Ngā Raru Whakaoti i roto i te Ahupūngao Taketake

9 Te huri i ngā tauine pāmahana (tauine Celsius Tauine Fahrenheit Tauine Kelvin)

1. 50 ^° C = ….. ^° F ?

otinga

I te pēhanga hauhautanga paerewa , ko te pūwāhi tio o te wai he 0 ^° C i te tauine Celsius me te 32 ^° F i te tauine Fahrenheit. I te pēhanga hauhautanga paerewa, ko te pūwāhi kohua o te wai he 100 ^° C i te tauine Celsius me te 212 ^° F i te tauine Fahrenheit.

0 ^o C = 32 ^o F me 1 00 ^o C = 212 ^o F. Ko te panonitanga o te 5 C ^o = te panonitanga o te 9 F ^o.

Mō te tauine Celsius, ka wehea te tawhiti i waenga i te 0 ^° C me te 100 ^° C kia 100 ngā āputa ōrite. Mō te tauine Fahrenheit, ka wehea te tawhiti i waenga i te 0 ^° C me te 100 ^° C kia 180 ngā āputa ōrite.

Ki ^te F = (180/100) Ki ^te C + 32

Ki ^te F = (9/5) Ki ^te C + 32

Ki ^te F = (9/5) 50 + 32

Ki ^te F = (9) 10 + 32

Ki ^te F = 90 + 32

Ki ^te F = 122

50 ^° C = 122 ^° F

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2. 86 ^o F = ….. ^o C ?

otinga

Ki ^te C = (100/180)(Ki ^te F – 32)

Ki ^te C = (5/9)(Ki ^te F – 32)

Ki ^a C = (5/9)(86 – 32)

Ki ^a C = (5/9)(54)

Ki ^a C = (5)(6)

Ki ^te C = 30

86 ^° F = 30 ^° C

3. 50 ^° C = ….. K ?

otinga

T = Ki ^C + 273

T = 50 + 273

T = 323

50 ^° C = 323 K

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4. 212 ^o F = ….. K ?

otinga

Ki ^te C = (100/180)(Ki ^te F – 32)

Ki ^te C = (5/9)(Ki ^te F – 32)

Ki ^a C = (5/9)(212 – 32)

Ki ^a C = (5/9)(180)

Ki ^a C = (5)(20)

Ki ^te C = 100

212 ^o F = 100 ^o C + 273

212 ^o F = 373 K

 

5. x ^o C = x ^o F

x = ….. ?

otinga

1: Te huri i te tauine Celsius ki te tauine Fahrenheit

2: Te huri i te tauine Fahrenheit ki te tauine Celsius

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6. 122°F = ….. Celsius

otinga

Ka taea te tuhi i te huringa i waenga i ngā tauine pāmahana e rua:

T _C = 5/9 (T _F – 32)

T _C = Te pāmahana i roto i te Celsius, T _F = te pāmahana i roto i te Fahrenheit

Te pāmahana i roto i te Celsius:

T _C = 5/9 (122 – 32) = T _C = 5/9 (90) = 5 (10)

T _C = 50 ^o C

7. E whakaatu ana te pikitia i raro nei i te ine pāmahana o tētahi wai mā te whakamahi i te inemahana tauine Fahrenheit! Mena ka inehia te pāmahana o te wai mā te whakamahi i te inemahana tauine Celsius, he aha te pāmahana o te wai?

Mōhiotia:

Tauine Fahrenheit (T _F ) = 95 ^o F

E hiahiatia ana: Tauine Celsius

Rongoā:

I te pēhanga o te 1 atm, ko te pūwāhi tio o te wai he 0 °C, ko te tauine Fahrenheit he 32 ^° F. I tetahi atu taha, ko te pūwāhi kohua o te wai mō te tauine Celsius he 100 ^° C, ko te tauine Fahrenheit he 212 ^° F.

I te tauine Celsius, i waenga i te 0 °C me te 100 °C he 100 °, i te tauine Fahrenheit ia i waenga i te 32 °F ki te 212 °F he 180 °.

T _C = 100/180 (T _F – 32)

T _C = 5/9 (T _F – 32)

T _C = 5/9 ( 95 – 32)

T _C = 5/9 ( 63 )

T _C = 315/9

T _C = 35 ^o C

8. E ai ki te pikitia i raro nei, tātaihia te pāmahana P i runga i te inemahana Celsius.

otinga

T_C = 100/180 (T_F - 32)

T _C = 5/9 (T _F – 32)

T _C = 5/9 (104 – 32)

T _C = 5/9 (72)

T _C = 360/9

T _C = 40 ^o C

9. Mēnā ko te pāmahana o te tauine Celsius e whakaaturia ana i te pikitia i raro nei, tātaihia te pāmahana o te tauine Fahrenheit e whakaaturia ana i te pikitia i raro nei.

Rongoā:

T^oF = (180/100) T^oC + 32

Ki ^te F = (9/5) Ki ^te C + 32

Ki ^te F = (9/5) 60 + 32

Ki ^te F = (9) 12 + 32

Ki ^te F = 108 + 32

Ki ^te F = 140

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

1. Kei te whakaatuhia te kauwhata o te kaha (F) me te roa (x ) i te pikitia i raro nei. Kimihia te pūmau puna!

otinga

Te tauira ture a Hooke :

k = F / x

F = te kaha (Newton)

k = pūmau puna (Newton/mita)

x = te huringa o te roa (mita)

Pūmau puna:

k = 10 / 0.02 = 20 / 0.04

k = 500 N/m

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2. Tāutuhia te pūmau puna.

otinga

Pūmau puna:

k = F / x

k = 5 / 0.01 = 10 / 0.02 = 15 / 0.03 = 20 / 0.04

k = 500 N/m

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3. Ko te roa taketake o te puna A he 60 cm, ā, ko te roa taketake o te puna B he 90 cm. Ko te pumau o te puna A he 100 N/m, ko te pumau o te puna B he 200 N/m. Ko te ōwehenga o te huringa o te roa o te puna A ki te huringa o te roa o te puna B ko…

Mōhiotia:

Pūmau o te puna A (k _A ) = 100 N/m

Pūmau o te puna B (kB ₎ = 200 N/m

Te kaha i runga i te puna A (F _A ) = F

Te kaha i runga i te puna B (F _B ) = F

E hiahiatia ana: Δl _A : Δl _B

Rongoā:

Te tauira ture a Hooke:

Δl = F / k

Δl = te huringa o te roa, F = te kaha, k = te pumau

Te huringa o te roa o te puna A:

Δl _A = F _A / k _A = F / 100

Te huringa o te roa o te puna B:

Δl _B = F _B / k _B = F / 200

Ko te ōwehenga o te huringa o te roa o te puna A ki te huringa o te roa o te puna B:

Δl _A : Δl _B

F/100 : F/200

1 / 100 : 1 / 200

1 / 1 : 1 / 2

2: 1

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4. Ka tōia he aho nairona, he 20 cm te roa taketake, e te kaha o te 10 N. Ko te huringa o te roa o te aho he 2 cm. Tātaihia te rahi o te kaha mēnā he 6 cm te huringa o te roa.

Mōhiotia:

Te kaha (F) = 10 N

Ko te panonitanga o te roa ( Δl ) = 2 cm = 0.02 m

E hiahiatia ana: te rahi o te kaha (F) mēnā ko Δl = 0.06 m.

Rongoā:

Pūmau:

k = F / Δl

k = 10 / 0.02 = 500 N/m

Te rahi o te kaha (F) mēnā ko Δl = 0.06 m:

F = kx

F = (500)(0.06)

F = 30N

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1. Te ture a Hooke
2. Te ahotea, te taumahatanga, te modulus a Young

Pānuitia atu

Te Taumahatanga o te Taumahatanga o Young – Ngā Raru me ngā Otinga

1. Ko te whānui o te aho nairona he 2 mm, e tōia ana e te kaha o te 100 N. Tātaihia te aho taumaha!

Mōhiotia:

Te kaha (F) = 100 N

Diameter (d) = 2 mm = 0.002 m

Pūtoro (r) = 1 mm = 0.001 m

E hiahiatia ana: Te ahotea

Rongoā:

Wāhanga:

A = π r ²

A = (3.14)(0.001 m) ² = 0.00000314 m ²

^A = 3.14 x 10 ^-6 m²

Te ahotea:

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2. Ko te roa taketake o tētahi taura he 100 cm, ā, ka kumea e tētahi kaha. Ko te huringa o te roa o te taura he 2 mm. Tātaihia te taumahatanga!

Mōhiotia:

Te roa taketake (l ₀ ) = 100 cm = 1 m

Ko te panonitanga o te roa (Δl) = 2 mm = 0.002 m

E hiahiatia ana: Te momo

Rongoā:

Te tereina s:

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3. He aho 4 mm te whānui, ā, ko te roa taketake he 2 m. Ka tōia te aho e te kaha o te 200 N. Mena ko te roa whakamutunga o te puna he 2.02 m, whakatauhia: (a) te ahotea (b) te taumahatanga (c) te modulus a Young

Mōhiotia:

Diameter (d) = 4 mm = 0.004 m

Pūtoro (r) = 2 mm = 0.002 m

Horahanga (A) = π r ² = (3.14)(0.002 m) ²

^{Horahanga (} A) = 0.00001256 m² ⁼ 12.56 x 10 ^-6 m²

Te kaha (F) = 200 N

Te roa taketake o te puna (l ₀ ) = 2 m

Ko te panonitanga o te roa (Δl) = 2.02 – 2 = 0.02 m

E hiahiatia ana: (a) Te ahotea (b) Te taumahatanga c) Te modulus a Young

Rongoā:

(a) Te ahotea

(b) Te Taumahatanga

(c) Te tauwehenga o Young

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4. Ko te whānui o te aho he 1 cm, ā, ko te roa taketake he 2 m. Ka tōia te aho e te kaha o te 200 N. Tātaihia te huringa o te roa o te aho! Ko te modulus a Young o te aho = 5 x 10 ⁹ N/m ²

Mōhiotia:

Te tauwehenga o Young (E) = 5 x 109 ^N / ^m2

Te roa taketake (l ₀ ) = 2 m

Te kaha (F) = 200 N

Diameter (d) = 1 cm = 0.01 m

Pūtoro (r) = 0.5 henimita = 0.005 m = 5 x 10 ^-3 m

Horahanga ( A) = π r² ⁼ (3.14)(5 x 10 ^-3 m) ² = (3.14)(25 x 10 ^-6 m² ⁾

^{Horahanga (} A) = 78.5 x 10 -6 ^m² = 7.85 x 10 ^{-5 m²}

E hiahiatia ana : Te huringa o te roa (Δl)

Rongoā:

Te tātai modulus a Young:

Te huringa o te roa :

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5. E 5 mita te teitei o te raima, ā, ko te whānui o te waeine he 3 m ³ e tautoko ana i te taumaha o te 30,000 kg. Whakatauhia (a) Te ahotea (b) Te taumahatanga (c) Te huringa o te teitei! Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ^2. Ko te modulus a Young o te raima = 20 x 10 ⁹ N/m ²

Mōhiotia:

Te modulus a Young o te raima = 20 x 109 ^N / ^m2

Teitei tīmatanga (l ₀ ) = 5 mita

Te horahanga o te waeine (A) = 3 ^m²

Taumaha (w) = mg = (30,000)(10) = 300,000 N

E hiahiatia ana: (a) Te ahotea (b) Te taumahatanga (c) Te panonitanga o te teitei!

Rongoā:

(a) Te ahotea

(b) Te Taumahatanga

(c) Te panonitanga o te teitei

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1. Te ture a Hooke
2. Te ahotea, te taumahatanga, te modulus a Young

Pānuitia atu

1. He pōro e piri ana ki te pito o te taura whakapae, e hurihia ana i roto i tētahi porowhita he 20 cm te whānui o te pūtoro. E 360° te porowhita ⁱ ia hekona. Tātaihia te rahi o te whakaterenga pūwaenga!

Mōhiotia:

Tere koki (ω ) = 360 ^o /hekona = 1 hurihanga/hekona = 6.28 rātiana/hekona

Pūtoro (r) = 20 henemita = 0.2 m

E hiahiatia ana: Te whakaterenga ā-pokapū (a _r )

Rongoā:

a _r = v ² / r —> v = r ω

a _r = (r ω) ² / r = r ² ω ² / r

a _r = r ω ²

a _s = whakaterenga ā-pokapū, v = tere rārangi, r = pūtoro, ω = tere koki

Te rahi o te whakaterenga pokapū :

a _r = r ω ² a _r = (0,2 m)( 6.28 rad/s)

a _r = 1.256 m/s ²

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2. E hurihuri ana tētahi wira, he 30 cm te whānui o tōna radius, i te tere o te 180 rpm. Tātaihia te whakaterenga ā-pokapū o tētahi pūwāhi i te taha o te wira!

Mōhiotia:

Pūtoro (r) = 30 henimita = 0.3 m

Tere koki ( ω ) = 180 hurihanga / 60 hēkona = 3 hurihanga / hēkona = (3)(6.28 rātiana) / hēkona = 18.84 rātiana/hēkona

E hiahiatia ana: te whakaterenga ā-pokapū ( a _r ) o r = 0.3 m

Rongoā:

Te rahi o te whakaterenga pokapū:

a _r = r ω ²

a _r = (0.3 m)(18.84 rad/s)

a _r = 5.65 m/s ²

3. E neke ana tētahi waka reihi i runga i tētahi ara porowhita he 50 mita te whānui. Mena he 72 km/h te tere o te waka, tautuhia te kaha o te whakaterenga ā-pokapū!

Mōhiotia:

Pūtoro (r) = 50 mita

Tere (v) = 72 km/h = (72)(1000 mita) / 3600 hēkona = 20 mita/hēkona

E hiahiatia ana : te rahi o te whakaterenga porotītaha (a _r )

Rongoā:

a _r = ^v2 / r = 202 ^/ 50 = 400 / 50 = 8 m/ ^s2

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4. Ko te tere whakaterenga pūrua mōrahi o tētahi motuka he 10 m/s² ^, nō reira ka taea e te motuka te huri me te kore e paheke i waho o te ara piko. Mena kei te neke te motuka i te tere pumau 108 km/h, he aha te radius o te piko kore-piko?

Mōhiotia:

Te whakaterenga ā-pokapū (a _r ) = 10 m/s ²

Te tere o te motuka (v) = 108 km/ h = (108)(1000) / 3600 = 30 mita s /h i runga i te d

E hiahiatia ana: te pūtoro (r)

Rongoā:

r = v ² / a _r

r = 30 ² / 10 = 900 / 10 = 90 mita s

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1. Te huri i ngā waeine koki hei tauira mō ngā raruraru me ngā otinga
2. Ngā tauira raruraru me ngā otinga mō te nekehanga koki me te nekehanga rārangi
3. Ngā tauira rapanga tere koki me te tere raina me ngā otinga
4. Ngā tauira rapanga whakaterenga koki me te whakaterenga raina me ngā otinga
5. Ngā tauira rapanga nekehanga porowhita ōrite me ngā otinga
6. Ngā raruraru tauira whakaterenga pūrua me ngā otinga
7. Ngā tauira o ngā nekehanga porowhita kore-taurite me ngā otinga

Pānuitia atu

1. Ka huri te wira, he 30 cm te whānui, i te pūmau 5 rad/s ^2. He aha te rahi o te whakaterenga rārangi o tētahi pūwāhi kei (a) 10 cm mai i te pokapū (b) 20 cm mai i te pokapū (c) i te taha o te wira?

Mōhiotia:

Pūtoro (r) = 30 henimita = 0.3 m

Whakaterenga koki ( α ) = 5 rad/s ²

E hiahiatia ana: whakaterenga rārangi (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m

Rongoā:

Te whanaungatanga i waenga i te whakaterenga rārangi (a) me te whakaterenga koki:

a = rα

(a) whakaterenga rārangi, r = 0.1 m

a = (0.1 m)(5 rad/s ² ) = 0.5 m/s ²

(b) whakaterenga rārangi, r = 0.2 m

a = (0.2 m)(5 rad/s ² ) = 1 m/s ²

(c) whakaterenga rārangi, r = 0.3 m

a = (0.3 m)(5 rad/s ² ) = 1.5 m/s ²

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2. He pūreirei he 50 cm te whānui. Mena ko te whakaterenga rārangi o tētahi pūwāhi kei te taha o te pūreire he 2 m/s² ^, tātaihia te whakaterenga koki o te pūreire!

Mōhiotia:

Pūtoro (r) = 50 henimita = 0,5 m

whakaterenga rārangi (a) = 2 m/s ²

E hiahiatia ana: te whakaterenga koki

Rongoā:

α = a / r = 2 / 0.5 = 4 rad/s ²

3. Ko ngā mata o te mīhini whakaranu he 20 cm te whānui, i te tīmatanga ka okioki. I muri i te 2 hēkona, ka huri ngā mata i te 10 rad/s. Tātaihia te rahi o te whakaterenga rārangi (a) he pūwāhi kei te 10 cm mai i te pokapū (b) he pūwāhi kei te taha o ngā mata.

Mōhiotia:

Pūtoro (r) = 20 henimita = 0.2 m

Ko te tere _{koki tīmatanga (} ωo ) = 0

_Ko te tere koki whakamutunga ( ωt ₎ = 10 ngā rātiana/hekona

Wā wā (t) = 2 hēkona

E hiahiatia ana: te whakaterenga rārangi o tētahi pūwāhi kei (a) r = 0.1 m (b) r = 0.2 m

Rongoā:

ωt = ωo + αt_​​

10 = 0 + α (2)

10 = 2 ā

α = 10 / 2

 α = 5 rad/s

(a) te whakaterenga rārangi o r = 0.1 m

a = r α = (0.1 m)(5 rad/s ² ) = 0.5 m/s ²

(b) te whakaterenga rārangi o r = 0.2 m

a = r α = (0.2 m)(5 rad/s ² ) = 1 m/s ²

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4. Ka whakaterea te wira, he 20 cm te radius, mō te 2 hēkona mai i te 20 rad/s ki te okioki. Tātaihia te rahi o te whakaterenga rārangi (a) he pūwāhi kei te 10 cm mai i te pokapū (b) he pūwāhi kei te 10 cm mai i te pokapū.

Mōhiotia:

Pūtoro (r) = 20 henimita = 0.2 m

Ko te tere koki tīmatanga ( ω _o ) = 20 rad/s

Ko te tere _{koki whakamutunga (} ωt ) = 0

Wā wā (t) = 2 hēkona

E hiahiatia ana: Ko te whakaterenga rārangi (a) r = 0.1 m (b) r = 0.2 m

Rongoā:

ωt = ωo + αt_​​

0 = 20 + α (2)

-20 = 2 ā

α = -20 / 2

 α = -10 rad/s

Ko te tohu kino e tohu ana kei te heke te tere koki.

(a) te whakaterenga rārangi o r = 0.1 m

a = r α = (0.1 m)(-10 rad/s ² ) = -1 m/s ²

(b) te whakaterenga rārangi o r = 0.2 m

a = r α = (0.2 m)(-10 rad/s ² ) = -2 m/s ²

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1. Te huri i ngā waeine koki hei tauira mō ngā raruraru me ngā otinga
2. Ngā tauira raruraru me ngā otinga mō te nekehanga koki me te nekehanga rārangi
3. Ngā tauira rapanga tere koki me te tere raina me ngā otinga
4. Ngā tauira rapanga whakaterenga koki me te whakaterenga raina me ngā otinga
5. Ngā tauira rapanga nekehanga porowhita ōrite me ngā otinga
6. Ngā raruraru tauira whakaterenga pūrua me ngā otinga
7. Ngā tauira o ngā nekehanga porowhita kore-taurite me ngā otinga

Pānuitia atu

1. Kei te porowhita ōrite te porowhita i te pito o te aho i roto i tētahi porowhita whakapae he 2 mita te whānui o te pūtoro i te tere koki pumau 10 rād/s. Tātaihia te rahi o te tere rārangi o tētahi pūwāhi kei:

(a) 0.5 mita mai i te pokapū

(b) 1 mita mai i te pokapū

(c) 2 mita mai i te pokapū

Mōhiotia:

Pūtoro (r) = 0.5 mita s, 1 mita, 3 mita

Ko te tere koki = 10 rātiana s /se āhua

E hiahiatia ana: Te tere raina

Rongoā:

v = rω

v = te tere rārangi , r = te pūtoro , ω = te tere koki

(a) Te tere rārangi (v) o tētahi pūwāhi kei r = 0.5 mita

v = r ω = (0.5 mita s )(10 rad/s) = 5 mita s /s āhua

(b) Te tere rārangi (v) o tētahi pūwāhi kei r = 1 mita

v = r ω = (1 mita)(10 rad/s) = 10 mita s /s āhua

(c) Te tere rārangi (v) o tētahi pūwāhi kei r = 2 mita s

v = r ω = (2 mita s )(10 rad/s) = 20 mita s /s āhua

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2. Ka huri ngā mata o te mīhini whakaranu i te tere o te 5000 rpm. Tātaihia te rahi o te tere raina:

(a) he pūwāhi kei te 5 cm mai i te pokapū

(b) he pūwāhi kei te 10 cm mai i te pokapū

Mōhiotia:

Pūtoro (r) = 5 henimita me te 10 henimita

Te tere koki (ω) = 5000 hurihanga / 60 hēkonaoro = 83.3 hurihanga / seāhuatanga = (83.3)(6.28 ngā rātiana) / seāhuatanga = 523.3 rātianas / seāhuatanga

E hiahiatia ana: Te rahi o te tere raina

Rongoā:

(a) Te rahi o te tere rārangi o tētahi pūwāhi kei te 0.05 m mai i te pokapū

v = r ω = (0.05 m)( 523.3 rad/s) = 26 m/s

(b) Te rahi o te tere rārangi o tētahi pūwāhi kei te 0,1 m mai i te pokapū

v = r ω = (0.1 m)( 523.3 rad/s) = 52 m/s

3. He pūwāhi kei te taha o te wira, 30 cm te radius, e karapoti ana i tētahi porowhita i te tere pūmau 10 mita/hekona.

He aha te rahi o te tere koki?

Mōhiotia:

Pūtoro ( r) = 30 henimita = 0.3 mita s

Ko te tere rārangi (v) = 10 mita s /s āhua

E hiahiatia ana: te tere koki

Rongoā:

ω = v / r = 10 / 0.3 = 33 ngā rātiana s /se āhua

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4. E 10 mita te tere o tētahi motuka he 50 henimita te whānui o ōna potae i roto i te 1 hēkona. He aha te tere koki?

Mōhiotia:

Pūtoro (r) = 0.25 mita

Ko te tere rārangi o tētahi pūwāhi i te taha o ngā potae (v) = 10 mita s /s āhua

E hiahiatia ana: Te tere koki

Rongoā:

ω = v / r = 10 / 0.25 = 40 ngā rātiana s /se āhua

5. Ko te tere koki o te wira 20 cm i roto i ngā rātiana he 120 rpm. He aha te tawhiti mēnā ka haere te motuka i roto i te 10 hēkona?

Mōhiotia:

Pūtoro (r) = 20 henimita = 0.2 mita s

Te tere koki = 120 whakahou / 60 hēkonangā āhuatanga = 2 whakahou / seāhuatanga = (2)(6.28) rātianas / seāhuatanga = 12.56 rātianas / seāhuatanga

E hiahiatia ana: tawhiti

Rongoā:

Te tere o te taha o te wira:

v = r ω = (0.2 mita s )(12.56 rātiana s /se āhua ) = 2.5 mita s /se āhua

2.5 mitas / seKo te tikanga o te cond he pūwāhi kei te taha o te haere o te wira. 2.5 mitas ia hēkona kotahi. I muri 10ngā āhuatanga, ka haere te pūwāhi 25 mitas.

Nō reira, ko te tawhiti he 25 mita s.

[irp]

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[wpdm_package id='439′]

1. Te huri i ngā waeine koki hei tauira mō ngā raruraru me ngā otinga
2. Ngā tauira raruraru me ngā otinga mō te nekehanga koki me te nekehanga rārangi
3. Ngā tauira rapanga tere koki me te tere raina me ngā otinga
4. Ngā tauira rapanga whakaterenga koki me te whakaterenga raina me ngā otinga
5. Ngā tauira rapanga nekehanga porowhita ōrite me ngā otinga
6. Ngā raruraru tauira whakaterenga pūrua me ngā otinga
7. Ngā tauira o ngā nekehanga porowhita kore-taurite me ngā otinga

Pānuitia atu

Te huri i ngā wae koki (tohu, rādian, hurihanga)

1. ¼ hurihanga = ….. ^o ( nekehanga ) ?

otinga

1 hurihanga = 360 ^°

½ hurihanga = 180 ^°

¼ hurihanga = 90 ^°

2. ½ hurihanga = …….. r pānuitanga?

otinga

1 rev = 2 π rad = 2(3.14) rad = 6.28 rad

½ hurihanga = pi rad = 3.14 rad

3. 180 ^° = ….. hurihanga ?

otinga

360 ^o = 1 hurihanga

180 ^o = ½ hurihanga

[irp]

4. 90 ^o = ….. rāti ?

otinga

360 ^o = 2 π rad = 2(3.14) rad = 6.28 rad

180 ^o = π rāti = 3.14 rāti

90 ^o = ½ π rad = ½ (3.14) = 1.57

5. 60 rāti = ….. hurihanga?

otinga

6.28 rad = 1 hurihanga

60 rad/6.28 = 9.55 hurihanga

6. 40 rāti= ….. ^o?

otinga

6.28 rad = 360 ^o

40 rad/6.28 = (6.37)(360 ^o ) = 2292.99 ^o

[irp]

Te nekehanga koki me te nekehanga rārangi

1. E 10 ngā rātiana e hurihurihia ana e te wira pahikara, he 60 henemita te whānui. He aha te nekehanga rārangi o tētahi pūwāhi i te taha o te wira?

Mōhiotia:

Pūtoro (r) = 30 henimita = 0.3 m

Koki (θ ) = 10 ngā rātiana

E hiahiatia ana: te nekehanga rārangi (l)

Rongoā:

l = rθ

l = (0.3 m)(10 rāti)

l = 3 mita

2. Ka huri te wira he 50 cm te radius i te 360 ^° . He aha te nekehanga rārangi o tētahi pūwāhi i te taha o te wira?

Mōhiotia:

Pūtoro (r) = 50 henimita = 0.5 mita

Koki ( θ ) = 360 ^o = 6.28 rātiana

E hiahiatia ana: te nekehanga rārangi (l)

Rongoā:

l = rθ

l = (0.5 m)(6.28 rāti)

l = 3.14 mita

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3. E 50 cm te whānui o te porowhita e hurihuri ana i ngā hurihanga e rua. He aha te nekehanga rārangi o tētahi pūwāhi i te taha o te wira?

Mōhiotia:

Pūtoro (r) = 50 henimita = 0,5 m

Koki ( θ ) = 2 hurihanga = (2)(6.28 rātiana) = 12.56 rātiana

E hiahiatia ana: te nekehanga rārangi (l)?

Rongoā:

l = rθ

l = (0.5 m)(12.56 rāti)

l = 6.28 mita

4. Kei te taha o te wira he 2 mita te radius, e neke ana i te 100 mita. Tātaihia te nekehanga koki.

Mōhiotia:

Pūtoro (r) = ½ (diameter) = ½ (2 mita) = 1 mita

nekehanga rārangi (l) = 100 mita

Rongoā:

(a) Te nekehanga koki (i roto i ngā rātiana)

θ = s / r = 100 / 1 = 100 ngā rātiana

(b) Te nekehanga koki (i roto i ngā nekehanga)

1 rātiana = 360 ^o

100 ngā rātiana = 100(360 ^o ) = 36,000 ngā rātiana

(c) Te nekehanga koki (i te hurihanga)

6.28 ngā rātiana = 1 hurihanga

36,000 / 6.28 = 5732,484 hurihanga

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5. Ka porowhitahia e tētahi matūriki tētahi porowhita mō te 10 mita, ka huri mō te 180 ^° . He aha te pūtoro?

Mōhiotia:

Nekehanga rārangi (l) = 10 mita

Koki ( θ ) = 180 ^o = 3.14 rātiana

E hiahiatia ana: te pūtoro (r)

Rongoā:

r = l / θ = 10 / 3.14 = 3.18 mita

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1. Te huri i ngā waeine koki hei tauira mō ngā raruraru me ngā otinga
2. Ngā tauira raruraru me ngā otinga mō te nekehanga koki me te nekehanga rārangi
3. Ngā tauira rapanga tere koki me te tere raina me ngā otinga
4. Ngā tauira rapanga whakaterenga koki me te whakaterenga raina me ngā otinga
5. Ngā tauira rapanga nekehanga porowhita ōrite me ngā otinga
6. Ngā raruraru tauira whakaterenga pūrua me ngā otinga
7. Ngā tauira o ngā nekehanga porowhita kore-taurite me ngā otinga

Pānuitia atu

1. Ka tere ōrite te wira, 1 mita te radius, i te 2 rad/s² ^. Tātaihia te whakaterenga koki me te tere koki o te wira, i muri i te 2 hēkona.

Mōhiotia:

Pūtoro (r) = 1 mita

Whakaterenga koki (α ) = 2 rad/s ²

E hiahiatia ana: te whakaterenga koki me te tere koki i muri i te 2 hēkona.

Rongoā:

(a) Te whakaterenga koki i roto i te 2 hēkona

He pumau te whakaterenga koki, nō reira i muri i te 2 hēkona, ko te whakaterenga koki o te wira he 2 rad/ ^s².

(b) Te tere koki i roto i te 2 hēkona

Ko te whakaterenga koki 2 rad/s ² te tikanga ka piki ake te tere koki mā te 2 rātiana/hekona i ia 1 hēkona. I muri i te 1 hēkona, ko te tere koki = 2 rātiana/hekona. I muri i te 2 hēkona, ko te tere koki = 4 rātiana/hekona.

[irp]

2. Ka tere tere te matūriki mai i te okioki ki te 60 rpm i roto i te 10 hēkona. Tātaihia te rahi o te whakaterenga koki!

Mōhiotia:

Ko te tere koki tīmatanga (ω _o ) = 0

Ko te tere koki whakamutunga ( ωt ₎ = 60 rpm = 60 hurihanga / 60 hēkona = 1 hurihanga / hēkona = 6,28 rātiana/hēkona

Wā wā (t) = 10 hēkona

E hiahiatia ana: Te whakaterenga koki ( α )

Rongoā:

ω _o = te tere koki tīmatanga, ω _t = te tere koki whakamutunga, α = te whakaterenga koki, t = te wā, θ = te koki.

ωt = ωo ₊ αt_​

6.28 = 0 + α (10)

6.28 = 10 ā

α = 6.28 / 10

α = 0.628 rad/s ²

Ko te rahi o te whakaterenga koki = 0.628 rad/s ²

3. Ka pōturi te tere o tētahi mea mai i te 20 rad/s ki te 10 rad/s i roto i te 4 hēkona. Tātaihia te rahi o te whakaterenga koki!

Mōhiotia:

Wā wā (t) = 4 hēkona

Ko te tere koki tīmatanga ( ω _o ) = 20 rad/s

_{Ko te} tere koki whakamutunga ( ωt ) = 10 rad/s

E hiahiatia ana : te rahi o te whakaterenga koki (α )

Rongoā:

ωt = ωo ₊ αt_​

10 = 20 + α (4)

10 – 20 = 4 ā

-10 = 4 ā

α = -10 / 4

α = – 2.5 rad/s ²

Ko te rahi o te whakaterenga koki he -2.5 rad/s² ^. Ko te tohu kino he tohu kei te whakaheke tere te mea. Whakaterenga = ka piki ake te tere koki, whakahekenga = ka heke te tere koki.

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4. Ka whakaterea tētahi mea mō te 2 hēkona mai i te 10 rad/s ki te 2 rad/s2 ^. Tātaihia te koki i porowhitahia e te mea!

Mōhiotia:

te tere koki tīmatanga ( ω _o ) = 10 rad/s

te whakaterenga koki (α ) = 2 rad/s ²

wā wā (t) = 2 hēkona

E hiahiatia ana: koki (θ)

Rongoā:

θ = ω _o + ½ α t ²

θ = (10)(2) + ½ (2)(2 ² )

θ = 20 + (1)(4) = 20 + 4

θ = 24 ngā rātiana

5. Ka pōturi te wira o tētahi motuka mai i te 20 rad/s ki te okioki i muri i te 20 rad i te takahuri. Tātaihia te rahi o te whakaterenga koki o te wira!

Mōhiotia:

te tere koki tīmatanga ( ω _o ) = 20 rad/s

te tere _{koki whakamutunga (} ωt ) = 0

Koki ( θ ) = 20 ngā rātiana

E hiahiatia ana: te rahi o te whakaterenga koki (α )

Rongoā:

ωt ₂ = ωo ² ₊ ² αθ

0 = 20 ² + 2 α (20)

0 = 400 + 40 ā

400 = – 40 ā

α = – 400 / 40

α = – 10 rad/s ²

6. He tokotoko PQ, he 60 cm te roa, e hurihuri ana i te pūwāhi Q hei tuaka hurihuri, ā, ko PQ hei pūtoro o te porowhita. I tere ake te tokotoko PQ mai i te okiokinga ki te 0.3 rad/s² ^. He aha te tere rārangi o te pūwāhi P i te t = 10 hēkona, mēnā ko te tūranga tīmatanga koki he 0.

Mōhiotia:

Te roa o te tokotoko PQ = te pūtoro o te porowhita (r) = 60 cm = 60/100 m = 0.60 m

Ko te tere koki tīmatanga (ω _o ) = 0 rad/s

Whakaterenga koki (α) = 0.3 rad s ^-2

Ko te tūranga koki tīmatanga (θ _o ) = 0

E hiahiatia ana: Tere rārangi (v) o te pūwāhi P i te t = 10 hēkona

Rongoā:

Ko te tere koki whakamutunga i muri i te 10 hēkona:

ω _t = ω _o + α t = 0 rad/s + (0.3 rad s ^-2 )(10 s) = 3 rad/s

Ko te tere raina whakamutunga i muri i te 10 hēkona:

v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s

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7. Ka huri tetahi mea me te tere tīmatanga o te 4 rad/s, ā, ko te whakaterenga koki he 0.5 rad/s² ^. He aha te tere o te mea i muri i te 4 hēkona.

Mōhiotia:

Ko te tere koki tīmatanga (ω _o ) = 4 rad/s

Whakaterenga koki (α) = 0.5 rad/s ²

Wā wā (t) = 4 hēkona

E hiahiatia ana: Te tere o te mea i muri i te 4 hēkona ( _ωt )

Rongoā:

ωt ₌ ωo ₊ αt

ωt = 4 + ₍ 0.5)(4)

ωt = 4 + ₂

ωt ₌ 6 rad/s

8. E toru ngā ngira o tētahi karaka pakitara, he 10 cm te whānui, ia ngira hei whakaatu i ngā hāora, ngā meneti me ngā hēkona. Te whakatairite i te maha o ngā huringa o te ngira hāora: te ngira meneti: te ngira tuarua.

A. 1 : 3 : 180

B. 1 : 12 : 720

C. 4 : 12 : 180

D. 4 : 12 : 720

Mōhiotia:

1 hāora = 60 meneti

12 hāora = (12)(60 meneti) = 720 meneti

Te tere koki o te ngira hāora = 1 hurihanga / 12 hāora = 1 hurihanga / 720 meneti

Te tere koki o te ngira meneti = 1 hurihanga / 1 hāora = 1 hurihanga / 60 meneti

Te tere koki o te ngira tuarua = 1 hurihanga / 1 meneti

E hiahiatia ana: Te whakataurite i te maha o ngā rauna o te ngira hāora: te ngira meneti: te ngira tuarua

Rongoā:

Te whārite o te nekehanga porowhita:

Tere koki = te maha o ngā hurihanga / te wā

Te maha o ngā hurihanga = te tere koki x te wā

I roto i taua wā anō, hei tauira, 1 meneti, e hia ngā hurihanga o te ngira hāora, te ngira meneti, me te ngira tuarua.

Te maha o ngā hurihanga o te ngira hāora = te tere koki x te wā = (1 hurihanga / 720 meneti)(1 meneti) = 1/720 hurihanga

Te maha o ngā hurihanga o te ngira meneti = te tere koki x te wā = (1 hurihanga / 60 meneti)(1 meneti) = 1/60 hurihanga

Te maha o ngā hurihanga o te ngira tuarua = te tere koki x te wā = (1 hurihanga / 1 meneti)(1 meneti) = 1/1 hurihanga

Te whakataurite i te maha o ngā hurihanga:

Te maha o ngā hurihanga o te ngira hāora: te maha o ngā hurihanga o te ngira meneti: te maha o ngā hurihanga o te ngira tuarua.

1/720 : 1/60 : 1/1

1/720 : 12/720 : 720/720

1:12:720

Ko te whakautu tika ko B.

9. He pōro e herea ana ki te taura. Ka hurihia te pōro kia neke i roto i te papa porowhita e whakarara ana ki te mata o te whenua. I tēnei nekehanga, ka tere ake te pōro nā te mea…..

A. Te waku hau

B. Taumaha o te pōro

C. Te kaha kume

D. Te kaha o te kaha ā-papa

Rongoā:

E ai ki te ture tuarua o te nekehanga a Newton, ka tere ake te tere o tētahi mea mēnā he kaha e puta mai ana. Ka honoa te pōro ki te taura, ā, ina huri te taura, ka huri anō hoki te pōro. Ina huri te pōro (ka neke te pōro i roto i te porowhita), ka pāngia te pōro e te tere porowhita. He tere porowhita porowhita ngā mea neke katoa. Ko te tere porowhita te take o te tere porowhita . Ko te kaha porowhita mō tēnei take ko te kaha kume.

Ko te whakautu tika ko C.

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[wpdm_package id='439′]

1. Te huri i ngā waeine koki hei tauira mō ngā raruraru me ngā otinga
2. Ngā tauira raruraru me ngā otinga mō te nekehanga koki me te nekehanga rārangi
3. Ngā tauira rapanga tere koki me te tere raina me ngā otinga
4. Ngā tauira rapanga whakaterenga koki me te whakaterenga raina me ngā otinga
5. Ngā tauira rapanga nekehanga porowhita ōrite me ngā otinga
6. Ngā raruraru tauira whakaterenga pūrua me ngā otinga
7. Ngā tauira o ngā nekehanga porowhita kore-taurite me ngā otinga

Pānuitia atu

1. E neke ana tētahi mea i roto i tētahi porowhita me te tere koki pumau o te 10 rad/s. Whakatauhia (a) Te tere koki i muri i te 10 hēkona (b) Te nekehanga koki i muri i te 10 hēkona.

Mōhiotia:

Tere koki (ω) = 10 rad/s

E hiahiatia ana:

(a) Tere koki (ω) i muri i te 10 hēkona.

(b) Koki (θ) i muri i te 10 hēkona

Rongoā:

(a) Tere koki (ω) i muri i te 10 hēkona

He mea porowhita te nekehanga kia ōrite , kia pumau te tere koki, 10 rad/s.

(b) Te nekehanga koki (θ)

Ko te tere koki pumau 10 rātiana/hēkona te tikanga he tata ki te 10 rātiana ia hekona te mea. I muri i te 10 hēkona, ko te mea tata ki te 10 x 10 rātiana = 100 rātiana.

[irp]

2. Ka neke porowhita tētahi matūriki me te tere pumau o te 10 m/s. Ko te whānui o te porowhita = 1 mita. Whakatauhia (a) Te tere o te matūriki i muri i te 5 hēkona (b) Te nekehanga o te matūriki i muri i te 5 hēkona (c) Te whakaterenga ā-pokapū.

Mōhiotia:

Te whānui o te porowhita (r) = 1 mita

Te tere o te matūriki (v) = 10 m/s

Rongoā:

(a) Te tere o te matūriki i muri i te 5 hēkona

He rite te nekehanga porowhita ōrite o te mea, ā, he pumau tonu te tere, 10 m/s.

(b) Te nekehanga o te matūriki i muri i te 5 hēkona

Ko te tikanga o te 10 mita/hēkona i ia 1 hēkona, ko te nekehanga o te matūriki = 10 mita. I muri i te 5 hēkona, ko te nekehanga o te matūriki = 5 x 10 mita = 50 mita.

(c) Te whakaterenga ā-pokapū (a _r )

a _r = ^v2 / r = 102 ^/ 1 = 100 / 1 = 100 m/ ^s2

3. He pōro e piri ana ki tētahi pito o te taura, e hurihia ana i roto i tētahi porowhita me te radius o te 2 mita i te tere pumau o te 60 rpm. Whakatauhia (a) te rahi o te tere koki i muri i te 2 hēkona (b) te nekehanga koki i muri i te 1 meneti.

Mōhiotia:

Te whānui o te porowhita (r) = 2 mita

Tere koki (ω) = 60 rpm = 60 hurihanga / 1 meneti

= 60 hurihanga / 60 hēkona = 1 hurihanga / hēkona = 2π rātiana / hēkona

= 2(3.14) ngā rātiana / hēkona= 6.28 ngā rātiana / hēkona

Rongoā:

(a) Tere koki (ω) i muri i te 2 hēkona

He pumau te tere koki, nō reira i muri i te 2 hēkona, ko te tere koki (ω) = 6.28 rātiana/hēkona

(b) Te nekehanga koki (θ)

Ko te tere koki = 1 hurihanga/hēkona, ko tōna tikanga i ia 1 hēkona, ka pāngia te pōro e te 1 hurihanga. I muri i te 60 hēkona, ka neke te pōro i te 60 hurihanga.

Ko te tere koki = 6.28 rātiana/hēkona, ko tōna tikanga i ia 1 hēkona, ka neke te pōro me te koki o te 6.28 rātiana. I muri i te 60 hēkona, ka neke te pōro i te 376.8 rātiana.

[irp]

4. E 120 ngā hurihanga ka hurihia e te wira pahikara i roto i te 60 hēkona. He aha te tere koki?

Rongoā:

(a) ngā hurihanga ia meneti (rpm)

120 hurihanga / 60 hēkona = 120 hurihanga / 1 meneti = 120 hurihanga / meneti = 120 rpm

(b) ngā nekehanga ia hekona ( ^o /s)

1 hurihanga = 360 ^° , 120 hurihanga = 43200 ^°

120 hurihanga / 60 hēkona = (120)(360 ^o ) / 60 hēkona = 43200 ^o / 60 hēkona = 720 ^o /hekona

(c) ngā rātiana ia hekona (rāti/h)

1 hurihanga = 6.28 rātiana

120 hurihanga / 60 hēkona = (120)(6.28) rātiana / 60 hēkona = 753.6 rātiana / 60 hēkona = 12.56 rātiana/hēkona.

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[wpdm_package id='439′]

1. Te huri i ngā waeine koki hei tauira mō ngā raruraru me ngā otinga
2. Ngā tauira raruraru me ngā otinga mō te nekehanga koki me te nekehanga rārangi
3. Ngā tauira rapanga tere koki me te tere raina me ngā otinga
4. Ngā tauira rapanga whakaterenga koki me te whakaterenga raina me ngā otinga
5. Ngā tauira rapanga nekehanga porowhita ōrite me ngā otinga
6. Ngā raruraru tauira whakaterenga pūrua me ngā otinga
7. Ngā tauira o ngā nekehanga porowhita kore-taurite me ngā otinga

Pānuitia atu

1. He pōro 0.1 -kg te taumaha, e piri ana ki te pito o tētahi taura whakapae, e hurihia ana i roto i tētahi porowhita he 50 cm te whānui o te pūtoro, ā , ko te tere koki o te pōro he 4 pūtoro s ^-1 . He aha te rahi o te kaha pokapū?

Mōhiotia:

Taumaha (m) = 100 karamu = 100/1000 kg = 1/10 kg = 0.1 kg

Tere koki ( ω) = 4 rātiana/ wāhanga

Pūtoro (r) = 50 henimita = 50/100 m = 0.5 m

E hiahiatia ana: Te kaha pokapū

Rongoā:

Ko te kaha pūrua te kaha kupenga e hua ai te whakaterenga pūrua :

∑ F = ma _r

∑ F = mv ² /r = m ω ² r

∑ F = te kaha kupenga = te kaha pokapū , m = te papatipu , v = te tere , ω = te tere koki , r = te pūtoro

∑ F = m ω ² r = (0.1)(4) ² (0.5) = (0.1)(16)(0,5) = 0.8 Ngā Newton

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2. Kei te hurihuri ōrite te pōro i roto i tētahi porowhita whakapae. Mēnā ka huri te tere ki te whā ngā wā o te uara tīmatanga, he aha te kaha o te kaha pokapū…..

Mōhiotia:

Papatipu = m

Tere = v

Tere tīmatanga = v _o

Pūtoro (r) = r

E hiahiatia ana: Te rahi o te kaha pokapū

Rongoā:

3. Kua hangaia he kōpiko whakarara o te pūtoro R kia taea ai e te motuka e tere ana i te tere 12 ms ^–1 te whakawhiti haumaru i te kokonga. Ko te tauwehenga o te waku pateko i waenga i te motuka me te rori = 0.4. He aha te pūtoro R. Te whakaterenga nā te kaha ā-papa ( g ) = 10 ms ^–2.

Mōhiotia:

Tere (v) = 12 m/s

Tauwehenga o te waku pateko ( μs ₎ = 0.4

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

E hiahiatia ana: Pūtoro (R)

Rongoā:

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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

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