Te mahi me te pūngao nekeneke – ngā raruraru me ngā otinga

Pūngao Mahi-Kinetika :

1. I tere ake te tere o tētahi waka 5000-kg mai i te tū ki te 20 m/s. Tātaihia te mahi kupenga i mahia ki runga i te waka.

Mōhiotia:

Taumaha (m) = 5000 kg

Tere tīmatanga (v _o ) = 0 m/s ( okiokinga waka )

Tere whakamutunga (vt ₎ = 20 m/s

E hiahiatia ana : whatunga

Rongoā:

Te mātāpono pūngao mahi-nekeneke :

W _kupenga = Δ EK

W _kupenga = ½ m (v _t ² – v _o ² )

W _kupenga = mahi kupenga

Δ EK = te huringa o te pūngao nekeneke

m = papatipu (kg),

vt = tere whakamutunga ₍ m/s),

v _o = te tere tīmatanga (m/s).

Whatunga:

W _kupenga = ½ m (v _t ² – v _o ² )

W _kupenga = ½ (5000)(20 ² – 0 ² )

W _kupenga = (2500)(400 – 0)

W _kupenga = (2500)(400)

W _kupenga = 1000,000 Joule

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2. I tere ake te tere o tētahi mea 10-kg mai i te 5 m/s ki te 10 m/s. Tātaihia te mahi kupenga i mahia ki te mea!

Mōhiotia:

Taumaha (m) = 10 kg

Tere tīmatanga (v _o ) = 5 m/s

Tere whakamutunga (vt ₎ = 10 m/s

E hiahiatia ana : whatunga

Rongoā:

Whatunga:

W _kupenga = Δ EK

W _kupenga = ½ m (v _t ² – v _o ² )

W _kupenga = ½ (10)(10 ² – 5 ² )

W _kupenga = (5)(100 – 25)

W _kupenga = (5)(75)

W _kupenga = 375 Joule

3. Ka whakahekehia te tere o tētahi motuka 2000-kg mai i te 10 m/s ki te 5 m/s. He aha te mahi i mahia ki te motuka?

Mōhiotia:

Papatipu o te motuka (m) = 2000 kg

Tere tīmatanga (v _o ) = 10 m/s

Tere whakamutunga (vt ₎ = 5 m/s

E hiahiatia ana: whatunga

Rongoā:

Whatunga:

W _kupenga = Δ EK

W _kupenga = ½ m (v _t ² – v _o ² )

W _kupenga = ½ (2000)(5 ² – 10 ² )

W _kupenga = (1000)(25 – 100)

W _kupenga = (1000)(-75)

W _kupenga = -75,000 Joule

E tohu ana te tohu tango ko te ahunga o te nekehanga he ritenga ke ki te ahunga o te kaha kupenga.

4. He kaha pumau 60-N i pā ki tētahi mea 10-kg te taumaha mō ngā hēkona 12. Ko te tere tīmatanga o tētahi mea he 6 m/s, ā, he rite te ahunga o te mea ki te ahunga o te kaha.

(1) Ko te mahi i mahia ki te mea he 30,240 Joules

(2) Ko te pūngao nekeneke whakamutunga he 30,240 joules

(3) Ko te mana he 2,520 Watt

(4) Ko te pikinga o te kaha nekeneke o te mea he 180 Joules

Ko ngā kōrero tika ko…

Mōhiotia:

Te kaha (F) = 60 N

Wā wā (t) = 12 hēkona

Papatipu o te mea (m) = 10 kg

Te tere tīmatanga (v _o ) = 6 m/s

E hiahiatia ana: Ngā kōrero tika

Rongoā:

Te whakaterenga o te mea:

