Ngā whakaoti rapanga i roto i ngā ture nekehanga a Newton – te ture nekehanga tuarua a Newton
1. I whakaterea he mea 1 kg te taumaha i te tere pumau 5 m/s2Whakatauhia te kaha kupenga e hiahiatia ana hei whakatere i te mea.
Mōhiotia:
Taumaha (m) = 1 kg
whakaterenga (a) = 5 m/s2
hiahia : te kaha kupenga (∑F)
Rongoā:
Ka whakamahia e mātou te ture tuarua a Newton hei tiki i te kaha kupenga.
∑F = ma
∑F = (1 kg)(5 m/s)2) = 5 kg m/s2 = 5 Niutona
2. Mass o tētahi mea = 1 kg, te kaha kupenga ∑F = 2 Newton. Whakatauhia te rahi me te ahunga o te whakaterenga o te mea….
Mōhiotia:
Taumaha (m) = 1 kg
Te kaha kupenga (∑F) = 2 Newton
hiahia : Te rahi me te ahunga o te whakaterenga (a)
Rongoā:
a = ∑F / m
ā = 2 / 1
a = 2 m/s2
Ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga (∑F)
3. Papatipu o te mea = 2 kg, F1 = 5 Newton, F2 = 3 Ngā Newton. Ko te rahi me te ahunga o te whakaterenga ko…
Mōhiotia:
Taumaha (m) = 2 kg
F1 = 5 Niutona
F2 = 3 Niutona
E hiahiatia ana: Te rahi me te ahunga o te whakaterenga (a)
Rongoā:
te kaha kupenga:
∑F = F1 - F2 = 5 – 3 = 2 Nītona
Te rahi o te whakaterenga:
a = ∑F / m
ā = 2 / 2
a = 1 m/s2
Te ahunga o te whakaterenga = te ahunga o te kaha kupenga = te ahunga o F1
4. Papatipu o te mea = 2 kg, F1 = 10 Newton, F2 = 1 Ngā Newton. Ko te rahi me te ahunga o te whakaterenga ko…
Mōhiotia:
Taumaha (m) = 2 kg
F2 = 1 Niutona
F1 = 10 Niutona
F1x =F1 whaimana 60o = (10)(0.5) = 5 Ngā Newton
hiahia : Te rahi me te ahunga o te whakaterenga (a)
Rongoā:
Te kaha kupenga:
∑F = F1x - F2 = 5 – 1 = 4 Nītona
Te rahi o te whakaterenga:
a = ∑F / m
ā = 4 / 2
a = 2 m/s2
Te ahunga o te whakaterenga = te ahunga o te kaha kupenga = te ahunga o F1x
5. F1 = 10 Newton, F2 = 1 Newton, m1 = 1 kg, mita2 = 2 kg. Ko te rahi me te ahunga o te whakaterenga ko…
Mōhiotia:
Taumaha 1 (m1) = 1 kirokaramu
Taumaha 2 (m2) = 2 kirokaramu
F1 = 10 Niutona
F2 = 1 Niutona
hiahia : Te rahi me te ahunga o te whakaterenga (a)
Rongoā:
Te kaha kupenga:
∑F = F1 - F2 = 10 – 1 = 9 Nītona
Te rahi o te whakaterenga:
a = ∑F / (m1 +m2)
ā = 9 / (1 + 2)
ā = 9 / 3
a = 3 m/s2
Ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga = te ahunga o F1
6.
He poraka 40-kg te taumaha i whakaterea ake e te kaha o te 200 N. Ko te whakaterenga o te poraka he 3 m/s2Whakatauhia te rahi o te kaha waku e pā ana ki te poraka.
A. 15 N
B. 40 N
C. 43 N
D. 80 N
Mōhiotia:
Taumaha (m) = 40 kg
Te kaha (F) = 200 N
Whakaterenga (a) = 3 m/s2
Hiahia: Te kaha waku (Fg)
Rongoā:
Ko te whārite o Te ture tuarua o te nekehanga a Newton
∑F = ma
∑F = te kaha kupenga, m = te papatipu, a = te whakaterenga
Ko te ahunga o te kaha F ki matau, ko te ahunga o te kaha waku ki maui (ko te ahunga o te kaha waku he ritenga kē ki te ahunga o te nekehanga o te mea).
Kōwhiria te taha matau hei pai, me te taha maui hei kino.
∑F = ma
Wh – Whg = mā
200 – Fg = (40)(3)
200 – Fg = 120
Fg = 200 - 120
Fg = 80 Niutona
Ko te whakautu tika ko D.
7. Whakatakotoria te poraka A he 100 karamu te taumaha ki runga ake i te poraka B he 300 karamu te taumaha, kātahi ka panaia te poraka B ki runga me te kaha 5 N poutū. Tātaihia te kaha noa i whakamahia e te poraka B ki te poraka A.
A. 1 N
B. 1.25 N
C. 2 N
D. 3 N
Mōhiotia:
Te Kaha (F) = 5 Newton
Te taumaha o te poraka A (mA) = 100 karamu = 0.1 kg
Te taumaha o te poraka B (mB) = 300 karamu = 0.3 kg
Te whakaterenga o te kaha ā-papa (g) = 10 m/s2
Taumaha o te poraka A (wA) = (0.1 kg)(10 m/s2) = 1 kg m/s2 = 1 Niutona
Taumaha o te poraka B (wB) = (0.3 kg)(10 m/s2) = 3 kg m/s2 = 3 Niutona
E hiahiatia ana: Te kaha noa i tukuna e te poraka B ki te poraka A
Rongoā:
He maha ngā kaha e pā ana ki ngā poraka e rua, e whakaaturia ana i te pikitia.
F = te kaha pana (mahi ki te poraka B)
wA = te taumaha o te poraka A (mahi ki te poraka A)
wB = te taumaha o te poraka B (mahi ki te poraka B)
NA = te kaha noa i tukuna e te poraka B ki te poraka A (Tuhinga ki te poraka A)
NA' = te kaha noa i tukuna e te poraka A ki te poraka B (Tuhinga ki te poraka B)
Whakamahia te ture nekehanga tuarua a Newton ki ngā poraka e rua:
∑F = ma
F – wA - wB +NA - NA' = (mA +mB) a
NA a NA' ko ngā kaha mahi-tauhohenga he rite te rahi engari he rerekē te ahunga, nō reira kua tangohia atu i te whārite.
F – wA - wB = (mA +mB) a
5 – 1 – 3 = (0.1 + 0.3) he
5 – 4 = (0.4) a
1 = (0.4) he
ā = 1 / 0.4
a = 2.5 m/s2
Whakamahia te ture nekehanga tuarua a Newton ki te poraka A:
∑F = ma
NA - wA = mA a
NA – 1 = (0.1)(2.5)
NA - 1 = 0.25
NA = 1 + 0.25
NA = 1.25 Niutona
Ko te whakautu tika ko B.
8. He mea e 4 N te taumaha e tautokona ana e te taura me te pūrei. Ka pā te kaha o te 2 N ki te poraka, ā, ka kumea tetahi pito o te taura e te kaha o te 9 N. Tātaihia te kaha kupenga e pā ana ki te mea X.
A. 3 N ki runga
B. 4 N ki raro
C. 9 N ki runga
D. 9 N ki raro
Mōhiotia:
Taumaha o X (wX) = 4 Niutona
Te kaha tō (F)x) = 2 Niutona
Te kaha kume (FT) = 9 Niutona
Hiahia: Ka pā te kaha kupenga ki te mea X
Rongoā:
Ngā kaha poutū whakarunga e pā ana ki te mea
He rite tonu te kaha kume i ngā wāhanga katoa o te taura. Nō reira, ko te kaha kume he 9 N.
Ngā kaha poutū ki raro e pā ana ki te mea
E rua ngā kaha e pā ana ki te mea X, ā, e rua ngā kaha e poutū ana ki raro, ko te wāhanga whakapae o te taumaha wx me te wāhanga whakapae o te kaha Fx.
Te pānga o te kaha kupenga ki te mea
FT - wX - Fx = 9 – 4 – 2 = 9 – 6 = 3
Ko te kaha kupenga e pā ana ki te mea X he 3 Newton, e anga whakarunga poutū ana ki runga.
Ko te whakautu tika ko A.
9. He mea e okioki ana i te tīmatanga i runga i tētahi mata whakapae maeneene. Ka pā te kaha o te 16 N ki te mea, ā, ka tere ake te mea i te 2 m/s2. Mena kei te tū te mea kotahi i runga i te mata whakapae taratara, nō reira ko te kaha waku e pā ana ki te mea he 2 N, tātaihia te whakaterenga o te mea mena ko te kaha ōrite o te 16 N e pā ana ki te mea.
A. 1.75 m/s2
B. 1.50 m/s2
C. 1.00 m/s2
D. 0.88 m/s2
Mōhiotia:
Te kaha (F) = 16 Newton = 16 kg m/s2
Whakaterenga (a) = 2 m/s2
Te kaha waku (Ffric) = 2 Newton = 2 kg m/s2
E hiahiatia ana: Te whakaterenga o te mea?
Rongoā:
Mata whakapae maeneene (kāore he kaha waku):
∑F = ma
F = ma
16 = (m) 2
m = 16 / 2
m = 8 kg
Ko te taumaha o te mea he 8 kirokaramu.
Mata whakapae taratara (he kaha waku kei reira):
∑F = ma
Wh – Whfric = mā
16 – 2 = 8 a
14 = 8
ā = 14 / 8
a = 1.75 m/s2
Ko te whakaterenga o te mea he 1.75 m/s2.
Ko te whakautu tika ko A.
10. Ka panaia e Tāme rāua ko Anaru tētahi mea ki runga i te papa maeneene. Ka panaia e Tāme te mea me te kaha o te 5.70 N. Mena ko te taumaha o te mea he 2.00 kg, ā, ko te whakaterenga e pā ana ki te mea he 2.00 ms.-2, kātahi ka whakatauhia te rahi me te ahunga o te mahi a te kaha e Tom.
A. 1.70 N, ā, ko tōna ahunga he ritenga kē ki te kaha i pā ki a Andre.w
B. 1.70 N, ā, ko tōna ahunga he rite ki te kaha i pā ki a Andrew
C. 2.30 N, ā, ko tōna ahunga he ritenga kē ki te kaha i pā ki a Andrew.
D. 2.30 N, ā, ko tōna ahunga he rite ki te kaha i pā ki a Andrew.
Mōhiotia:
Te kaha pana i whakahaerehia e Andrew (F)1) = 5.70 Niutona
Papatipu o te mea (m) = 2.00 kg
Whakaterenga (a) = 2.00 m/s2
E hiahiatia ana: Te rahi me te ahunga o te kaha i mahia e Tom (F2)?
Rongoā:
Whakamahia te ture tuarua o te nekehanga a Newton:
∑F = ma
F1 +F2 = mā
5.70 + F2 = (2)(2)
5.70 + F2 = 4
F2 = 4 - 5.70
F2 = – 1.7 Nūtene
I tohuhia e te tohu tango (F2) he ritenga kē ki te mahi pana kaha a Andrew (F1).
Ko te whakautu tika ko A.
11. Mena he ōrite te taumaha o te poraka, ko tēhea ahua e whakaatu ana i te whakaterenga iti rawa?
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Te kaha kupenga A:
ΣF = 4 N + 2 N – 3 N = 6 N – 3 N = 3 Newtons, whakatemauī
Te kaha kupenga B:
ΣF = 2 N + 3 N – 4 N = 5 N – 4 N = 1 Newtons, whakamatau
Te kaha kupenga C:
ΣF = 4 N + 3 N – 2 N = 7 N – 2 N = 5 Newtons, whakamatau
Te kaha kupenga D:
ΣF = 3 N + 4 N + 2 N = 9 Newtons, whakatikai
Ko te whārite o te ture tuarua a Newton:
ΣF = ma
a = ΣF / m
a = whakaterenga, ΣF = kaha kupenga, m = papatipu
I runga i te tātai i runga ake nei, he rite tonu te tere whakaterenga (a) ki te kaha kupenga (ΣF) me te rite whakamuri ki te papatipu (m). Mena he ōrite te papatipu o tētahi mea, ko te nui ake o te kaha ka puta, ko te nui ake o te tere whakaterenga, ko te iti iho rānei o te kaha ka puta, ko te iti iho o te tere whakaterenga.
I runga i te tātaitanga i runga ake nei, ko te kaha kupenga iti rawa ko te 1 Newton, nō reira ko te whakaterenga hoki te mea iti rawa.
Ko te whakautu tika ko B.
12. Ka pā ētahi kaha ki tētahi mea he 20 kg te taumaha, e whakaaturia ana i te pikitia i raro nei.
Whakatauhia te whakaterenga o te mea.
Mōhiotia:
Papatipu o te mea (m) = 20 kg
Topa kupenga (ΣF) = 25 N + 30 N – 15 N = 40 N
Hiahia: Te whakaterenga o tētahi mea
Rongoā:
Te whakaterenga o te mea i tatauhia mā te whakamahi i te whārite o te ture tuarua a Newton:
ΣF = ma
a = ΣF / m = 40 N / 20 kg = 2 N/kg = 2 m/s2
13. Ko tēhea kōrero i raro nei e whakaahua ana i te ture tuatoru o Newton?
(1) I pana whakamua ngā pāhihi i te wā i pēhi ohorere ai te pahi
(2) Bngā pukapuka i runga i te pepa kāore e hinga ana ina tere te kume o te pepa
(3) I te wā e takaro ana i te papa reti, ka pana te waewae i te whenua ki muri, ka paheke whakamua te papa reti.
(4) Oka panaia whakamuri ngā waka, ka neke whakamua ngā waka
Rongoā:
(1) Te ture tuatahi a Newton
(2) Te ture tuatahi a Newton
(3) Te ture tuatoru a Newton
(4) Te ture tuatoru a Newton
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- Papatipu me te taumaha
- Te kaha noa
- Te ture tuarua o te nekehanga a Newton
- Te kaha waku
- Te nekehanga i runga i te mata whakapae me te kore he kaha waku
- Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
- Te nekehanga i runga i te papa whakarara me te kore he kaha waku
- Te nekehanga i runga i te papa whakarara taratara me te kaha waku
- Te nekehanga i roto i te ararewa
- Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
- E rua ngā tinana he rite te rahi o te whakaterenga
- Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
- Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
- Te nekehanga ōrite i roto i te porowhita whakapae
- Te kaha pokapū i roto i te nekehanga porowhita ōrite
Pānuitia atu
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