1. Ka tōia e te tangata tētahi poraka 2 m i runga i tētahi mata whakapae mā te kaha pumau F = 20 N. Tātaihia te mahi i mahia e te kaha F e pā ana ki te poraka.
Mōhiotia:
Te kaha (F) = 20 N
Nekehanga (s) = 2 m
Koki (θ ) = 0
E hiahiatia ana : Mahi (W)
Rongoā:
W = F d cos θ = (20)(2)(cos 0) = (20)(2)(1) = 40 Joules
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2. He kaha F = 10 N e pā ana ki tētahi pouaka 1 m te roa i runga i tētahi mata whakapae. Ka pā te kaha ki tētahi koki 30 ° e whakaaturia ana i te pikitia i raro nei. Tātaihia te mahi i mahia e te kaha F!
Mōhiotia :
Te kaha (F) = 10 N
Ko te kaha whakapae (F x ) = F cos 30 o = (10)(0.5√3) = 5√3 N
Nekehanga (d) = 1 mita
E hiahiatia ana : Mahi (W)?
Otinga :
W = F x d = (5√3)(1) = 5√3 Ngā Joule
3. Ka taka noa te tinana mai i te okiokinga, mai i te teitei o te 2 m. Mena ko te whakaterenga nā te kaha ā-papa he 10 m/s² , tātaihia te mahi i mahia e te kaha ā-papa!
Mōhiotia:
Papatipu o te mea (m) = 1 kg
Teitei (h) = 2 m
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
E hiahiatia ana: Te mahi i mahia e te kaha o te kaha ā-papa (W)
Rongoā:
W = F d = wh = mgh
W = (1)(10)(2) = 20 Joule
W = mahi, F = kaha, d = tawhiti, w = taumaha , h = teitei, m = papatipu, g = whakaterenga nā te kaha ā-papa.
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4. Kei te honoa tētahi mea 1-kg ki tētahi puna, ā, ka roa ake kia 2 cm. Mēnā ko te whakaterenga nā te kaha ā-papa he 10 m/s 2 , tautuhia (a) te pūmau puna (b) te mahi i mahia e te kaha puna ki runga i te mea
Mōhiotia:
Taumaha (m) = 1 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te toronga (x) = 2 cm = 0.02 m
Taumaha (w) = mg = (1 kg)(10 m/s² ) = 10 kg m/ s² = 10 N
E hiahiatia ana: Te pūmau puna me te mahi i mahia e te kaha puna
Rongoā:
(a) Pūmau puna
Te tauira o te ture a Hooke :
F = kx.
k = F / x = w / x = mg / x
k = (1)(10) / 0.02 = 10 / 0.02
k = 500 N/m
(b) te mahi i mahia e te kaha o te puna
W = – ½ kx 2
W = – ½ (500)(0.02) 2
W = – (250)(0.0004)
W = -0.1 Joule
Ko te tohu tango e tohu ana ko te ahunga o te kaha o te puna he ritenga ke ki te ahunga o te nekehanga o te mea.
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5. Ka whakaterea ake tētahi pouaka e te kaha F = 10 N i runga i te nekehanga 2 m. He taratara te papa, ā, he kaha waku F k = 2 N te mea e puta ai. Tātaihia te mahi kupenga i mahia ki runga i te pouaka.
Mōhiotia:
Te kaha (F) = 10 N
Te kaha o te waku nekeneke (F k ) = 2 N
Nekehanga (d) = 2 m
E hiahiatia ana: Whatunga (W kupenga )
Rongoā:
Te mahi i mahia e te kaha F:
W 1 = F d cos 0 = (10)(2)(1) = 20 Joules
Te mahi i mahia e te kaha o te waku nekeneke (F k ):
W 2 = F k d = (2)(2)(cos 180) = (2)(2)(-1) = -4 Joule
Whatunga:
W kupenga = W 1 – W 2
W kupenga = 20 – 4
W kupenga = 16 Joule
6. He aha te mahi i mahia e te kaha F ki runga i te poraka?
Mōhiotia:
Te Kaha (F) = 12 Newton
Nekehanga (d) = 4 mita
E hiahiatia ana: Mahi (W)
Rongoā:
W = F d = (12 Newton)(4 mita) = 48 N m = 48 Joules
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7. Ka panaia tētahi poraka e te kaha o te 200 N. Ko te nekehanga o te poraka he 2 mita. He aha te mahi i mahia ki te poraka?
Mōhiotia:
Te Kaha (F) = 200 Newton
Nekehanga (d) = 2 mita
E hiahiatia ana: Mahi (W)
Rongoā:
Mahi:
W = Fs
W = (200 Newton)(2 mita)
W = 400 N m
W = 400 Joule
8. E hiahia ana te taraiwa o te sedan ki te whakatū i tana waka kia 0.5 m te tawhiti ki mua i te taraka, e 10 m te tawhiti mai i te tūranga o te sedan. He aha te mahi e hiahiatia ana e te sedan?
Mōhiotia:
Nekehanga (d) = 10 mita – 0.5 mita = 9.5 mita
Te Kaha (F) = 50 Newton
E hiahiatia ana: Mahi (W)
Rongoā:
W = Fs
W = (50 Newton)(9.5 mita)
W = 475 N m
W = 475 Joule
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9.
Ko te mahi i mahia e Tom rāua ko Jerry kia taea ai e te motuka te neke tae atu ki te 4 mita. Ko ngā kaha i tukuna e Tom rāua ko Jerry he 50 N me te 70 N.
Mōhiotia:
Nekehanga (s) = 4 mita
Te kaha kupenga (F) = 50 Newton + 70 Newton = 120 Newton
E hiahiatia ana: Mahi (W)
Rongoā:
W = Fs = (120 Newton)(4 mita) = 480 N m = 480 Joules
10. Ka tōia e te taraiwa tētahi motuka kia neke te motuka ki te 1000 cm. He aha te mahi i mahia ki te motuka?
Mōhiotia:
Te Kaha (F) = 250 Newton
Nekehanga (s) = 1000 cm = 1000/100 mita = 10 mita
E hiahiatia ana: Mahi (W)
Rongoā:
W = Fs = (250 Newton)(10 mita) = 2500 N m = 2500 Joules
11. E ai ki te pikitia i raro nei, mēnā ko te mahi i mahia e te kaha kupenga he 375 Joules, whakatauhia te nekehanga o te mea.
Mōhiotia:
Mahi (W) = 375 Joule
Te topa kupenga ( ΣF) = 40 N + 10 N – 25 N = 25 Newtons ( whaka-tikanga )
E hiahiatia ana: Te nekehanga ( d )
Rongoā:
Te whārite o te mahi:
W = Fs
Te nekehanga o te mea:
d = W / F = 375 Joule / 25 Newton
d = 15 mita s
12. Ko ngā mahi i raro nei kāore e whai hua ko …
A. Panahia tētahi mea kia 10 mita te tawhiti
B. Panahia he motuka kia neke ra ano
C. Panahia he pakitara
D. I tōia he pouaka
Rongoā:
Te whārite o te mahi:
W = ΣFs
W = mahi , F = kaha , d = nekehanga
E ai ki te tauira o runga ake nei, ka oti te mahi mā te kaha, ā, ka puta he nekehanga.
Ko te whakautu tika ko C.
1 3. Ka panaia e Andrew tētahi mea me te kaha o te 20 N kia neke ai te mea i roto i te nekehanga porowhita me te radius o te 7 mita. Tātaihia te mahi i mahia e Andrew mō ngā nekehanga porowhita e rua ngā whakarea.
A. 0 Joules
B. 1400 Joules
C. 1540 Joule
D. 1760 Joule
Rongoā:
Ki te panaia e te tangata te tūru wīra kia rua ngā nekehanga porohita, ka hoki te tangata me te tūru wīra ki tōna tūranga taketake, nō reira he kore te nekehanga o te tangata.
Nekehanga = 0, nō reira ko te mahi = 0.
Ko te whakautu tika ko A.
14. Ka panaia e tetahi tetahi mea ki runga i te papa me te kaha o te 350 N. E 70 N te kaha waku o te papa. Tātaihia te mahi i mahia e te kaha hei neke i te mea ki tawhiti atu i te 6 mita.
A. 45 J
B. 72 J
C. 1680 J
D. 2580 J
Mōhiotia:
Te kaha o te pana (F) = 350 Newtons
Te kaha waku (F fric ) = 70 Newton
Te nekehanga o te mea (ngā mea) = 6 mita
E hiahiatia ana: Mahi (W)
Rongoā:
E rua ngā kaha e pā ana ki te mea, ko te kaha pana (F) me te kaha waku (F fric ). He rite te ahunga o te kaha pana ki te nekehanga o te mea nā te mea he mahi pai te kaha pana. I tētahi atu ringa, he rerekē te ahunga o te kaha waku me te nekehanga o te mea, nō reira he mahi kino te kaha waku.
