Ka hoʻoikaika a me ka ikaika

Inā ʻoe e paʻi i kahi puke ma luna o ka papaʻaina a hiki i ka neʻe ʻana o ka puke a laila hana ʻoe hana i loko o ka puke. Inā hāʻule kahi mea i luna o ka honua no ka mea ua huki ʻia e ka ikaika umekaumaha o ka honua, a laila hana ka ikaika umekaumaha o ka honua ma luna o ka mea. I ka ʻaoʻao ʻē aʻe, inā ʻoe e paʻi i kahi mea me kou ikaika a pau a pulu ʻoe i ka hou akā inā ʻaʻole neʻe ka mea a laila ʻaʻole ʻoe i hana i kekahi hana ma luna o ka mea. I ke ola o kēlā me kēia lā, ʻōlelo kekahi poʻe ua hana ʻoe i ka hoʻoikaika a i ʻole ka hana nui e paʻi ana i ka mea, akā e like me ke kālaikūlohea, ʻaʻole ʻoe e hana i kekahi hana ma ka mea no ka mea ʻaʻole ʻike ka mea i ka neʻe ʻana.

Hiki ke hana ʻia ka hana ma luna o kahi mea e kahi ikaika mau (ʻo ka nui a me ke kuhikuhi o ka ikaika e mau ana) a i ʻole kahi ikaika loli (ʻo ka nui a me ke kuhikuhi o ka ikaika e loli mau ana). ʻO kahi laʻana o kahi ikaika me kahi nui a me ke kuhikuhi mau ʻo ia ka ikaika umekaumaha e hana ana ma luna o kahi mea ke kokoke ka mea i ka ʻili o ka Honua. Ke hāʻule manuahi kahi mea kokoke i ka ʻili o ka Honua, ʻo ka nui a me ke kuhikuhi o ka wikiwiki hāʻule manuahi o ka mea e mau ana no ka mea ʻo ka nui a me ke kuhikuhi o ka ikaika umekaumaha e hoʻolalelale ana i ka mea he mau. ʻO kahi laʻana o kahi ikaika me kahi nui loli (ʻo ke kuhikuhi o ka ikaika e mau ana) ʻo ia ikaika puna. Inā ʻoe e kīkoʻo i kahi pūnāwai, ʻo ka nui o ka hoʻonui ʻana o ka lōʻihi, ʻo ka paʻakikī o kou huki ʻana. ʻAʻole mau ka nui o ka ikaika i hoʻokau ʻia ma luna o ka pūnāwai i ka wā e kīkoʻo ana ka pūnāwai. ʻO kekahi laʻana ʻē aʻe i ka wā e neʻe ai kahi rocket i ka lewa a hoʻi paha i ka ʻili o ka Honua. I ka neʻe ʻana o ka rocket, loli ka nui o ka ikaika umekaumaha e hana ana ma luna o ia mea me ka huinahā o ka mamao mai ke kikowaena o ka Honua.

Ma ke ʻano makemakika, ua wehewehe ʻia ka hana i hana ʻia e ka ikaika mau ma luna o kahi mea ma ke ʻano he huahana o ka neʻe ʻana i hoʻonui ʻia e ka ikaika a i ʻole ka ʻāpana o ka ikaika ma ke kuhikuhi o ka neʻe ʻana o ka mea.

ʻAʻole hiki ke helu ʻia ka hana i hana ʻia e kahi ikaika paʻa ʻole e like me ka pūnāwai me ka hoʻohana ʻana i ke ʻano hana no ka hana e kahi ikaika paʻa. Inā hoʻolōʻihi ʻia ka pūnāwai, i ka hoʻolōʻihi ʻana o ka pūnāwai, e ʻoi aku ka nui o ka ikaika tensile e pono ai e hoʻolōʻihi i ka pūnāwai. Pēlā nō, inā e ʻomi ʻia ka pūnāwai, i ka wā e ʻoi aku ka paʻa o ka pūnāwai, ʻoi aku ka nui o ka ikaika paʻi e pono ai. I ka lōʻihi o ke kaomi ʻia a i ʻole ke hoʻolōʻihi ʻia o ka pūnāwai, e loli ka ikaika pūnāwai mai 0 (x = 0) a i ka palena kiʻekiʻe (F = kx) no laila ua helu ʻia ka ikaika pūnāwai me ka hoʻohana ʻana i ka awelika.

Laʻana pilikia

1. Nā Nīnau Hoʻokolohua Lahui 2018

Aia kahi poloka o ke kaumaha m ma luna o kahi ʻili pālahalaha laumania. Aia ka poloka ma ke kūlana (1) a huki ʻia e ka ikaika F i ke kūlana (2) i loko o kahi manawa t e like me ka mea i hōʻike ʻia ma ke kiʻi.

Ma ka hoʻololi ʻana i ka nuipa a me ka ikaika, loaʻa nā ʻikepili penei:

Mai ka papa ma luna, ʻo ka hana i hana ʻia e nā mea mai ka nui a i ka liʻiliʻi he…

Pahana

Ua ʻike ʻia:

Ka wikiwiki mua (v_o) = 0

Ua nīnau ʻia:

Pane:

Haʻilula hana:

W = Fs ………. Formula 1

Haʻilula GLBB:

s = v_o t + 1/2 ma²

s = 1/2 ma²

E pani i haʻilula 1

W = F (1/2 ma²) ………. Formula 2

Haʻilula hoʻoikaika:

F = ma

a = F / m

E pani i haʻilula 2

W = 0,5 F (F/m) t²

W = 0,5 (F²/m) t² .......... Formula 3

E hoʻohana i ke ʻano hana 3 e helu ai i ka nui o ka hana.

1) W = 0,5 (F²/m) t² = 0,5 (3²/12)(4²) = (0,5)(9/12)(16) = (9/12) 8 = 6

2) W = 0,5 (F²/m) t² = 0,5 (4²/16)(3²) = (0,5)(16/16)(9) = (1) 4,5 = 4,5

3) W = 0,5 (F²/m) t² = 0,5 (5²/20)(2²) = (0,5)(25/20)(4) = (1,25) 2 = 2,5

4) W = 0,5 (F²/m) t² = 0,5 (6²/24)(1²) = (0,5)(36/24)(1) = (1,5) 0,5 = 0,75

ʻO ka hana i hana ʻia e nā mea mai ka mea nui a i ka mea liʻiliʻi he 1, 2, 3, 4.

2. Nā Nīnau Hoʻokolohua Lahui 2017 no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana

Ke paheʻe nei kahi pahu me ke kaumaha o 6 kg ma ka wikiwiki o 8 m/s.^-1 ma luna o kahi mokulele hilig ʻino me kahi kihi o ka hilig α e kūʻē i kahi ʻili pālahalaha. Inā he 5 N ka ikaika friction e hana ana ma luna o ka pahu a he ʻeleʻele uliuli ʻo α = 3/4, a laila ʻo ka ikaika F e pono e hoʻopili ʻia e hoʻōki i ka pahu ma lalo o ka mokulele inclined he…

A. 15 N

B. 25 N

C. 45 N

D. 55 N

E. 69,4 N

Pahana

Ua ʻike ʻia:

Ka nuipa o ka pahu (m) = 6 kg

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

Ka wikiwiki mua o ka pahu (v_o) = 8 m/s

Ka wikiwiki hope loa o ka pahu (v_t) = 0 m/s (pono ka pahu e kū ma mua o ka hiki ʻana i ka lalo o ka mokulele inclined)

Ka ikaika kuʻi (F _kāwele) = 5 N

ʻO ka ʻaoʻao mua α = ʻaoʻao lalo / ʻaoʻao mua = 3/4

ʻO ke kiʻekiʻe haʻahaʻa = 5 mika

Ua nīnau ʻia: F

Pane:

Ke kumumanaʻo hana-ikehu mīkini:

Hana i hana ʻia e ka ikaika non-conservative = loli i ka ikehu mechanical

ʻO ka hana i hana ʻia e ka ikaika non-conservative = loli i ka ikehu kinetic a me ka ikehu hiki.

Aia ʻelua mau mana kūpaʻa ʻole, ʻo ia hoʻi ka friction kinetic a me ka mana F.

ʻO ka hana i hana ʻia e ka ikaika friction kinetic ma ka pahu:

W = -(F_nā)(s) = -(5)(5) = -25

Maikaʻi ʻole no ka mea ʻo ke kuhikuhi o ka ikaika friction e kūʻē ana i ke kuhikuhi o ka neʻe ʻana o ka pahu.

Ka hana i hana ʻia e ka ikaika F:

W = (F)(s) = (F)(5) = -5F

Maikaʻi ʻole no ka mea ʻo ke kuhikuhi o ka ikaika F ua kūʻē i ke kuhikuhi o ka neʻe ʻana o ka pahu.

Ka loli ʻana o ka ikehu kinetic:

ΔEK = 1/2 m (v_t² - v_o²) = 1/2 (6)(0² - 8²) = (3)(0-64) = (3)(-64) = -192

Ka loli ʻana o ka ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha:

ΔEP = mgh = (6)(10)(-3) = -180

he maikaʻi ʻole ʻo h no ka mea aia ke kūlana hope loa ma lalo o ke kūlana mua

Ke kumumanaʻo hana-ikehu mīkini:

W_nc = ΔEM

W_nā + W_F = ΔEP + ΔEK

-25 – 5F = -180 -192

-25 – 5F = -372

-5F = -372 + 25

-5F = – 347

F = -347 / -5

F = 69,4 Newton

ʻO ka pane pololei ʻo E.

