ahupūngao

1. Papatipu o te mea = 2 kg, whakaterenga nā te kaha ā-papatipu = 9.8 m/s2 ^, tauwehenga o te waku pūmau = 0.2, tauwehenga o te waku nekeneke = 0.1. Kei te okioki te mea, kei te whakaterenga rānei? Mena kei te whakaterenga te mea, kimihia (a) te kaha kupenga (b) te rahi me te ahunga o te whakaterenga o te pouaka!

otinga

Mōhiotia:

Taumaha (m) = 2 kg

Te whakaterenga nā te kaha ā-papa (g) = 9.8 m/s ²

Tauwehenga o te waku pateko ( μs ₎ = 0.2

Tauwehenga o te waku nekeneke ( μk ₎ = 0.1

Taumaha (w) = mg = (2)(9.8) = 19.6 Ngā Newton

Ko te wāhanga whakapae o te taumaha (w _x ) = w sin 30 ^o = (19.6)(0.5) = 9.8 Newton

Ko te wāhanga poutū o te taumaha (w _y ) = w cos 30 ^o = (19.6)(0.5√3) = 9.8√3 Ngā Newton

Te kaha noa (N) = w _y = 9.8√3 Ngā Newton

Te kaha o te waku pūmau (f _s ) = (0.2)(9.8√3) = 1.96√3 Newton = 3.39 Newton

Te kaha o te waku nekeneke (f _k ) = (0.1)(9.8√3) = 0.98√3 Newton = 1.69 Newton

Rongoā:

Kei te okioki te mea mēnā ko te w _x < f _s , kei te neke iho te mea mēnā ko te w _x > f _s.

wx = 9.8 Newton me fs _{= 3.39} Newton.

(a) te kaha kupenga

∑ F = w _x – f _k = 9.8 – 1.69 = 8.11 Ngā Newton

(b) te rahi me te ahunga o te whakaterenga

∑ F = ma

8.11 = (2) he

ki = 4.05

Ko te rahi o te whakaterenga = 4.05 m/s2 ^me te ahunga o te whakaterenga = ki raro.

[irp]

2. Papatipu o te mea = 4 kg, whakaterenga nā te kaha ā-papatipu = 9,8 m/s2 ^. Tauwehenga o te waku nekeneke = 0.2 me te tauwehenga o te waku pūmau = 0.4. Te rahi o te kaha F = 40 Newtons. Kei te okioki te mea, kei te paheke rānei ki raro? Mena ka paheke te mea, kimihia (a) te kaha kupenga (b) te rahi me te ahunga o te whakaterenga!

otinga

Mōhiotia:

Taumaha (m) = 4 kg

Te whakaterenga nā te kaha ā-papa (g) = 9.8 m/s ²

Ko te tauwehenga o te waku pateko ( μs ₎ = 0.4

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

Taumaha (w) = mg = (4)(9.8) = 39.2 Ngā Newton

Ko te wāhanga whakapae o te taumaha (w _x ) = w sin 30 ^o = (39.2)(0.5) = 19.6 Newtons

Ko te wāhanga poutū o te taumaha (w _y ) = w cos 30 ^o = (392)(0..5√3) = 19.6√3 Ngā Newton

Ko te kaha noa (N) = w _y = 19.6√3 Ngā Newton = 33.95 Ngā Newton

te kaha waku pumau (f _s ) = μ _s N = (0,4)(33.95) = 13.58 Newtons

Te kaha waku nekeneke (f _k ) = μ _k N = (0.2)(33.95) = 6.79 Newtons

F = 40 Newton

Rongoā:

Ka paheke te mea ki raro mēnā ko F < w _x + f _s . Ka paheke te mea ki runga mēnā ko F > w _x + f _s.

F = 40 Ngā Newton, w _x = 19.6 Ngā Newton me f _s = 13.58 Ngā Newton.

He nui ake a F i te wx ₊ fs _, nō reira ka paheke ake te mea.

(a) Te kaha kupenga

∑ F = F – w _x – f _k = 40 – 19.6 – 6.79 = 13.61 Ngā Newton

(b) Te rahi me te ahunga o te whakaterenga

∑ F = ma

6.4 = (4) he

ki = 1.6

Ko te rahi o te whakaterenga he 1.6 m/s² ^, ā, ko te ahunga o te whakaterenga kei runga.

[irp]

[wpdm_package id='481′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

1. Te taumaha o te pouaka = 2 kg, te whakaterenga nā te kaha ā-papatipu = 9.8 m/s ^2. Kimihia (a) te kaha kupenga e whakatere ana i te pouaka ki raro (b) te rahi o te whakaterenga o te pouaka.

otinga

Mōhiotia:

Taumaha (m) = 2 kg

Te whakaterenga nā te kaha ā-papa (g) = 9.8 m/s ²

Taumaha (w) = mg = (2)(9.8) = 19.6 Newton

w _x = w sin 30 = (19.6)(0.5) = 9.8 Ngā Newton

w _y = w cos 30 = (19.6)(0.5√3) = 9.8√3 Ngā Newton

Rongoā:

(a) Ko te kupenga mō te ce e whakateretere ana i te pouaka

He maeneene te papa piko, nō reira kāore he kaha waku. Ko te kaha anake e pā ana ki te mea ko te w _x.

∑ F = _wx

∑ F = 9.8 Newton

(b) te rahi o te whakaterenga

∑ F = ma

9.8 = (2) he

ā = 9.8 / 2

a = 4.9 m/s ²

Ko te kaha o te whakaterenga he 4.9 m/s² ^, ko te ahunga o te whakaterenga kei raro.

[irp]

2. He maeneene te papa piko , nō reira kāore he kaha waku . Ko te papatipu o te mea he 3 kg, ko te whakaterenga nā te kaha ā-papa he 9.8 m/s² ^. Tātaihia te rahi o te kaha F mēnā (a) kei te okioki te mea (b) kei te neke te mea ki raro me te whakaterenga pumau o te 2 m/s² ⁽ c) kei te neke te mea ki runga me te whakaterenga pumau o te 2 m/ ^s².

otinga

Mōhiotia:

Taumaha (m) = 3 kg

Te whakaterenga nā te kaha ā-papa (g) = 9.8 m/s ²

Taumaha (w) = mg = (3)(9.8) = 29.4 Ngā Newton

w _x = w sin 30 = (29.4)(0.5) = 14.7 Ngā Newton

w _y = w cos 30 = (29.4)(0.5√3) = 14.7√3 Ngā Newton

Rongoā:

(a) Te rahi o te kaha F mēnā kei te takoto kau te mea

E ai ki te ture nekehanga tuatahi a Newton , mēnā kei te okioki tetahi mea, ko te kaha kupenga e pā ana ki taua mea he kore.

∑ F = 0

F – w _x = 0

W = _wx

F = 14.7 Newton

(b) Te rahi o te kaha F mēnā kei te neke whakararo tetahi mea i te pūmau 2 m/s ²

∑ F = ma

w _x – F = ma

14.7 – F = (3)(2)

14.7 – F = 6

F = 14.7–6

F = 8.7 Newton

(c) Te rahi o te kaha F mēnā kei te neke ake tētahi mea i te pūmau 2 m/s ²

∑ F = ma

F – w _x = ma

F – 14.7 = (3)(2)

F – 14.7 = 6

F = 14.7 + 6

F = 20.7 Newton

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[wpdm_package id='479′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

1. Ko te taumaha o te pouaka 1 he 2 kg, ko te taumaha o te pouaka 2 he 4 kg, ko te whakaterenga o te kaha ā-papa he 10 m/s2 ^, ko te rahi o te kaha F he 40 Newtons. Ko te tauwehenga o te waku nekeneke i waenga i te pouaka 1 me te papa he 0.2, ā, ko te tauwehenga o te waku nekeneke i waenga i te pouaka 2 me te papa he 0.3. Kimihia (a) Te rahi me te ahunga o te whakaterenga o te pouaka (b) Te rahi o te kaha i tukuna e te pouaka 1 ki te pouaka 2 (F ₁₂ ) me te rahi o te kaha i tukuna e te pouaka 2 ki te pouaka 1 (F ₂₁ ).

otinga

Mōhiotia:

Taumaha o te pouaka 1 (m1 ₎ = 2 kg

Taumaha o te pouaka 2 (m2 ₎ = 4 kg

Te whakaterenga o te kaha ā-papa (g) = 10 m/ ^s² ,

Ko te kaha F = 40 Newton,

Te tauwehenga o te waku nekeneke i waenga i te pouaka 1 me te papa ( μ _k1 ) = 0.2

Te tauwehenga o te waku nekeneke i waenga i te pouaka 2 me te papa ( μ _k2 ) = 0.3

Te taumaha o te pouaka 1 (w1 ₎ = m1 _karamu = (2)(10) = 20 Newton

Te taumaha o te pouaka 2 (w ₂ ) = m ₂ karamu = (4)(10) = 40 Newtons

Ko te kaha noa i pā ki te pouaka 1 (N ₁ ) = w ₁ = 20 Newtons

Ko te kaha noa i pā ki te pouaka 2 (N ₂ ) = w ₂ = 40 Newtons

Ko te kaha o te waku nekeneke i pā ki te pouaka 1 (f _k1 ) = ( μ _k1 )(N ₁ ) = (0.2)(20) = 4 Newtons

Ko te kaha o te waku nekeneke i pā ki te pouaka 2 (f _k2 ) = ( μ _k1 )(N ₂ ) = (0.3)(40) = 12 Newtons

Rongoā:

(a) Te rahi me te ahunga o te whakaterenga o te pouaka

ΣF = ma

F – f _k1 – f _k2 = (m ₁ + m ₂ ) a

40 – 4 – 12 = (2 + 4) he

24 = 6

ā = 24 / 6

a = 4 m/s ²

Te ahunga o te whakaterenga = te ahunga o te kaha kupenga = whaka-matau.

(b) Te rahi o te kaha i tukuna e te pouaka 1 ki runga i te pouaka 2 (F ₁₂ ) me te rahi o te kaha i tukuna e te pouaka 2 ki runga i te pouaka 1 (F ₂₁ ).

Tātaihia te rahi o F ₁₂ :

ΣF = ma

F ₁₂ – f _k2 = (m ₂ ) a

F ₁₂ – 12 = (4)(4)

F ₁₂ – 12 = 16

F ₁₂ = 16 + 12

F ₁₂ = 28 Newton

Ko te F ₁₂ me te F ₂₁ he kaha mahi me te kaha tauhohe e pā ana ki ngā mea rerekē. He rite te rahi o te F ₁₂ me te F ₂₁ , he rite te ahunga, he rerekē hoki.

F ₁₂ = 28 Ngā Newton = F ₂₁ = 28 Ngā Newton.

[irp]

2. Ko te taumaha o te pouaka 1 he 2 kg, ko te taumaha o te pouaka 2 he 4 kg, ko te whakaterenga o te kaha ā-papa he 10 m/s² ^, ko te kaha F he 40 N. Ko te tauwehenga o te waku nekeneke i waenga i te pouaka 1 me te papa he 0.2, ā, ko te tauwehenga o te waku nekeneke i waenga i te pouaka 2 me te papa he 0.3. Whakatauhia (a) Te rahi me te ahunga o te whakaterenga (b) Te kume i roto i te taura e hono ana i ngā pouaka. Kaua e aro ki te taumaha o te taura.

Mōhiotia:

Taumaha o te pouaka 1 (m1 ₎ = 2 kg

Taumaha o te pouaka 2 (m2 ₎ = 4 kg

Te whakaterenga o te kaha ā-papa (g) = 10 m/ ^s² ,

Ko te kaha F = 40 Newton,

Ko te tauwehenga o te waku nekeneke i waenga i te pouaka 1 me te papa he 0.2 ( μ _k1 ) = 0.2

Ko te tauwehenga o te waku nekeneke i waenga i te pouaka 2 me te papa he 0.2 ( μ _k2 ) = 0.3

Te taumaha o te pouaka 1 (w ₁ ) = m ₁ karamu = (2)(10) = 20 Newtons

Te taumaha o te pouaka 2 (w ₂ ) = m ₂ karamu = (4)(10) = 40 Newtons

Ko te kaha noa i pā ki te pouaka 1 (N ₁ ) = w ₁ = 20 Newtons

Ko te kaha noa i pā ki te pouaka 2 (N ₂ ) = w ₂ = 40 Newtons

Ko te kaha o te waku nekeneke i pā ki te pouaka 1 (f _k1 ) = ( μ _k1 )(N ₁ ) = (0.2)(20) = 4 Newtons

Ko te kaha o te waku nekeneke i pā ki te pouaka 2 (f _k2 ) = ( μ _k1 )(N ₂ ) = (0.3)(40) = 12 Newtons

Rongoā:

(a) te rahi me te ahunga o te whakaterenga

ΣF = ma

F – f _k1 – f _k2 = (m ₁ + m ₂ ) a

40 – 4 – 12 = (2 + 4) he

24 = 6

ā = 24 / 6

a = 4 m/s ²

Ko te rahi o te whakaterenga he 4 m/s² ^, ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga = whaka-matau.

(b) Te kukū o te taura

Ko ngā kaha e pā ana ki te pouaka 1 i te taha whakapae ko te kume 1 (T ₁ ) ki te taha matau, me te kaha o te waku nekeneke 1 (f _{k 1} ) ki te taha maui. Whakamahia te ture tuarua a Newton:

ΣF = ma

T ₁ – f _k1 = m ₁ a

T ₁ – 4 = (2)(4)

T ₁ – 4 = 8

T ₁ = 8 + 4 = 12 Newton

Ko ngā kaha e pā ana ki te pouaka 2 i te ahunga whakapae ko te kume 2 (T ₂ ) ki maui me te kaha o te waku nekeneke 2 (f _{k 2} ) ki matau. Whakamahia te ture tuarua a Newton :

ΣF = ma

F – T ₂ – f _k2 = m ₂ a

40 – T ₂ – 12 = (4)(4)

28 – T ₂ = 16

T ₂ = 28 – 16 = 12 Newton

Ko te kume i roto i te taura e hono ana i ngā pouaka = T ₁ = T ₂ = T = 12 Newton.

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[wpdm_package id='493′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Te nekehanga o ngā tinana e honoa ana e ngā taura me ngā pūrei
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

1. Ko te taumaha o te mea 1 he 2 kg, ko te taumaha o te mea 2 he 4 kg, ko te whakaterenga o te kaha ā-papa he 10 m/s² ^, ko te rahi o te kaha F he 12 Newton. Tātaihia te rahi me te ahunga o te whakaterenga o ngā mea.

Mōhiotia:

m1 = ₂ kg, m2 ₌ 4 kg, karamu = 10 m/s2 ^, F = 12 Newton

E hiahiatia ana : he

Rongoā:

Σ F = ma

F = (m1 ₊ m2 ₎ a

12 = (2 + 4) he

12 = 6

ā = 12 / 6

a = 2 m/s ²

Ko te rahi o te whakaterenga he 2 m/s² ^, ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga = whaka-matau.

[irp]

2. Ko te taumaha o te mea 1 he 2 kg, ko te taumaha o te mea 2 he 4 kg, ko te whakaterenga o te kaha ā-papa he 10 m/s² ^, ko te rahi o te kaha F he 24 N. Tātaihia te rahi me te ahunga o te whakaterenga.

Mōhiotia:

m1 = ₂ kg, m2 ₌ 4 kg, karamu = 10 m/s2 ^, F = 24 Newton

E hiahiatia ana: te whakaterenga (a)

Rongoā:

Σ F = ma

F = (m1 ₊ m2 ₎ a

24 = (2 + 4) he

24 = 6

ā = 24 / 6

a = 4 m/s ²

Ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga = whaka-matau.

[irp]

[wpdm_package id='474′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

Ngā raruraru i whakatauhia i roto i ngā ture nekehanga a Newton – Te kaha o te waku pūmau me te waku nekeneke

1. Kei runga i te papa whakapae tētahi mea e takoto ana. Ko te tauwehenga o te waku pumau ko te 0.4 , ā, ko te whakaterenga o te kaha ā-papa ko te 9.8 m/s² ^. Whakatauhia (a) Te kaha mōrahi o te waku pumau (b) Te kaha iti rawa o F

otinga

Mōhiotia:

Taumaha (m) = 1 kg

Ko te tauwehenga o te waku pateko (μ _s ) = 0.4

Ko te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

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

Te kaha noa (N) = w = 10 Newton

E hiahiatia ana:

(a) Te kaha mōrahi o te waku pumau (b) Te kaha iti rawa o F

Rongoā:

(a) Te kaha mōrahi o te waku pumau

f _s = μ _s N

fs ₌ (0.4)(9.8 N) = 3.92 Ngā Newton

(b) Te kaha iti rawa o F

Mena ka pā te kaha F ki te mea engari kāore te mea e nekehia, me rite te kaha o te waku pumau ki te papa e pā ana ki te mea. Mena ka tīmata te mea ki te neke, ā, ka hipa atu i te kaha o te waku pumau, me rite te kaha o te waku nekeneke. Ka tīmata te mea ki te neke mena he nui ake te kaha F i te kaha mōrahi o te waku pumau.

Nō reira, ko te kaha iti rawa o F = te kaha mōrahi o te waku pateko = 3.92 Newtons.

[irp]

2. Ka tōia te pouaka 1 kg i runga i te mata whakapae e te kaha F, nō reira kei te neke te pouaka i te tere pumau. Mena ko te tauwehenga waku nekeneke he 0.1, tautuhia te rahi o te kaha F! (g = 9.8 m/s ² )

Mōhiotia:

_{Ko te tauwehenga waku nekeneke} ( μk ) = 0.1

Te taumaha o te pouaka (m) = 1 kg

Te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

Taumaha (w) = mg = (1 kg)(9.8 m/s² ⁾ = 9.8 kg m/s² ⁼ 9.8 Newton

Te kaha noa (N) = w = 9.8 Newton

E hiahiatia ana : F

Rongoā:

E ai ki te ture tuatahi a Newton , ki te kore he kaha kupenga e pā ki tētahi mea, ka noho tonu ia mea i tōna āhua okiokinga, i tōna tere pumau rānei i roto i te rārangi tika.

Nō reira, ki te neke te mea i te tere pumau , me kore he kaha kupenga ( Σ F = 0) . Ka pāngia te mea e te kaha F i te ahunga tika, kia pāngia ai te mea e te kaha o te waku nekeneke ki te taha maui.

∑ F = 0

F – f _k = 0

F = _fk

Te kaha o te waku nekeneke:

f _k = μ _k N = (0.1)(9.8 N) = 0.98 Newtons

ka neke te mea me te tere pumau, F = f _k = 0.98 Newtons

[irp]

3. Ka paheke tetahi mea i raro i tētahi papa whakarara me te tere pumau. Tāutuhia te tauwehenga waku nekeneke ( _μk ) . g = 9.8 m/ ^s2

otinga

w = taumaha, w _x = wāhanga whakapae o te taumaha, ngā pūwāhi i te taha o te pari, w _y = wāhanga poutū o te taumaha, poutū ki te papa pari, N = kaha noa, f _k = te kaha o te waku nekeneke.

Mōhiotia:

Taumaha (m) = 1 kg

Te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

taumaha (w) = mg = (1 kg)(9.8 m/s² ⁾ = 9.8 kg m/s² ⁼ 9.8 Newton

w _x = w sin 30 ^o = (9.8 N)(0.5) = 4.9 Ngā Newton

w _y = w cos 30 ^o = (9.8 N)(0.5) √ 3 = 4.9 √ 3 Ngā Newton

Te kaha noa (N) = w _y = 4.9 √ 3 Ngā Newton

E hiahiatia ana : te tauwehenga waku nekeneke ( μk ₎

Rongoā:

Ka paheke te mea i raro i tētahi papa hianga me te tere pumau kia kore ai te kaha kupenga e rite ki te 0.

∑ F = 0

wx – _{fk =} 0

wx = _fk​

w _x = μ _k N

5 = μk ₍ 5 √ 3 )

μ _k = 5 / 5 √ 3

μ _k = 1 / √ 3

μk ₌ 0.58

[irp]

[wpdm_package id='472′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Te nekehanga o ngā tinana e honoa ana e ngā taura me ngā pūrei
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

Ngā whakaoti rapanga i roto i ngā ture nekehanga a Newton – te ture nekehanga tuarua a Newton 

1. I whakaterea tētahi mea 1 kg te taumaha i te tere pumau 5 m/s2 ^. Tātaihia te kaha kupenga e hiahiatia ana hei whakatere i te mea.

Mōhiotia:

Taumaha (m) = 1 kg

Whakaterenga (a) = 5 m/s ²

E hiahiatia ana : 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/s ² = 5 Newton

[irp]

2. Papatipu o tētahi mea = 1 kg, 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

E hiahiatia ana : Te rahi me te ahunga o te whakaterenga (a)

Rongoā:

a = ∑F / m

ā = 2 / 1

a = 2 m/s ²

Ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga (∑F)

[irp]

3. Papatipu o te mea = 2 kg, F1 ₌ 5 Newton, F2 ₌ 3 Newton. Ko te rahi me te ahunga o te whakaterenga ko…

Mōhiotia:

Taumaha (m) = 2 kg

F ₁ = 5 Newton

F ₂ = 3 Newton

E hiahiatia ana: Te rahi me te ahunga o te whakaterenga (a)

Rongoā:

te kaha kupenga:

∑ F = F ₁ – F ₂ = 5 – 3 = 2 Ngā Newton

Te rahi o te whakaterenga:

a = ∑F / m

ā = 2 / 2

a = 1 m/s ²

Te ahunga o te whakaterenga = te ahunga o te kaha kupenga = te ahunga o F ₁

[irp]

4. Papatipu o te mea = 2 kg, F1 ₌ 10 Newton, F2 ₌ 1 Newton. Ko te rahi me te ahunga o te whakaterenga ko…

Mōhiotia:

Taumaha (m) = 2 kg

F ₂ = 1 Newton

F ₁ = 10 Newton

F _1x = F ₁ cos 60 ^o = (10)(0.5) = 5 Ngā Newton

E hiahiatia ana : Te rahi me te ahunga o te whakaterenga (a)

Rongoā:

Te kaha kupenga:

∑ F = F _1x – F ₂ = 5 – 1 = 4 Ngā Newton

Te rahi o te whakaterenga:

a = ∑F / m

ā = 4 / 2

a = 2 m/s ²

Te ahunga o te whakaterenga = te ahunga o te kaha kupenga = te ahunga o F _1x

[irp]

5. F ₁ = 10 Newton, F ₂ = 1 Newton, m ₁ = 1 kg, m ₂ = 2 kg. Ko te rahi me te ahunga o te whakaterenga ko…

Mōhiotia:

Taumaha 1 (m1 ₎ = 1 kg

Taumaha 2 (m2 ₎ = 2 kg

F ₁ = 10 Newton

F ₂ = 1 Newton

E hiahiatia ana : Te rahi me te ahunga o te whakaterenga (a)

Rongoā:

Te kaha kupenga:

∑ F = F ₁ – F ₂ = 10 – 1 = 9 Ngā Newton

Te rahi o te whakaterenga:

a = ∑F / ( _m1 + _m2 )

ā = 9 / (1 + 2)

ā = 9 / 3

a = 3 m/s ²

Ko te ahunga o te whakaterenga = te ahunga o te kaha kupenga = te ahunga o F ₁

[irp]

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/ s² ^. Tātaihia 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/s ²

E hiahiatia ana: Te kaha waku (F _g )

Rongoā:

Te whārite o te ture nekehanga tuarua 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

F – F _g = ma

200 – F _g = (40)(3)

200 – F _g = 120

F _g = 200 – 120

F _g = 80 Newton

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 tukuna e te poraka B ki runga i te poraka A.

A. 1 N

B. 1.25 N

C. 2 N

D. 3 N

Mōhiotia:

Te Kaha (F) = 5 Newton

Taumaha o te poraka A (m _A ) = 100 karamu = 0.1 kg

Taumaha o te poraka B (m _B ) = 300 karamu = 0.3 kg

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

Taumaha o te poraka A (w _A ) = (0.1 kg)(10 m/s ² ) = 1 kg m/s ² = 1 Newton

Taumaha o te poraka B (w _B ) = (0.3 kg)(10 m/s ² ) = 3 kg m/s ² = 3 Newtons

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)

w _A = taumaha o te poraka A (mahi ki te poraka A)

w _B = taumaha o te poraka B (mahi ki te poraka B)

N _A = te kaha noa i tukuna e te poraka B ki te poraka A (Whakahaere ki te poraka A)

N _A ' = te kaha noa i tukuna e te poraka A ki te poraka B (Whakahaere ki te poraka B)

Whakamahia te ture nekehanga tuarua a Newton ki ngā poraka e rua:

∑ F = ma

F – w _A – w _B + N _A – N _A ' = (m _A + m _B ) a

Ko te N _A me te N _A ' he kaha mahi-tauhohenga e rite ana te rahi engari he rerekē te ahunga, nō reira kua tangohia atu i te whārite.

F – w _A – w _B = (m _A + m _B ) 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/s ²

Whakamahia te ture nekehanga tuarua a Newton ki te poraka A:

∑ F = ma

N _A – w _A = m _A a

N _A – 1 = (0.1)(2.5)

NA – ₁ = 0.25

NA = 1 + _0.25

NA = 1.25 _{Ngā Niutoni}

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 (w _X ) = 4 Newton

Te kaha tō (F _x ) = 2 Newton

Te kaha kume (F _T ) = 9 Newton

E hiahiatia ana: Ka pā te kaha kupenga ki te mea

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 heke poutū ana ki raro, ko te wāhanga whakapae o te taumaha w _x me te wāhanga whakapae o te kaha F _x.

Te pānga o te kaha kupenga ki te mea

W _T – w _X – W _x = 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 tū ana i te tīmatanga i runga i tētahi mata whakapae maeneene. Ka pā te kaha 16 N ki te mea, ā, ka tere ake te mea i te 2 m/s ^2. Mena ko te mea kotahi e tū ana i runga i tētahi mata whakapae taratara, ā, ko te kaha waku e pā ana ki te mea he 2 N, tātaihia te tere o te mea mena ka pā te kaha 16 N ki te mea.

A. 1.75 m/s ²

B. 1.50 m/s ²

C. 1.00 m/s ²

D. 0.88 m/s ²

Mōhiotia:

Te kaha (F) = 16 Newton = 16 kg m/s ²

Whakaterenga (a) = 2 m/s ²

Te kaha waku (F _fric ) = 2 Newtons = 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

F – F _fric = ma

16 – 2 = 8 a

14 = 8

ā = 14 / 8

a = 1.75 m/s ²

Ko te whakaterenga o te mea he 1.75 m/ ^s².

Ko te whakautu tika ko A.

10. Ka panaia e Tāmu rāua ko Anaru tētahi mea ki runga i te papa maeneene. Ka panaia e Tāmu te mea me te kaha o te 5.70 N. Mena ko te papatipu o te mea he 2.00 kg, ā, ko te whakaterenga e pā ana ki te mea he 2.00 ms ^-2 , tātaihia te rahi me te ahunga o te kaha e pā ana ki a Tāmu.

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 mahia e Andrew (F ₁ ) = 5.70 Newton

Papatipu o te mea (m) = 2.00 kg

Whakaterenga (a) = 2.00 m/s ²

E hiahiatia ana: Te rahi me te ahunga o te kaha i pā ki a Tom (F ₂ )?