∑F = ma

60 = 10

a = 60 / 10 = 6 m/s ²

Te tere whakamutunga:

vt = v _o + _i

vt = 6 + ₍ 6)(12)

v _t = 6 + 72

v _t = 78 m/s

Ko te tawhiti i haerea i roto i te 12 hēkona:

s = v _o t + 1/2 i te ²

s = (6)(12) + 1/2 (6)(12) ²

s = 72 + (3)(144)

s = 72 + 432

s = 504 mita

(1) Mahi i mahia mā te kaha

W = F s = (60)(504) = 30,240 Joule

(2) Te pūngao nekeneke whakamutunga

KE = 1/2 mv _t ² = 1/2 (10)(78) ² = (5)(6084) = 30,420 Joules

(3) Te Kaha

P = W / t = 30,240 / 12 = 2,520 Joule/hēkona

(4) Te pikinga o te pūngao nekeneke

ΔKE = 1/2 mv _t ² – 1/2 mv _o ² = 1/2 m (v _t ² – v _o ² ) = 1/2 (10)(78 ² – 6 ² ) = 5 (6084 –36) = 5 (6048)

ΔKE = 30,240 Joule

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5. Ko te mahi nui ka oti mā te tau o te mea…

Rongoā:

Mahi kupenga = huringa o te pūngao nekeneke

W _kupenga = ½ m (v _t ² – v _o ² )

Ko te mahi nui ake:

W ₁ = ½ (8)(4 ² – 2 ² ) = (4)(16 – 4) = (4)(12) = 48 Ngā Joule

W ₂ = ½ (8)(5 ² –3 ² ) = (4)(25 – 9) = (4)(16) = 64 Ngā Hīora

W ₃ = ½ (10)(6 ² – 5 ² ) = (5)(36 – 25) = (5)(11) = 55 Ngā Joule

W ₄ = ½ (10)(4 ² – 0 ² ) = (5)(16 – 0) = (5)(16) = 80 Ngā Joule

W ₅ = ½ (20)(3 ² – 3 ² ) = (10)(9 – 9) = (10)(0) = 0 Ngā Joule

6. E haere ana tētahi waka 4000-kg i te rārangi tika i te 25 m/s. Ka whakahekehia te tere o te waka kia 15 m/s te tere whakamutunga o te waka. He aha te mahi i mahia ki te waka?

Mōhiotia:

Taumaha (m) = 4000 kg

Ko te tere tīmatanga (v _o ) = 25 m/s

Ko te tere whakamutunga (v _t ) = 15 m/s

E hiahiatia ana : Te mahi i mahia ki te motuka

Rongoā:

W _kupenga = ½ m (v _t ² – v _o ² ) = ½(4000)(15 ² -25 ² ) = (2000)(225-625) = (2000)(-400) = -800,000 Joule = -800 kJ

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7. He pōro e whiua ana ki te taha whakararo, 0.1-kg te taumaha, i te tere 6 m/s mai i te teitei o te 5 mita. Mēnā ko te whakaterenga o te kaha ā-papa he 10 m/s² ^, he aha te kaha nekeneke o te pōro i te teitei o te 2 mita?

Mōhiotia:

Taumaha (m) = 0.1 kg

Ko te panonitanga o te teitei (h) = 5 m – 2 m = 3 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te pūngao nekeneke i te teitei o te 2 mita.

Rongoā:

Ka taea te mārama ki te nekehanga pere mā te tātari motuhake i ngā wāhanga whakapae me ngā wāhanga poutū o te nekehanga. Ka tātarihia te nekehanga i te ahunga whakapae hei nekehanga tere pumau , ā, ka tātarihia te nekehanga i te ahunga poutū hei nekehanga hinga kore utu, hei nekehanga poutū rānei.

Ko te pūngao ā-pūkaha tīmatanga = te pūngao pūmanawa ā-papa.

PE = mgh = (0.1)(10)(3) = 3 Joule.

Ko te pūngao miihini whakamutunga = te pūngao nekeneke.

KE = 3 Joule.

8. Ka tere ake te waka 1000-kg mai i te tūnga, ā, ka haere i te 5 m/s. He aha te mahi e mahia ana e te waka?

Mōhiotia:

Taumaha (m) = 1000 kg

Te tere tīmatanga (v _o ) = 0

Te tere whakamutunga (vt ₎ = 5 m/s

E hiahiatia ana: Mahi (W) i mahia e te motuka

Rongoā:

W _kupenga = ½ m (v _t ² – v _o ² )

Ngā mahi i mahia e te motuka:

W _kupenga = ½ (1000)(5 ² – 0 ² ) = (500)(25 – 0) = (500)(25) = 12,500 Joule

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9. Ka whiua poutū ake tētahi pōro 500-karamu mai i te mata o te whenua me te tere tīmatanga o te 10 m/s² ^. Ko te whakaterenga nā te kaha ā-papa he 10 ms ^-2 . He aha te mahi i mahia e te kaha taumaha ina tae te pōro ki te teitei mōrahi?

Mōhiotia :

Taumaha o te pōro (m) = 500 karamu = 0.5 kg

Te tere tīmatanga (v _o ) = 10 m/s ²

Te tere whakamutunga (vt ₎ = 0 (te tere i te pūwāhi teitei rawa)

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Mahi (W) mā te taumaha

Rongoā:

Ko te mahi kupenga i mahia e te kaha kupenga ki runga i tētahi mea = te huringa o te pūngao nekeneke.

W _kupenga = ΔEK = EK _t – EK _o

Wnet = ½ mv _t ² – ½ mv _o ² = ½ m (v _t ² – v _o ² )

KE _t = te pūngao nekeneke whakamutunga, KE _o = te pūngao nekeneke tīmatanga, m = te papatipu o te mea, v _t = te tere whakamutunga o te mea, v _o = te tere tīmatanga o te mea.

Whatunga:

W _kupenga = ½ m (v _t ² – v _o ² ) = ½ (0.5)(0 ² – 10 ² )

W _kupenga = (0.25)(-100) = -25 Joules

Ko te tohu tango e tohu ana ko te ahunga o te nekehanga he ritenga kē ki te taumaha o te pōro. He poutū te ahunga o te pōro, ā, he tika tonu te ahunga o te taumaha.

10. Ka taka noa tetahi mea 1-kg te taumaha me te rerekētanga teitei = 2.5 mita. Ko te tere o te kaha ā-papa he 10 ms ^-2 . He aha te mahi i mahia ki te mea?

Mōhiotia:

Taumaha o te pōro (m) = 1 kg

Te tere tīmatanga (v _o ) = 0 m/s

Teitei (h) = 2.5 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Mahi kupenga i te wā e nekehia ana

Rongoā:

Te tere whakamutunga o te pōro ( _vt )

I tatauhia mā te whakamahi i te whārite o te nekehanga taka noa. E mōhiotia ana: Te whakaterenga nā te kaha ā-papa (g) = 10 m/s² ^, Ko te huringa teitei o te pōro (h) = 2.5 mita. E hiahiatia ana: Te tere whakamutunga.

v _t ² = 2 gh = 2(10)(2.5) = 2(25)

vt = _√2 (25)

vt ₌ 5√2

Mahi kupenga = te huringa o te pūngao nekeneke

W _kupenga = ΔEK = ½ m (v _t ² – v _o ² ) = ½ (1){(5√2) ² – 0 ² }

W _kupenga = ½ (25)(2) = 25 Joule

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11. E 72 km/haora te tere o te haere o tētahi mea 2-kg. I muri i te haere i te 400 mita, ko te tere whakamutunga o te mea he 144 km/haora. Ko te whakaterenga nā te kaha ā-papatipu he 10 ms ^-2 . Kimihia te mahi kupenga.