3. Nā Nīnau Hoʻokolohua Lahui 2017 no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana

Heʻe iho kahi poloka 10 kg mai kahi A ma waena o B a kū ma kahi C e like me ka mea i hōʻike ʻia ma ke kiʻi. ʻO ke koina o ka friction kinetic ma waena o ka poloka a me ka ʻili ʻino he 0,2, no laila ʻo ka lōʻihi o ke ala ABC…

A. 250 kenimika

B. 200 kenimika

C. 150 kenimika

D. 100 kenimika

E. 80 kenimika

Pahana

Ua ʻike ʻia:

Ka nuipa o ka poloka (m) = 10 kg

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

Kaumaha o ka poloka (w) = mg = (10 kg)(10 m/s)²) = 100 Newton

Ke kiʻekiʻe o ka mokulele hilig (h) = 30 kenimika = 0,3 mika

ʻO ka lōʻihi o ka mokulele hilig (s) = 50 kenimika = 0,5 mika

Ka helu o ka haʻalulu kinetic (μ_k) = 0,2

Ka ikaika kuʻi kinetic (f_k) = μ_k N= μ_k w = (0,2)(100 N) = 20 N

Ua nīnau ʻia: Ka lōʻihi o ke ala ABC

Pane:

E noʻonoʻo i ka neʻe ʻana o ka mea mai ke kiko AB.

Ikehu mechanical mua ma ke kiko A = ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha = mgh = (10)(10)(0,3) = (10)(3) = 30 Joules

Ikehu mīkini hope loa ma ke kiko B = ikehu kinetic

Ke kānāwai o ka mālama ʻana i ka ikehu mechanical:

Ikehu mīkini mua = ikehu mīkini hope loa

30 Joules = Ikehu kinetic

No laila, ʻo ka ikehu kinetic ma ke kiko B = 30 Joules.

E noʻonoʻo i ka neʻe ʻana o ka mea mai ke kiko BC.

ʻŌlelo ke kumumanaʻo hana-ikehu ua like ka hana i hana ʻia e kahi ikaika non-conservative me ka loli o ka ikehu mechanical o ka mea. Ka loli o ka ikehu mechanical = ka ikehu mechanical hope loa - ka ikehu mechanical mua. Ma ke ʻano makemakika:

W_NC = ΔEM

W_NC = EM₂ – EM₁

Aia ka mea ma luna o kahi ʻili pālahalaha i ʻole ka ikehu hiki ke umekaumaha. Ikehu mechanical (EM) = ikehu kinetic (EK).

Ikehu kinetic mua (EK)₁) = ikehu kinetic ma ke kiko B = 30 Joules

Ikehu kinetic hope loa (EK)₂) = ikehu kinetic ma ke kiko C = 0 (ua kū ka poloka).

ʻO ka hana i hana ʻia e ka ikaika kūpaʻa ʻole o BC ʻo ia ka hana i hana ʻia e ka ikaika friction kinetic.

W_NC = – f_k s = – 20 s

Jadi

W_NC = EK₂ – EK₁

– 20 kekona = 0 - 30

– 20 kekona = – 30

20 kekona = 30

s = 30/20 = 3/2 = 1,5 mika = 1,5 x 100 kenimika = 150 kenimika.

Ka lōʻihi o ke ala ABC = 50 kenimika + 150 kenimika = 200 kenimika.

ʻO ka pane pololei ʻo B.

4. Nīnau Hoʻokolohua Lahui SMA/MA Physics 2014/2015 Helu 8

E nānā i ke kiʻi aʻe! Paheʻe ka poloka ma luna o kahi mokulele inclined ʻino me ka coefficient friction o 0,4. Inā g = 10 ms^-2 No laila, ʻo ka wikiwiki o ka poloka i kona pā ʻana i ka lalo o ka mokulele inclined he...

H. 2√5 ms^-1

B. 2√7 ms^-1

C. 2√14 ms^-1

D. 2√19 ms^-1

E. 2√23 ms^-1

Pahana

ʻOiai e nānā ana i ke kiʻi ma lalo

Ua ʻike ʻia:

Ke kiʻekiʻe mua (h_o) = 6 mika

Ke kiʻekiʻe hope loa (h_t) = 0 mika

Ka wikiwiki mua (v_o) = 0 (i ka wā mua, ua mau nō ka poloka)

Ka helu o ka haʻalulu kinetic (μ_k) = 0,4 (paheʻe ka poloka i hiki ai i ke koina o ka friction kinetic, ʻaʻole ke koina o ka friction static)

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms^-2

hele θ = i lalo/hili = 8/10

ʻĀpana kaumaha ma ke kuhikuhi kū pololei = w_y = w cos θ = mg cos θ = m (10)(8/10) = m (10)(4/5) = m (40/5) = 8 m

Ikaika maʻamau = N = w_y = 8 m

Ka ikaika kuʻi kinetic = f_k = μ_k N= μ_k w_y = (0,4)(8 mika) = 3,2 mika

Ua nīnau ʻia: Ka wikiwiki hope loa (v_t)

Pane:

ʻŌlelo ke kumumanaʻo hana-ikehu ua like ka hana i hana ʻia e kahi ikaika non-conservative ma luna o kahi mea me ka loli o ka ikehu mechanical o ka mea. ʻO kahi laʻana o ka ikaika non-conservative ka friction kinetic.

W_nc = ΔEM

W_nc = ΔEK + ΔEP

ʻIkepili:

W_nc = Hana i hana ʻia e nā mana ʻaʻole conservative, ΔEM = Ka loli ʻana o ka ikehu mechanical, ΔEK = Ka loli o ka ikehu kinetic, ΔEP = Ka loli o ka ikehu hiki.

Ka loli ʻana o ka ikehu kinetic:

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

Ka loli ʻana o ka ikehu hiki:

ΔEP = mg (h_t -h_o) = m (10)(0-6) = m (10)(-6) = – 60 m

Nā hana i hana ʻia e ka friction kinetic:

Wnc = – f_k s = – (3,2 m)(10) = – 32 m

He maikaʻi ʻole ia no ka mea hana ka ikaika friction kinetic i ka hana maikaʻi ʻole, kahi e kūʻē ai ke kuhikuhi o ka ikaika friction kinetic (i luna) i ke kuhikuhi o ka neʻe ʻana o ka mea (i lalo).

E helu i ka wikiwiki hope loa (v_t):

Wnc = ΔEK + ΔEP

- 32 ka m = 1/2 mv_t² - 60 ka m

- 32 ka m = m (1/2 v)_t² - 60)

- 32 = 1/2 v_t² - 60

– 32 + 60 = 1/2 v_t²

28 = 1/2 v_t²

2 (28) = v_t²

56 = v_t²

v_t = √4.14

v_t = 2√14 ms^-1

ʻO C ka pane pololei.

5. Nīnau Hoʻokolohua Lahui SMA/MA Physics 2014/2015 Helu 8

E nānā i ke kiʻi ma ka ʻaoʻao!

Heʻe kekahi poloka i lalo ma luna o kahi mokulele hilo ʻinoʻino, a hiki i ka wāwae o ka mokulele hilo i ka wikiwiki o 10 m/s.^-1Inā he 2 N ka ikaika friction e hana ana a he 10 ms ka g^-2, a laila ʻo ka waiwai o h ʻo ….

A. 10 m

B. 8 m

C. 6 m

D. 4 m

E. 2 m

Pahana

Ua ʻike ʻia:

Ka nuipa o ka poloka (m) = 1 kg

Ka wikiwiki mua (v_o) = 0 (i ka wā mua, ua mau nō ka poloka)

Ka wikiwiki hope loa (v_t) = 10 ms^-1

Ke kiʻekiʻe mua (h_o) = h

Ke kiʻekiʻe hope loa (h_t) = 0

Ka ikaika kuʻi kinetic (f_k) = 2 N

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms^-2

Ua nīnau ʻia: Kiʻekiʻe (h)

Pane:

Nā hana i hana ʻia e ka friction kinetic:

Wnc = – f_k s = – (2)(15) = – 30

He maikaʻi ʻole ia no ka mea hana ka ikaika friction kinetic i ka hana maikaʻi ʻole, kahi e kūʻē ai ke kuhikuhi o ka ikaika friction kinetic (i luna) i ke kuhikuhi o ka neʻe ʻana o ka mea (i lalo).

Ka loli ʻana o ka ikehu kinetic:

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

Ka loli ʻana o ka ikehu hiki:

ΔEP = mg (h_t -h_o) = (1)(10)(0-h) = (10)(-h) = -10 h

ʻO ke ʻano hana no ka mechanical work-energy theorem:

Wnc = ΔEK + ΔEP

– 30 = 50 – 10 hola

10 h = 50 + 30

10 hola = 80

h = 80/10

h = 8 mika

ʻO ka pane pololei ʻo B.