Rongoā:

Whakamahia te ture tuarua o te nekehanga a Newton:

∑ F = ma

F ₁ + F ₂ = mā

5.70 + F ₂ = (2)(2)

5.70 + F ₂ = 4

F ₂ = 4 – 5.70

F ₂ = – 1.7 Newton

I tohu te tohu tango ko (F ₂ ) kei te ritenga kē atu i te mahi a te kaha pana a Andrew (F ₁ ).

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?

otinga

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.

[irp]

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

E hiahiatia ana: 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/s ²

[irp]

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) Kāore ngā pukapuka i runga i te pepa e taka ana ina tōia teretia te pepa

(3) I te wā e tākaro ana i te papa reti, ka panaia te whenua e te waewae ki muri, ka paheke whakamua te papa reti.

(4) Ka 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

[wpdm_package id='470′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

Ngā raruraru kua whakatauhia i roto i ngā ture nekehanga a Newton – Te kaha noa 

1. He mea e takoto ana i runga i tētahi tēpu, e whakaaturia ana i te pikitia i raro nei. Ko te papatipu o te mea he 1 kg. Ko te whakaterenga o te kaha ā-papa he 9.8 m/s ^2. Tātaihia te kaha noa i pā ki te mea e te tēpu.

Mōhiotia:

Taumaha (m) = 1 kg

Te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

Taumaha (w) = mg = (1 kg)(9.8 m/s² ⁾ = 9.8 kg m/s² ⁼ 9.8 Newton

E hiahiatia ana: te kaha noa (N)

Rongoā:

Kei runga i te tēpu te mea e takoto ana, nō reira ko te kaha kupenga i runga i te mea he kore (te ture tuatahi, tuarua rānei a Newton). Ka mahi poutū te taumaha o te mea ki raro, ki waenganui o te Ao. Me whai kaha anō ki runga i te mea hei taurite i te kaha ā-papa . Kei runga i te tēpu te mea e takoto ana, kia puta ai tēnei kaha ki runga. Ko te kaha e puta ana i te tēpu ka kiia he kaha noa (N). Ko te tikanga o te noa he poutū.

Kōwhiria te ahunga whakarunga hei ahunga-y pai. Ko te kaha kupenga i runga i te mea ko:

∑ Fy = 0

N – w = 0

N = w

N = mg

N = 9.8 Niutona

Ko te kaha noa e pā ana ki te mea e whakamahia ana e te tēpu he 9.8 N ki runga.

[irp]

2. E rua ngā mea e takoto ana i runga i tētahi tēpu. Te taumaha o te mea 1 (m1 ₎ = 1 kg, te taumaha o te mea 2 (m2 _{) = 2 kg, te whakaterenga nā te kaha ā-papa (g) =} ^9.8 m/s2 . Tātaihia te rahi me te ahunga o te kaha noa e pā ana ki te m2 _ki te m1 _me te kaha noa e pā ana ki te tēpu ki te _m2.

otinga

Mōhiotia:

Taumaha o te mea 1 (m1 ₎ = 1 kg

Taumaha o te mea 2 (m2 ₎ = 2 kg

Te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

Taumaha o te mea 1 (w1 ₎ = m1 _karamu = (1)(9.8 m/s2 ⁾ = 9.8 kg m/s2 ⁼ 9.8 Newtons

Taumaha o te mea 2 (w ₂ ) = m ₂ karamu = (2)(9.8 m/s ² ) = 19.6 kg m/s ² = 19.6 Newtons

E hiahiatia ana: N ₁ me N ₂

Rongoā:

(a) Te kaha noa i tukuna e m ₂ ki te m ₁ (N ₁ )

N ₁ = w ₁ = 9.8 Newton

Kei runga te ahunga o N _{1 .}

(b) Te kaha noa i tukuna e te tēpu ki runga i te m ₂ (N ₂ )

N ₂ = w ₁ + w ₂ = 9.8 Ngā Newton + 19.6 Ngā Newton = 29.4 Ngā Newton

Kei runga te ahunga o N _{2 .}

[irp]

3. He mea e takoto ana i runga i te tēpu. Ko te taumaha o te mea he 2 kg, ko te whakaterenga nā te kaha ā-papa he 9.8 m/s² ^. Ko te rahi o te kaha F he 10 Newtons. Kimihia te rahi me te ahunga o te kaha noa e tukuna ana e te tēpu ki runga i te mea.

otinga

Mōhiotia:

Taumaha o te mea (m) = 2 kg

Te whakaterenga nā te kaha ā-papa (g) = 9.8 m/s ²

Taumaha (w) = mg = (2 kg)(9.8 m/s² ⁾ = 19.6 kg m/s² ⁼ 19.6 Newton

Te Kaha F (F) = 10 Newton

E hiahiatia ana : te rahi me te ahunga o te kaha noa (N)

Rongoā:

ko te ahunga o te kaha noa kei runga.

Te rahi o te kaha noa:

∑ F = 0

N – F – w = 0

N = F + w

N = 10 Ngā Newton + 20 Ngā Newton

N = 30 Niutona

[irp]

4. He mea e takoto ana i runga i te tēpu. Ko te papatipu o te mea he 1 kg, ko te whakaterenga nā te kaha ā-papa he 9,8 m/s² ^, ko te kaha F1 _he 10 N, ā, ko te kaha F2 _he 20 N. Tātaihia te rahi me te ahunga o te kaha noa e pā ana ki te tēpu ki te mea. g = 9.8 m/ ^s²

otinga

Mōhiotia:

Taumaha (m) = 1 kg

Te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

Taumaha (w) = mg = (1 kg)(9.8 m/s² ⁾ = 9.8 kg m/s² ⁼ 9.8 Newton

F ₁ = 10 Newton

F ₂ = 20 Newton

E hiahiatia ana: te rahi me te ahunga o te kaha noa (N)

Rongoā:

Ko te ahunga o te kaha noa kei runga.

