ahupūngao

Ngā Raru Whakaoti i roto i te Nekehanga Raina – Ngā mea e hinga noa ana

1. He mea i taka iho i te tihi o te pari. Ka kitea e pā ana ki te whenua i raro i muri i te 3 hēkona. Tātaihia tōna tere i mua tata tonu i te pā ki te whenua. Ko te tere o te kaha ā-papa he 10 m/s ^2. Kaua e aro ki te ātete wai.

Mōhiotia:

Te tere tīmatanga (v _o ) = 0 (i taka te mea)

Wā wā (t) = 3 hēkona

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

E hiahiatia ana: Te tere whakamutunga ( _vt )

Rongoā:

Ko te whakaterenga nā te kaha ā-papa i te mata o te whenua, ko tōna rahi he 9.8 m/s² ^. Hei whakangāwari i ngā tataunga, ka whakamahia e mātou te 10 m/ ^s².

10 m/s ² , 10 m/s / 1 hēkona rānei, ko te tikanga ka piki haere te tere i roto i te wā mā te 10 m/s i ia hēkona.

I muri i te 1 hēkona, ko te tere o te mea = 10 m/s

I muri i te 2 hēkona, ko te tere o te mea = 20 m/s

I muri i te 3 hēkona, ko te tere o te mea = 30 m/s.

Ka taea hoki e tātou te whakamahi i ngā 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

Kāore he tere tīmatanga o te hinganga kore utu (v _o = 0), nō reira ka taea te whakarerekē i te whārite i runga ake nei e whakaaturia ana i raro nei:

Whārite o te nekehanga taka noa :

vt ₌ gt ………… 1

h = ½ gt ² ………… 2

v _t ² = 2 gh ………….. 3

vt ₌ gt

vt = ₍ 10)(3)

v _t = 30 m/s

Ko te tere whakamutunga he 30 m/s

[irp]

2. Ka taka noa te tinana mai i te okiokinga, mai i te teitei o te 25 m. Kimihia (a) Te tere o tana pā ki te whenua. (b) Te wā e pau ana ki te tae ki te whenua.

Ko te whakaterenga nā te kaha ā-papa i te mata o Papatūānuku he 10 m/ ^s².

Mōhiotia:

Teitei (h) = 5 mita

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

E hiahiatia ana:

(a) Te tere whakamutunga ( _vt )

(b) Te wā (t)

Rongoā:

Te whārite o te hinganga kore utu:

vt ₌ gt

h = ½ gt ²

v _t ² = 2 gh

(a) Te tere whakamutunga ( _vt )

v _t ² = 2 gh = 2(10)(5) = 100

v _t = 10 m/s

(b) Te wā (t)

h = ½ gt ²

5 = ½ (10) t ²

5 = 5 t ²

t ² = 5/5 = 1

t = 1 hēkona

[irp]

3. He pōro i taka mai i te teitei. Kimihia (a) Te Whakaterenga (b) Te Tawhiti i muri i te 3 hēkona (c) Te wā i te rangi mēnā ko te tere whakamutunga he 20 m/s. Te Whakaterenga nā te kaha ā-papatipu = 10 m/s ²

Mōhiotia :

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

E hiahiatia ana:

(a) Te Whakaterenga (a)

(b) Te tawhiti , te teitei rānei (h) mēnā ko te wā i pahemo (t) = 3 hēkona

(c) Te wā (t) mēnā ko te v _t = 20 m/s

Rongoā:

Te whārite o te hinganga kore utu:

vt ₌ gt

h = ½ gt ²

v _t ² = 2 gh

(a) Te Whakaterenga (a)

Whakaterenga = whakaterenga nā te kaha ā-papatipu = 10 m/s2 ^. Ko tōna tikanga he pikinga tere mā te 10 m/s ia hekona.

