ahupūngao

Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga hinga noa – ngā raruraru me ngā otinga

1. Ka taka noa tetahi tinana 1-kg mai i te tūnga, mai i te teitei o te 80 m. Ko te tere o te kaha ā-papa he 10 m/s² ^. He aha te pūngao nekeneke ina pā te tinana ki te whenua.

Mōhiotia:

Taumaha (m) = 1 kg

Teitei (h) = 80 m

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

E hiahiatia ana: te pūngao nekeneke ina pā te tinana ki te whenua

Rongoā:

Ko te pūngao ā-pūkaha tīmatanga (ME _o) = te pūngao pūmanawa ā-papa (PE)

M E _o= P E = mgh = (1)(10)(80) = 800 Joule

Ko te pūngao miihini whakamutunga (M E _t) = te pūngao nekeneke (K E )

Te mātāpono o te tiaki i te pūngao miihini :

ME o = ME _t

P E = K E

800 = K E

Ko te pūngao nekeneke whakamutunga ko 800 Joules.

[irp]

2. Ka taka noa tētahi tinana 4-kg te taumaha mai i te tūnga, mai i te teitei o te 10 m. Ko te tere o te kaha ā-papa he 10 ms ^–2 . He aha te pūngao nekeneke me te tere i te 5 mita i runga ake i te whenua.

Mōhiotia:

Ko te panonitanga o te teitei (h) = 10 – 5 = 5 mita s

Taumaha (m) = 4 kg

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

E hiahiatia ana: Pūngao nekeneke i te 5 mita i runga ake i te whenua me te tere i te 5 mita i runga ake i te whenua

Rongoā:

(a) Pūngao nekeneke i te 5 mita i runga ake i te whenua

Ko te pūngao miihini tīmatanga (M E _o) = te pūngao pūmanawa ā-papa (P E )

M E _o= P E = mgh = (4)(10)(5) = 200 Joule

Ko te pūngao miihini whakamutunga (EM _t) = te pūngao nekeneke (EK)

M E _t= K E

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga.

ME o = ME _t

200 = K E

Ko te pūngao nekeneke i te 5 mita i runga ake i te whenua he 200 Joules.

(b) te tere i te 5 mita i runga ake i te whenua

Ko te pūngao miihini tīmatanga (M E _o) = te pūngao miihini whakamutunga (M E _t)

P E = K E

200 = ½ mv ²

2(200) / 4 = v ²

100 = v ²

v = √100

v = 10 m/s

Ko te tere o te tinana i te 5 mita i runga ake i te whenua he 10 m/s.

[irp]

3. Ka taka noa te māngo mai i te tūnga, mai i te teitei o te 2 mita. Ko te tere o te kaha ā-papa he 10 ms ^–2 . Tātaihia te tere o te māngo ina pā ki te whenua.

Mōhiotia:

Teitei (h) = 2 mita s

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

E hiahiatia ana: te tere o te māngo ina pā ki te whenua.

Rongoā:

Ko te pūngao miihini tīmatanga (M E _o) = te pūngao pūmanawa ā-papa (P E )

M E = P E = mgh = m (10)(2) = 20 m

Ko te pūngao miihini whakamutunga (M E _t) = te pūngao nekeneke (K E )

M E _t= K E = ½ mv ²

Ko te mātāpono o te tiaki i te pūngao ā-pūkaha e kī ana ko te pūngao ā-pūkaha tīmatanga = te pūngao ā-pūkaha whakamutunga.

ME o = ME _t

20 m = ½ mv ²

20 = ½ v ²

2(20) = ^v2

40 = v ²

v = √40 = √(4)(10) = 2√10 m/ s

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Pānuitia atu

Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga poutū i te hinganga kore utu – ngā raruraru me ngā otinga

1. Ka whiua e te tangata tētahi kōhatu 1-kg ki runga i te tere 2 m/s i a ia e tū ana i te taha o te pari kia taka ai te kōhatu ki te take o te pari 40 mita i raro iho. He aha te pūngao nekeneke o te kōhatu i te 10 mita i runga ake i te whenua? Te whakaterenga nā te kaha ā-papatipu g = 10 m/ ^s2.

Mōhiotia:

Taumaha (m) = 1 kg

Te tere tīmatanga (v _o) = 2 m/s

Te panonitanga o te teitei = 40 – 10 = 30 mita

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

E hiahiatia ana: te kaha nekeneke o te kōhatu i te 10 mita i runga ake i te whenua

Rongoā:

Te pūngao miihini tuatahi

Ko te pūngao pūmanawa ā-papa tuatahi (EP) = mgh = (1)(10)(30) = 300 Joules

Ko te pūngao nekeneke tīmatanga (KE) = ½ mv _o² = ½ (1)(2) ² = ½ (4) = 2 Joule

Ko te pūngao miihini tuatahi = te pūngao pūmanawa ā-papa tuatahi + te pūngao nekeneke tuatahi = 300 + 2 = 302 Joule.

