Nā pilikia i hoʻoponopono ʻia ma ke ʻano Physics kumu

Nā pilikia i hoʻoponopono ʻia ma ka neʻe laina - nā mea hāʻule manuahi

1. Ua hāʻule kahi mea mai luna mai o ka pali. ʻIke ʻia e paʻi i ka honua ma lalo ma hope o 3 kekona. E hoʻoholo i kona wikiwiki ma mua o ka paʻi ʻana i ka honua. ʻO ka wikiwiki o ke koʻikoʻi he 10 m/s ^2. Hoʻowahāwahā i ke kū'ē wai.

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 0 (ua hāʻule ka mea)

Ka manawa (t) = 3 kekona

Ka wikiwiki o ke koʻikoʻi (g) = 10 m/s ²

Makemake ʻia: Ka wikiwiki hope loa ( _vt )

Lōlā:

ʻO ka wikiwiki ma muli o ke koʻikoʻi ma ka ʻili o ka honua, ʻo kona nui he 9.8 m/s ^2. I mea e maʻalahi ai ka helu ʻana, hoʻohana mākou i 10 m/s ².

10 m/s ² a i ʻole 10 m/s / 1 kekona, ʻo ia hoʻi, e piʻi linear ka wikiwiki i ka manawa ma 10 m/s i kēlā me kēia kekona.

Ma hope o 1 kekona, ʻo ka wikiwiki o ka mea = 10 m/s

Ma hope o 2 kekona, ʻo ka wikiwiki o ka mea = 20 m/s

Ma hope o 3 kekona, ʻo ka wikiwiki o ka mea = 30 m/s.

Hiki iā mākou ke hoʻohana i nā kaulike kinematic no ka neʻe ʻana ma kahi wikiwiki mau , e like me ka mea i hōʻike ʻia ma lalo nei.

vt = v _o + _ma

s = v _o t + ½ ma ²

vt ₂ = v _o ^{2 +} 2 es

ʻAʻohe wikiwiki mua o ka hāʻule manuahi (v _o = 0), no laila hiki ke hoʻololi ʻia ke kaulike ma luna e like me ka mea i hōʻike ʻia ma lalo nei:

Ka hoʻohālikelike o ka neʻe hāʻule manuahi :

vt = _gt ………… 1

h = ½ gt ² ………… 2

vt _{2 =} ² gh ………….. 3

vt = _gt

vt ₌ (10)(3)

vt = 30 m/ _s

ʻO ka wikiwiki hope loa he 30 m/s

ʻAʻole maopopo

2. Hāʻule kūʻokoʻa ke kino mai ka hoʻomaha ʻana, mai ke kiʻekiʻe o 25 m. E huli (a) Ka wikiwiki o kona kuʻi ʻana i ka honua. (b) Ka manawa e hiki ai i ka honua.

ʻO ka wikiwiki ma muli o ke koʻikoʻi ma ka ʻili o ka Honua he 10 m/ ^s².

ʻIke ʻia:

Kiʻekiʻe (h) = 5 mika

Ka wikiwiki o ke koʻikoʻi (g) = 10 m/s ²

Makemake ʻia:

(a) Ka wikiwiki hope loa ( _vt )

(b) Ka manawa (t)

Lōlā:

Ka hoʻohālikelike o ka hāʻule manuahi:

vt = _gt

h = ½ gt ²

vt _{2 =} ² gh

(a) Ka wikiwiki hope loa ( _vt )

vt _{2 =} ² gh = 2(10)(5) = 100

vt = 10 m/ _s

(b) Ka manawa (t)

h = ½ gt ²

5 = ½ (10) t ²

5 = 5 t ²

t ² = 5/5 = 1

t = 1 kekona

ʻAʻole maopopo

3. Ua hāʻule kahi pōpō mai kahi kiʻekiʻe. E huli (a) Ka wikiwiki (b) Ka mamao ma hope o 3 kekona (c) Ka manawa ma ka lewa inā he 20 m/s ka wikiwiki hope loa. Ka wikiwiki ma muli o ke koʻikoʻi = 10 m/s ²

ʻIke ʻia :

Ka wikiwiki o ke koʻikoʻi (g) = 10 m/s ²

Makemake ʻia:

(a) Hoʻolalelale (a)

(b) Ka mamao a i ʻole ke kiʻekiʻe (h) inā ua hala ka manawa (t) = 3 kekona

(c) Ka manawa mamao (t) inā v _t = 20 m/s

Lōlā:

Ka hoʻohālikelike o ka hāʻule manuahi:

vt = _gt

h = ½ gt ²

vt _{2 =} ² gh

(a) Hoʻolalelale (a)

Ka wikiwiki = ka wikiwiki ma muli o ke koʻikoʻi = 10 m/s ^2. ʻO ia hoʻi ka piʻi ʻana o ka wikiwiki ma 10 m/s i kekona.

