11 Ngā Tauira o Ngā Pātai Hihiri Hurihuri
Te Wā o te Kāhua
1. He tokotoko tino māmā, 140 cm te roa. E toru ngā kaha e pā ana ki te tokotoko, F1 = 20 Newton, F2 = 10 N, me F3 = 40 N, ia ia me te ahunga me te tūranga e whakaaturia ana i te pikitia. Ko te rahi o te nekehanga kaha e meinga ai te tokotoko kia huri huri noa i tōna pokapū papatipu ko...
A. 40 Nm
B. 39 Nm
C. 28 Nm
D. 14 Nm
E. 3 Nm
Kōrero
E mōhiotia ana:
Kei waenganui o te tokotoko te pokapū o te papatipu o te tokotoko.
Te roa o te tokotoko (l) = 140 cm = 1,4 mita
Kaha 1 (F 1 ) = 20 N, ringa kaha 1 (l 1 ) = 70 cm = 0,7 mita
Te kaha 2 (F 2 ) = 10 N, te ringa o te kaha 2 (l 2 ) = 100 cm – 70 cm = 30 cm = 0,3 mita
Kaha 3 (F 3 ) = 40 N, ringa kaha 3 (l 3 ) = 70 cm = 0,7 mita
Pātai: Te rahi o te au o te kaha e meinga ai te tokotoko kia hurihuri i tōna pokapū papatipu
Whakautu:
Mā te au o te kaha 1 ka huri te tokotoko ki te taha matau. Nō reira, he kino te au o te kaha 1.
τ 1 = F 1 l 1 = (20 N)(0,7 m) = -14 N m
Mā te au o te kaha 2 ka huri te tokotoko ki te taha maui. Nō reira, he pai te au o te kaha 2.
τ 2 = F 2 l 2 = (10 N)(0,3 m) = 3 N m
Mā te au o te kaha 3 ka huri te tokotoko ki te taha matau. Nō reira, he kino te au o te kaha 3.
τ 3 = F 3 l 3 = (40 N)(0,7 m) = -28 N m
Te hua o te au o te kaha:
Στ = -14 Nm + 3 Nm – 28 Nm = – 42 Nm + 3 Nm = -39 Nm
Ko te rahi o te nekehanga kaha he 39 mita Newton. Ko te tohu kino e tohu ana ka huri te tokotoko ki te taha maui.
Ko te whakautu tika ko B.
2. Ko te tokotoko AB, kāore e arohia tōna papatipu, kua whakatakotoria whakapaetia, ā, e toru ngā kaha e pāngia ana e ia e ngā kaha e whakaaturia ana i te pikitia. Ko te hua o te kaha e pā ana ki te tokotoko ina hurihia i runga i te tuaka i D ko… (sin 53 o = 0,8)
A. 2,4 N m
B. 2,6 N m
C. 3,0 N m
D. 3,2 N m
E. 3,4 N m
Kōrero
E mōhiotia ana :
Kei te pūwāhi D te tuaka hurihuri, te tuaka takahuri rānei.
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
I pātaihia : Te hua o te au o te kaha
Whakautu :
τ 1 = F 1 l 1 = (10 N)(0,32 m) = 3,2 Nm
(he pai nā te mea ka huri te poraka i te taha maui o te karaka nā tēnei au o te kaha)
τ 1 = F 2 l 2 = (10√2 N)( 0,1√2 m) = -2 Nm
(kino nā te mea ka huri te poraka i te taha matau nā tēnei au o te kaha)
τ 1 = F 2 l 2 = (20 N)(0,1 m) = 2 Nm
(he pai nā te mea ka huri te poraka i te taha maui o te karaka nā tēnei au o te kaha)
Te hua o te au o te kaha:
Στ = τ 1 – τ 1 + τ 3
Στ = 3,2 Nm – 2 Nm + 2 Nm
Στ = 3,2 Nm
Ko te whakautu tika ko D.
3. Ko te tokotoko AB, kāore e arohia tōna papatipu, kua whakatakotoria whakapaetia, ā, e toru ngā kaha e pāngia ana e ia e ngā kaha e whakaaturia ana i te pikitia. Ko te hua o te kaha e pā ana ki te tokotoko ina hurihia i runga i te tuaka i D ko… (sin 53 o = 0,8)
A. 2,4 Nm
B. 2,6 Nm
C. 3,0 Nm
D. 3,2 Nm
E. 3,4 Nm
Kōrero
E mōhiotia ana :
Kei D te tuaka hurihuri.