Mōhiotia:

Papatipu o te mea (m) = 2 kg

Te tere tīmatanga (v _o ) = 72 km/haora = 20 m/s

Te tere whakamutunga (vt ₎ = 144 km/h = 40 m/s

Tawhiti (s) = 400 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te whatunga

Rongoā:

Te mahi kupenga = ngā huringa o te pūngao nekeneke

W _kupenga = ΔEK = ½ m (v _t ² – v _o ² ) = ½ (2)(40 ² – 20 ² }

W _kupenga = ½ (2)(1600 – 400) = 1200 Joules

12. Ka haere tētahi mea 2-kg te taumaha i te 2 ms ^–1 . Ko te mahi i mahia ki te mea he 21 Joules. He aha te tere whakamutunga o te mea?

Mōhiotia:

Taumaha (m) = 2 kg

Te tere tīmatanga (v _o ) = 2 m/s

Mahi (W) = 21 Joule

E hiahiatia ana: te tere whakamutunga ( _vt )

Rongoā:

W _kupenga = ΔEK

W _kupenga = 1/2 mv _t ² -1/2 mv _o ²

W _kupenga = 1/2 m (v _t ² – v _o ² )

21 = 1/2 (2) (v _t ² – 2 ² )

21 = (v _t ² – 2 ² )

21 = v _t ² – 4

v _t ² = 21 + 4 = 25

vt ₌ √25

v _t = 5 m/s

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1 3 . Ka pā te kaha pumau 8 N ki tētahi mea he 16 kg te taumaha. Mēnā i te tīmatanga ka okioki te mea, tātaihia te tere o te mea i muri i te pānga o te kaha ki te mea mō te 4 hēkona.

Mōhiotia:

Te kaha pumau (F) = 8 Newton

Papatipu o te mea (m) = 16 kg

Te tere tīmatanga o te mea (v _o ) = 0 m/s

Ka pā te kaha o te wā ki te mea (t) = 4 hēkona

E hiahiatia ana: Te tere whakamutunga (v _t )

Rongoā:

Mahi = Te huringa o te pūngao nekeneke

W = KE whakamutunga – KE tīmatanga

W = ½ mv _t ² – ½ mv _o ²

W = ½ mv _t ² – 0

W = ½ mv _t ² —— Whārite 1

Mahi = Kaha x Nekehanga

W = F d

W = 8 rā

Whakamahia te whārite o te nekehanga rārangi kore-taurite i raro nei hei tatau i te nekehanga (d):

d = v _o t + ½ i te ²

d = nekehanga, v _o = tere tīmatanga, t = wā, a = whakaterenga

d = 0 + ½ i te ² = ½ i te ² —-> a = (v _t – v _o ) / t = v _t / t

d = ½ (v _t / t) t ²

^d = ½ (v _t ) t

Hurihia te nekehanga (d) i runga i te whārite o te Mahi me te nekehanga (d) i roto i tēnei whārite:

W = 8 rā

W = 8(1/2)(v _t )(t)

W = (4)(v _t )(t) —— whārite 2

Whārite 1 = Whārite 2

W = W

½ mv _t ² = (4)(v _t )(t)

½ mv _t = (4)(t)

½ (16)(v _t ) = 4(4)

8 v _t = 16

vt ₌ 16 / 8

v _t = 2 mita/hekona

14. Hei whakanui ake i te tere o tētahi mea kia 2 ngā wā o tōna tere tīmatanga, tautuhia te mahi e hiahiatia ana i roto i te tukanga…

Mōhiotia:

Papatipu o te mea (m) = 1 kg

Tere tīmatanga (v _o ) = 1 m/s

Tere whakamutunga (vt ₎ = 2 x tere tīmatanga = 2 x 1 = 2 m/s

E hiahiatia ana: Mahi

Rongoā:

Te pūngao nekeneke tuatahi:

KE tuatahi = ½ mv _o ² = ½ (1)(1) ² = ½ (1)(1) = ½ (1) = 0.5

Ko te pūngao nekeneke whakamutunga ina piki te tere o te mea kia 2 ngā wā o tōna tere tīmatanga:

KI te whakamutunga = ½ mv _t ² = ½ (1)(2) ² = ½ (4) = 2

Te ariā o te pūngao mahi-nekeneke:

Mahi = Te huringa o te pūngao nekeneke

Mahi = Te pūngao nekeneke whakamutunga – te pūngao nekeneke tuatahi

Mahi = 2 – 0.5

Mahi = 1.5

Ko te pūngao nekeneke tīmatanga = 0.5

Mahi = 3 x 0.5 = 1.5

E toru ngā whakarea o te mahi e hiahiatia ana o tōna pūngao nekeneke tīmatanga.