Te mahi i mahia e te kaha pana:
W = F d = (350 Newton)(6 mita) = 2100 Newton-mita = 2100 Joules
Te mahi i mahia e te kaha waku:
W = – (F fric )(s) = – (70 Newton)(6 mita) = – 420 Newton-mita = – 420 Joules
Te whatunga:
W kupenga = 2100 Joule – 420 Joule
W kupenga = 1680 Joule
Ko te whakautu tika ko C.
15. Ka panaia tētahi mea e te kaha whakapae o te 14 Newton i runga i te papa taratara me te kaha waku o te 10 Newton. Tātaihia te mahi kupenga o te neke i te mea tae noa ki te 8 mita.
A. 0.5 Joules
B. 3 Joules
C. 32 Joule
D. 192 Joule
Mōhiotia:
Te kaha pana (F) = 14 Newton
Te kaha waku (F fric ) = 10 Newton
Te nekehanga o te mea (d) = 8 mita
E hiahiatia ana: Mahi (W)
Rongoā:
E rua ngā kaha e pā ana ki tētahi mea, ko te kaha pana (F) me te kaha waku (F fric ).
He rite te ahunga o te kaha pana ki te nekehanga o te mea, ā, ka mahi pai te kaha pana. I tētahi atu ringa, he rerekē te ahunga o te kaha waku ki te nekehanga o te mea, ā, ka mahi kino te kaha waku.
Te mahi i mahia e te kaha pana:
W = Fs = (14 Newton)(8 mita) = 112 mita Newton = 112 Joules
Te mahi i mahia e te kaha waku:
W = – (F fric )(s) = – (10 Newton)(8 mita) = – 80 mita Newton = – 80 Joules
Te whatunga:
W kupenga = 112 Joule – 80 Joule
W kupenga = 32 Joule
Ko te whakautu tika ko C.
16. Tāutuhia te mahi kupenga i runga i te pikitia i raro nei.
A. 360 Joules
B. 450 Joules
C. 600 Joule
D. 750 Joule
Rongoā:
Mahi = Kaha (F) x nekehanga (d)
Mahi = Te horahanga o te tapatoru 1 + te horahanga o te tapawhā hāngai + te horahanga o te tapatoru 2
Work = 1/2(40-0)(3-0) + (40-0)(9-3) + 1/2(40-0)(12-9)
Mahi = 1/2(40)(3) + (40)(6) + 1/2(40)(3)
Mahi = (20)(3) + 240 + (20)(3)
Mahi = 60 + 240 + 60
Mahi = 360 Joule
Ko te whakautu tika ko A.
17. Ka purua poutūtia te rakau, 60 cm te roa, ki te whenua. Ka whiua te rakau ki te hama 10-kg mai i te teitei o te 40 cm i runga ake i te tihi o te rakau. Mena ko te kaha ātete toharite o te whenua he 2 x 103 N , ā, ko te whakaterenga nā te kaha ā-papa he 10 m/s2 , kātahi ka uru katoa te rakau ki roto i te whenua i muri i te…. pānga.
A. 4
B. 16
C. 28
D. 30
Mōhiotia:
Taumaha o te hama (m) = 10 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m / s2
Taumaha o te hama (w) = mg = (10)(10) = 100 kg m/s 2
Te nekehanga o te hama i mua i te pānga ki te rakau (d) = 40 cm = 0.4 mita
Ko te ātete o te rakau (F) = 2 x 103 N = 2000 N
Te roa o te rakau = 60 henimita = 0.6 mita
E hiahiatia ana: Ka uru katoa te rakau ki roto i te whenua i muri i te… pānga.
Rongoā:
Ko te mahi i mahia ki te hama ina neke te hama ki te tawhiti o te 0.4 mita ko:
W = F d = ws = (100 N)(0.4 m) = 40 Nm = 40 Joules
Te mahi i mahia e te kaha ātete o te whenua:
W = F d = (2000 N)(0.6 m) = 1200 Nm = 1200 Joule
Ka uru katoa te rakau ki roto i te whenua i muri i te… pānga.
1200 Joule / 40 Joule = 30
Ko te whakautu tika ko D.
[wpdm_package id='1192′]
- Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
- Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
- Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
- Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
- Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
- Ngā raruraru hiko me ngā otinga
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
- Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere
