Te nekehanga hurihuri - ngā raruraru me ngā otinga

Te nekehanga hurihuri - ngā raruraru me ngā otinga

Tuhinga

1. He kurupae 140 cm te roa. E toru ngā kaha e pā ana ki te kurupae, F ₁ = 20 N, F ₂ = 10 N, me F ₃ = 40 N, me te ahunga me te tūranga e whakaaturia ana i te pikitia i raro nei. He aha te taipana e meinga ai te kurupae kia huri huri noa i te pokapū o te papatipu o te kurupae?

Mōhiotia:

Kei waenganui o te kurupae te pokapū o te papatipu.

Te roa o te kurupae (l) = 140 cm = 1.4 mita

Te kaha 1 (F ₁ ) = 20 N, te ringa rīwhi 1 (l ₁ ) = 70 cm = 0.7 mita

Te kaha 2 (F ₂ ) = 10 N, te ringa rīwhi 2 (l ₂ ) = 100 cm – 70 cm = 30 cm = 0.3 mita

Te kaha 3 (F ₃ ) = 40 N, te ringa rīwhi 3 (l ₃ ) = 70 cm = 0.7 mita

E hiahiatia ana: Te rahi o te taipana

Rongoā:

Ka hurihia te kurupae e te taipana 1 ki te taha matau, nō reira kua tohua he tohu kino ki te taipana 1.

τ ₁ = F ₁ l ₁ = (20 N)(0.7 m) = -14 N m

Ka hurihia te hihi e te taipana 2 ki te taha maui, nō reira ka tohaina he tohu pai ki te taipana 2.

τ ₂ = F ₂ l ₂ = (10 N)(0.3 m) = 3 N m

Ka huri te taipana 3 ki te taha matau, nō reira kua tohua he tohu pai ki te taipana 3.

τ ₃ = F ₃ l3 = (40 N)(0.7 m) = -28 N m

Te taipana kupenga:

Στ = -14 Nm + 3 Nm – 28 Nm = – 42 Nm + 3 Nm = -39 Nm

Ko te rahi o te taipana he 39 N m. Ko te ahunga o te hurihanga o te hihi ki te taha matau, nō reira kua tohua he tohu kino.

2. He aha te pānga o te taipana kupenga ki te kurupae? Ko te tuaka hurihuri i te pūwāhi D. (sin 53 ^o = 0.8)

Mōhiotia:

Te tuaka hurihuri i te pūwāhi D

F ₁ = 10 N me l ₁ = r ₁ hara θ = (40 cm)(hara 53 ^o ) = (0.4 m)(0.8) = 0.32 mita

F ₂ = 10√2 N me l ₂ = r ₂ hara θ = (20 cm)(hara 45 ^o ) = (0.2 m)(0.5√2) = 0.1√2 mita

F ₃ = 20 N me l ₃ = r ₁ hara θ = (10 cm)(hara 90 ^o ) = (0.1 m)(1) = 0.1 mita

E hiahiatia ana: Te taipana kupenga

Rongoā:

τ ₁ = F ₁ l ₁ = (10 N)(0.32 m) = 3.2 Nm

(Ka huri te hihi taipana 1 ki te taha maui o te karaka, nō reira ka tohua he tohu pai ki te taipana 1)

τ ₂ = F ₂ l ₂ = (10√2 N)( 0.1√2 m) = -2 Nm

(Ka huri te hihi o te taipana 2 ki te taha matau, nō reira ka tohua e tātou he tohu kino ki te taipana 2)

τ ₃ = F ₂ l ₂ = (20 N)(0.1 m) = 2 Nm

(Ka huri te hihi taipana 3 ki te taha maui o te karaka, nō reira ka tohua he tohu pai ki te taipana 3)

Te taipana kupenga:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3.2 Nm – 2 Nm + 2 Nm

Στ = 3.2 Nm

3. He aha te taipana kupenga mēnā ko te tuaka hurihuri i te pūwāhi D. (sin 53 ^o = 0.8)

Mōhiotia:

Te tuaka hurihuri i te pūwāhi D.

Te tawhiti i waenganui i a F ₁ me te tuaka hurihuri (r _AD ) = 40 cm = 0.4 m

Te tawhiti i waenganui i a F ₂ me te tuaka hurihuri (r _BD ) = 20 cm = 0.2 m

Te tawhiti i waenganui i a F ₃ me te tuaka hurihuri (r _CD ) = 10 cm = 0.1 m

F ₁ = 10 Newton

F ₂ = 10√2 Newton

F ₃ = 20 Newton

Sin 53 ^o = 0.8

E hiahiatia ana: Te taipana kupenga

Rongoā:

Te wā o te kaha 1

Στ ₁ = (F ₁ )(r hara _AD 53 ^o ) = (10 N)(0.4 m)(0.8) = 3.2 Nm

(Ka huri te hihi taipana 1 ki te taha maui o te karaka, nō reira ka tohua he tohu pai ki te taipana 1)

Te wā o te kaha 2

Στ ₂ = (F ₂ )(r _BD hara 45 ^o ) = (10√2 N)(0.2 m)(0.5√2) = -2 Nm

(Ka huri te hihi o te taipana 2 ki te taha matau, nō reira ka tohua e tātou he tohu kino ki te taipana 2)

Te wā o te kaha 3

Στ ₃ = (F ₃ )(r _CD hara 90 ^o ) = (20 N)(0.1 m)(1) = 2 Nm

(Ka huri te hihi taipana 2 ki te taha maui o te karaka, nō reira ka tohua he tohu pai ki te taipana 3)

Te taipana kupenga:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3.2 – 2 + 2

Στ = 3.2 mita Newton

Te wā o te korekore

4. Te roa o te waea = 12 m, l ₁ = 4 m. Kaua e aro ki te taumaha o te waea. He aha te wā o te inertia o te pūnaha?

Mōhiotia:

Papatipu o A (mA ₎ = 0.2 kg

Papatipu o B (m _B ) = 0.6 kg

Te tawhiti i waenganui i a A me te tuaka hurihuri (r _A ) = 4 mita

Te tawhiti i waenganui i a B me te tuaka hurihuri (r _B ) = 12 – 4 = 8 mita

E hiahiatia ana: Te wā o te korekore o te pūnaha

Rongoā:

Te wā o te korekore o A

I _A = (m _A )(r _A ² ) = (0.2)(4) ² = (0.2)(16) = 3.2 kg m ²

Te wā o te korekore o B

I _B = (m _B )(r _B ² ) = (0.6)(8) ² = (0.6)(64) = 38.4 kg m ²

Te wā o te korekore o te pūnaha:

I = I _A + I _B = 3.2 + 38.4 = 41.6 kg m ²

Ngā hihiri hurihuri

5. Ka pāngia he kaha 6-N ki tētahi taura e takai ana i tētahi pūrei he taumaha M = 5 kg, ā, ko te pūtoro R = 20 cm. He aha te whakaterenga koki o te pūrei? He rango totoka ōrite te pūrei.

Mōhiotia:

Te Kaha (F) = 6 Newton

Taumaha (M) = 5 kg

Pūtoro (R) = 20 henimita = 20/100 m = 0.2 m

E hiahiatia ana: Te whakaterenga koki (α)

Rongoā:

Te wā o te kaha:

τ = FR = (6 Newton)(0.2 mita) = 1.2 N m

Te wā o te korehau mō te rango totoka:

I = 1/2 MR ²

I = 1/2 (5 kg)(0.2 m) ²

I = 1/2 (5 kg)(0.04 ^m² )

I = 1/2 (0.2)

I = 0.1 kg ^m².

Te whakaterenga koki:

τ = I α

α = τ / I = 1.2 / 0.1 = 12 rad s ^-2

6. He poraka taumaha = 4 kg e iri ana i tētahi taura e takai ana i tētahi pūreirei taumaha = 8 kg, ā, ko te pūtoro R = 10 cm. Ko te whakaterenga nā te kaha ā-papatipu he 10 ms ^-2 . He aha te whakaterenga rārangi o te poraka? He rango totoka ōrite te pūreirei.

Mōhiotia:

Te taumaha o te pūrei (m) = 8 kg

Te whānui o te pūrakau (r) = 10 cm = 0.1 m

Taumaha o te poraka (m) = 4 kg

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

Taumaha (w) = mg = (4 kg)(10 m/s² ⁾ = 40 kg m/s² ⁼ 40 Newton

E hiahiatia ana: Te whakaterenga taka noa o te poraka

Rongoā:

Te wā o te korekore o te rango totoka:

I = 1/2 MR2 ⁼ 1/2 (8 kg)(0.1 m) ² = (4 kg)(0.01 m2 ⁾ = 0.04 kg ^m2

Te wā o te kaha:

τ = F r = (40 N)(0.1 m) = 4 Nm

Te whakaterenga koki:

Στ = I α

4 = 0.04 ā

α = 4 / 0.04 = 100

Te whakaterenga rārangi:

a = r α = (0.1)(100) = 10 m/s ²

7. He poraka he m te taumaha e iri ana i tētahi taura e takai ana i tētahi pūreirei. Mena ko te whakaterenga taka noa o te poraka he am/s ² , he aha te wā o te korehau o te pūreirei?

Mōhiotia:

taumaha = w = mg

Ringa rīpene = R

Ko te whakaterenga koki = α

Ko te whakaterenga taka noa o te poraka = a ms ^-2

E hiahiatia ana: Te wā o te korekore o te pūrakau (I)

Rongoā:

Ko te hononga i waenga i te whakaterenga raina me te whakaterenga koki:

a = Rα

α = a / R

Te wā o te koretake:

τ = I α

I = τ : α = τ : a / R = τ (R / a) = τ R a ^-1

Te nekehanga koki

8. E neke ana tētahi matūriki 0.2-karamu i roto i tētahi porowhita i te tere pumau o te 10 m/s. Ko te radius o te porowhita he 3 cm. He aha te nekehanga koki o te matūriki?

Mōhiotia:

Papatipu o te matūriki (m) = 0.2 karamu = 2 x 10 ^-4 kg

Tere koki (ω) = 10 rad s ^-1

Pūtoro (r) = 3 henimita = 3 x 10 ^-2 mita

E hiahiatia ana: Te nekehanga koki o te matūriki

Rongoā:

Te whārite o te nekehanga koki:

L = I ω

I = te nekehanga koki, I = te nekehanga o te korekore, ω = te tere koki

Te wā o te korekore (mō ngā matūriki):

I = mr ² = (2 x 10 ^-4 )(3 x 10 ^-2 ) ² = (2 x 10 ^-4 )(9 x 10 ^-4 ) = 18 x 10 ^-8

Te nekehanga koki:

L = I ω = (18 x 10 ^-8 )(10 rāti s ^-1 ) = 18 x 10 ^-7 kg m ² s ^-1

1. He aha te nekehanga hurihuri?
   • WhakautuKo te nekehanga hurihuri e pā ana ki te nekehanga o tētahi mea huri noa i tētahi tuaka pumau. Koinei te momo nekehanga e neke porowhita ana ia pūwāhi o te mea huri noa i te tuaka.
2. He aha te hononga o te tere rārangi ki te tere koki i roto i te nekehanga hurihuri?
   • Whakautu: Tere rārangi ($v$) o tētahi pūwāhi i roto i tētahi mea hurihuri he rite tonu ki tōna tawhiti ($r$) mai i te tuaka hurihuri me te tere koki ($\omega$) o te mea. Ko te whanaungatanga e homai ana e $v=rTuhinga\omega$.
3. He aha te wā o te inertia, ā, he aha tōna hononga ki te nekehanga hurihuri?
   • WhakautuKo te wā o te korekore he rite ki te hurihanga o te papatipu i roto i te nekehanga rārangi. Ka ine i te ātete o te mea ki ngā huringa o tōna āhua hurihanga. Ko te wā o te korekore e whakawhirinaki ana ki te papatipu o te mea me tōna tohatoha e pā ana ki te tuaka hurihanga.
4. He pēhea te pānga o te ture nekehanga tuatahi a Newton ki te nekehanga hurihuri?
   • WhakautuPērā i te mea e neke ana te mea rārangi, ka noho tonu te mea hurihuri i roto i taua āhua mēnā kāore he kaha o waho e pāngia e ia.
5. He aha te hiranga o te radius o te hurihuri?
   • WhakautuKo te pūtoro hurihuri he ine i te tohatoha o te papatipu o tētahi mea mai i tōna tuaka hurihuri. Ko te tikanga, e whakaahua ana i te tawhiti o te papatipu katoa o te mea mai i te tuaka me kukū kia rite te kaha o te inertia ki te tohatoha taketake.
6. He aha te nekehanga koki, ā, me pēhea te tiaki i tēnei?
   • WhakautuKo te nekehanga koki te ōrite hurihuri o te nekehanga rārangi. Ko te hua o te nekehanga korekore o te mea me tōna tere koki. I roto i tētahi pūnaha kati, ka noho pūmau te nekehanga koki katoa mēnā kāore he taipana o waho e pāngia ana, e whakaatu ana i te tiakitanga o te nekehanga koki.
7. He pēhea te awe o te taipana ki te nekehanga hurihuri?
   • WhakautuKo te taipana te ōrite o te hurihanga o te kaha. Ka puta he huringa i roto i te nekehanga hurihanga o tētahi mea. Ko te whanaungatanga e homai ana e te ture tuarua a Newton mō te hurihanga: $\tau =ITuhinga\alpha$, i reira $\tau$ ko te taipana, $I$ ko te wā o te korekore, ā, $\alpha$ ko te whakaterenga koki.
8. He aha te rerekētanga o te pokapū papatipu mai i te pokapū hurihuri?
   • WhakautuAhakoa ka taea te ōrite, ko te pokapū o te papatipu te pūwāhi e taea ai te kī he kukū te papatipu katoa o tētahi mea hei tātai i roto i te nekehanga rārangi, ko te pokapū ia o te hurihanga ko te pūwāhi (te tuaka rānei) e huri ai tētahi mea.
9. He aha te tūranga o te kaha pokapū i roto i te nekehanga hurihuri?
   • WhakautuKo te kaha pūrua te kaha kupenga e pā ana ki tētahi mea e neke ana i te ara porowhita, e anga ana ki te pokapū o te hurihanga. Koia te kawenga mō te pupuri i tētahi mea i tōna ara piko me te aukati i a ia kei neke i te rārangi tika nā te koretake.

10. He aha te hononga o te pūngao nekeneke hurihuri ki te wā o te inertia me te tere koki?

    • WhakautuKo te pūngao nekeneke hurihuri ko te pūngao e puta mai ana i te hurihuri o tētahi mea huri noa i tētahi tuaka. Ka homai e te tātai: KE_{rotational​}=1/2 ​I ω², i reira $I$ ko te wā o te korekore me te $\omega$ ko te tere koki.