7 Ngā Tauira o ngā Raru Momentum Koki
Te nekehanga koki
1. Kei tētahi mea te wā o te korekore 2 kg m2 ā, ka huri i runga i tētahi tuaka pumau me tere koki 1 rad/s. E hia te nui? te nekehanga koki taua mea?
Kōrero
E mōhiotia ana:
Te wā o te korenga o te kaha (I) = 2 kg m2
Tere koki (ω) = 1 rad/s
I pātaihia: Te nekehanga koki (L)
Whakautu:
Tātai nekehanga koki:
L = I ω
Whakaahuatanga: L = te nekehanga koki (kg m2/s), I = te tere o te korenga o te kaha (kg m2), ω = tere koki (rad/s)
Te nekehanga koki:
L = I ω = (2)(1) = 2 kg m2/s
2. He 2 kg te taumaha o tētahi pūrei kōpae totoka, ā, he 0,1 mita te whānui. Mēnā ka huri te pūrei i runga i tōna tuaka me te tere koki pumau o te 2 rad/hēkona, he aha te nekehanga koki o te pūrei?
Kōrero
E mōhiotia ana:
Te taumaha o te porotaka kōpae totoka (m) = 2 kirokaramu
Te whānui o te pūrei kōpae totoka (r) = 0.1 mita
Tere koki (ω) = 2 rātiana/hekona
I pātaihia: Te nekehanga koki o te pūrakau
Whakautu:
Ko te tātai mō te wā o te korekore o tētahi kōpae totoka mēnā ka huri i runga i tētahi tuaka e whakaaturia ana i te pikitia:
I = 1/2 mr2
Whakaahuatanga: I = te tere o te korenga o te kaha (kg m2), m = papatipu (kg), r = pūtoro (mita)
Te wā o te korekore o te kōpae totoka:
I = 1/2 (2)(0,1)2 = (1)(0,01) = 0,01 kg m2
Te nekehanga koki:
L = I ω = (0,01)(2) = 0,02 kg m2/s
3. He pōro totoka, he 2 kg te taumaha, ā, he 0,2 mita te whānui, e hurihuri ana i tōna tuaka me te tere koki o te 4 rad/s. Tātaihia te nekehanga koki o te pōro totoka!
Kōrero
E mōhiotia ana:
Te taumaha o te pōro totoka (m) = 2 kirokaramu
Te whānui o te porowhita totoka (r) = 0,2 mita
Tere koki (ω) = 4 rātiana/hekona
I pātaihia: Te nekehanga koki o te porowhita totoka
Whakautu:
Ko te tātai mō te wā o te korehau o tētahi pōro totoka mēnā ka huri i runga i tētahi tuaka e whakaaturia ana i te pikitia:
I = (2/5) mr2
Whakaahuatanga: I = te tere o te korenga o te kaha (kg m2), m = papatipu (kg), r = pūtoro (mita)
Te wā o te korekore o te porowhita totoka:
I = (2/5)(2)(0,2)2 = (4/5)(0,04) = 0,032 kg m2
Te nekehanga koki o te porowhita totoka:
L = I ω = (0,032)(4) = 0,128 kg m2/s
4. He mea e neke ana i roto i tētahi porowhita he 1 kg te taumaha me te tere koki pumau o te 2 rad/s. Tātaihia te nekehanga koki mēnā he 10 cm te radius o te ara o te matūriki.
Kōrero
E mōhiotia ana:
Papatipu o te mea (m) = 1 kirokaramu
Te whānui o te porowhita totoka (r) = 10 cm = 10/100 = 0,1 mita
Tere koki (ω) = 2 rātiana/hekona
I pātaihia: Te nekehanga koki
Whakautu:
Ko te tātai mō te wā o te korekore o te matūriki:
Ahau = Mr.2 = (1)(0,1)2 = (1)(0,01) = 0,01 kg m2
Te nekehanga koki:
L = I ω = (0,01)(2) = 0,02 kg m2/s
Te ture tiaki o te nekehanga koki
5. Ka huri tuatahi tētahi kōpae porotaka totoka ōrite i runga i tōna tuaka me te tere koki o te 5 rad/s. He whakarara te papa o te kōpae ki te papa whakapae. Ko te papatipu me te radius o te kōpae he 2 kg me te 0,2 mita. Mēnā ka whakatakotoria he mowhiti he papatipu o te 0,1 kg me te radius o te 0,2 mita ki runga i te kōpae, kei reira te pokapū o te mowhiti i runga ake i te pokapū o te kōpae, ka huri tahi te kōpae me te mowhiti me te tere koki o…
Kōrero
E mōhiotia ana:
Taumaha o te rango totoka (m1) = 2 kirokaramu
Te whānui o te rango totoka (r1) = 0,2 mita
Te tere koki o te rango totoka (ω1) = 5 rāti/hēkona
Papatipu mowhiti (m2) = 0,1 kirokaramu
Te pūtoro o te mowhiti (r)2) = 0,2 mita
I pātaihia: Te tere koki o ngā rango me ngā mowhiti
Whakautu:
Te kaha o te korenga o te rango totoka: I = 1⁄2 m1 r12 = 1⁄2 (2)(0,2)2 = (1)(0,04) = 0,04 kg m2
Te wā o te korekore o te mowhiti: I = mr2 = (0,1)(0,2)2 = (0,1)(0,04) = 0,004 kg m2
Te wā o te korekore o te rango totoka me te mowhiti (I) = 0,04 + 0,004 = 0,044 kg m2
Te nekehanga koki tīmatanga (L1) = Te nekehanga koki whakamutunga (L2)
I1 ω1 = Ahau2 ω2
(0,04)(5) = (0,044)(ω2)
(0,2) = (0,044)(ω2)
ω2 = 0,2 : 0,044
ω2 = 4,5 rāti/hēkona
6. Ka hurihuri te kanikani poi me ōna ringa e totoro ana ki te roa o te 150 cm me te tere koki o te 10 radians/hēkona. Kātahi ka piko te kanikani i ōna ringa ki te roa o te 75 cm i te tuke. He aha te tere koki whakamutunga?
Kōrero
E mōhiotia ana:
Pūtoro 1 (r1) = 150 henimita = 1,5 mita
Pūtoro 2 (r2) = 75 henimita = 0,75 mita
Tere koki 1 (ω1) = 10 rāti/hēkona
I pātaihia: Tere koki 2 (ω2)
Whakautu:
Te wā tuatahi o te korekore: I1 = Mr.12 = (m)(1,5)2 = 2,25 m
Te wā whakamutunga o te korenga o te kaha: I2 = Mr.22 = (m)(0,75)2 = 0,5625 m
Te nekehanga koki tīmatanga (L1) = Te nekehanga koki whakamutunga (L2)
I1 ω1 = Ahau2 ω2
(2,25 m)(10) = (0,5625 m)(ω2)
22,5 mita = (0,5625 mita)(ω2)
22,5 = (0,5625)(ω2)
ω2 = 22,5/0,5625
ω2 = 40 rāti/hēkona
7. Ka huri tuatahi tētahi kōpae porotaka totoka ōrite i runga i tōna tuaka me te tere koki o te 4 rad s.-1Ko te papatipu me te radius o te kōpae he 1 kg me te 0,5 m. Mēnā ka whakatakotoria he mowhiti ki runga i te kōpae, ko tōna papatipu me tōna radius he 0,2 kg me te 0,1 m, ā, ko te pokapū o te mowhiti kei runga ake i te pokapū o te kōpae porotaka totoka, ka huri tahi te kōpae porotaka totoka me te mowhiti me te tere koki...
A. 1 rad/s
B. 2 rad/s
C. 3 rad/s
D. 4 rad/s
E. 5 rad/s
Kōrero :
Te Wā o te Āhuakore rango totoka: I = ½ mr2 = ½ (1 kg)(0,5 m)2 = (0,5)(0,25) = 0,125 kg m2
Te Wā o te Āhuakore o te mowhiti: I = mr2 = (0,2 kg)(0,1 mita)2 = (0,2)(0,01) = 0,002 kg m2
Te Momentum Koki Tuatahi (L)1) = Te Manawa Koki Whakamutunga (L2)
I1 ω1 = Ahau2 ω2
(0,125 kg m2)(4 rad/s) = (0,125 kg m2 + 0,002 kg m2)(ω2)
(0,5) = (0,127)(ω2)
ω2 = 0,5 : 0,127
ω2 = 4 rāti/hēkona
Ko te whakautu tika ko D.
