10 Ngā Āhuatanga Hihiri e hono ana mā te taura ki runga i te pūrei Mīhini Atwood – Ngā Raru me ngā Otinga
1. Poraka A he 5 kg te taumaha , kei runga i te papa whakapae maeneene. Poraka B he 3 kg te taumaha e iri ana i tetahi pito o te taura e hono ana ki te poraka A i runga i te pūreirei. Ko te tere o te kaha ā-papa he 10 m/s2 . He aha te tere o te tere o ngā poraka e rua?
Mōhiotia:
Te taumaha o te poraka A (mA) = 5 kirokaramu
Taumaha o te poraka B (m B ) = 3 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka B (w B ) = m B g = (3)(10) = 30 Newton
E hiahiatia ana: Te whakaterenga o ngā poraka e rua (a)
Rongoā:
He maeneene te papa whakapae, nō reira kāore he kaha waku. Ko te kaha e whakatere ana i ngā poraka e rua ko te taumaha o te poraka B.
ΣF = ma
w B = (m A + m B ) a
30 = (5 + 3) he
30 = 8
ā = 30 / 8
a = 3.75 m/s 2
2.
I runga i te ahua i runga ake nei, 
(1) te whakaterenga o te mea = 0
(2) ka neke te mea i te tere pumau
(3) te mea e okioki ana
(4) ka neke te mea mena he iti ake te taumaha o te mea i te kaha e kukume ana i te mea.
Rongoā:
(1) Ko te whakaterenga o te mea = 0.
Te kaha kupenga:
∑ F = ma –> whakaterenga (a) = 0
∑ F = 0
F 1 + F 2 – F 3 = 12 + 24 – 36 = 36 – 36 = 0 N
(2) Ka neke te mea i te tere pumau
Ko te kore whakaterenga he tikanga kei te okioki te mea, kei te neke rānei i te tere pumau.
(3) te mea e okioki ana
Ko te kore o te kaha kupenga he tikanga kei te okioki te mea.
(4) ka neke te mea mena he iti ake te taumaha o te mea i te kaha e kukume ana i te mea.
Ka pā te taumaha ki te ahunga poutū, ko te kaha kukume ia ka pā ki te ahunga whakapae.
Ka neke te mea i te ahunga whakapae, nō reira ko ngā kaha whakapae anake e pā ana ki te mea ka nekehia
3. Mena ko te tauwehenga o te waku nekeneke i waenga i te poraka A me te mata o te tēpu he 0.1. Ko te whakaterenga nā te kaha ā-papa he 10 m/s2, kāti he aha te kaha e pā ana ki te poraka A kia neke ai te pūnaha ki maui i roto i te 2 m/ s2.
Mōhiotia:
Te taumaha o te poraka A (mA) = 30 kirokaramu
taumaha o te poraka A (w A ) = (30 kg)(10 m/s 2 ) = 300 kg m/s 2 , 300 Newton rānei
Taumaha o te poraka B (m B ) = 20 kg
taumaha o te poraka B (w B ) = (20 kg)(10 m/s 2 ) = 200 kg m/s 2 , 200 Newton rānei
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Tauwehenga o te waku nekeneke ( μk ) = 0.1
Te whakaterenga o te pūnaha (a) = 2 m/s 2 (ki te taha maui)
Te kaha o te waku nekeneke (f k ) = μ k N = μ k w A = (0.1)(300) = 30 Newtons
E hiahiatia ana: Te rahi o te kaha F
Rongoā:
Te ture tuarua a Newton:
ΣF = ma
Ka neke te mea A ki te taha maui:
F – f k – w B = (m A + m B ) a
F – 30 – 200 = (30 + 20)(2)
F – 230 = (50)(2)
F – 230 = 100
F = 230 + 100
F = 330 Newton
4. E rua ngā mea, ko A = 2 kg me B = 6 kg, e herea ana ki tētahi pito o te taura ki runga i tētahi pūrei, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , he aha te whakaterenga o te mea B?
Mōhiotia:
Papatipu o te mea A (mA) = 2 kg, mB = 6 kg, karamu = 10 m/s2
taumaha o te mea A (w A ) = (m A )(g) = (2)(10) = 20 N
taumaha o te mea B (w B ) = (m B )(g) = (6)(10) = 60 N
E hiahiatia ana: Te whakaterenga o te ahanoa b (te whakaterenga o te pūnaha).
Rongoā:
w B > w A kia neke whakararo te mea B, kia neke whakarunga te mea A
ΣF = ma
w B – w A = (m A + m B ) a
60 – 20 = (2 + 6) he
40 = (8) he
a = 5 m/s 2
5. E rua ngā mea e honoa ana e te taura i runga i te pūrei maeneene, e whakaaturia ana i te pikitia i raro nei. Mena ko m 1 = 1 kg, m 2 = 2 kg, ā, ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , he aha te kaha kume T?
Mōhiotia:
Papatipu o te mea 1 (m1) = 1 kirokaramu
Taumaha o te mea 2 (m² ) = 2 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
taumaha o te mea 1 (w1 ) = m1 karamu = (1 kg)(10 m/s2 ) = 10 kg m/s2 , 10 rānei ngā Newton
taumaha o te mea 2 (w2 ) = m2 karamu = (2 kg)(10 m/s2 ) = 20 kg m/s2 , 20 Newton rānei
E hiahiatia ana: Te kaha kume (T)?
Rongoā:
w 2 > w 1 nō reira ka neke a m 2 ki raro , ka neke a m 1 ki runga.
Te ture tuarua o te nekehanga a Newton :
ΣF = ma
w 2 – w 1 = (m 1 + m 2 ) a
20 – 10 = (1 + 2) a
10 = (3) he
a = 3.3 m/s 2
Te whakaterenga o te pūnaha = 3.3 m/ s².
Ka neke whakararo a m2 :
w 2 – T 2 = m 2 a
20 – T 2 = (2)(3.33)
20 – T 2 = 6.66
T 2 = 20 – 6.66
T 2 = 13.3 Newton
Ka neke ake a m1 :
T 1 – w 1 = m 1 a
T 1 – 10 = (1)(3.3)
T 1 – 10 = 3.33
T 1 = 10 + 3.33
T 1 = 13.3 Newton
Ko te kaha kume (T) = 13.3 Newton.
6. Te taumaha o te m1 = 6 kg, ā, te taumaha o te m2 = 4 kg. He maeneene te mata whakapae. Ko te tere o te kaha ā-papa he 10 m/s2 . He aha te tere o te pūnaha?
Mōhiotia:
Papatipu o m1 = 6 kirokaramu
papatipu o m 2 = 4 kg
te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
taumaha o te w1 = m1 karamu = (6 kg)(10 m/s2 ) = 60 kg m/s2 , 60 Newton rānei
taumaha o te w2 = m2 karamu = (4 kg)(10 m/s2 ) = 40 kg m/s2 , 40 Newton rānei
E hiahiatia ana: Te whakaterenga o te pūnaha (a)
Rongoā:
m 1 i runga i tētahi papa whakapae maeneene, kāore he waku, kia tere ake ai te pūnaha i te taumaha o te poraka 2.
Whakamahia te ture tuarua a Newton:
∑ F = ma
w 2 = (m 1 + m 2 ) a
40 N = (6 kg + 4 kg) a
40 N = (10 kg) a
a = 40 N / 10 kg
a = 4 m/s 2
7. E rua ngā poraka, ko te taumaha o ia poraka he 2 kg, e honoa ana e te taura i runga i te pūreirei, e whakaaturia ana i te pikitia i raro nei. He maeneene te papa whakapae me te pūreirei. Mena ka tōia te poraka B e te kaha whakapae o te 40 Newtons, he aha te whakaterenga o te poraka? Ko te whakaterenga nā te kaha ā-papa he 10 m/ s².
Mōhiotia:
te papatipu o te poraka A (mA) = te papatipu o te poraka B (mB) = 2 kirokaramu
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te kaha o F = 40 N
taumaha o te mea A (w A ) = mg = (2)(10) = 20 N
E hiahiatia ana: Te whakaterenga o te pūnaha (a)?
Rongoā:
Whakamahia te ture tuarua a Newton:
∑ F = ma
F – w A = (m A + m B ) a
40 – 20 = (2 + 2) he
20 = (4) he
ā = 20 / 4
a = 5 m/s 2
8. Te taumaha o te poraka A = 2 kg me te taumaha o te poraka B = 1 kg. I te tīmatanga ka okioki te poraka B, kātahi ka whakatereterehia ki raro tae noa ki te taunga ki te whenua. Ko te whakateretere nā te kaha ā-papa he 10 m/s 2. He aha te rahi o te kaha kume.
Mōhiotia:
Te taumaha o te poraka A (mA) = 2 kirokaramu
Taumaha o te poraka B (m B ) = 1 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka B (w B ) = m B g = (1)(10) = 10 Newton
E hiahiatia ana: Te rahi o te kaha kume (T)
Rongoā:
Kaua e aro ki te kaha o te waku.
Te whakaterenga o te pūnaha (a)
∑ F = ma
w B = (m A + m B ) a
10 = (2 + 1) he
10 = 3
ā = 10/3
Te kaha kume (T)
Te kaha kume i runga i te poraka A:
∑ F = ma
T = m A a = (2)(10/3) = 20/3 = 6.7 Ngā Newton
Te kaha kume i runga i te poraka B:
∑ F = ma
w B – T = m B a
10 – T = (1)(10/3)
10 – T = 3.3
T = 10 – 3.3 = 6.7 Newton
Ko te kaha kume (T) = 6.7 Newton
9. Te taumaha o te poraka A = 2 kg me te taumaha o te poraka B = 1 kg. Ko te kaha waku i waenga i te mea A me te papa whakapae = 2.5 Newton. Kaua e aro ki te waku i runga i te pūre me te taura. He aha te whakaterenga o ngā poraka e rua.
Mōhiotia:
Te taumaha o te poraka A (mA) = 2 kirokaramu
Taumaha o te poraka B (m B ) = 1 kg
Te kaha waku i waenganui i te raka a me te papa whakapae (f kA ) = 2.5 Newtons
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka (w B ) = m B g = (1)(10) = 10 Newton
E hiahiatia ana: Te whakaterenga o ngā poraka e rua (a)
Rongoā:
Whakamahia te ture tuarua a Newton:
∑ F = ma
w B – f k = (m A + m B ) a
10 – 2.5 = (2 + 1) he
7.5 = 3
ā = 7.5 / 3
a = 2.5 m/s 2
10. Te taumaha o te poraka a = 30 kg, e takoto ana i runga i te papa whakapae e hono ana ki te poraka B me te taumaha o te 10 kg i runga i te pūreirei. He aha te whakaterenga o te pūnaha? Ko te whakaterenga nā te kaha ā-papatipu he 10 ms -2.
Mōhiotia:
Te taumaha o te poraka A (mA) = 30 kirokaramu
Taumaha o te poraka B (m B ) = 10 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
taumaha o te poraka B (w B ) = m B g = (10)(10) = 100 Newton
E hiahiatia ana: Te whakaterenga o te pūnaha (a)
Rongoā:
∑ F = ma
w B = (m A + m B ) a
100 = (30 + 10) he
100 = 40
ā = 100 / 40
a = 2.5 m/s 2