Te rahi o te kaha noa:

∑ F = 0

N – F ₂ – w + F ₁ = 0

N = F2 ₊ w – _F1

N = 20 Ngā Niutoni + 9.8 Ngā Niutoni – 10 Ngā Niutoni

N = 19.8 Niutona

[irp]

5. Papatipu o te mea (m) = 2 kg, whakaterenga o te kaha ā-papa (g) = 9.8 m/s² ^, koki = 30 ^° . Kimihia te rahi me te ahunga o te kaha noa i pā ki te mea.

Rongoā:

Ko w te taumaha, ko wx _te wāhanga whakapae o te taumaha, ko _wy te wāhanga poutū o te taumaha, ko N te kaha noa.

Mōhiotia:

papatipu (m) = 2 kg

te whakaterenga o te kaha ā-papa (g) = 9.8 m/s ²

taumaha (w) = mg = (2 kg)(9.8 m/s² ⁾ = 19.6 kg m/s² ⁼ 19.6 Newton

w _x = w sin 60 ^o = (19.6 N)(0.5) √ 3 = 9.8 √ 3 Ngā Newton

w _y = w cos 60 = (19.6 N)(0.5) = 9.8 Newton

E hiahiatia ana: te kaha noa (N)

Rongoā:

∑ F = 0

N – w _y = 0

N = w _y

N = 9.8 Niutona

[irp]

[wpdm_package id='467′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

Ngā whakaoti rapanga i roto i ngā ture nekehanga a Newton – te papatipu me te taumaha

1. Ko te taumaha o te papatipu 1 kg i te mata o te Ao ko… karamu = 9.8 m/s ²

Mōhiotia:

Taumaha (m) = 1 kg

Ko te whakaterenga nā te kaha ā-papa i te mata o te Ao (g) = 9.8 m/s ²

E hiahiatia ana: taumaha (w)

Rongoā:

w = mg

m = papatipu (Ko te waeine SI mō te papatipu ko te kirokaramu, kg)

g = te whakaterenga nā te kaha ā-papa (Ko te waeine SI o g ko m/s ² )

w = taumaha (Ko te waeine SI o w ko kg m/s ² , ko Newton rānei)

Taumaha:

w = (1 kg)(9.8 m/s² ⁾ = 9.8 kg m/s² ⁼ 9.8 Newton

[irp]

2.

(a) Tuhia te kaha o te papa taumaha (taumaha) e pā ana ki te mea ina okioki te mea i runga i te tēpu, e whakaaturia ana i te pikitia (a).

(b) Tuhia te kaha o te taumaha (taumaha) me ōna wāhanga e pā ana ki tētahi mea e reti ana i raro i tētahi papa whakarara , e whakaaturia ana i te ahua (b)

otinga

Ko te ahunga o te taumaha e anga ana ki raro, ki waenganui o Papatūānuku.

w _x = te wāhanga whakapae o te taumaha, ā, w _y = te wāhanga poutū o te taumaha

[irp]

3. Ko te taumaha o tētahi pouaka he 1 kg, ā, ko te whakaterenga nā te kaha ā-papa he 9.8 m/s² ^. Kimihia (a) te taumaha (b) te wāhanga whakapae me te wāhanga poutū o te taumaha.

otinga

Taumaha: w = mg = (1 kg)(9.8 m/s² ⁾ = 9.8 kg m/s² ⁼ 9.8 Newton

Ko te wāhanga whakapae o te taumaha:

w _x = w sin 30 ^o = (9,8 N)(0,5) = 4.9 Ngā Newton

Ko te wāhanga poutū o te taumaha:

w _y = w cos 30 ^o = (9.8 N)(0.5√3) = 4.9√3 Ngā Newton

[irp]

[wpdm_package id='458′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite

Pānuitia atu

Ngā Raru Whakaoti i roto i te Nekehanga Raina – Te nekehanga ki runga, ki raro hoki i te hinganga kore utu

1. Ka whiua e te tangata tētahi pōro ki runga i te rangi me te tere tīmatanga o te 20 m/s. Tātaihia te teitei o tōna rere. Kaua e aro ki te ātete wai. Te whakaterenga nā te kaha ā-papa (g) = 10 m/ ^s2.

otinga

Ka whakamahia e mātou tētahi o ēnei whārite kinematic mō te nekehanga i te whakaterenga pumau , e whakaaturia ana i raro nei.

vt = v _o + _i

s = v _o t + ½ i te ²

v _t ² = v _o ² + 2 hei

Mōhiotia:

Ka whiriwhiria e tātou te ahunga whakarunga hei pai, ā, ko te ahunga whakararo hei kino.

Te tere tīmatanga (v _o ) = 20 m/s (pai ake ki runga)

Te whakaterenga o te kaha ā-papa (g) = – 10 m/s ² (kino ki raro).

Te tere whakamutunga (vt ₎ = 0 (he kore tōna tere mō tētahi wā poto i te pūwāhi teitei)

Teitei mōrahi (h)

Rongoā:

vt ₂ = v _o ^{2 + 2} gh

0 = (20 ² ) + 2(-10) hāora

0 = 400 – 20 hāora

400 = 20 hāora

h = 400 / 20 = 40 / 2 = 20 mita

[irp]

2. Ka whiua e te tangata tētahi kōhatu ki runga i te tere 20 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 100 mita i raro.

(a) Kia pēhea te roa o te taenga o te pōro ki te pūtake o te pari (b) Te tere whakamutunga i mua tata tonu i te pānga o te kōhatu ki te whenua. Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ^2. Kaua e aro ki te ātete wai.

Mōhiotia:

Ka whiriwhiria e tātou te ahunga whakarunga hei pai, ā, ko te ahunga whakararo hei kino.

Teitei (h) = -100 mita (kino nā te mea kei raro iho te tūranga whakamutunga i te tūranga tīmatanga)

Te tere tīmatanga (v _o ) = 20 m/s (pai ake ki runga)

Te whakaterenga o te kaha ā-papa (g) = -10 m/s ² (kino ki raro)

E hiahiatia ana:

(a) Te wā i te rangi, te wā rānei (t)

(b) Te tere whakamutunga ( _vt )

Rongoā:

(a) Te wā (t)

Mōhiotia:

Teitei (h) = -100 mita (kino nā te mea kei raro iho te tūranga whakamutunga i te tūranga tīmatanga)

Te tere tīmatanga (v _o ) = 20 m/s (pai ki runga), Te whakaterenga o te kaha ā-papa (g) = -10 m/s ² (kino ki raro).

h = v _o t + ½ gt ²

-100 = (20) t + ½ (-10) t ²

-100 = 20 t – 5 t ²

-5 t ² + 20 t + 100 = 0

Ka whakamahia e mātou te tātai tapawhā:

(b) Te tere whakamutunga

vt ₂ = v _o ^{2 + 2} gh

v _t ² = (20 ² ) + 2 (-10)(-100)

v _t ² = 400 + 2000

v _t ² = 2400

v _t = 49 m/s

[irp]

[wpdm_package id='515′]

[wpdm_package id='517′]

1. Te tawhiti me te nekehanga
2. Te tere toharite me te tere toharite
3. Tere pumau
4. Whakatere tonu
5. Nekehanga hinga noa
6. Te nekehanga ki raro i te hinganga kore utu
7. Te nekehanga ki runga, ki raro hoki i te hinganga kore utu

Pānuitia atu

Ngā Raru Whakaoti i roto i te Nekehanga Raina – Te nekehanga ki raro i te hinganga kore utu

1. Ka whiua poutūtia tētahi pōro ki raro me te tere tīmatanga 10 m/s, ā, ka tae ki te whenua i roto i te 2 hēkona. Kimihia te tere whakamutunga i mua tata tonu i te pānga o te pōro ki te whenua. Te whakaterenga o te kaha ā-papa (g) = 10 m/s2 ^. Kaua e aro ki te ātete wai.

Mōhiotia:

Te tere tīmatanga (v _o ) = 10 m/s

Te wā i hipa (t) = 2 hēkona

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

E hiahiatia ana: Te tere whakamutunga ( _vt )

Rongoā:

Ko te whakaterenga 10 m/s ² te tikanga he pikinga tere mā te 10 m/s ia hekona. I muri i te 3 hēkona, ko te tere = 30 m/s.

Te tere whakamutunga = 10 m/s + 20 m/s = 30 m/s.

Ngā whārite kinematic mō te nekehanga i te whakaterenga pumau , e whakaaturia ana i raro nei:

vt = v _{o + i ………} . 1

h = v _o t + ½ i te ² ………. 2

v _t ² = v _o ² + 2 ah ……. 3

vt = v _{o +} g t

vt = 10 + ₍ 10)(2)

v _t = 10 + 20 = 30 m/s

Te tere whakamutunga = v _t = 30 m/s

[irp]

2. Ka whiua poutūtia iho tētahi kōhatu mai i tētahi piriti me te tere tīmatanga o te 5 m/s, ā, ka tae ki te wai i roto i te 2 hēkona. Tātaihia te teitei o te piriti.

Mōhiotia:

Te tere tīmatanga (v _o ) = 5 m/s

Te wā i hipa (t) = 2 hēkona

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

E hiahiatia ana: te teitei o te piriti (h)

Rongoā:

h = v _o t + ½ gt ²

h = (5)(2) + ½ (10)(2) ²

h = 10 + (5)(4)

h = 10 + 20

h = 30 mita

[irp]

3. Ka whiua poutūtia tētahi pōro ki raro me te tere tīmatanga 10 m/s mai i te teitei o te 80 mita. Kimihia (a) Te wā i te rangi (b) Te tere whakamutunga i mua tata tonu i te pānga o te pōro ki te whenua.

Mōhiotia:

teitei (h) = 80 mita

Te tere tīmatanga (v _o ) = 10 m/s

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

E hiahiatia ana:

(a) Te wā (t)

(b) Te tere whakamutunga ( _vt )

Rongoā:

(a) Te wā (t)

Te tere whakamutunga:

vt ₂ = v _o ^{2 + 2} gh

v _t ² = (10) ² + 2(10)(80) = 100 + 1600 = 1700

v _t = 41 m/s

Wā wā (t):

vt = v _{o +} g t

41 = 10 + (10)(t)

41 – 10 = 10 t

31 = 10 tāra

t = 31 / 10 = 3,1 hēkona

(b) Te tere whakamutunga ( _{vt )}?

vt ₌ 41 m/s

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[wpdm_package id='513′]

[wpdm_package id='517′]

1. Te tawhiti me te nekehanga
2. Te tere toharite me te tere toharite
3. Tere pumau
4. Whakatere tonu
5. Nekehanga hinga noa
6. Te nekehanga ki raro i te hinganga kore utu
7. Te nekehanga ki runga, ki raro hoki i te hinganga kore utu

Pānuitia atu