Kumumanaʻo hana-ikehu Ka ikaika mālama ʻole Ka neʻe ʻana ma luna o ka mokulele inclined me ka friction - Nā pilikia a me nā hoʻonā

2 Kumumanaʻo hana-ikehu Ka ikaika mālama ʻole Ka neʻe ʻana ma luna o ka mokulele inclined me ka friction - Nā pilikia a me nā hoʻonā

1. Paheʻe kahi poloka i lalo i kahi mokulele hilig me ka friction. He aha ka poloka ka wikiwiki ke paʻi ka poloka i ka honua? ʻO ke koina o ka ʻūmiʻi kinetic he 0.4. ʻO ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s².

ʻIke ʻia:

Ke kiʻekiʻe mua (h_o) = 6 mika

Ke kiʻekiʻe hope loa (h_t) = 0 mika

Ka wikiwiki mua (v_o) = 0 (poloka mua i ka wā hoʻomaha)

Ka helu o ka haʻalulu kinetic (μ_k) = 0.4

ʻO ka wikiwiki ma muli o ka umekaumaha (g) = 10 ms^-2

cos θ = adj/hyp = 8/10

ʻO ka ʻāpana kū pololei o kaumaha = w_y = w cos θ = mg cos θ = m (10)(8/10) = m (10)(4/5) = m (40/5) = 8 m

ka ikaika maʻamau = N = w_y = 8 m

ʻO ka ikaika o ka friction kinetic = f_k = μ_k N = μ_k w_y = (0.4)(8 mika) = 3.2 mika

Makemake ʻia: Ka wikiwiki hope loa (v_t)

Lōlā:

ʻŌlelo ke kumumanaʻo ikehu hana-mechanical ʻo ka hana i hana ʻia e nā mana nonconservative e hana ana ma kahi mea ua like ia me ka loli holoʻokoʻa o ka ikehu kinetic a me ka ikehu hiki.

W_nc = ΔEM

W_nc = ΔEK + ΔEP

W_nc = Hana i hana ʻia e ka ikaika mālama ʻole, ΔEM = Ka loli i loko ka ikaika mechanical, ΔEK = Ka loli o ka ikehu kinetic, ΔEP = Ka loli o ka ikehu hiki.

ʻO ka loli i loko ikehu kinetic :

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

ʻO ka loli i loko ikehu hiki :

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

Ka hana i hana ʻia e ka mana o ka hakakā kinetic:

W_nc = – f_k s = – (3.2 m)(10) = – 32 m

Hōʻike ka hōʻailona minus he maikaʻi ʻole ka hana i hana ʻia e ka ikaika o ka friction kinetic ma ka poloka.

E hoʻoholo i ka wikiwiki hope loa (v_t):

W_nc = ΔEK + ΔEP

– 32 m = 1/2 mv_t² - 60 ka m

– 32 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

2.

Heʻe iho kahi poloka ma luna o kahi mokulele hilig me ka friction. ʻO ka wikiwiki hope loa o ka poloka i kona pā ʻana i ka honua he 10 m/s²Inā he 2 N ka ikaika kuʻi a he 10 m/s ka wikiwiki ma muli o ke koʻikoʻi²He aha ke kiʻekiʻe o h?

ʻIke ʻia:

Ka nuipa o ka poloka (m) = 1 kg

Ka wikiwiki mua (v_o) = 0 (poloka mua i ka wā hoʻomaha)

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

Ke kiʻekiʻe mua (h_o) = h

Ke kiʻekiʻe hope loa (h_t) = 0

Ka ikaika o ka haʻalulu kinetic (f_k) = 2 N

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

Makemake ʻia: kiʻekiʻe (h)

Lōlā:

Hana ʻia ka hana e ka ikaika o ka friction kinetic:

W_nc = – f_k d = – (2)(15) = – 30

Hōʻike ka hōʻailona minus he maikaʻi ʻole ka hana i hana ʻia e ka ikaika o ka friction kinetic ma ka poloka.

Ka loli 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 o ka ikehu hiki:

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

ʻO ke kaulike o ke kumumanaʻo ikehu hana-mekanika:

W_nc = ΔEK + ΔEP

– 30 = 50 – 10 hola

10 h = 50 + 30

10 hola = 80

h = 80/10

h = 8 mika

1. He aha ke kumumanaʻo o ka hana-ikehu?
   • pane mai: ʻŌlelo ke kumumanaʻo hana-ikehu e like ka hana i hana ʻia ma kahi mea me ka loli o kona ikehu kinetic. Ma ke ʻano makemakika, $W=\Delta KE$, kahi $W$ ua pau ka hana a $\Delta KE$ ʻo ia ka loli o ka ikehu kinetic.
2. Pehea ka ʻokoʻa o ka mana nonconservative mai ka mana conservative?
   • pane mai: ʻO ka ikaika nonconservative, e like me ka friction, e hopena i ka nalowale o ka ikehu mechanical mai kahi ʻōnaehana, ma ke ʻano maʻamau o ka wela. I ka hoʻohālikelike ʻana, ʻo nā ikaika conservative, e like me ke umekaumaha a i ʻole ka ikaika puna, ʻaʻole e hoʻopau i ka ikehu mechanical akā hiki ke hoʻololi iā ia ma waena o ka ikehu hiki a me ka ikehu kinetic i loko o ka ʻōnaehana.
3. Pehea ka hopena o ka friction i ka hana i hana ʻia ma kahi mea e neʻe ana ma kahi mokulele hilig?
   • pane mai: Hana ka haʻihaʻi ma ke kuhikuhi kūʻē i ka neʻe ʻana o ka mea. ʻO ke ʻano kēia, hana ka haʻihaʻi i ka hana maikaʻi ʻole ma ka mea, e hōʻemi ana i kona ikehu kinetic a i ʻole e hoʻonui ana i ka nui o ka hana waho e pono ai e hoʻoneʻe iā ia i luna o ka piʻi.
4. No ke aha i loli ʻole ai ka ikehu hiki o kahi mea ma muli o nā mana nonconservative?
   • pane mai: Pili ka ikehu hiki ke hana ʻia me nā ikaika conservative, a pili kona loli i nā kūlana mua a me ka hope wale nō, ʻaʻole ma ke ala i hele ʻia. Hiki i nā ikaika nonconservative ke hoʻololi i ka ikehu kinetic o kahi mea akā ʻaʻohe ona ikehu hiki ke hana ʻia e pili ana.
5. Pehea e hoʻohuli ai ke kihi o ka hili i ka neʻe ʻana o kahi mea ma luna o kahi mokulele hili me ka friction?
   • pane mai: ʻO ke kiʻekiʻe o ke kihi o ka ʻūlū ʻana, ʻo ka nui o ka ʻāpana o ka ikaika umekaumaha e hana like ana me ka mokulele. ʻO kēia ka mea e paʻakikī ai ke hoʻomaha a neʻe paha i luna o ka mokulele, a maʻalahi hoʻi e hoʻolalelale i lalo o ka mokulele. Hana ka haʻalulu e kūʻē i kēia neʻe ʻana, akā lilo kona hopena i mea liʻiliʻi i ka piʻi ʻana o ke kihi.
6. No ke aha ʻaʻole e wikiwiki mau nā mea ma kahi mokulele i hoʻokiʻekiʻe ʻia me ka friction?
   • pane mai: Ma muli o ke alo o ka friction, i ka neʻe ʻana o ka mea, ua hoʻololi ʻia kekahi o ka ikehu hiki ke umekaumaha i wela. I ka hopena, e kaulike ʻia ka ikaika ma muli o ka umekaumaha e kūlike ana me ka mokulele e ka ikaika frictional, a e neʻe ka mea me ka wikiwiki mau a i ʻole e hoʻomaha.
7. Hiki ke hoʻihoʻi ʻia ka hana i hana ʻia e ka mana kūʻokoʻa?
   • pane mai: ʻO ka hana i hana ʻia e nā mana nonconservative e hoʻololi pinepine ʻia i nā ʻano ikehu e like me ka wela, kahi mea paʻakikī ke hoʻololi hou i ikehu mechanical pono. I ka hapa nui o nā hiʻohiʻona kūpono, ua manaʻo ʻia kēia ikehu he "nalowale" i ka ʻōnaehana.
8. He aha ka mea e hoʻoholo ai i ka nui o ka ikaika frictional ma kahi mokulele inclined?
   • pane mai: Hoʻoholo ʻia ka ikaika frictional ma kahi mokulele inclined e ka ikaika maʻamau (perpendicular) a me ke coefficient o ka friction ma waena o nā ʻili. Hāʻawi ʻia e ffrictionʻO=μ×fnormalʻO, kahi $\mu$ ʻo ia ke koina o ka friction.
9. No ke aha i wehewehe ʻia ai ka ikehu hiki ke loaʻa he ʻole ma kekahi mau kiko kuhikuhi?
   • pane mai: He ana pili ka ikehu hiki. Ma ka wehewehe ʻana i kahi kiko kuhikuhi kahi he ʻole ka ikehu hiki, hāʻawi ia i kahi kumu kūlike no ka helu ʻana i nā loli i ka ikehu hiki no nā kūlana like ʻole e pili ana i kēlā kuhikuhi.
10. Pehea e loli ai ka neʻe ʻana o kahi mea ma luna o kahi mokulele hiʻona inā ʻaʻohe friction?

• pane mai: Me ka ʻole o ka friction, ʻo ka ikaika wale nō e hana ana ma ka mea ma ka mokulele ʻo ia ka ʻāpana o ke umekaumaha e like me ke kūlou ʻana. ʻO ka hopena, e wikiwiki ka mea i lalo o ka mokulele ma muli wale nō o kēia ikaika a ʻaʻole e hiki i kahi wikiwiki mau ke ʻole e hana ʻia e kekahi ikaika waho ʻē aʻe.