(b) Te tawhiti, te teitei rānei (h) i muri i te t = 3 hēkona

h = ½ gt ² = ½ (10)(3) ² = (5)(9) = 45 mita

(c) Te wā i hipa (t) mēnā ko te v _t = 20 m/s

vt ₌ gt

20 = (10) t

t = 20 / 10 = 2 hēkona

[irp]

[wpdm_package id='511′]

[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 Whakatau i roto i te Nekehanga Raina – Te Whakaterenga Pūmau

1. Ka tere ake te tere o tētahi waka mai i te tū ki te 20 m/s i roto i te 10 hēkona. Tātaihia te tere o te waka!

otinga

Mōhiotia:

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

Wā wā (t) = 10 hēkona

Te tere whakamutunga (vt ₎ = 20 m/s

E hiahiatia ana : Te whakaterenga (a)

Rongoā:

vt = v _o + _i

20 = 0 + (a)(10)

20 = 10

ā = 20 / 10

a = 2 m/s ²

[irp]

2. Kei te whakaheke tere te motuka mai i te 30 m/s ki te okioki i roto i te 10 hēkona. Tātaihia te whakaterenga o te motuka.

otinga

Mōhiotia:

Te tere tīmatanga (v _o ) = 30 m/s

Te tere whakamutunga (vt ₎ = 0

Wā wā (t) = 10 hēkona

E hiahiatia ana: whakaterenga (a)

Rongoā:

vt = v _o + _i

0 = 30 + (a)(10)

– 30 = 10 a

ā = – 30 / 10

a = -3 m/s ²

Ka puta te tohu kino nā te mea he iti iho te tere whakamutunga i te tere tīmatanga.

[irp]

3. Ka tīmata te motuka, ā, ka tere ake i te 4 m/s ² pūmau i roto i te 1 hēkona. Tātaihia te tere me te tawhiti i muri i te 10 hēkona.

otinga

(a) Tere

Ko te whakaterenga 4 m/s2 ^te tikanga ka piki ake te tere mā te 4 m/s ia 1 hēkona. I muri i te 2 hēkona, ko te tere o te motuka he 8 m/s. I muri i te 10 hēkona, ko te tere o te motuka he 40 m/s.

(b) Tawhiti

Mōhiotia:

Te tere tīmatanga (v _o ) = 0

Te tere whakamutunga (vt ₎ = 40 m/s

Whakaterenga (a) = 4 m/s ²

E hiahiatia ana: Tawhiti

Rongoā:

s = v _o t + ½ i te ² = 0 + ½ (4)(10 ² ) = (2)(100) = 200 mita

[irp]

4. Ka tere te motuka i te tere pumau 10 m/s, kātahi ka whakaheke i te tere pumau 2 m/s2 ^tae noa ki te okiokinga. Tātaihia te wā i pau me te tawhiti o te motuka i mua i te okiokinga.

Mōhiotia:

Te tere tīmatanga (v _o ) = 10 m/s

Tere (a) = -2 m/s ² (Ka puta te tohu kino nā te mea he iti iho te tere whakamutunga i te tere tīmatanga)

Te tere whakamutunga (vt ₎ = 0 (okiokinga)

E hiahiatia ana: Te wā me te tawhiti

Rongoā:

(a) Te wā (t)

vt = v _o + _i

0 = 10 + (-2)(t)

0 = 10 – 2 t

10 = 2 tāra

t = 10 / 2 = 5 hēkona

(b) Tawhiti

v _t ² = v _o ² + 2 hei

0 = 10 ² + 2(-2) s

0 = 100 – 4 hēkona

100 = 4 hēkona

s = 100 / 4 = 25 mita

[irp]

5. E 40 m/s te tere o te haere o tētahi motuka, ka whakaheke tere i te 4 m/s ² pūmau tae noa ki te okioki. Tātaihia te tere me te tawhiti i muri i te whakaheke tere i roto i te 10 hēkona!

otinga

Mōhiotia:

Te tere tīmatanga (v _o ) = 40 m/s

Whakaterenga (a) = -4 m/s ²

Wā wā (t) = 10 hēkona

E hiahiatia ana: te tere whakamutunga (vt ₎ me te tawhiti (s)

Rongoā:

(a) Te tere whakamutunga

v _t = v _o + at = 40 + (-4)(10) = 40 – 40 = 0 m/s

Ko te tikanga o te 0 m/s he okiokinga mō te motuka.

(b) Tawhiti

s = v _o t + ½ i te ² = (40)(10) + ½ (-4)(10 ² ) = 400 + (-2)(100) = 400 – 200 = 200 mita

[irp]

6. Tātaitia te tawhiti i muri i te 10 hēkona!

otinga

Tawhiti: s = vt = (10-0)(5-0) = (10)(5) = 50 mita

7. Tātaitia te tawhiti i muri i te 4 hēkona!

otinga

Tawhiti = horahanga tapawhā + horahanga tapatoru

Tawhiti = (8-0)(8-0) + ½ (16-8)(8-0) = (8)(8) + ½ (8)(8) = 64 + 32 = 96 mita

8. Whakatauhia te tawhiti o te motuka i muri i te 4 hēkona!

otinga

Tawhiti = horahanga tapatoru = ½ (4-0)(8-0) = ½ (4)(8) = 16 mita

9. E neke ana tētahi motuka i te tere 90 km/h i mua i tētahi motuka pirihimana e tū ana i te taha o te rori. Kotahi meneti i muri mai, ka whaia e te motuka pirihimana te tere 0.8 m/s² ^. Kia pēhea te tawhiti e tae atu ai te motuka pirihimana ki te motuka?

Mōhiotia:

Ko te tere o te motuka (v) = 90 km/h = 90,000 mita / 3600 hēkona = 25 mita/h

Wā wā (t) = 1 meneti = 60 hēkona

Te tere o te motuka a ngā pirihimana (a) = 0.8 m/s ²

Te tere tīmatanga o te motuka a ngā pirihimana (v _o ) = 0 m/s

E hiahiatia ana: Te tawhiti i haerea e te motuka a ngā pirihimana

Rongoā:

Ka neke te motuka i te tere pumau. Te tawhiti i haerea e te motuka:

Te tawhiti tīmatanga:

s = vt = (25)(60) = 1500 mita

Te tawhiti whakamutunga:

s = vt = (25)(t)

Tapeke tawhiti = 1500 + 25 t

Ka tere tonu te neke o te motuka a ngā pirihimana. Te tawhiti i haerea e te motuka a ngā pirihimana:

s = v _o t + ½ i te ² = (0)(t) + ½ (0.8)(t ² ) = 0 + 0.4 t ² = 0.4 t ²

Ina tae te motuka a ngā pirihimana ki te motuka, ka rite te tawhiti i haerea e te motuka a ngā pirihimana ki te tawhiti i haerea e te motuka.

Te tawhiti i haerea e te motuka = ​​te tawhiti i haerea e te motuka pirihimana

1500 + 25 t = 0.4 t ²

0.4 tāra ² – 25 tāra – 1500 = 0

Whakamahia te tātai tapawhā:

Te tawhiti i haerea e te motuka a ngā pirihimana:

s = 0.4 t ² = (0.4)(100 ² ) = (0.4)(10,000) = 4000 mita s = 4 kiromita

10. Ka neke te motuka i te tere pumau 24 m/s kia mau tonu te whakahekenga o te tere ki te 0.952 m/s2 ^. Tātaihia te tere o te motuka i muri i te tawhiti o te 250 mita.

Mōhiotia:

Te tere tīmatanga (v _o ) = 24 m/s

Whakaterenga (a) = – 0.952 m/s ² ( kua hainatia te tohu kino nā te mea kua whakaroahia )

Tawhiti ( d ) = 250 mita s

E hiahiatia ana: Te tere o te motuka i muri i te 250 mita s

Rongoā:

Mōhiotia: te tere tīmatanga (v_o), whakatere (a), tawhiti (d), e hiahiatia ana: te tere whakamutunga (v_t) nō reira whakamahia te whārite o v_t² = v_o² +2 ki d

v _t = te tere whakamutunga , v _o = te tere tīmatanga , a = te whakaterenga , d = te tawhiti

v _t ² = (24) ² + (2)(-0.952)(250)

v _t ² = 576 – 476

v _t ² = 100

vt = _√100

v _t = 10 m/s

[irp]

[wpdm_package id='507′]

[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 Whakatau i roto i te Nekehanga Raina – Te Tere Pūmau

1. Ka tere te haere o tētahi motuka i te 10 m/s te tere pumau. Tātaihia te tawhiti i muri i te 10 hēkona me te 60 hēkona.

otinga

Ko te tere pumau 10 mita/hekona te tikanga ka haere te motuka i te 10 mita i ia 1 hekona.

I muri i te 2 hēkona, ka haere te motuka i te 20 mita,

I muri i te 5 hēkona, ka haere te motuka i te 50 mita,

I muri i te 10 hēkona, ka haere te motuka mō te 100 mita ,

I muri i te 60 hēkona, ka haere te motuka i te 600 mita.

[irp]

2. E haere ana tētahi motuka i te huarahi tika i te tere pumau 72 km/h. Tātaihia te tawhiti o te motuka i muri i te 2 meneti me te 5 meneti.

otinga

72 kiromita/h = (72)(1000 mita) / 3600 hēkona = 72,000 / 3600 hēkona = 20 mita/hēkona.

Ko te tere pumau i te 20 mita/hekona te tikanga ka haere te motuka i te 20 mita i ia 1 hekona.

I muri i te 120 hēkona, 2 meneti rānei, ka haere te motuka i te 20 mita x 120 = 2400 mita ,

I muri i te 300 hēkona, i te 5 meneti rānei, ka haere te motuka i te 20 mita x 300 = 6000 mita.

[irp]

3. Ka haere te tinana i te huarahi tika mō te 100 mita i roto i te 50 hēkona. Tātaihia te tere o te tinana.

otinga

100 mita / 50 hēkona = 10 mita / 5 hēkona = 2 mita/hekona.

4. Whakatauhia te tere e ai ki te hoahoa i raro nei….

otinga

Tere = Tawhiti / wā i pau

Tere = 2 mita / 1 hēkona = 4 mita / 2 hēkona = 6 mita / 3 hēkona = 8 mita / 4 hēkona = 2 mita/hekona.

5. Ka whakatata ngā motuka A me B tetahi ki tetahi i runga i ngā ara whakarara. Ina 100 mita te tawhiti i waenganui i ngā motuka e rua, ka neke te motuka A i te tere pumau o te 10 m/s, ka neke te motuka B i te tere pumau o te 40 m/s. Tātaihia (a) te tawhiti o te motuka A i mua i te taha o te motuka B (b) te wā i mua i te taha o te motuka B i te motuka A.

otinga

Ka neke te motuka A me te tere pumau i te 10 mita/hekona, ko te tikanga ka neke te motuka A tae atu ki te 10 mita i ia 1 hēkona. I muri i te 2 hēkona, ka neke te motuka A tae atu ki te 20 mita.

Ka neke a Waka B me te tere pumau i te 40 mita/hekona, ko te tikanga ka neke a Waka B tae atu ki te 40 mita i ia 1 hēkona. I muri i te 2 hēkona, ka neke a Waka B tae atu ki te 80 mita.

20 mita + 80 mita = 100 mita.

(a) Ko te tawhiti o te motuka A i mua i te taha o te motuka B he 20 mita. Ko te tawhiti o te motuka B i mua i te taha o te motuka A he 80 mita.

(b) Ko te wā i waenganui i te motuka B me te motuka A he 2 hēkona. Ko te wā i waenganui i te motuka A me te motuka B he 2 hēkona

5. Mena e whakaatu ana te ine tere o tētahi motuka i te 108 km/h, tātaihia te tawhiti i haerea e te motuka i roto i te meneti kotahi.

Rongoā:

He taputapu te ine tere. Ko te tere o te motuka he 108 km/h.
108 kiromita/h = (108) (1000 mita) / 3600 hēkona = 30 mita/hēkona.

1 meneti = 60 hēkona

Ko te tere o te motuka he 30 mita ia hēkona, ko te tikanga ka neke te motuka ki te 30 mita i roto i te 1 hēkona.

I muri i te 1 hēkona, ka neke te motuka ki te tawhiti o te 1 x 30 mita = 30 mita.

I muri i te 2 hēkona, ka neke te motuka ki te tawhiti e 2 x 30 mita = 60 mita.

I muri i te 60 hēkona, ka neke te motuka ki te tawhiti e 60 x 30 mita = 1800 mita.

6. Ka whiua tika atu e Tom tētahi pōro ki a Andrew . E 10.08 mita te tawhiti o Tom rāua ko Andrew . Ka whiua whakapaetia te pōro , ā, ka neke i te 20 m/ s (kaua e aro ki te kaha ā-papa). Ka whiua e Andrew te pōro 4.00 x 10 ^-3 hēkona i muri i te whiunga o te pōro. Mēnā ka neke te kaiwhiu i te tere pumau o te 5.00 m/s, ka whiua te pōro e te kaiwhiu i muri i te nekenga o te kaiwhiu ki te…

Mōhiotia:

Ko te tawhiti i waenganui i a Tom rāua ko Andrew = 10.08 mita

Te tere o te pōro (v) = 20 m/s

Ko te wā (t) = 4 x 10 ^-3 hēkona = 0.004 hēkona

Te tere o te kaipatu (v) = 5 m / s

Hiahia: Ka pā te pōro e te kaiwhiu i muri i te nekenga o te pōro ki...

Rongoā:

Te tawhiti o te pōro:

s1 = vt = (20 ₎ (0.004) = 0.08 mita

Te tawhiti o te kaiwhiu:

s2 = vt ₌ 5 t

Te tawhiti o te pōro + te tawhiti o te kaiwhiu = te tawhiti i waenganui i a Tom rāua ko Andrew.

0.08 + 5 t = 10.08

5 t = 10.08 – 0.08

5 t = 10

t = 10/5

t = 2 hēkona

Te tawhiti o te kaiwhiu:

s2 = vt = 5 t = (5) (2) = 10 _mita

7. Kei te whaia e te kaiwhai tētahi tia me tana motuka. E 72 km/h te tere o te neke o te motuka, ā, e 64.8 km/h te tere o te oma o te tia. I te 2012 mita te tawhiti i waenganui i te motuka me te tia, ka pupuhi te kaiwhai i tana pū. E 200 m/h te tere o ngā matā i puta mai i te pū. Whakatauhia te wā i pupuhihia ai te tia.

A. 0.5 hēkona

B. 1 hēkona

C. 1.25 hēkona

D. 1.5 hēkona

Mōhiotia:

Tere o te motuka (v _b ) = 72 km/h = (72)(1000 m) / 3600 s = 20 m/s

Te tere o te tia (v _r ) = 64.8 km/h = (64.8)(1000 m) / 3600 s = 64800 m / 3600 s = 18 m/h

Ina pupuhihia te matā, ko te tawhiti i waenganui i te motuka me te tia (ngā) = 202 mita

Tere o te pupuhi (v _p ) = 20 m/s + 200 m/s = 220 m/s

Ko ngā patu e puritia ana e ngā kaiwhai i roto i tētahi motuka e tere ana me te tere o te 20 m/s, kia tāpirihia ai hoki te tere o te motuka ki te tere o te matā.

E hiahiatia ana: Whakatauhia te wā e pupuhihia ana te tia

Rongoā:

Whakaarohia ngā motuka me ngā tia e neke ana i te tere pumau.

Whārite: v = s / t, s = vt rānei

v = tere, s = tawhiti, t = wā

Tawhiti = 202 + X _r = 202 + v _r t = 202 + 18 t

Tawhiti = Y _p = v _p t = 220 t

Te tawhiti i haerea e te tia = te tawhiti i haerea e te matā

202 + 18 tāra = 220 tāra

202 = 220 tāra – 18 tāra

202 = 202 tāra

t = 202/202

t = 1 hēkona

Ko te whakautu tika ko B.

[irp]

[wpdm_package id='507′]

[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 Whakatau i roto i te Nekehanga Raina – Te tere toharite me te tere toharite

1. Ka haere tētahi motuka i te huarahi tika ki te rawhiti mō te 100 mita i roto i te 4 hēkona, kātahi ka haere ki te hauauru mō te 50 mita i roto i te 1 hēkona. Tātaihia te tere toharite me te tere toharite.

otinga

Tawhiti = 100 mita + 50 mita = 150 mita

Nekehanga = 100 mita – 50 mita = 50 mita, ki te rawhiti.

Te wā i hipa = 4 hēkona + 1 hēkona = 5 hēkona.

Tere toharite = Tawhiti / wā i pahemo = 150 mita / 5 hēkona = 30 mita/hekona.

Tere toharite = Nekehanga / wā i hipa = 50 mita / 5 hēkona = 10 mita/hekona.

[irp]

2. E 4 mita te hikoi a te tangata ki te rawhiti i roto i te 1 hēkona, kātahi ka hikoi 3 mita ki te raki i roto i te 1 hēkona. Tātaihia te tere toharite me te tere toharite.

otinga

Tawhiti = 4 mita + 3 mita = 7 mita

Te nekehanga = = mita, ki te raki mā rāwhiti.

Te wā i pahemo = 1 hēkona + 1 hēkona = 2 hēkona.

Tere toharite = tawhiti / wā i pau = 7 mita / 2 hēkona = 3.5 mita/hēkona

Te tere toharite = te nekehanga / te wā i pahemo = 5 mita / 2 hēkona = 2.5 mita/hēkona

[irp]

3. Ka haereere te kai-oma i tētahi ara tapawhā rite, ko te roa = 50 mita, ko te whānui = 20 mita. I muri i tana haereere i te ara tapawhā rite e rua ngā wā, ka hoki te kai-oma ki te tīmatanga. Mena ko te wā i pau = 100 hēkona, tātaihia te tere toharite me te tere toharite.

otinga

Te porowhita o te tapawhā hāngai = 2(50 mita) + 2(20 mita) = 100 mita + 40 mita = 140 mita.

Ka haereere i te tapawhā rite e 2 ngā wā = 2(140 mita) = 280 mita.

Tawhiti = 280 mita.

Nekehanga = 0 mita . ( hoki te kai-oma ki te pūwāhi tīmatanga)

Tere toharite = tawhiti / wā i pau = 280 mita / 100 hēkona = 2.8 mita/hekona.

Te tere toharite = te nekehanga / te wā i pahemo = 0 / 100 hēkona = 0.

[irp]

[wpdm_package id='505′]

[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 raruraru kua whakatauhia i roto i ngā whārite – te whakatau i te hua o ngā whārite e rua mā te whakamahi i ngā wāhanga o te whārite

1. F ₁ = 6 N, F ₂ = 10 N. Tātaihia te hua o te whārite.

otinga

F _1x = F ₁ cos 60 ^o = (6)(0.5) = 3 N ( he pai nā te mea he rite te ahunga ki te tuaka x )

F _2x = F ₂ cos 30 ^o = (10)(0.5 √ 3) = 5 √ 3 = (5)(1.372) = -8.66 N (kino nā te mea he rite te ahunga ki te tuaka -x)

F _1y = F ₁ sin 60 ^o = (6)(0.5 √ 3) = 3 √ 3 ​​​​= (3)(1.372) = 4.116 N ( he pai nā te mea he rite te ahunga ki te tuaka y )

F _2y = F ₂ sin 30 ^o = (10)(0.5 ) = -5 N (kino nā te mea he rite te ahunga ki te tuaka -y)

F _x = F _1x – F _2x = 3 – 8.66 = -5.66 N

F _y = F _1y – F _2y = 4.116 – 5 = -0.884 N

 

Ko te hua o ēnei kaha e rua ko 5.7 N.

[irp]

2. F ₁ = 4 N, F ₂ = 4 N, F ₃ = 8 N. Tātaihia te hua o te whārite.

otinga

F_1x =F₁ whaimana 60^o = (4)(0.5) = 2 N (he pai nā te mea he rite te ahunga ki te tuaka x)

F _2x = -4 N (kino nā te mea he rite te ahunga ki te tuaka -x)

F _3x = F ₃ cos 60 ^o = (8)(0.5) = 4 N ( he pai nā te mea he rite te ahunga ki te tuaka x )

F_1y =F₁ hara 60^o = (4)(0.5√3) = 2√3 N (he pai nā te mea he rite te ahunga ki te tuaka-y)

F _2y = 0

F_3y =F₃ hara 60^o = (8)(0.5√3) = -4√3 N (kino nā te mea he rite te ahunga ki te tuaka -y)

F _x = F _1x – F _2x + F _3x = 2 – 4 + 4 = 2 N

F_y =F_1y +F_2y - F_3y = 2√3 + 0 – 4√3 = -2√3 N

Ko te hua o ēnei kaha e toru ko 5.7 N.

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Whakatauhia te hua o te i roto i te rārangi whārite
2. Whakatauhia ngā wāhanga whārite
3. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te ariā Pythagorean
4. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te whārite cosine
5. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i ngā wāhanga o ngā whārite

Pānuitia atu

Ngā raruraru kua whakatauhia i roto i ngā whārite – te whakatau i te hua o ngā whārite e rua mā te whakamahi i te whārite cosine

1. F ₁ = 10 N me F ₂ = 20 N. Tātaihia te hua o te whārite.

[irp]

2. A ₁ = 15 me A ₂ = 9. Ko te koki i waenganui i ngā whārite e rua he 60 ^° . Tātaihia te whārite ka puta.

otinga

[irp]

3. v ₁ = 5 me v ₂ = 12. Ko te koki i waenganui i ngā whārite e rua he 90 ^° . Tātaihia te whārite ka puta.

otinga

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Whakatauhia te hua o te i roto i te rārangi whārite
2. Whakatauhia ngā wāhanga whārite
3. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te ariā Pythagorean
4. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te whārite cosine
5. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i ngā wāhanga o ngā whārite

Pānuitia atu

Ngā raruraru kua whakatauhia i roto i ngā whārite – te whakatau i te hua o ngā whārite e rua mā te whakamahi i te ariā Pythagorean

1. Tāutuhia te hua o ngā whārite nekehanga e rua e whakaaturia ana i te pikitia i raro nei.

[irp]

2. Kimihia te hua o ngā kaha e rua , 12 N me te 5 N.

[irp]

3. E 4 mita te hikoi a tētahi ākonga ki te hauauru, kātahi ka 6 mita ki te raki, me te 4 mita ki te hauauru. Kimihia te nekehanga o te ākonga.

otinga

Ko te nekenga he 10 mita ki te raki mā uru.

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Whakatauhia te hua o te i roto i te rārangi whārite
2. Whakatauhia ngā wāhanga whārite
3. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te ariā Pythagorean
4. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te whārite cosine
5. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i ngā wāhanga o ngā whārite

Pānuitia atu

Ngā rapanga kua whakatauhia i roto i ngā whārite – te whakatau i ngā wāhanga whārite

1. Ka hangaia he koki 30 ^° ki te tuaka-x e te kaha o te 20 Newton. Kimihia ngā wāhanga x me te y o te kaha.

otinga

F _x = F cos 30 ^o = (20)(cos 30 ^o ) = (20)(0.5 √ 3 ) = 10 √ 3 Ngā Newton

F _y = F hara 30 ^o = (20)(hara 30 ^o ) = (20)(0.5) = 10 Newtons

[irp]

2. Ka hangaia e F ₁ = 20 he koki 30 o a Newton ^me te tuaka y, ā, ka hangaia e F ₂ = 30 he koki 60 o a Newton ^me te tuaka -x. Kimihia ngā wāhanga x me y o F ₁ me F ₂.

otinga

F _1x = F ₁ cos 60 ^o = (20)(cos 60 ^o ) = (20)(0.5) = -10 Newton (kino nā te mea he rite te ahunga ki te tuaka -x)

F _2x = F ₂ cos 60 ^o = (30)(cos 60 ^o ) = (30)(0.5) = -15 Newton (kino nā te mea he rite te ahunga ki te tuaka -x)

F_1y =F₁ hara 60^o = (20)(hara 60^o) = (20)(0.5√3) = 10√3 Newton (he pai nā te mea he rite te ahunga ki te tuaka-y)

F_2y =F₂ hara 60^o = (30)(hara 60^o) = (30)(0.5√3) = -15√3 Newton (kino nā te mea he rite te ahunga ki te tuaka -y)

[irp]

3. F1 ₌ 2 N, F2 ₌ 4 N, F3 ₌ 6 N. Kimihia ngā wāhanga x me y o _F1 , _F2 me _F3!

otinga

F _1x = F ₁ cos 60 ^o = (2)(cos 60 ^o ) = (2)(0.5) = 1 Newton (he pai nā te mea he rite te ahunga ki te tuaka x)

F_2x =F₂ cos 30^o = (4)(cos 30^o) = (4)(0.5√3) = -2√3 Newton (kino nā te mea he rite te ahunga ki te tuaka -x)

F _3x = F ₃ cos 60 ^o = (6)(cos 60 ^o ) = (6)(0.5) = 3 Newton (he pai nā te mea he rite te ahunga ki te tuaka x)

F_1y =F₁ hara 60^o = (2)(hara 60^o) = (2)(0.5√3) = √3 Newton (he pai nā te mea he rite te ahunga ki te tuaka-y)

F _{2 y} = F ₂ sin 3 0 ^o = (4)(sin 30 ^o ) = (4)(0.5) = 2 Newton (he pai nā te mea he rite te ahunga ki te tuaka y)

F_3y =F₃ hara 60^o = (6)(hara 60^o) = (6)(0.5√3) = -3√3 Newton (kino nā te mea he rite te ahunga ki te tuaka -y)

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Whakatauhia te hua o te i roto i te rārangi whārite
2. Whakatauhia ngā wāhanga whārite
3. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te ariā Pythagorean
4. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te whārite cosine
5. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i ngā wāhanga o ngā whārite

Pānuitia atu

Ngā rapanga kua whakatauhia i roto i ngā whārite – te whakatau i te hua o roto i te whārite rārangi

1. Ka hikoi te tauira ki te raki tae atu ki te 10 mita te tawhiti, kātahi ka hikoi ki te tonga tae atu ki te 4 mita te tawhiti. Ko te nekehanga o te tauira ko…

otinga

R = 10 mita – 4 mita = 6 mita

Ko te rahi o te nekehanga he 6 mita, ko te ahunga o te nekehanga ko te raki.

2. F ₁ = 10 N, F ₂ = 15 N. Tātaihia te hua o te whārite…

otinga

R = 10 N + 15 N = 25 Newton

Ko te rahi o te irahiko hua ko 25 Newton, ko te ahunga o te irahiko hua ko te rawhiti, ko te matau rānei.

[irp]

3. F ₁ = 4 N, F ₂ = 8 N. Tātaihia te hua o te whārite…

otinga

R = 8 N – 4 N = 4 Newton

Ko te rahi o te irahiko hua ko 4 Newton, ko te ahunga o te irahiko hua ko te rawhiti, ko te matau rānei.

4. F ₁ = 10, F ₂ = 15 N, F ₃ = 5 N. Tātaihia te hua o te whārite…

otinga

R = 10 N + 5 N – 15 N = 0

Ko te rahi o te whārite hua ko te 0.

[irp]

[wpdm_package id='542′]

[wpdm_package id='554′]

1. Whakatauhia te hua o te i roto i te rārangi whārite
2. Whakatauhia ngā wāhanga whārite
3. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te ariā Pythagorean
4. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i te whārite cosine
5. Whakatauhia te hua o ngā whārite e rua mā te whakamahi i ngā wāhanga o ngā whārite

Pānuitia atu