(b) Ka mamao a i ʻole ke kiʻekiʻe (h) ma hope o t = 3 kekona

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

(c) Ka manawa i hala (t) inā v _t = 20 m/s

vt = _gt

20 = (10) t

t = 20 / 10 = 2 kekona

ʻAʻole maopopo

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[wpdm_package id='517′]

1. Ka mamao a me ka neʻe ʻana
2. ʻO ka wikiwiki awelika a me ka wikiwiki awelika
3. Ka wikiwiki mau
4. Hoʻolalelale mau
5. Neʻe hāʻule manuahi
6. Neʻe i lalo i ka hāʻule manuahi
7. Neʻe i luna a i lalo i ka hāʻule manuahi

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma ka neʻe laina - ka wikiwiki mau

1. Hoʻolalelale kekahi kaʻa mai ka hoʻomaha a i 20 m/s i loko o 10 kekona. E hoʻoholo i ka hoʻolalelale o ke kaʻa!

pāʻoihana

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 0 (hoʻomaha)

Ka manawa (t) = 10 kekona

Ka wikiwiki hope loa (vt ₎ = 20 m/s

Makemake ʻia : Hoʻolalelale (a)

Lōlā:

vt = v _o + _ma

20 = 0 + (a)(10)

20 = 10 a

a = 20 / 10

a = 2 m/s ²

ʻAʻole maopopo

2. Ke hoʻēmi nei kekahi kaʻa mai 30 m/s a hoʻomaha i loko o 10 kekona. E hoʻoholo i ka wikiwiki o ke kaʻa.

pāʻoihana

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 30 m/s

Ka wikiwiki hope loa (vt ₎ = 0

Ka manawa (t) = 10 kekona

Makemake ʻia: hoʻolalelale (a)

Lōlā:

vt = v _o + _ma

0 = 30 + (a)(10)

– 30 = 10 a

a = – 30 / 10

a = -3 m/s ²

ʻIke ʻia ka hōʻailona maikaʻi ʻole no ka mea ʻoi aku ka liʻiliʻi o ka wikiwiki hope ma mua o ka wikiwiki mua.

ʻAʻole maopopo

3. Hoʻomaka a hoʻolalelale kekahi kaʻa i ka wikiwiki mau o 4 m/s ² i 1 kekona. E hoʻoholo i ka wikiwiki a me ka mamao ma hope o 10 kekona.

pāʻoihana

(a) Ka wikiwiki

ʻO ka hoʻolalelale ʻana he 4 m/s ² ʻo ia hoʻi ka hoʻonui ʻia o ka wikiwiki he 4 m/s i kēlā me kēia 1 kekona. Ma hope o 2 kekona, ʻo ka wikiwiki o ke kaʻa he 8 m/s. Ma hope o 10 kekona, ʻo ka wikiwiki o ke kaʻa he 40 m/s.

(b) Ka mamao

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 0

Ka wikiwiki hope loa (vt ₎ = 40 m/s

Hoʻolalelale (a) = 4 m/s ²

Makemake ʻia: Ka mamao

Lōlā:

s = v _o t + ½ ma ² = 0 + ½ (4)(10 ² ) = (2)(100) = 200 mika

ʻAʻole maopopo

4. Holo ke kaʻa ma ka wikiwiki mau o 10 m/s, a laila hoʻēmi i ka wikiwiki ma ka wikiwiki mau o 2 m/s ² a hiki i ka hoʻomaha. E hoʻoholo i ka manawa i hala a me ka mamao o ke kaʻa ma mua o ka hoʻomaha.

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 10 m/s

Hoʻolalelale (a) = -2 m/s ² (ʻIke ʻia ka hōʻailona maikaʻi ʻole no ka mea ʻoi aku ka liʻiliʻi o ka wikiwiki hope ma mua o ka wikiwiki mua)

Ka wikiwiki hope loa (vt ₎ = 0 (hoʻomaha)

Makemake ʻia: Ka manawa a me ka mamao

Lōlā:

(a) Ka manawa (t)

vt = v _o + _ma

0 = 10 + (-2)(t)

0 = 10 – 2 t

10 = 2 t

t = 10 / 2 = 5 kekona

(b) Ka mamao

vt ₂ = v _o ^{2 +} 2 es

0 = 10 ² + 2(-2) s

0 = 100 – 4 kekona

100 = 4 kekona

s = 100 / 4 = 25 mika

ʻAʻole maopopo

5. Holo kekahi kaʻa ma 40 m/s, hoʻēmi i ka wikiwiki ma ke ʻano mau 4 m/s ² a hiki i ka hoʻomaha. E hoʻoholo i ka wikiwiki a me ka mamao ma hope o ka hoʻēmi ʻana i loko o 10 kekona!

pāʻoihana

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 40 m/s

Hoʻolalelale (a) = -4 m/s ²

Ka manawa (t) = 10 kekona

Makemake ʻia: ka wikiwiki hope loa (vt ₎ a me ka mamao (s)

Lōlā:

(a) Ka wikiwiki hope loa

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

ʻO 0 m/s ke ʻano o ka hoʻomaha ʻana o ke kaʻa.

(b) Ka mamao

s = v _o t + ½ ma ² = (40)(10) + ½ (-4)(10 ² ) = 400 + (-2)(100) = 400 – 200 = 200 mika

ʻAʻole maopopo

6. E hoʻoholo i ka mamao ma hope o 10 kekona!

pāʻoihana

Ka mamao: s = vt = (10-0)(5-0) = (10)(5) = 50 mika

7. E hoʻoholo i ka mamao ma hope o 4 kekona!

pāʻoihana

Ka mamao = ʻāpana huinahā + ʻāpana huinakolu

Ka mamao = (8-0)(8-0) + ½ (16-8)(8-0) = (8)(8) + ½ (8)(8) = 64 + 32 = 96 mika

8. E hoʻoholo i ka mamao o ke kaʻa ma hope o 4 kekona!

pāʻoihana

Ka mamao = ʻāpana huinakolu = ½ (4-0)(8-0) = ½ (4)(8) = 16 mika

9. Neʻe kekahi kaʻa ma ka wikiwiki o 90 km/h ma mua o kahi kaʻa mākaʻi e kū ana ma ka ʻaoʻao o ke alanui. I hoʻokahi minuke ma hope mai, alualu ke kaʻa mākaʻi ma ka wikiwiki o 0.8 m/s² ^. Pehea ka mamao o ka hiki ʻana o ke kaʻa mākaʻi i ke kaʻa?

ʻIke ʻia:

ʻO ka wikiwiki o ke kaʻa (v) = 90 km/hola = 90,000 mika / 3600 kekona = 25 mika/kekona

Ka manawa (t) = 1 minuke = 60 kekona

Ka wikiwiki o ke kaʻa o nā mākaʻi (a) = 0.8 m/s ²

Ka wikiwiki mua o ke kaʻa o nā mākaʻi (v _o ) = 0 m/s

Makemake ʻia: Ka mamao i hele ʻia e ke kaʻa o nā mākaʻi

Lōlā:

Neʻe ke kaʻa i ka wikiwiki mau. Ka mamao i hele ʻia e ke kaʻa:

Ka mamao mua:

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

Ka mamao hope loa:

s = vt = (25)(t)

Ka huina mamao = 1500 + 25 t

Neʻe ka kaʻa o nā mākaʻi me ka wikiwiki mau. Ka mamao i hele ʻia e ke kaʻa o nā mākaʻi:

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

Ke hiki aku ke kaʻa o ka mākaʻi i ke kaʻa, ua like ka mamao i hele ʻia e ke kaʻa o ka mākaʻi me ka mamao i hele ʻia e ke kaʻa.

Ka mamao i hele ʻia e ke kaʻa = ka mamao i hele ʻia e ke kaʻa o nā mākaʻi

1500 + 25 t = 0.4 t ²

0.4 t ² – 25 t – 1500 = 0

E hoʻohana i ke ʻano quadratic:

Ka mamao i hele ʻia e ke kaʻa o nā mākaʻi:

s = 0.4 t ² = (0.4)(100 ² ) = (0.4)(10,000) = 4000 mika s = 4 km

10. Neʻe kekahi kaʻa ma kahi paleki mau 24 m/s i loaʻa iā ia ka deceleration mau o 0.952 m/s ^2. E hoʻoholo i ka wikiwiki o ke kaʻa ma hope o kahi mamao o 250 mika.

ʻIke ʻia:

Ka wikiwiki mua (v _o ) = 24 m/s

Ka wikiwiki (a) = – 0.952 m/s ² ( hōʻailona maikaʻi ʻole no ka mea ka hoʻēmi ʻana )

Ka mamao ( d ) = 250 mika s

Makemake ʻia: Ka wikiwiki o ke kaʻa ma hope o 250 mika s

Lōlā:

ʻIke ʻia: ka wikiwiki mua (v_o), ka piʻi (a), mamao (d), makemake ʻia: ka wikiwiki hope loa (v_t) no laila e hoʻohana i ka hoohalike o v_t² = v_o² + 2 a d

vt ₌ ka wikiwiki hope loa , vo ₌ ka wikiwiki mua , a = ka wikiwiki , d = ka mamao

v _t ² = (24) ² + (2)(-0.952)(250)

v _t ² = 576 – 476

vt ₂ = ¹⁰⁰

vt ₌ √100

vt = 10 m/ _s

ʻAʻole maopopo

[wpdm_package id='507′]

[wpdm_package id='517′]

1. Ka mamao a me ka neʻe ʻana
2. ʻO ka wikiwiki awelika a me ka wikiwiki awelika
3. Ka wikiwiki mau
4. Hoʻolalelale mau
5. Neʻe hāʻule manuahi
6. Neʻe i lalo i ka hāʻule manuahi
7. Neʻe i luna a i lalo i ka hāʻule manuahi

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma ka neʻe laina - ka wikiwiki mau

1. Holo ke kaʻa ma ka wikiwiki mau o 10 m/s. E hoʻoholo i ka mamao ma hope o 10 kekona a me 60 kekona.

pāʻoihana

ʻO ka wikiwiki mau he 10 mika/kekona, ʻo ia hoʻi ka holo ʻana o ke kaʻa i 10 mika i kēlā me kēia 1 kekona.

Ma hope o 2 kekona, holo ke kaʻa i 20 mika,

Ma hope o 5 kekona, holo ke kaʻa i 50 mika,

Ma hope o 10 kekona, holo ke kaʻa i 100 mika.

Ma hope o 60 kekona, holo ke kaʻa i 600 mika.

ʻAʻole maopopo

2. Holo kekahi kaʻa ma ke alanui pololei ma ka wikiwiki mau o 72 km/h. E hoʻoholo i ka mamao o ke kaʻa ma hope o 2 mau minuke a me 5 mau minuke.

pāʻoihana

72 km/h = (72)(1000 mika) / 3600 kekona = 72,000 / 3600 kekona = 20 mika/kekona.

ʻO ka wikiwiki mau ma 20 mika/kekona, ʻo ia hoʻi, holo ke kaʻa i 20 mika i kēlā me kēia 1 kekona.

Ma hope o 120 kekona a i ʻole 2 mau minuke, hele ke kaʻa i 20 mika x 120 = 2400 mika ,

Ma hope o 300 kekona a i ʻole 5 mau minuke, holo ke kaʻa i 20 mika x 300 = 6000 mika.

ʻAʻole maopopo

3. Hele ke kino ma ke alanui pololei no 100 mika i loko o 50 kekona. E hoʻoholo i ka wikiwiki o ke kino.

pāʻoihana

100 mika / 50 kekona = 10 mika / 5 kekona = 2 mika/kekona.

4. E hoʻoholo i ka wikiwiki e like me ke kiʻikuhi ma lalo nei….

pāʻoihana

Māmā = Ka mamao / ka manawa i hala

Ka māmā holo = 2 mika / 1 kekona = 4 mika / 2 kekona = 6 mika / 3 kekona = 8 mika / 4 kekona = 2 mika/kekona.

5. Hoʻokokoke nā kaʻa A a me B kekahi i kekahi ma nā ala like. Ke 100 mika ka mamao ma waena o nā kaʻa ʻelua, neʻe ke kaʻa A ma ka wikiwiki mau o 10 m/s, neʻe ke kaʻa B ma ka wikiwiki mau o 40 m/s. E hoʻoholo (a) ka mamao o ke kaʻa A ma mua o ka hala ʻana o ke kaʻa B (b) ka manawa ma mua o ka hala ʻana o ke kaʻa B i ke kaʻa A.

pāʻoihana

Neʻe ke kaʻa A me ka wikiwiki mau ma 10 mika/kekona, ʻo ia hoʻi, neʻe ke kaʻa A a hiki i 10 mika i kēlā me kēia 1 kekona. Ma hope o 2 kekona, neʻe ke kaʻa A a hiki i 20 mika.

Neʻe ke kaʻa B me ka wikiwiki mau ma 40 mika/kekona, ʻo ia hoʻi, neʻe ke kaʻa B a hiki i 40 mika i kēlā me kēia 1 kekona. Ma hope o 2 kekona, neʻe ke kaʻa B a hiki i 80 mika.

20 mika + 80 mika = 100 mika.

(a) ʻO ka mamao o ke kaʻa A ma mua o ka hala ʻana o ke kaʻa B he 20 mika. ʻO ka mamao o ke kaʻa B ma mua o ka hala ʻana o ke kaʻa A he 80 mika.

(b) ʻO ka manawa o ke kaʻa B ma mua o ka hala ʻana o ke kaʻa A he 2 kekona. ʻO ka manawa o ke kaʻa A ma mua o ka hala ʻana o ke kaʻa B he 2 kekona

5. Inā hōʻike ka speedometer o ke kaʻa i 108 km/h, e hoʻoholo i ka mamao i hele ʻia e ke kaʻa i hoʻokahi minuke.

Lōlā:

He mea hana ka speedometer no ke ana ʻana i ka wikiwiki. ʻO ka wikiwiki o ke kaʻa he 108 km/hola.
108 km / h = (108) (1000 mika) / 3600 kekona = 30 mika/kekona.

1 minuke = 60 kekona

ʻO ka wikiwiki o ke kaʻa he 30 mika/kekona, ʻo ia hoʻi, neʻe ke kaʻa a hiki i 30 mika i loko o 1 kekona.

Ma hope o 1 kekona, neʻe ke kaʻa a hiki i ka mamao o 1 x 30 mika = 30 mika.

Ma hope o 2 kekona, neʻe ke kaʻa a hiki i ka mamao o 2 x 30 mika = 60 mika.

Ma hope o 60 kekona, neʻe ke kaʻa a hiki i ka mamao o 60 x 30 mika = 1800 mika.

6. Hoʻolei pololei ʻo Tom i kahi pōpō iā Andrew . Ua hoʻokaʻawale ʻia ʻo Tom lāua ʻo Andrew a hiki i 10.08 mika . Hoʻolei ʻia ka pōpō ma ka ʻaoʻao pālahalaha a neʻe i 20 m/ s (hoʻowahāwahā i ke koʻikoʻi). Paʻi ʻo Andrew i ka pōpō 4.00 x 10 ^-3 kekona ma hope o ka hoʻolei ʻia ʻana o ka pōpō. Inā neʻe ka mea hahau i ka wikiwiki mau o 5.00 m/s, paʻi ʻia ka pōpō e ka mea hahau ma hope o ka neʻe ʻana o ka mea hahau a hiki i…

ʻIke ʻia:

ʻO ka mamao ma waena o Tom lāua ʻo Andrew = 10.08 mika

Ka wikiwiki o ka pōpō (v) = 20 m/s

ʻO ka manawa ma waena (t) = 4 x 10 ^-3 kekona = 0.004 kekona

Ka wikiwiki o ka mea hahau (v) = 5 m / s

Makemake: Ua pā ʻia ka pōpō e ka mea hahau ma hope o ka neʻe ʻana o ka pōpō a hiki i kahi...

Lōlā:

Ka mamao o ka pōpō:

s ₁ = vt = (20) (0.004) = 0.08 mika

Ka mamao o ka mea hahau:

s2 = vt ₌ 5 t

Ka mamao o ka pōpō + ka mamao o ka mea hahau = ka mamao ma waena o Tom lāua ʻo Andrew.

0.08 + 5 t = 10.08

5 t = 10.08 – 0.08

5 t = 10

t = 10/5

t = 2 kekona

Ka mamao o ka mea hahau:

s ₂ = vt = 5 t = (5) (2) = 10 mika

7. Ke alualu nei kekahi mea hahai holoholona me kāna kaʻa i kahi dia. Neʻe ke kaʻa ma 72 km/h a holo ka dia ma ka wikiwiki o 64.8 km/h. I ka wā he 2012 mika ka mamao ma waena o ke kaʻa a me ka dia, ua kī ka mea hahai holoholona i kāna pū panapana. Nā pōkā mai loko mai o ka pū ma 200 m/s. E hoʻoholo i ka manawa o ka pana ʻia ʻana o ka dia.

A. 0.5 kekona

B. 1 s

C. 1.25 kekona

D. 1.5 kekona

ʻIke ʻia:

Ka wikiwiki o ke kaʻa (v _b ) = 72 km/h = (72)(1000 m) / 3600 s = 20 m/s

Ka wikiwiki o ka dia (v _r ) = 64.8 km/h = (64.8)(1000 m) / 3600 s = 64800 m / 3600 s = 18 m/s

Ke kī ʻia ka pōkā, ʻo ka mamao ma waena o ke kaʻa a me ka dia (s) = 202 mika

Ka wikiwiki o ke ahi (v _p ) = 20 m/s + 200 m/s = 220 m/s

Nā mea kaua i paʻa ʻia e nā mea hahai holoholona i loko o kahi kaʻa e neʻe ana me ka wikiwiki o 20 m/s i hoʻohui ʻia ai ka wikiwiki o ke kaʻa i ka wikiwiki o ka pōkā.

Makemake ʻia: E hoʻoholo i ka manawa o ka pana ʻia ʻana o ka dia

Lōlā:

E noʻonoʻo i nā kaʻa a me nā dia e neʻe ana i ka wikiwiki mau.

Kaulike: v = s / t a i ʻole s = vt

v = ka wikiwiki, s = ka mamao, t = ka wā manawa

Ka mamao = 202 + X _r = 202 + v _r t = 202 + 18 t

Mamao = Y _p = v _p t = 220 t

Ka mamao i hele ʻia e ka dia = ka mamao i hele ʻia e ka pōkā

202 + 18 t = 220 t

202 = 220 t – 18 t

202 = 202 t

t = 202/202

t = 1 kekona

ʻO ka pane pololei ʻo B.

ʻAʻole maopopo

[wpdm_package id='507′]

[wpdm_package id='517′]

1. Ka mamao a me ka neʻe ʻana
2. ʻO ka wikiwiki awelika a me ka wikiwiki awelika
3. Ka wikiwiki mau
4. Hoʻolalelale mau
5. Neʻe hāʻule manuahi
6. Neʻe i lalo i ka hāʻule manuahi
7. Neʻe i luna a i lalo i ka hāʻule manuahi

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma ka neʻe laina - ka wikiwiki awelika a me ka wikiwiki awelika

1. Holo kekahi kaʻa ma ke alanui pololei i ka hikina no 100 mika i loko o 4 kekona, a laila hele i ke komohana no 50 mika i loko o 1 kekona. E hoʻoholo i ka wikiwiki awelika a me ka wikiwiki awelika.

pāʻoihana

Ka mamao = 100 mika + 50 mika = 150 mika

Ka neʻe ʻana = 100 mika – 50 mika = 50 mika, ma ka hikina.

Ka manawa i hala = 4 kekona + 1 kekona = 5 kekona.

Ka wikiwiki awelika = Ka mamao / ka manawa i hala = 150 mika / 5 kekona = 30 mika/kekona.

ʻO ka wikiwiki awelika = Ka neʻe ʻana / ka manawa i hala = 50 mika / 5 kekona = 10 mika/kekona.

ʻAʻole maopopo

2. Hele kekahi kanaka i 4 mika hikina i 1 kekona, a laila hele i 3 mika ʻākau i 1 kekona. E hoʻoholo i ka wikiwiki awelika a me ka wikiwiki awelika.

pāʻoihana

Ka mamao = 4 mika + 3 mika = 7 mika

Ka hoʻoneʻe ʻana = = mika, ma ka ʻākau hikina.

Ka manawa i hala = 1 kekona + 1 kekona = 2 kekona.

ʻO ka wikiwiki awelika = ka mamao / ka manawa i hala = 7 mika / 2 kekona = 3.5 mika/kekona

ʻO ka wikiwiki awelika = ka neʻe ʻana / ka manawa i hala = 5 mika / 2 kekona = 2.5 mika/kekona

ʻAʻole maopopo

3. Ke holo nei kekahi mea holo a puni kahi ala huinahā me ka lōʻihi = 50 mika a me ka laulā = 20 mika. Ma hope o ka holo ʻana a puni ke ala huinahā ʻelua manawa, hoʻi ka mea holo i kahi hoʻomaka. Inā ua hala ka manawa = 100 kekona, e hoʻoholo i ka wikiwiki awelika a me ka wikiwiki awelika.

pāʻoihana

Ka pōʻai o ka huinahā like = 2 (50 mika) + 2 (20 mika) = 100 mika + 40 mika = 140 mika.

Kaʻapuni a puni ka huinahā like 2 manawa = 2 (140 mika) = 280 mika.

Ka mamao = 280 mika.

Ka neʻe ʻana = 0 mika . ( mea holo e hoʻi i kahi hoʻomaka)

Ka wikiwiki awelika = ka mamao / ka manawa i hala = 280 mika / 100 kekona = 2.8 mika/kekona.

ʻO ka wikiwiki awelika = ka neʻe ʻana / ka manawa i hala = 0 / 100 kekona = 0.

ʻAʻole maopopo

[wpdm_package id='505′]

[wpdm_package id='517′]

1. Ka mamao a me ka neʻe ʻana
2. ʻO ka wikiwiki awelika a me ka wikiwiki awelika
3. Ka wikiwiki mau
4. Hoʻolalelale mau
5. Neʻe hāʻule manuahi
6. Neʻe i lalo i ka hāʻule manuahi
7. Neʻe i luna a i lalo i ka hāʻule manuahi

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma nā vectors - e hoʻoholo i ka hopena o ʻelua vectors me ka hoʻohana ʻana i nā ʻāpana o ka vector

1. F ₁ = 6 N, F ₂ = 10 N. E hoʻoholo i ka vector hopena.

pāʻoihana

F _1x = F ₁ cos 60 ^o = (6)(0.5) = 3 N ( maikaʻi no ka mea he kuhikuhi like kona me ke axis x )

F _2x = F ₂ cos 30 ^o = (10)(0.5 √ 3) = 5 √ 3 = (5)(1.372) = -8.66 N (maikaʻi ʻole no ka mea ua like kona kuhikuhi me ke axis -x)

F _1y = F ₁ sin 60 ^o = (6)(0.5 √ 3) = 3 √ 3 ​​​​= (3)(1.372) = 4.116 N ( maikaʻi no ka mea he kuhikuhi like kona me ke axis y )

F _2y = F ₂ sin 30 ^o = (10)(0.5 ) = -5 N (maikaʻi ʻole no ka mea ua like kona kuhikuhi me ke axis -y)

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

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

 

ʻO ka hopena o kēia mau ikaika ʻelua he 5.7 N.

ʻAʻole maopopo

2. F ₁ = 4 N, F ₂ = 4 N, F ₃ = 8 N. E hoʻoholo i ka vector hopena.

pāʻoihana

F_1x =F₁ ka helu 60^o = (4)(0.5) = 2 N (maikaʻi no ka mea he kuhikuhi like kona me ke axis x)

F _2x = -4 N (maikaʻi ʻole no ka mea he kuhikuhi like kona me ke axis -x)

F _3x = F ₃ cos 60 ^o = (8)(0.5) = 4 N ( maikaʻi no ka mea ua like kona kuhikuhi me ke axis x )

F_1y =F₁ hewa 60^o = (4)(0.5√3) = 2√3 N (maikaʻi no ka mea he kuhikuhi like kona me ke axis y)

F _2y = 0

F_3y =F₃ hewa 60^o = (8)(0.5√3) = -4√3 N (maikaʻi ʻole no ka mea, ua like kona kuhikuhi me ke axis -y)

ʻO 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

ʻO ka hopena o kēia mau ikaika ʻekolu he 5.7 N.

ʻAʻole maopopo

[wpdm_package id='542′]

[wpdm_package id='554′]

1. E hoʻoholo i ka hopena o loko o kahi vector laina
2. E hoʻoholo i nā ʻāpana vector
3. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka Pythagorean theorem
4. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka hoohalike cosines
5. E hoʻoholo i ka hopena o ʻelua mau vectors me ka hoʻohana ʻana i nā ʻāpana o nā vectors

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma nā vectors - e hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka hoʻohālikelike cosines

1. F ₁ = 10 N a me F ₂ = 20 N. E hoʻoholo i ka vector hopena.

ʻAʻole maopopo

2. A ₁ = 15 a me A ₂ = 9. ʻO ke kihi ma waena o nā vectors ʻelua he 60 ^o . E hoʻoholo i ka vector hopena.

pāʻoihana

ʻAʻole maopopo

3. v ₁ = 5 a me v ₂ = 12. ʻO ke kihi ma waena o nā vectors ʻelua he 90 ^o . E hoʻoholo i ka vector hopena.

pāʻoihana

ʻAʻole maopopo

[wpdm_package id='542′]

[wpdm_package id='554′]

1. E hoʻoholo i ka hopena o loko o kahi vector laina
2. E hoʻoholo i nā ʻāpana vector
3. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka Pythagorean theorem
4. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka hoohalike cosines
5. E hoʻoholo i ka hopena o ʻelua mau vectors me ka hoʻohana ʻana i nā ʻāpana o nā vectors

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma nā vectors - e hoʻoholo i ka hopena o ʻelua vectors me ka hoʻohana ʻana i ka Pythagorean theorem

1. E hoʻoholo i ka hopena o nā vectors neʻe ʻelua e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei.

ʻAʻole maopopo

2. E huli i ka hopena o nā ikaika ʻelua , 12 N a me 5 N.

ʻAʻole maopopo

3. Hele kekahi haumāna i 4 mika i ke komohana, a laila 6 mika i ke kūkulu ʻākau a me 4 mika i ke komohana. E huli i ka neʻe ʻana o ka haumāna.

pāʻoihana

He 10 mika ka neʻe ʻana , ma ke komohana ʻākau.

ʻAʻole maopopo

[wpdm_package id='542′]

[wpdm_package id='554′]

1. E hoʻoholo i ka hopena o loko o kahi vector laina
2. E hoʻoholo i nā ʻāpana vector
3. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka Pythagorean theorem
4. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka hoohalike cosines
5. E hoʻoholo i ka hopena o ʻelua mau vectors me ka hoʻohana ʻana i nā ʻāpana o nā vectors

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma nā vectors - hoʻoholo i nā ʻāpana vector

1. Hana kahi ikaika o 20 Newton i kahi kihi o 30 ^o me ke axis-x. E huli i nā ʻāpana x a me y o ka ikaika.

pāʻoihana

ʻO F _x = F cos 30 ^o = (20)(cos 30 ^o ) = (20)(0.5 √ 3 ) = 10 √ 3 Newtons

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

ʻAʻole maopopo

2. Hana ʻo F ₁ = 20 Newton i kahi kihi o 30 ^o me ke axis y a hana ʻo F ₂ = 30 Newton i kahi kihi o 60 ^o me ke axis -x. E huli i nā ʻāpana x a me y o F ₁ a me F ₂.

pāʻoihana

F _1x = F ₁ cos 60 ^o = (20)(cos 60 ^o ) = (20)(0.5) = -10 Newtons (maikaʻi ʻole no ka mea he kuhikuhi like kona me ke axis -x)

F _2x = F ₂ cos 60 ^o = (30)(cos 60 ^o ) = (30)(0.5) = -15 Newtons (maikaʻi ʻole no ka mea he kuhikuhi like kona me ke axis -x)

F_1y =F₁ hewa 60^o = (20)(hewa 60^o) = (20)(0.5√3) = 10√3 ʻO Newton (maikaʻi no ka mea he like kona kuhikuhi me ke axis y)

F_2y =F₂ hewa 60^o = (30)(hewa 60^o) = (30)(0.5√3) = -15√3 ʻO Newton (maikaʻi ʻole no ka mea he like kona kuhikuhi me ke axis -y)

ʻAʻole maopopo

3. F ₁ = 2 N, F ₂ = 4 N, F ₃ = 6 N. E huli i nā ʻāpana x a me y o F ₁ , F ₂ a me F ₃!

pāʻoihana

F _1x = F ₁ cos 60 ^o = (2)(cos 60 ^o ) = (2)(0.5) = 1 Newtons (maikaʻi no ka mea he kuhikuhi like kona me ke axis x)

F_2x =F₂ hele 30^o = (4)(cos 30^o) = (4)(0.5√3) = -2√3 ʻO Newton (maikaʻi ʻole no ka mea he kuhikuhi like kona me ke axis -x)

F _3x = F ₃ cos 60 ^o = (6)(cos 60 ^o ) = (6)(0.5) = 3 Newtons (maikaʻi no ka mea he kuhikuhi like kona me ke axis x)

F_1y =F₁ hewa 60^o = (2)(hewa 60^o) = (2)(0.5√3) = √3 ʻO Newton (maikaʻi no ka mea he like kona kuhikuhi me ke axis y)

F _{2 y} = F ₂ sin 3 0 ^o = (4)(sin 30 ^o ) = (4)(0.5) = 2 Newtons (maikaʻi no ka mea he kuhikuhi like kona me ke axis y)

F_3y =F₃ hewa 60^o = (6)(hewa 60^o) = (6)(0.5√3) = -3√3 ʻO Newton (maikaʻi ʻole no ka mea he kuhikuhi like kona me ke axis -y)

ʻAʻole maopopo

[wpdm_package id='542′]

[wpdm_package id='554′]

1. E hoʻoholo i ka hopena o loko o kahi vector laina
2. E hoʻoholo i nā ʻāpana vector
3. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka Pythagorean theorem
4. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka hoohalike cosines
5. E hoʻoholo i ka hopena o ʻelua mau vectors me ka hoʻohana ʻana i nā ʻāpana o nā vectors

heluhelu hou

Nā pilikia i hoʻoponopono ʻia ma nā vectors - e hoʻoholo i ka hopena o loko o kahi vector laina

1. Hele kekahi haumāna i ka ʻākau a hiki i 10 mika a laila i ka hema a hiki i 4 mika. ʻO ka neʻe ʻana o ka haumāna he…

pāʻoihana

R = 10 m – 4 m = 6 mika

ʻO ka nui o ka neʻe ʻana he 6 mika, ʻo ke kuhikuhi o ka neʻe ʻana he ʻākau.

2. F ₁ = 10 N, F ₂ = 15 N. E hoʻoholo i ka vector hopena…

pāʻoihana

R = 10 N + 15 N = 25 Newton

ʻO ka nui o ka vector hopena he 25 Newtons, ʻo ke kuhikuhi o ka vector hopena he hikina a ʻākau paha.

ʻAʻole maopopo

3. F ₁ = 4 N, F ₂ = 8 N. E hoʻoholo i ka vector hopena…

pāʻoihana

R = 8 N – 4 N = 4 Newton

ʻO ka nui o ka vector hopena he 4 Newtons, ʻo ke kuhikuhi o ka vector hopena he hikina a ʻākau paha.

4. F ₁ = 10, F ₂ = 15 N, F ₃ = 5 N. E hoʻoholo i ka vector hopena…

pāʻoihana

R = 10 N + 5 N – 15 N = 0

ʻO ka nui o ka vector hopena he 0.

ʻAʻole maopopo

[wpdm_package id='542′]

[wpdm_package id='554′]

1. E hoʻoholo i ka hopena o loko o kahi vector laina
2. E hoʻoholo i nā ʻāpana vector
3. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka Pythagorean theorem
4. E hoʻoholo i ka hopena o nā vectors ʻelua me ka hoʻohana ʻana i ka hoohalike cosines
5. E hoʻoholo i ka hopena o ʻelua mau vectors me ka hoʻohana ʻana i nā ʻāpana o nā vectors

heluhelu hou