Ko te tawhiti i waenganui i a F 1 me te tuaka hurihuri (r AD ) = 40 cm = 0,4 m
Ko te tawhiti i waenganui i a F 2 me te tuaka hurihuri (r BD ) = 20 cm = 0,2 m
Ko 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
Pātai : Te hua o te au o te kaha mēnā ka hurihia te tokotoko i runga i te tuaka i D
Whakautu :
Tātaihia te au o te kaha i puta mai i ia kaha.
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
He pai te au o te kaha 1 nā te mea ko te ahunga o te hurihanga o te tokotoko i puta mai i te au o te kaha 1 he taha maui.
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
He kino te au o te kaha 2 nā te mea ko te ahunga o te hurihanga o te tokotoko i puta mai i te au o te kaha 2 kei te ahunga kotahi ki te hurihanga o ngā ringaringa karaka.
Te wā o te kaha 3
Στ 3 = (F 3 )(r CD hara 90 o ) = (20 N)(0,1 m)(1) = 2 Nm
He pai te au o te kaha 3 nā te mea ko te ahunga o te hurihanga o te tokotoko i puta mai i te au o te kaha 3 he taha maui.
Te hua o te au o te kaha
Στ = Στ 1 + Στ 2 + Στ 3
Στ = 3,2 – 2 + 2
Στ = 3,2 mita Newton
Ko te whakautu tika ko D.
Te Wā o te Āhuakore
4. Whakaarohia te ahua o ngā pōro e rua e honoa ana e te waea. Ko te roa o te waea = 12 m, l 1 = 4 m, ā, kāore te papatipu o te waea e arohia, nō reira ko te rahi o te nekehanga o te inertia o te pūnaha ko…
A. 52,6 kg m2
B. 41,6 kg m²
C. 34,6 kg m²
D. 22,4 kg m²
E. 20,4 kg m²
Kōrero
E mōhiotia ana :
Papatipu o te pōro A (m A ) = 0,2 kg
Taumaha o te pōro B (m B ) = 0,6 kg
Ko te tawhiti i waenganui i te pōro A me te tuaka hurihuri (r A ) = 4 mita
Ko te tawhiti i waenganui i te pōro B me te tuaka hurihuri (r B ) = 12 – 4 = 8 mita
Pātai : Te wā o te korekore (I) o te pūnaha
Whakautu :
Te wā o te korekore o te pōro 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 te pōro 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 tētahi pūnaha matūriki :
I = I A + I B = 3,2 + 38,4 = 41,6 kg m 2
Ko te whakautu tika ko B.
Te Ture Tuarua a Newton mō te Nekehanga Hurihuri
5. Tirohia te ahua o tētahi wira totoka ōrite i te taha. Ka takaihia he aho ki te taha o te wira, kātahi ka tōia te pito o te aho ki te kaha F o te 6 N. Mena he 5 kg te taumaha o te wira, ā, he 20 cm te whānui o tōna pūtoro, ko te whakaterenga koki o te wira ko…
A. 0,12 rāti s-2
B. 1,2 rāti s –2
C. 3,0 rāti s –2
D. 6,0 rāti s –2
E. 12,0 rāti s –2
Kōrero
E mōhiotia ana:
Te kaha kume (F) = 6 Newton
Papatipu wira (M) = 5 kg
Te pūtoro o te wira (R) = 20 henimita = 20/100 m = 0,2 m
Pātai: Te whakaterenga koki o te wira (α)
Whakautu:
Tātaihia te au o te kaha:
τ = FR = (6 Newton)(0,2 mita) = 1,2 mita Newton
Tātaihia te wā o te koretake:
Ko te tātai mō te wā ātete o tētahi wira totoka i te āhua o tētahi kōpae, pereti rānei, ko 1/2 MR2 = 1/2 (5 kg)(0,2 m) 2 = 1/2 (5 kg)(0,04 m2 ) = 1/2 (0,2) = 0,1 kg m2.
Tātaihia te whakaterenga koki mā te whakamahi i te tātai hihiri hurihuri:
τ = I α
α = τ / I = 1,2 / 0,1 = 12 rad s -2
Ko te whakautu tika ko E.
6. He porotaka kōpae totoka, he 8 kg te taumaha, he 10 cm te whānui, kua takaihia ki te taha o te taura me te kawenga 4 kg e herea ana ki tētahi pito (g = 10 ms -2 ). Ko te whakaterenga o te nekehanga whakararo o te kawenga ko...
A. 2,5 ms –2
B. 5,0 ms –2
C. 10,0 ms –2
D. 20,0 ms –2
E. 33,3 ms –2
Kōrero
E mōhiotia ana:
Taumaha o te pūrei kōpae totoka (m) = 8 kg
Te whānui o te porotaka kōpae totoka (r) = 10 cm = 0,1 mita
Papatipu o te kawenga (m) = 4 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te kawenga (w) = mg = (4 kg)(10 m/s 2 ) = 40 kg m/s 2 = 40 Newton
Pātai: Te whakaterenga o te nekehanga whakararo o te kawenga
Whakautu:
Tātaihia te wā o te korehau o tētahi kōpae totoka:
I = 1/2 MR2 = 1/2 (8 kg)(0,1 m) 2 = (4 kg)(0,01 m2 ) = 0,04 kg m2
Tātaihia te au o te kaha:
τ = F r = (40 N)(0,1 m) = 4 Nm
Tātaihia te whakaterenga koki mā te whakamahi i te tātai ture tuarua a Newton mō te nekehanga hurihuri:
Στ = I α
4 = 0,04 ā
α = 4 / 0,04 = 100
Tātaihia te whakaterenga o te nekehanga whakararo o te kawenga:
a = r α = (0,1)(100) = 10 m/s 2
Ko te whakautu tika ko C.
7. He pūreirei totoka me te papatipu (M) me te radius (R) e whakaaturia ana i te pikitia! Kotahi te pito o te taura kore papatipu e takaihia ana ki te pūreirei, ko tetahi atu pito o te taura e whakairihia ana ki te kawenga o te m kg, ko te whakaterenga koki o te pūreirei (α) mēnā ka tukuna te kawenga. Mēnā ka tāpirihia he wahi kirihou A me te papatipu o te 1⁄2 M ki te pūreirei, kia puta ai te whakaterenga koki ōrite me hanga te kawenga…. (I pūreirei = 1/2 MR 2 )
A. 3/4 m kg
B. 3/2 m kg
C. 2 mita kg
D. 3 mita kg
E. 4 m kg
Kōrero
E mōhiotia ana :
papatipu kawenga = m
Taumaha kawenga = w = mg
Papatipu o te pūraka totoka = M
Te whānui o te pūraka totoka = R
Te whakaterenga koki o te pūrakau = α
I pātaihia :
Ki te piki te papatipu o te pūreirei ki te M + M/2 = 3M/2, ā, ko te whakaterenga koki o te pūreirei = α, he aha te papatipu o te kawenga?
Whakautu :
Te wā o te korekore o te pūrakau me te kore he kirihou:
I = 1/2 MR 2 = 0,5 MR 2
Te wā o te korekore o te pūrakau + te kirihou:
Ahau = 1/2 (3M/2) R 2 = (3M/4) R 2 = 0,75M R 2
Te wā o te kaha:
τ = FR
Te ture tuarua a Newton mō te nekehanga hurihuri:
Στ = I α
w R = I α
mg R = I α
α = mg R / I
Hei whakaputa i te whakaterenga koki ōrite, me hanga te papatipu o te kawenga….. Whakakapia a α i te whārite 2 ki a α i te whārite 1:
Ko te whakautu tika ko B.
8.. Kei te whakaatuhia he pūre i hangaia ki tētahi mea totoka me te taura e takai ana i tōna taha o waho e whakaaturia ana i te pikitia. Kāore i te arohia te waku o te pūre ki te taura me te waku i tōna tuaka hurihuri. Mena ka neke te kawenga ki raro me te whakaterenga pumau a ms -2 , ko te uara o te wā o te inertia o te pūre he ōrite ki….
A. I = τ α R
B. I = τ α -1 R
C. I = τ a R
D. I = τ a -1 R -1
E. I = τ a R -1
Kōrero
E mōhiotia ana:
Te kaha = w = mg
Ringa kaha = R
Whakaterenga koki = α
Te whakaterenga o te kawenga = a ms -2
Pātai: Te wā o te korekore o te pūrakau (I)
Whakautu:
Te whanaungatanga i waenga i te whakaterenga rārangi me te whakaterenga koki:
a = Rα
α = a / R
Ka tatauhia te wā o te inertia mā te whakamahi i te tātai:
τ = I α
I = τ : α = τ : a / R = τ (R / a) = τ R a -1
Kāore he whakautu tika.
