huringa o te roa o te puna ōrite :

∆x = w / k

∆x = 1 : 400/3 = 1 x 3/400 = 3/400 = 0.0075 m = 0.75 henimita

Te pumau o te puna

3. He aha te pūmau o te puna e ai ki ngā raraunga kei te ripanga i raro nei.

Rongoā:

Te whārite o te ture a Hooke:

k = F / Δx

Te pūmau o te puna:

k = 0.98 / 0.0008 = 1.96 / 0.0016 = 2.94 / 0.0024 = 3.92 / 0.0032 = 1.225 N/m

4. E toru ngā puna e honoa ana i roto i te raupapa-whakarara e whakaaturia ana i te pikitia i raro nei. Ko ngā pūmau o te puna k ₁ = k ₂ = 3 Nm ⁻¹ me te k ₃ = 6 Nm ⁻¹ . He aha te pūmau o te pūmau ōrite o te puna?

Mōhiotia:

Pūmau o te puna 1 (k ₁ ) = pūmau o te puna 2 (k ₂ ) = 3 Nm ⁻¹

Pūmau o te puna 3 (k ₃ ) = 6 Nm ⁻¹

E hiahiatia ana: te pūmau o te puna ōrite (k)

Rongoā:

E honoa ana te puna 1 (k1 ₎ me te puna 2 (k2 ₎ i te taha whakarara. Ko te Pūmau o te puna ōrite:

kp ₌ k1 + k2 ₌ 3 + 3 = 6 _Nm ⁻¹

Kei te hono raupapa te puna p (k _P ) me te puna 3 (k _{3 ). Ko te pūmau o te puna ōrite:}

1/k _s = 1/k _p + 1/k ₃ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6

k _s = 6/2 = 3 Nm ⁻¹

Ko te pūmau o te ōrite o te puna = 3 Nm ⁻¹.

5. He puna ko te roa o L, e tōia ana e te taumaha o w. E ai ki ngā raraunga i te ripanga i raro nei, he aha te pūmau o te puna ōrite:

Rongoā:

k = F / Δx

Te pūmau o te puna:

k = 10 / 0.02 = 20 / 0.04 = 30 / 0.06 = 40 / 0.08 = 500 N/m

6. E ai ki ngā raraunga kei te ripanga i raro nei, he aha te pūmau o te puna ōrite:

Rongoā:

k = F / Δx = w / Δx = mg / Δx

k = te pūmau o te ngāwari, w = te taumaha, m = te papatipu, g = te whakaterenga nā te kaha ā-papatipu, Δx = te huringa o te roa

Pūmau puna:

k = 2 / 0.05 = 4 / 0.1 = 6 / 0.15 = 8 / 0.20 = 10 / 0.25 = 40 N/m

7. Mena ko k ₁ = 4k, he aha te pūmau o te puna ōrite?

Rongoā:

E rua ngā puna e honoa ana i te taha whakarara. Ko te pūmau o te puna ōrite:

kp ₌ k + k = 2k

E rua ngā puna e honoa ana i roto i te raupapa. Ko te pūmau o te puna ōrite

1/k _s = 1/k _p + 1/k ₁ = 1 / 2k + 1 / 4k = 2 / 4k + 1 / 4k = 3 / 4k

k _s = 4k/3

8. E ai ki ngā raraunga kei te ripanga i raro nei, he aha te pūmau o te puna ōrite:

Rongoā:

Te whārite o te ture a Hooke:

k = F / ΔL

Te pūmau o te puna:

k = 2 / 0.0050 = 3 / 0.0075 = 4 / 0.01 = 400 Nm ^-1

9. Ko te pūmau iti rawa ko…

otinga

Te whārite o te ture a Hooke:

k = F / Δx

k = te pūmau o te ngāwari, F = te kaha, Δx = te huringa o te roa

Te pūmau o te ngāwari:

k _A = F / Δx = 1 / 0.05 = 20 N/m

kB = F / Δx = 2 / 0.025 = 80 N/ _m

kC = F / Δx = 1 / 0.025 = 40 N/ _m

k _D = F / Δx = 2 / 0.05 = 40 N/m

k _E = F / Δx = 2 / 0.25 = 8 N/m

10. He aha te pūmau nui rawa atu e ai ki ngā raraunga kei te ripanga i raro nei.

Rongoā:

Ko te whārite o te ture a Hooke:

k = F / Δx

k _A = 7 / 0.035 = 200 Nm ^-1

kB = 8 / 0.025 = 320 _Nm ^-1

kC = 6 / 0.020 = 300 _Nm ^-1

kD = 9 / 0.045 = 200 _Nm ^-1

k _E = 10 / 0.033 = 303 Nm ^-1

Ko te pūmau nui rawa ko 320 Nm ^-1.

11. E whakaatu ana te kauwhata i raro nei i te hononga i waenga i te panonitanga o te kaha (ΔF) me te pikinga o te roa (Δx). He aha te kauwhata e whakaatu ana i te pūmau iti rawa o te ngāwari?

otinga

Te whārite o te ture a Hooke:

k = F / Δx

Δx = te huringa o te roa, F = te kaha, k = te pūmau o te ngāwari

Te pūmau o te ngāwari:

k _A = F / Δx = 1 / 8 = 0.125

k _B = F / Δx = 8 / 3 = 2.7

kC = F / Δx = 6 / 6 = ₁

k _D = F / Δx = 3 / 5 = 0.6

k _E = F / Δx = 2 / 4 = 0.5

12. Ko tēhea kauwhata h kei a ia ngā pūmau rapa nui rawa atu?

Rongoā:

Pūmau o te ngāwari :

kA ₌ F / Δx = 50 / 10 = 5

k _B = F / Δx = 50 / 0.1 = 500

kC = F / Δx = 5 / 0.1 = ₅₀

k _D = F / Δx = 500 / 0.1 = 5000

k _E = F / Δx = 500 / 10 = 50

Te pūngao pūmanawa o te puna:

13. E whakaatu ana te kauwhata i raro nei i te whanaungatanga i waenga i te kaha me te huringa o te roa o te puna. He aha te kaha pūmanawa o te puna, e ai ki te kauwhata i raro nei.

Mōhiotia:

F = 40N

x = 0.08 mita

E hiahiatia ana : Te pūngao pūmanawa o te puna

Rongoā:

Te pūmau o te puna:

k = F / Δx = 40 / 0.08 = 500 N/m

Te pūngao pūmanawa o te puna:

PE = 1/2 kx ² = 1/2 (500)(0.08) = (250)(0.08) = 20 Joules

14. Kua tāpirihia he poraka 2-kg ki te puna. Mena ko te pikinga o te roa o te puna he 5 cm, ā, ko te whakaterenga nā te kaha ā-papa he 10 m/s² ^, he aha te kaha pūmanawa o te puna?

Mōhiotia:

Ko te pikinga o te roa (Δx) = 5 cm = 0.05 mita

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

Papatipu o te poraka (m) = 2 kg

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

E hiahiatia ana: te pūngao pūmanawa o te puna

Rongoā:

Te pūmau o te ngāwari:

k = w / Δx = 20 / 0.05 = 400 N/m

Te pūngao pūmanawa o te puna:

PE = ½ k Δx ² = ½ (400)(0.05) ² = (200)(0.0025)

PE = 0.5 Joule

15. Ko te huringa o te roa o te puna he 5 cm ina kumea e te kaha 20-N. He aha te kaha pūmanawa o te puna ina he 10 cm te huringa o te roa o te puna.

Mōhiotia:

Ko te panonitanga o te roa (Δx) = 5 cm = 0.05 mita

Te Kaha (F) = 20 Newton

E hiahiatia ana : Te pūngao pūmanawa o te puna

Rongoā:

Te pūmau o te puna:

k = F / Δx = 20 / 0.05 = 400 N/m

Ko te pūngao pūmanawa o te puna ina Δx = 10 cm = 0.1 m:

PE = ½ k Δx ² = ½ (400)(0.1) ² = (200)(0.01)

PE = 2 Joule

Taumaha o te mea

16. E whā ngā puna, ko te pūmau o ia puna he 800 N/m, e honoa ana i roto i te raupapa-whakarara, e whakaaturia ana i te pikitia. Kei te honoa tētahi poraka ki te puna. Ko te huringa o te roa o ngā puna katoa he 5 cm. He aha te taumaha o ngā poraka.

Mōhiotia:

k1 = k2 ₌ k3 ₌ k4 _{= 800} N m ⁻¹

Δx = 5 henimita = 0.05 m

E hiahiatia ana: te taumaha o te poraka (w)

Rongoā:

Whakatauhia te pūmau o te puna ōrite

Koanga 1 (k₁), puna 2 (k₂) me te puna 3 (k₃) e honoa ana i te taha whakarara. Ko te pūmau o te puna ōrite:

kp ₌ k1 ₊ k2 + k3 ₌ 800 + 800 + 800 = 2400 _Nm ⁻¹

Kei te hono raupapa te puna p (k _P ) me te puna 4 (k _{4 ). Ko te pūmau o te puna ōrite:}

1/k _s = 1/k _p + 1/k ₄ = 1/2400 + 1/800 = 1/2400 + 3/2400 = 4/2400

k _s = 2400/4 = 600 Nm ⁻¹

Ko te pūmau o te puna ōrite ko 600 Nm ^-1

Whakatauhia te taumaha o te mea:

Te whārite o te ture a Hooke:

F = k Δx, w = k Δx rānei

Taumaha o te mea:

w = (600 Nm ^-1 )(0.05 m) = 30 Ngā Niutona

17. E whā ngā puna e honoa ana i roto i te raupapa-whakarara. Ko te pūmau o ia puna he 1600 N/m. Kua tāpirihia he poraka i te mutunga o te puna, e whakaaturia ana i te pikitia. Ko te pikinga o te roa o ngā puna katoa he 5 cm. He aha te taumaha o ngā poraka?

Mōhiotia:

k1 = k2 ₌ k3 ₌ k4 _{= 1600} N m ⁻¹

Δx = 5 henimita = 0.05 m

E hiahiatia ana: te taumaha o te poraka

Rongoā:

Whakatauhia te pūmau o te puna ōrite

Koanga 1 (k₁), puna 2 (k₂) me te puna 3 (k₃) e honoa ana i te taha whakarara. Ko te pūmau o te puna ōrite:

k _P = k ₁ + k ₂ + k ₃ = 1600 + 1600 + 1600 = 4800 Nm ⁻¹

Kei te hono raupapa te puna p (k _P ) me te puna 4 (k _{4 ). Ko te pūmau o te puna ōrite:}

1/k _s = 1/k _p + 1/k ₄ = 1/4800 + 1/1600 = 1/4800 + 3/4800 = 4/4800

k _s = 4800/4 = 1200 Nm ⁻¹

Ko te pūmau o te puna ōrite ko 1200 Nm ^-1

Whakatauhia te taumaha o te mea:

Te whārite o te ture a Hooke:

F = k Δx, w = k Δx rānei

Taumaha o te mea:

w = (1200 Nm ^-1 )(0.05 m) = 60 Ngā Niutona

1. He aha te Ture a Hooke?
   • whakahoki: E whakaahua ana te Ture a Hooke i te whanaungatanga i waenga i te kaha e pā ana ki tētahi mea pīwariwari me te āhua rerekē e puta mai ana (ko te roa, ko te pēhitanga rānei te tikanga). Ina koa, e kī ana ko te kaha e hiahiatia ana hei pēhi, hei whakaroa rānei i tētahi puna he rite tonu ki te tawhiti e totorohia ana, e pēhia ana rānei, ki te kore e hipa i te rohe pīwariwari.
2. He aha te tikanga ina kīia kua eke te rauemi ki tōna rohenga ngāwari?
   • whakahoki: Ina tae te rauemi ki tōna rohe ngāwari, ko te tikanga kāore e hoki anō ki tōna āhua taketake, ki tōna rahi taketake rānei i muri i te tangohanga o te kaha whakarerekē. I tua atu i tēnei wāhi, ka noho kirihou te rauemi, ā, ka whakarerekē tonu pea.
3. He aha te hononga o te pūmau puna (k) ki te pakari o te puna?
   • whakahoki: Ko te pūmau puna (k) he ine i te pakari o te puna. Ko te uara nui o te k e tohu ana i te puna pakari ake, ko te tikanga he nui ake te kaha e hiahiatia ana hei whakapēke i tōna āhua i tētahi nui kua whakaritea, ko te k iti ake e tohu ana i te puna ngāwari ake, ngāwari ake rānei.
4. He aha ngā waeine o te pūmau puna i roto i te pūnaha SI?
   • whakahoki: I roto i te pūnaha SI, ko ngā waeine mō te pūmau puna (k) ko ngā Newton ia mita (N/m).
5. He aha i kiia ai te whanonga e whakaahuatia ana e te Ture a Hooke he mea rārangi?
   • whakahoki: E kiia ana te whanonga he rārangi tika nā te mea he rārangi tika te whanaungatanga i waenga i te kaha i whakamahia (F) me te nekehanga (x), me te whanaungatanga e hoatu ana ko $F=kx$, ina ko k he pūmau mō tētahi rauemi, mō tētahi puna rānei kua hoatu.
6. E pā ana te ture a Hooke ki ngā puna anake?
   • whakahoki: Kāo, e pā ana te Ture a Hooke ki ngā rauemi rapa katoa e rerekē ana te āhua me te kaha e whakamahia ana, tae noa ki tōna rohe rapa. Ahakoa he tauira noa ngā puna, ka taea hoki e ētahi atu rauemi pēnei i ngā here rapa, ngā konganuku i raro i ngā rerekētanga iti, me ētahi kiko koiora te whakaatu i te whanonga e whakaahuatia ana e te Ture a Hooke.
7. He aha te mea ka tupu mēnā ka totorohia tētahi rauemi ki tua atu i tōna rohe ngāwari engari kāore i te rawaka hei whati?
   • whakahoki: Ki te totorohia tētahi rauemi ki tua atu i tōna rohe pīngore engari kāore i te whati, ka rerekē te āhua kirihou. Ko te tikanga o tēnei, ina tangohia te kaha, e kore te rauemi e hoki katoa ki tōna āhua taketake, ā, ka toe tonu ētahi rerekētanga tuturu.
8. He aha te hononga o ngā ariā o te ahotea me te pehanga ki te Ture a Hooke?
   • whakahoki: Ko te ahotea te kaha e pā ana ki ia wāhanga horahanga, ā, ko te taumahatanga te whakarerekētanga whanaunga o tētahi rauemi. E ai ki te Ture a Hooke mō te ahotea me te taumahatanga, he rite tonu te ahotea ki te taumahatanga, ko te pūmau ōritetanga ko te modulus Young o te rauemi. He huarahi anō tēnei hei whakaatu i te whanaungatanga rārangi i waenga i te kaha me te whakarerekētanga, engari mō ngā rauemi papatipu kaua ko ngā puna anake.
9. He aha te Modulus a Young, ā, he aha tōna hononga ki te ngāwari?
   • whakahoki: Ko te Modulus a Young, e tohuhia ana e te reta $E$, he ine i te pakari o tētahi rauemi e pā ana ki te kume, ki te pēhanga rānei. E whakaahua ana i te kaha o te rauemi ki te ātete i te whakarerekētanga i raro i te kaha e pā ana. Ko te Young's Modulus teitei ake e tohu ana i tētahi rauemi pakari ake, ā, e tautuhia ana ko te ōwehenga o te ahotea ki te taumahatanga.
10. Ka taea te whakaahua i ngā rauemi katoa e te Ture a Hooke?

• whakahoki: Kāo, ehara i te mea ko ngā rauemi katoa e whanonga ana i runga i te Ture a Hooke. He maha ngā rauemi, inā koa ko ngā mea kāore i te raina, he viscoelastic, he kirihou rānei, kāore e whakaatu i te whanaungatanga raina i waenga i te ahotea me te taumahatanga. Ko te Ture a Hooke he whakaahuatanga tino pai, ā, he tino tika mō ngā whakarerekētanga iti o ngā rauemi elastic.