Te pūngao miihini whakamutunga

Ko te pūngao miihini whakamutunga = te pūngao nekeneke whakamutunga = te pūngao pūmanawa ā-papa tuatahi + te pūngao nekeneke tuatahi = 300 + 2 = 302 Joule.

[irp]

2. Ka whiua e te tangata tētahi mea 1-kg ki runga ki te rangi me te tere tīmatanga o te 10 m/s. Tātaihia (a) te pūngao pūmanawa ā-papa i te teitei mōrahi (b) te teitei mōrahi.

Ko te whakaterenga nā te kaha ā-papa he 10 m/s ²

Mōhiotia:

Taumaha (m) = 1 kg

Te tere tīmatanga (v _o ) = 10 m/s

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

E hiahiatia ana : te pūngao pūmanawa ā-papa i te teitei mōrahi me te teitei mōrahi

Rongoā:

(a) te pūngao pūmanawa ā-papa i te teitei mōrahi

Te pūngao miihini tuatahi:

Ko te pūngao miihini tuatahi (ME) = te pūngao nekeneke tuatahi (KE) = ½ mv _o² = ½ (1)(10) ² = ½ (100) = 50 Joule.

Te pūngao miihini whakamutunga:

Ko te pūngao miihini whakamutunga (ME) = te pūngao pūmanawa ā-papa (PE)

Te mātāpono o te tiaki i te pūngao miihini:

Ko te pūngao miihini tuatahi = te pūngao miihini whakamutunga

KE = PE

50 = PE

Ko te pūngao pūmanawa ā-papa he 50 Joule.

(b) Te teitei mōrahi

PE = mgh

50 = (1)(10) hāora

50 = 10 hāora

h = 50 / 10 = 5 mita

Ko te teitei mōrahi he 5 mita i runga ake i te whenua.

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Pānuitia atu

Pūngao pūmanawa o te puna rapa – ngā raruraru me ngā otinga

1. E honoa ana tētahi papatipu 2-kg ki tētahi puna. Mena he 4 cm te roa o te puna, tautuhia te pūngao pūmanawa o te puna rapa . Ko te whakaterenga nā te kaha ā-papatipu he 10 m/ ^s².

Mōhiotia:

Taumaha (m) = 2 kg

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

Taumaha (w) = mg = (2)(10) = 20 N

Te toronga (x) = 4 cm = 0.04 m

E hiahiatia ana: Pūngao pūmanawa o te puna rapa

Rongoā:

Te tauira o te ture a Hooke :

F = kx

F = kaha, k = pūmau puna, x = te huringa o te roa o te puna

Pūmau puna:

k = w / x = 20 / 0.04 = 500 N/m

Pūngao pūmanawa o te puna rapa:

PE = ½ kx ² = ½ (500)(0.04) ² = (250)(0.0016) = 0.4 Joules

Otinga kē atu:

PE = ½ kx ² = ½ (w / x) x ² = ½ wx = ½ mgx

w = taumaha, m = papatipu, x = te huringa o te roa o te puna

PE = ½ (2)(10)(0.04) = (10)(0.04) = 0.4 Joules.

[irp]

2. Ko te roa o te puna i totorohia e te kaha F = 50 N he 10 cm. He aha te pūngao pūmanawa o te puna rapa mēnā he 12 cm te roa o te puna.

Mōhiotia:

Te toronga (x) = 10 cm = 0.1 m

Te kaha (F) = 50 N

E hiahiatia ana : Te pūngao pūmanawa o te puna rapa

Rongoā:

Pūmau puna:

k = F / x = 50 / 0.1 = 500 N/m

Ko te pūngao pūmanawa o te puna rapa mēnā he 12 cm te roa o te puna:

PE = ½ kx ² = ½ (500)(0.12) ² = (250)(0.0144) = 3.6 Joules.

[irp]

3. Ko te kauwhata o F vs x e whakaaturia ana i te pikitia i raro nei. He aha te pūngao pūmanawa o te puna rapa, mēnā ko te roa o te puna he 10 cm.

Pūngao pūmanawa o te puna rapa - ngā raruraru me ngā otinga 1

Mōhiotia:

Te kaha (F) = 5 N

Te roa o te puna (x) = 2 cm = 0.02 m

E hiahiatia ana: Te pūngao pūmanawa o te puna rapa mēnā ko te roanga o te puna he 0.1 m.

Rongoā:

Pūmau puna:

k = F / x = 5 / 0.02 = 250 N/m

Ko te pūngao pūmanawa o te puna rapa mēnā ko te roanga o te puna he 0.1 m:

PE = ½ kx ² = ½ (250)(0.1) ² = (125)(0.01) = 1.25 Joules.

4. Ka peke tetahi kaitākaro ki runga i tētahi pūoro puna he 500 N te taumaha, ka whakapotohia te puna kia 4 cm. Tātaihia te nui o te pūngao pūmanawa hei akiaki i te kaitākaro.

A. 20 Joules

B. 10 Joules

C. 5 Joule

D. 2 Joule

Mōhiotia:

Te kaha (F) = 500 N

Ko te panonitanga o te roa o te puna (Δx) = 4 cm = 0.04 m

E hiahiatia ana: Te pūngao pūmanawa o te puna

Rongoā:

Tātaihia te pūmau rapa o tētahi puna mā te whakamahi i te whārite o te ture a Hooke:

k = F / Δx = 500 N / 0.04 m = 12500 N/m

Te pūngao pūmanawa rapa o te puna:

PE = ½ k Δx ² = ½ (12500)(0.04) ² = (6250)(0.0016)

PE = 10 Joule

Ko te whakautu tika ko B.

5. Ina whakairihia he puna me te taumaha 500 karamu, ka piki ake tōna roa mā te 5 cm. Tātaihia tōna pūmau me tōna pūngao pūmanawa.

Mōhiotia:

Taumaha o te mea (m) = 500 karamu = (500/1000) kg = 5/10 kg = 0.5 kg

Whakaterenga (g) = 10 m/s ²

Taumaha o te mea (w) = mg = (0.5 kg)(10 m/s² ⁾ = 5 kg m/s² ⁼ 5 Newton

Ko te panonitanga o te roa o te puna (Δx) = 5 cm = 0.05 m

E hiahiatia ana: te pūmau o te puna (k) me te pūngao pūmanawa (PE)

Rongoā:

Tuatahi, tatauhia te pūmau o te puna mā te whakamahi i te whārite o te ture a Hooke:

k = w / Δx = 5 N / 0.05 m = 100 N/m

Te pūngao rapa o te puna:

PE = ½ k Δx ² = ½ (100)(0.05) ² = (50)(0.0025)

PE = 0.125 Joule

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Pānuitia atu

Pūngao pūmanawa ā-papa – ngā raruraru me ngā otinga

1. He takanga kore utu o te tinana 1-kg mai i te okiokinga, mai i te teitei o te 10 m.

Whakatauhia:

(a) Te mahi i mahia e te kaha o te taumaha

(b) Te panonitanga o te pūngao pūmanawa ā-papa

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

Pūngao pūmanawa ā-papa – ngā raruraru me ngā otinga 1 Mōhiotia:

Taumaha (m) = 1 kg

Teitei (h) = 10 m

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

Taumaha (w) = mg = (1 kg)(10 m/s ² ) = 10 N

Rongoā:

(a) Te mahi i mahia e te kaha o te taumaha

W = wh = mgh

W = (1)(10)(10) = 100 Joule

(b) Te panonitanga o te pūngao pūmanawa ā-papa

He ōrite te huringa o te pūngao pūmanawa ā-papa ki te mahi e mahia ana e te ā-papa.

Δ EP = 100 Joule

[irp]

2. Ka paheke iho tētahi mea 10 N i runga i te papa whakarara maeneene mā te 2 mita te roa. Tātaihia te mahi i mahia e te taumaha kaha!

Pūngao pūmanawa ā-papa – ngā raruraru me ngā otinga 2 Mōhiotia:

taumaha (w) = 10 N

w _x= w hara θ = (10)(hara 30 ^o ) = (10)(0.5) = 5 N

d = 2 mita

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

E hiahiatia ana: te mahi i mahia e te taumaha kaha

Rongoā:

W = F d = w _x d = (5)(2) = 10 Joule

Otinga kē atu:

Sin 30 ^o = h / d

0.5 = hāora / 2

h = (0.5)(2)

h = 1 mita

Te mahi i mahia e te taumaha me te kaha;

W = F d = wh = (10 N)(1 m) = 10 N m = 10 Joules

[irp]

3. He mea 1,500 karamu te taumaha, e 20 mita te teitei i runga ake i te whenua , e taka noa ana ki te whenua. He aha te kaha pūmanawa ā-papa o te mea? Ko te tere o te ā-papa nā te kaha ā-papa he 10 m/ ^s².

Mōhiotia:

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

Taumaha (m) = 1500 karamu = 1500/1000 kirokaramu = 1.5 kirokaramu

Teitei (h) = 20 mita

E hiahiatia ana: Te pūngao pūmanawa ā-papa

Rongoā:

PE = mgh = (1.5 kg)(10 m/s² ⁾ (20 m) = 300 kg m² ^/ s² ⁼ 300 Joules

4. E ai ki te pikitia i raro nei, mēnā ko te taumaha o te mea 1 he 2 kg, ā, ko te taumaha o te mea 2 he 4 kg, ko te whakataurite i te pūngao pūmanawa o te mea 1 me te mea 2 he …..