15. E neke ana tētahi motuka he 1500 kg te taumaha me te tere o te 36 km/haora i runga i tētahi rori whakapae rārangi, maeneene hoki. I tere ake te motuka ki te 72 km/haora. Tātaihia te mahi e hiahiatia ana hei whakatere i te motuka.

Mōhiotia:

Taumaha o te motuka (m) = 1500 kg

Te tere tīmatanga o te motuka (v _o ) = 36 km/haora = 36,000 mita / 3600 hēkona = 10 mita/hekona

Te tere whakamutunga o te motuka (vt ₎ = 72 km/haora = 72,000 mita / 3600 hēkona = 20 mita/hekona

E hiahiatia ana: He mahi e hiahiatia ana hei whakatere i te motuka

Rongoā:

Te ariā o te pūngao mahi-nekeneke:

W = EK whakamutunga – EK tīmatanga

W = ½ mv _t ² – ½ mv _o ² = ½ m (v _t ² –v _o ² )

W = ½ (1500)(20 ² – 10 ² )

W = ½ (1500)(400 – 100)

W = ½ (1500)(300)

W = (1500)(150)

W = 225,000 Joule

16. Ka neke tuatahi tētahi mea he 2 kg te taumaha i te tere o te 72 km/haora ^-1 . I muri i tana neke i te rori whakapae tika tae atu ki te 400 m, ko te tere o te mea he 144 km/haora ^-1 . Tātaihia te tapeke o te mahi i runga i te mea.

Mōhiotia:

Papatipu o te mea (m) = 2 kg

Tere tīmatanga (v _o ) = 72 km/haora = 72,000 mita / 3600 hēkona = 20 m/s

Tere whakamutunga (vt ₎ = 144 km/h = 144,000 mita / 3600 hēkona = 40 m/h

Te nekehanga o te mea = 400 mita

E hiahiatia ana: Mahi kupenga i runga i te mea

Rongoā:

E ai ki te ariā o te pūngao mahi-nekeneke, ko te pānga o te mahi kupenga ki tētahi mea he rite tonu ki te huringa o te pūngao nekeneke o te mea.

W kupenga = KI whakamutunga – KI tīmatanga

W kupenga = ½ mv _t ² – ½ mv _o ²

W kupenga = ½ m (v _t ² – v _o ² )

W kupenga = ½ (2)(40 ² – 20 ² )

W kupenga = 1600 – 400

W kupenga = 1200 Joule

Whakamārama:

W = Mahi, KE = pūngao nekeneke

Te kaha Kinetic

17. He matā 10-karamu e neke ana i te tere pumau 100 m/s. He aha te pūngao nekeneke o te matā?

Mōhiotia:

Taumaha o te matā (m) = 10 karamu = 10/1000 kirokaramu = 1/100 kirokaramu = 0.01 kirokaramu

Te tere o te matā (v) = 100 mita/hekona

E hiahiatia ana: Pūngao nekeneke

Rongoā:

KE = 1/2 mv ²

KE = 1/2 (0,01 kg)(100 m/s) ²

KE = 1/2 (0,01 kg)(10.000 m ² /s ² )

KE = (0,01 kg)(5000 m ² /s ² )

KE = 50 kg ^m² / ^s²

KE = 50 Joule

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1. Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
2. Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
3. Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
4. Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
5. Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
6. Ngā raruraru hiko me ngā otinga
7. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
8. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
9. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
10. Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
11. Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere