3 Ngā Pātai mō te Whārite Taura
1. E whakaatu ana te pikitia i raro nei i ētahi poraka e toru, arā, ko A, ko B me C, kei runga i tētahi papa whakapae maeneene. Mēnā ko te papatipu A = 1 kg, ko te papatipu B = 2 kg, ko te papatipu C = 2 kg, ā, ko F = 10 N, tātaihia te ōwehenga o te kume i roto i te taura i waenganui i a A me B ki te kume i roto i te taura i waenganui i a B me C.
Mōhiotia:
Ko te papatipu o A (mA ) = 1 kg
Taumaha B (m B ) = 2 kg
Ko te papatipu o C (m C ) = 2 kg
Te kaha kume (F) = 10 N
E hiahiatia ana: T AB : T BC
Rongoā:
Tātaihia te whakaterenga o te pūnaha mā te whakamahi i te tātai Ture Tuarua a Newton:
ΣF = ma
F = (m A + m B + m C ) a
10 = (1 + 2 + 2) he
10 = 5
ā = 10 / 5
a = 2 m/s 2
Whakamahia te tātai kume taura hei tatau i te T AB
ΣF = ma
T AB = m A a = 1 (2) = 2 Ngā Newton
Whakamahia te tātai kume taura hei tatau i te T BC
ΣF = ma
T BC = (m A + m B ) a = (1 + 2) (2) = (3)(2) = 6 Ngā Newton
2. Kei te honoa te Taonga A he 6 kg te taumaha me te Taonga B he 3 kg te taumaha mā te taura e whakaaturia ana. Mena ko te tauwehenga o te waku he 0.3, ā, ko te karamu = 10 m/s 2 , tautuhia te whakaterenga o te taonga me te kume i roto i ngā taura o ia poraka.
Kua mohiotia:
Ko te papatipu o te mea A (m A ) = 6 kg
Ko te papatipu o te mea B (m B ) = 3 kg
Tauwehenga o te waku o te poraka A (µk ) = 0.3
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te taumaha o te poraka A (w A ) = m A g = (6)(10) = 60 N
Te kaha noa i runga i te poraka A (N A ) = w A = 60 N
Te taumaha o te poraka B (w B ) = m B g = (3)(10) = 30 N
E hiahiatia ana: Te whakaterenga o te pūnaha (a) me te kukū i roto i te taura (T)
Rongoā:
Tātaihia te kaha waku nekeneke, arā, te kaha waku ina neke te poraka A:
F k = µ k N A = (0,3)(60) = 18 Newtons
Tātaihia te whakaterenga o te pūnaha (a):
ΣF = ma
wB – Fk = (mA + mB ) a
30 – 18 = (6 + 3) he
12 = 9
a = 12 / 9 = 1,3 m/s 2
Tātaihia te kume o te aho i runga i te poraka A (T A ):
ΣF = ma
T A – F k = (m A ) a
T A – 18 = (6)(1,3)
T A – 18 = 7,8
TA = 7,8 + 18 = 25,8 Ngā Newton
Tātaihia te kumekume o te taura i runga i te kurupae B (T B ):
ΣF = ma
w B – T B = m B (a)
30 – T B = 3 (1,3)
30 – T B = 3,9
T B = 30 – 3,9
T B = 26,1 Ngā Newton
3. E rua ngā mea A me B, he 5 kg te taumaha, he 3 kg te taumaha, e honoa ana e tētahi pūreirei kore-waku. Ka pāngia te pūreirei e te kaha P ki runga. Mena kei te tū ngā poraka e rua i te tuatahi ki runga i te papa, he aha te whakaterenga o te poraka A, mena ko te rahi o P he 60 N?
Tātaihia hoki te kume o te taura i runga i ngā poraka A me B.
Kua mohiotia:
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Ko te papatipu o A (mA ) = 5 kg
Te taumaha o te poraka A (w A ) = m A g = (5)(10) = 50 Newton
Taumaha B (m B ) = 3 kg
Te taumaha o te poraka B (w B ) = m B g = (3)(10) = 30 Newton
Te Kaha P = 60 N
E hiahiatia ana: Te whakaterenga o te pūnaha o ngā kurupae A me B (a) me te kume o te taura i runga i te kurupae A (T A ) me te kurupae B (T B )
Rongoā:
Tātaihia te whakaterenga o te pūnaha mā te whakamahi i te tātai Ture Tuarua a Newton.
ΣF = ma
w A – w B = (m A + m B ) a
50 – 30 = (5 + 3) he
20 = 8
ā = 20 / 8
a = 2,5 m/s 2
Whakamahia te tātai kaha kume hei tatau i te kume i roto i te taura.
Te kumekume o te taura i te poraka A:
ΣF = ma
w A – T A = m A a
50 – T A = 5 (2,5)
50 – TA = 12,5
T A = 50 – 12,5 = 37,5 Ngā Newton
Te kumekume o te taura i te poraka B:
ΣF = ma
T B – w B = m B a
T B – 30 = 3 (2,5)
T B – 30 = 7,5
T B = 7,5 + 30 = 37,5 Ngā Newton