Mōhiotia:

Papatipu o te mea 1 (m₁) = 2 kirokaramu Pūngao pūmanawa ā-papa – ngā raruraru me ngā otinga 5

Papatipu o te mea 2 (m2 ₎ = 4 kirokaramu

Teitei 1 (h ₁ ) = 12 mita

Teitei 2 (h ₂ ) = 9 mita

E hiahiatia ana: Te whakataurite i te pūngao pūmanawa o te mea 1 me te mea 2

Rongoā:

PE = mgh

m = papatipu (ko tōna waeine ā-ao ko te kirokaramu, he whakarāpopototanga ki te kg)

g = te whakaterenga nā te kaha ā-papa (ko tōna waeine ā-ao ko ngā mita ia hekona tapawhā, he whakarāpopototanga m/s ² )

h = teitei (ko tōna waeine ā-ao ko te mita, he whakarāpopototanga m)

PE = pūngao pūmanawa ā-papa (ko tōna waeine ā-ao ko kg m ² /s ² , ko Joule rānei)

Te pūngao pūmanawa ā-papa o te mea 1:

EP ₁ = m ₁ gh ₁ = (2)(g)(12) = 24 g

Te pūngao pūmanawa ā-papa o te mea 2:

EP ₂ = m ₂ gh ₂ = (4)(g)(9) = 36 g

Te whakataurite i te pūngao pūmanawa o te mea 1 me te mea 2:

PE ₁ : PE ₂

24 karamu : 36 karamu

24: 36

12/24 : 12/36

2: 3

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Pānuitia atu

Te mātāpono o te mahi-pūngao miihini – ngā raruraru me ngā otinga

1. Ka heke te tere o tētahi pouaka 2-kg mai i te 10 m/s ki te okioki. Ko te tauwehenga o te waku nekeneke ko te 0.2. Ko te whakaterenga nā te kaha ā-papatipu ko te 10 m/s2 ^. He aha te rahi o te nekehanga?

Te mātāpono o te mahi-pūngao mīhini – ngā raruraru me ngā otinga 2

Mōhiotia;

Taumaha (m) = 2 kg

Te tere tīmatanga (v _o) = 10 m/s

Te tere whakamutunga (vt ₎= 0 m/s

Ko te tauwehenga o te waku nekeneke ( _μk) = 0.2

Taumaha (w) = mg = (1 kg)(10 m/s² ⁾ = 10 kg m/s² ⁼ 10 N

E hiahiatia ana: Te rahi o te nekehanga (d)

Rongoā:

Te mātāpono mahi-pūngao mīhini :

W _nc= ΔEM

W _nc= ΔEK + ΔEP

W _nc= ½ m (v _t² – v _o² ) + mgh

W _nc= te mahi i mahia e te kaha kore-pūmau e pā ana ki te mea

ΔEK = te huringa o te pūngao nekeneke

ΔEP = te huringa o te pūngao pūmanawa

m = papatipu

v = te tere

g = te whakaterenga nā te kaha ā-papa

h = te huringa o te teitei

Ko te panonitanga o te teitei h = 0, nō reira ko ΔEP = 0

W _nc= ΔEK

Ngā mahi i mahia e te kaha kore-pūmau:

W _nc= -F _cd = – μ _kN d = – μ _kwd = – μ _kmgd

W _nc= -(0.2)(2)(10)(s)

W _nc= – (4)(2)

Ko te tohu tango e tohu ana ko te ahunga o te kaha waku nekeneke he ritenga ke ki te ahunga o te nekehanga.

Te huringa o te pūngao nekeneke:

ΔEK = ½ m (v _t² – v _o² ) = ½ (2)(0 – 10 ² ) = 0 – 100 = -100

Te rahi o te nekehanga:

W _nc= ΔEK

– 4 hēkona = – 100

s = -100/-4

s = 25 m

[irp]

2. Ka paheke iho tētahi poraka i runga i tētahi papa whakarara. Ko te tauwehenga o te waku nekeneke ko te 0.4. Ko te whakaterenga nā te kaha ā-papa ko te g = 10 ms ^-2 . Tātaihia te tere whakamutunga ina pā te poraka ki te whenua.

Mōhiotia: Te mātāpono o te mahi-pūngao mīhini – ngā raruraru me ngā otinga 3

Teitei tīmatanga (h _o) = 6 m

Teitei whakamutunga ( _t) = 0 m

Te tere tīmatanga (v _o) = 0

Ko te tauwehenga o te waku nekeneke ( _μk) = 0.4

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

cos θ = 8/10

Ko te wāhanga poutū o te taumaha = w _y= w cos θ = mg cos θ = m (10) (8/10) = m (10)(4/5) = m (40/5) = 8 m

Te kaha noa = N = w _y= 8 m

Te kaha o te waku nekeneke = f _k= μ _kN = μ _kw _y= (0.4)(8 m) = 3.2 m

E hiahiatia ana: Te tere whakamutunga ( _vt)

Rongoā:

Te mātāpono o te mahi-pūngao mīhini – ngā raruraru me ngā otinga 4 Te mātāpono mahi-pūngao mīhini:

W _nc= Δ EM

W _nc= Δ EK + Δ EP

Te huringa o te pūngao nekeneke:

ΔEK = 1/2 m (v_t² -v_o²) = 1/2 m (v_t² - 0) = 1/2 mv_t²

Te huringa o te pūngao pūmanawa:

Δ EP = mg (h _t– h _o) = m (10)(0-6) = m (10)(-6) = – 60 m

Te mahi i mahia e te kaha o te waku nekeneke:

W _nc= – f _ks = – ( 3.2 m)(10) = – 32 m

Ko te tohu tango e tohu ana ko te ahunga o te kaha o te waku nekeneke he ritenga ke ki te ahunga o te nekehanga.

Ko te tere whakamutunga (vt ₎:

W _nc= Δ EK + Δ EP

– 32 m = 1/2 mv _t² – 60 m

– 32 m = m (1/2 v _t² – 60)

– 32 = 1/2 v _t² – 60

– 32 + 60 = 1/2 v _t²

28 = 1/2 v _t²

2 (28) = v _t²

56 = v _t²

vt = √4.14

v _t= 2 √14 ms ^-1

[irp]

3. Ka paheke iho tētahi poraka i runga i tētahi papa whakarara. Ko te tere tīmatanga he 0 m/s, ā, ko te tere whakamutunga he 10 ms ^-1 . Mena ko te kaha o te waku nekeneke he 2 N, ā, ko te whakaterenga nā te kaha ā-papatipu g = 10 ms ^-2 , he aha te teitei (h)?

Mōhiotia: Te mātāpono o te mahi-pūngao mīhini – ngā raruraru me ngā otinga 5

Taumaha (m) = 1 kg

Te tere tīmatanga (v _o) = 0 (te okiokinga poraka)

Te tere whakamutunga (vt ₎= 10 ms ^-1

Teitei tīmatanga (h _o) = h

Teitei whakamutunga ( _t) = 0

Te kaha o te waku nekeneke (f _k) = 2 N

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

Teitei e hiahiatia ana: Teitei (h)

Rongoā:

Te mahi i mahia e te kaha o te waku nekeneke:

W _nc= – f _ks = – (2 )(15) = – 30

Ko te tohu tango e tohu ana ko te ahunga o te kaha o te waku nekeneke he ritenga ke ki te ahunga o te nekehanga.

Te huringa o te pūngao nekeneke:

ΔEK = 1/2 m (v_t² -v_o²) = 1/2 (1)(10² - 0) = 1/2 (10²) = 1/2 (100) = 50

Te huringa o te pūngao pūmanawa:

Δ EP = mg (h _t– h _o) = (1)(10)(0-h) = (10)(-h) = -10 h

Te mātāpono mahi-pūngao mīhini:

W _nc= Δ EK + Δ EP

– 30 = 50 – 10 hāora

10 hāora = 50 + 30

10 hāora = 80

h = 80/10

h = 8 mita

4. Ki te neke iho tētahi poraka i tētahi papa whāiti, kāti….
A. He nui ake te mahi i mahia e te kaha ā-papa i runga i te poraka i te huringa o te pūngao pūmanawa o te poraka
B. Ka piki ake te pūngao miihini
C. Ka whakaitihia te nui o te pūngao nekeneke me tōna pūngao pūmanawa
D. Ka oti te mahi mā te kaha waku e rite ana ki te huringa o te pūngao nekeneke o te poraka
otinga

He hē a A

Ko te mahi i mahia e te kaha o te papatipu i runga i te poraka he rite ki te huringa o te pūngao pūmanawa papatipu o tētahi poraka.

He hē a B

Mena he maeneene te papa whakarara- c , he pumau tonu te pūngao ā-pūmanawa o te poraka. Ina kei te tihi o te papa whakarara, ā, kāore anō kia neke, he ōrite te pūngao ā-pūmanawa o te poraka ki te pūngao pūmanawa ā-papa. Kei te okioki tonu te poraka, nō reira he kore tōna pūngao nekeneke. Ina neke iho i te papa whakarara, ka whakaitihia te teitei o te poraka, nō reira ka whakaitihia hoki te pūngao pūmanawa ā-papa. Ka heke te pūngao pūmanawa ā-papa nā te mea ka huri ki te pūngao nekeneke. Ahakoa ka huri te pūngao pūmanawa ā-papa ki te pūngao nekeneke, he pumau tonu te pūngao ā-pūmanawa.

Mena he taratara te papa piko, ka heke te pūngao ā-pūkaha o te poraka nā te mahi kino a te kaha waku. He kaha kore-pūmau te kaha waku. Ka heke te pūngao ā-pūkaha o te mea nā te mahi a te kaha kore-pūmau ki runga i tētahi mea.

He tika a C

He taratara te papa piko, nō reira he kaha waku e wero ana i te nekehanga o te poraka. He kaha kore-pūmau te kaha waku. E kī ana te ariā mahi-pūngao mīhini ko te mahi i mahia e te kaha kore-pūmau (hei tauira, te kaha waku) he ōrite ki te huringa o te pūngao mīhini. I tēnei whai, kei te heke te pūngao mīhini.

Ko te pūngao ā-pūkaha o te poraka = te pūngao pūmanawa ā-papa + te pūngao nekeneke.

He hē a D.

Ko te mahi i mahia e te kaha waku i runga i te poraka he rite ki te huringa o te pūngao miihini o te poraka, ehara i te huringa o te pūngao nekeneke o te poraka. He pono kei te wero te kaha waku i te nekehanga o te poraka, ā, ka whakaitihia te tere o te poraka, ka whakaitihia hoki te pūngao nekeneke o te poraka. Engari kia mōhio koe ko te pūngao nekeneke o te poraka i ahu mai i te pūngao pūmanawa ā-papa. Nō reira, he pono te kī ko te mahi i mahia e te kaha waku he rite ki te huringa o te pūngao miihini (ka heke te pūngao miihini).

Ko te whakautu tika ko C.

5. Ka pāngia tētahi mea i runga i te papa taratara, ā, ka neke mō te 3 hēkona, kātahi ka tū. Mena ko te taumaha e mōhiotia ana o te mea he 10 karamu, ko te kaha waku i waenganui i te mea me te papa he 2 kirodina. Tātaihia te mahi i mahia e te kaha waku.

A. 0.18 J

B. -0.18 J

C. 0.36 J

D. -0.36 J

Mōhiotia:

Wā wā (t) = 3 hēkona

Tere whakamutunga (vt ₎= 0 m/s (e okioki ana te mea)

Taumaha o te mea (m) = 10 karamu = 10/1000 kg = 1/100 kg = 0.01 kg

Te kaha waku (F) = 2 kirotini = 2 x 10 ³ dynes

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

Rongoā:

Te hurihanga o ngā waeine kaha:

1 Newton = 1 x 10 ⁵ dyne

1 tāne = 1 / 10 ⁵ Ngā Newton = 1 x 10 ^-5 Ngā Newton = 10 ^-5 Ngā Newton

Te kaha waku (F) = 2 x 10 ³ dyne = 2 x 10 ³ x 10 ^-5 Newton = 2 x 10 ^-2 Newton = 2/100 Newton = 0.02 Newton

E ai ki te ariā mahi-pūngao mīhini, ka mahia te mahi e tētahi kaha kore-pūmau i runga i tētahi mea e ōrite ana ki te huringa o te pūngao mīhini o taua mea.

Ki te neke tetahi mea i runga i te papa whakarara, ko te pūngao ā-pūmanawa (ME) = te pūngao pūmanawa ā-papa (PE) + te pūngao nekeneke (KE). Engari ki te neke noa te mea i runga i te papa whakapae, ā, kāore he huringa teitei, ko te pūngao ā-pūmanawa = te pūngao nekeneke. I runga i te papa whakapae, he kore te pūngao pūmanawa ā-papa nā te mea kāore he huringa teitei.

He kaha kore-pūmau te kaha waku. Ko te tikanga ka whakaitihia e te kaha waku te tere o te mea me te pūngao nekeneke o te mea. Ka taea te whakatau ko te mahi i mahia e te kaha waku ki runga i te mea he rite ki te hekenga o te pūngao miihini.

Pāngarau:

Mahi (W) = Te huringa o te pūngao ā-ringa (ΔEM)

Fs = ΔEP + ΔEK

Fs = mg Δh + ½ m ( _vt² – _vo² )

Fs = mg (0) + ½ m (0 ² – v _o² )

Fs = 0 + ½ m (– (v _o² ))

F s = – ½ mv _o² ———— Whārite 1

Whakaahuatanga: F = te kaha waku, d = te nekehanga, m = te papatipu, v ₌te tere tīmatanga

Kāore anō kia mōhiotia te nekehanga (d) me te tere tīmatanga (v _{o ) nā te mea ka tatauhia tuatahitia te v}_ote d rānei. Ko te mahi i mahia e te kaha waku ka tatauhia mā te whakamahi i tētahi o ngā whārite i muri i te mōhiotia o te v _o te d rānei.

Ko te whārite o te nekehanga (d) i runga i te nekehanga rārangi kore-taurite:

v _t² = v _o² + 2 (-a) s

Ko te tere whakamutunga (vt ₎= 0, ā, ko te whakaterenga (a) he tohu kino nā te mea kua whakaroahia te tere o te mea (kua whakaitihia te tere o te mea).

0 = v_o² – 2 ngā pānuitanga

v_o² = 2 pānuitanga

d = v _o² / 2 a ———— Whārite 2

Hurihia a d i te whārite 2 ki a d i te whārite 1:

F d = – ½ mv _o²

F (v _o² /2a) = – ½ mv _o²

(F/2a) v _o² = – ½ mv _o²

F/2a = – ½ m

F = (2)(a)(-1/2)(m)

F = – (a)(m)

a = – (F / m)

a = – 0.02 Ngā Newton / 0.01 kirokaramu

a = – 2 Newton/kirokaramu

a = – 2 m/s ²

Whārite hei tatau i te tere tīmatanga (v _o) i roto i te nekehanga rārangi kore-taurite:

vt = v _o+ i —–> Tere whakamutunga (v _t) = 0, Whakaterenga (a) = 2 m/s ² , wā (t) = 3 _hēkona

0 = v _o+ (-2)(3)

0 = v _o– 6

v _o= 6 mita/hekona

Te mahi (W) i mahia e te kaha waku:

W = – ½ mv _o² = -1/2 (0.01)(6 ² ) = -1/2 (0.01)(36)

W = -1/2 (0.36)

W = – 0.18 Joule

Ko te mahi i mahia e te kaha waku he tohu kino, arā, ka whakaitihia te pūngao miihini o te mea e te mahi.

Mena e mōhiotia ana ko d, ka taea te tatau i te mahi mā te whakamahi i te whārite o W = F d.

Ko te whakautu tika ko B.

[wpdm_package id='1178′]

Pānuitia atu

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 _t² – v _o² )

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 _t² – v _o² )

W _kupenga= ½ (5000)(20 ² – 0 ² )

W _kupenga= (2500)(400 – 0)

W _kupenga= (2500)(400)

W _kupenga= 1000,000 Joule

[irp]

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 _t² – v _o² )

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 _t² – v _o² )

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 _t² = 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 _t² – 1/2 mv _o² = 1/2 m (v _t² – v _o² ) = 1/2 (10)(78 ² – 6 ² ) = 5 (6084 –36) = 5 (6048)

ΔKE = 30,240 Joule

[irp]

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

Pūngao nekeneke – ngā raruraru me ngā otinga 1

Rongoā:

Mahi kupenga = huringa o te pūngao nekeneke

W _kupenga = ½ m (v _t² – v _o² )

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 _t² – v _o² ) = ½(4000)(15 ² -25 ² ) = (2000)(225-625) = (2000)(-400) = -800,000 Joule = -800 kJ

[irp]

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: Pūngao nekeneke – ngā raruraru me ngā otinga 2

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 _t² – v _o² )

Ngā mahi i mahia e te motuka:

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

[irp]

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 _t² – ½ mv _o² = ½ m (v _t² – v _o² )

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 _t² – v _o² ) = 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 _t² = 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 _t² – v _o² ) = ½ (1){(5√2) ² – 0 ² }

W _kupenga = ½ (25)(2) = 25 Joule

[irp]

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 _t² – v _o² ) = 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 _t² -1/2 mv _o²

W _kupenga = 1/2 m (v _t² – v _o² )

21 = 1/2 (2) (v _t² – 2 ² )

21 = (v _t² – 2 ² )

21 = v _t² – 4

v _t² = 21 + 4 = 25

vt ₌ √25

v _t = 5 m/s

[irp]

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 _t² – ½ mv _o²

W = ½ mv _t² – 0

W = ½ mv _t² —— 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 _ot + 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 _t² = (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 _o² = 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 _t² = 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 _t² – ½ mv _o² = ½ m (v _t² –v _o² )

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 _t² – ½ mv _o²

W kupenga = ½ m (v _t² – v _o² )

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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Pānuitia atu

Ngā mahi i mahia mā te kaha - ngā raruraru me ngā otinga

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.

Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 1

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

[irp]

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!

Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 2

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 _xd = (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.

[irp]

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.

[irp]

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.

Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 3

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 _kd = (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: Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 1

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

[irp]

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: Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 2

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

[irp]

Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 3

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: Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 4

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.

Ngā mahi i mahia mā te kaha – ngā raruraru me ngā otinga 11

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 mahi

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.

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Pānuitia atu

Te ture a Kepler – ngā raruraru me ngā otinga

1. Ko te tawhiti o te Ao i te Rā he 149.6 x 106 ^km , ā, ko te wā o te hurihanga o te Ao he 1 tau. Tātaihia te T ² / r ³

Mōhiotia:

T = 1 tau, r = 149.6 x 10 ⁶ km

E hiahiatia ana : T ² / r ³ = … ?

Otinga :

k = T² /r³= 1² / (149.6 x 10⁶)³ = 1 / (3348071.9 x 10¹⁸) = 2.98 x 10^-25tau²/km³

[irp]

2. Pūmau whānui (G) = 6.67 x 10 ^-11 Nm² /kg² ^me^te 1.99 x ^10⁻¹ kg o te Rā.

Te ture a Kepler – ngā raruraru me ngā otinga 2

[irp]

3. Ko te tawhiti toharite o te Ao mai i te Rā ko 149.6 x 10 ⁶ km, ā, ko te tawhiti toharite o Merkuri mai i te Rā ko 57.9 x 10 ⁶ km. Ko te wā o te hurihanga o te Ao ko 1 tau, he aha te wā o te hurihanga o Merkuri?

Mōhiotia:

r o Papatūānuku = 149.6 x 10 ⁶ km

r o te mercury = 57.9 x 10 ⁶ km

T o Papatūānuku = 1 tau

E hiahiatia ana: T o te konukōrei?

Rongoā:

Te ture a Kepler – ngā raruraru me ngā otinga 3

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Pānuitia atu

Te amiorangi tukutahi-whenua – ngā raruraru me ngā otinga

1. He aha te teitei o tētahi amiorangi geosynchronous i runga ake i te mata o Papatūānuku?

G = pūmau whānui = 6.67 x 10 ^-11 N ^m² / ^kg²

M = Papatipu o te Ao = 5.97 x ¹⁰²⁴ kg

T = 24 hāora = 24 (3600 hēkona) = 86,400 hēkona = 8.64 x 10 ⁴ hēkona

otinga

Amiorangi tukutahi-whenua - ngā raruraru me ngā otinga 1

Te teitei o te amiorangi i runga ake i te mata o Papatūānuku = 4.22 x 10 ⁷ m = 4.22 x 10 ⁴ km = 42,200 km

Te teitei o te amiorangi i runga ake i te mata o Papatūānuku = 6.38 x 10 ⁶ m = 6.38 x 10 ³ km = 6380 km

Te teitei o te amiorangi i runga ake i te mata o te Ao = te tawhiti o te amiorangi mai i te pokapū o te Ao – te pūtoro o te Ao

Te teitei o te amiorangi i runga ake i te mata o te Ao = 42,200 km – 6380 km

Te teitei o te amiorangi i runga ake i te mata o te Ao = 35,820 km

[irp]

2. He aha te tere o tētahi amiorangi geosynchronous?

Pūmau whānui (G) = 6.67 x 10 ^-11 N ^m² / ^kg²

Papatipu o te Ao (m _E) = 5.97 x ¹⁰²⁴ kg

Ko te tawhiti i waenganui i te amiorangi me te pokapū o Papatūānuku (r) = 4.22 x ¹⁰⁷ m

otinga

Amiorangi tukutahi-whenua - ngā raruraru me ngā otinga 2

whakamahia rānei tēnei whārite

Amiorangi tukutahi-whenua - ngā raruraru me ngā otinga 3

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Pānuitia atu

Te ture ā-papatipu ā-ao a Newton – ngā raruraru me ngā otinga

1. Ko te tawhiti i waenganui i te tangata 40-kg me te tangata 30-kg he 2 m. He aha te rahi o te kaha ā-papa e pā ana ki tētahi ki tētahi? Pūmau whānui = 6.67 x 10 ^-11 N ^m² / ^kg²

Mōhiotia:

m1 = ₄₀kg, m2 _{= 30 kg, r}⁼ 2 m, G = 6.67 x 10 ^-11 N m2 ^/ kg2

E hiahiatia ana: te rahi o te kaha ā-papa (F)?

Rongoā:

Te ture a Newton mō te kaha ā-ao – ngā raruraru me ngā otinga 1

[irp]

2. Ko te tawhiti i waenganui i a Papatūānuku me te Marama (r) he 3.84 x 108 ^m . He aha te kaha o te kaha ā-papa e pā ana ki tētahi ki tētahi?

Mōhiotia:

Papatipu o te Ao (m _E) = 5.97 x ¹⁰²⁴ kg

Papatipu o te Marama (m _M) = 7.35 x ¹⁰²² kg

Ko te tawhiti i waenganui i te pokapū o Papatūānuku me te pokapū o te Marama (r) = 3.84 x ¹⁰⁸ m

Pūmau whānui (G) = 6.67 x 10 ^-11 N ^m² / ^kg²

E hiahiatia ana: Te rahi o te kaha ā-papa (F)

Rongoā:

Te ture a Newton mō te kaha ā-ao – ngā raruraru me ngā otinga 2

[irp]

3. He aha te tawhiti mai i te Ao, ko te rahi o te kaha ā-papa o te Ao me te Marama he kore?

Mōhiotia:

Papatipu o te Ao = 5.97 x ¹⁰²⁴ kg

Papatipu o te Marama = 7.35 x ¹⁰²² kg

Ko te tawhiti i waenganui i te pokapū o Papatūānuku me te pokapū o te Marama (r) = 3.84 x 108 ^m.

Pūmau whānui ( G) = 6.67 x 10 ^-11 N ^m² / ^kg²

E hiahiatia ana: te tawhiti mai i te Ao

Rongoā:

Te ture a Newton mō te kaha ā-ao – ngā raruraru me ngā otinga 3

Kore te kaha ā-papatipu kupenga.

Te ture a Newton mō te kaha ā-ao – ngā raruraru me ngā otinga 4

Whakamahia te tātai tapawhā:

A = – 6.35

B = – 7.68 x 10 ⁸

C = 87.76 x 10 ^-14

Te ture a Newton mō te kaha ā-ao – ngā raruraru me ngā otinga 5

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Pānuitia atu