9. Kei te whakaatuhia he pūrei i hangaia ki tētahi mea totoka me te taura e takai ana i tōna taha o waho e whakaaturia ana i te pikitia. Kāore te waku o te pūrei i arohia. Mena ko te wā o te inertia o te pūrei I = β, ā, ka kumea te taura ki te kaha pumau F, ko te uara o F he ōrite ki….
A. F = α. β. R 
B. F = α. β2 . R
C. F = α. (β. R) -1
D. F = α . β . (R) -1
E. F = R. (α.β) -1
Kōrero
E mōhiotia ana:
Te kaha tō = F
Te wā o te korekore o te pūraka = β
Te whakaterenga koki o te pūrakau = α
Te pūtoro o te pūrakau = R
Pātai: He ōrite te uara o F ki….
Whakautu:
Te tātai ture tuarua a Newton mō te nekehanga hurihuri:
Στ = β α ———- Whārite 1
Whakaahuatanga tātai:
Στ = Momeniti hua o te kaha (torque)
β = Te wā o te korekore
α = Whakaterenga koki
Te hua o te au o te kaha e pā ana ki te pūrei:
Στ = FR ———-> Whārite 2
Whakaahuatanga tātai:
F = te kaha kume
R = Te tawhiti mai i te pūwāhi mahi a te kaha F ki te tuaka hurihuri = te pūtoro o te porotaka
Whakakapia te Στ i te whārite 1 me te Στ i te whārite 2:
Στ = β . α
F. R = β. α
F = (β . α) / R
F = β. α. (R -1 )
Ko te whakautu tika ko D.
Te nekehanga koki
10. He matūriki he 0,2 karamu te taumaha e neke ana i roto i te porowhita me te tere koki pumau o te 10 rad s -1 . Mena he 3 cm te radius o te ara o te matūriki, ko te nekehanga koki o te matūriki ko...
A. 3 × 10 –7 kg m 2 s -1
B. 9 × 10 –7 kg m 2 s -1
C. 1,6 × 10 –6 kg m 2 s -1
D. 1,8 × 10 –4 kg m 2 s -1
E. 4,5 × 10 –3 kg m 2 s -1
Kōrero
E mōhiotia ana:
Papatipu matūriki (m) = 0,2 karamu = 2 x 10 -4 kg
Te tere koki (ω) = 10 rad s -1
Te whānui o te ara matūriki (r) = 3 cm = 3 x 10 -2 mita
I pātaihia: Te nekehanga koki o te matūriki
Whakautu:
Tātai nekehanga koki:
L = I ω
Whakaahuatanga: I = te nekehanga koki, I = te nekehanga o te korekore, ω = te tere koki
Te wā o te korenga o te 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
Ko te nekehanga koki ko:
L = I ω = (18 x 10 -8 )(10 rāti s -1 ) = 18 x 10 -7 kg m 2 s -1
Kāore he whakautu tika.
11. Ka hurihuri te kaihaka me ōna ringa e totoro ana ki te roa o te 160 cm. Kātahi ka pikohia ōna ringa ki ngā tuke ki te roa o te 80 cm. Mena ka mau tonu te tere koki o te kaihaka, ko tōna nekehanga raina ko...
A. tonu
B. ka haurua te rahi taketake
Ka huri a C. hei 3/4 o te rahi taketake
E rua ngā wā ka nui ake te rahi o D. i te mea taketake
E whā ngā wā ka nui ake te rahi o E. i te mea taketake
Kōrero
E mōhiotia ana:
Pūtoro 1 (r 1 ) = 160 henemita
Pūtoro 2 (r 2 ) = 80 henemita
Tere koki 1 (ω 1 ) = ω
Tere koki 1 (ω 2 ) = ω
I pātaihia: Te nekehanga rārangi
Whakautu:
Tere raina 1:
v 1 = r 1 ω 1 = (160 cm) ω
Tere raina 2:
v 2 = r 2 ω 2 = (80 cm) ω
Te nekehanga rārangi 1:
p = mv 1 = m (160 cm) ω
Te nekehanga rārangi 2:
p = mv 2 = m (80 cm) ω
Nō reira ka 1/2 te whakarea o te nekehanga rārangi i te taketake.
Ko te whakautu tika ko B.
Pūtake pātai:
Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa
