Nā nīnau hoʻohālike e pili ana i ke kānāwai o ka mālama ʻana i ka ikehu mechanical

16 mau laʻana o nā nīnau ma ke kānāwai o ka mālama ʻana i ka ikehu mīkini

ʻO ke kānāwai o ka mālama ʻana i ka ikehu mechanical i ka neʻe hāʻule manuahi

1. Hāʻule kūʻokoʻa kahi niu me ke kaumaha o 2 kg mai ke kiʻekiʻe o 6 mika. ʻO ka ikehu kinetic o ka niu i kona hiki ʻana i ka lepo he… g = 10 m/s²
Pahana
Ua ʻike ʻia :
Ka nuipa o ka niu (m) = 2 kg
Kiʻekiʻe (h) = 6 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic (EK)
Pane :

Ikehu mīkini mua
Inā hāʻule manuahi kahi mea, ʻaʻohe ona wikiwiki mua. No ka mea, ʻaʻohe wikiwiki mua, ʻaʻohe ikehu kinetic mua. I ka wā mua, aia ke kiʻekiʻe o ka mea i 6 mika, no laila, ʻoiaʻiʻo, loaʻa i ka mea ka ikehu hiki ke hoʻopaʻa ʻia i ka umekaumaha mua. No laila, ʻo ka ikehu mechanical mua (EM)_o) ʻo ia ka ikehu hiki ke hoʻopaʻa ʻia ka umekaumaha (EP).
EM_o = EP = mgh = (2)(10)(6) = 120 Joules

Ikehu mīkini hope loa
Ke neʻe i lalo, emi ke kiʻekiʻe o kahi mea, no laila e emi ana kona ikehu hiki ke umekaumaha. ʻAʻole nalowale ka ikehu hiki ke umekaumaha akā ua hoʻololi ʻia i ikehu kinetic. Ke hiki i ka honua, ua like ke kiʻekiʻe o ka mea me ke kiʻekiʻe o ka honua (h = 0), no laila ʻo kona ikehu hiki ke umekaumaha he ʻole (h = 0, no laila EP = mgh = 0). Hoʻololi ʻia nā ikehu hiki ke umekaumaha a pau i ikehu kinetic. No laila, ʻo ka ikehu mechanical hope loa (EM)_t) ʻo ia ka ikehu kinetic (EK).
EM_t = EK = ½ mv²

Ke kānāwai o ka mālama ʻana i ka ikehu mechanical :
Ikehu mīkini mua = ikehu mīkini hope loa
EM_o = EM_t
EP = EK
120 = EK
ʻO ka ikehu kinetic o ka niu ke hiki i ka lepo he 100 Joules.

2. He pōpō me ke kaumaha o 2 kg hāʻule manuahi mai ke kūlana A e like me ka mea i hōʻike ʻia ma ke kiʻi. (g = 10 ms^-2). I ka hiki ʻana i ke kiko B, ua like ka ikehu kinetic me 2 manawa o ka ikehu hiki, no laila ke kiʻekiʻe o ke kiko B mai ka honua mai…

A. 80 m
B. 70 m
C. 60 m
D. 40 m
E. 30 m

Pahana
Ua ʻike ʻia :
Ka nuipa o ka pōpō (m) = 2 kg
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms^-2
Kiʻekiʻe A (h)_A) = 90 mika
Ua nīnau ʻia Kiʻekiʻe B (h)_B)
Pane :

Ketika bola tiba di titik B, energi kinetik bola di titik B sama dengan 2 kali energi potensial gravitasi bola di titik B.
EK = 2 EP
½ mv² = 2 mg/h_B
½ v² = 2 gh_B
v² = 2(2)(10) hola_B
v² = 40 hola_B
Hītū ka wikiwiki (v) ka pōpō i kona hiki ʻana i kahi B ma hope o ka hāʻule ʻana mai kahi A.
v² = 2 gh = 2(10)(90–h_B) = 20(90–h_B)
Hoʻololi v² ma ka hoohalike ma luna me v² ma kēia kaulike.
v² = 40 hola_B
20(90–h)_B) = 40 hola_B
1800-20 h_B = 40 hola_B
1800 = 40 hola_B + 20 hola_B
1800 = 60 hola_B
h_B = 1800/60
h_B = 30 mika
ʻO ka pane pololei ʻo E.

3. Hāʻule kūʻokoʻa kahi mea me ke kaumaha o 1 kg mai luna mai o kahi hale papa he 80 mika ke kiʻekiʻe. Inā hoʻowahāwahā ʻia ka friction me ka ea a ʻo ka wikiwiki ma muli o ke umekaumaha (g) he 10 m/s² No laila, ʻo ka ikehu kinetic o ka mea i kona hiki ʻana i ka ʻili honua he...
Pahana
Ua ʻike ʻia :
Nuipaʻa (m) = 1 kg
Kiʻekiʻe (h) = 80 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic (EK) o kahi mea ke hiki ka mea i ka ʻili honua
Pane :
Hāʻule manuahi nā mea no laila ʻaʻohe wikiwiki mua o ka mea. No laila, i ka wā e kiʻekiʻe ai he 80 mika, loaʻa i ka mea ka ikehu hiki ke hoʻopaʻa ʻia akā ʻaʻohe ikehu kinetic o ka mea (v = 0 no laila EK = ½ mv² = 0). No laila, ʻo ka ikehu mechanical mua (EM)_o) = ikehu hiki ke hoʻonui ʻia ka umekaumaha (EP).

EM _o = EP = mgh = (1)(10)(80) = 800 Joules

I ka wā hāʻule manuahi, hoʻololi ʻia ka ikehu hiki ke umekaumaha i ikehu kinetic. Ke paʻi kahi mea i ka honua, hoʻololi ʻia kona ikehu hiki ke umekaumaha āpau i ikehu kinetic. No laila, ke hiki i ka honua, loaʻa i ka mea ka ikehu kinetic akā ʻaʻohe ikehu hiki ke umekaumaha (h = 0, no laila EP = mgh = 0). No laila, ʻo ka ikehu mechanical hope loa (EM _t ) = ikehu kinetic (EK)

ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu kinetic hope loa.
EM_o = EM_t
EP = EK
800 = EK
ʻO ka ikehu kinetic (EK) o ka mea i kona hiki ʻana i ka honua he 800 Joules.

4. Hāʻule kūʻokoʻa kahi mea mai kahi kiʻekiʻe o 10 mika ma luna o ka honua. Inā he 4 kg ke kaumaha o ka mea a ʻo ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms ^–2 , a laila ʻo ka ikehu kinetic a me ka wikiwiki o ka mea ma ke kiʻekiʻe o 5 mika ma luna o ka honua…

Pahana
Ua ʻike ʻia :
Ka loli o ke kiʻekiʻe (h) = 10 – 5 = 5 mika
Nuipaʻa (m) = 4 kg
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic o kahi mea ma ke kiʻekiʻe o 5 mika
Pane :
(a) Ka ikehu kinetic o kahi mea ma ke kiʻekiʻe o 5 mika
Ikehu mīkini mua (EM)_o) = ikehu hiki ke hoʻonui ʻia ka umekaumaha (EP)
EM_o = EP = mgh = (4)(10)(5) = 200 Joules
Ikehu mīkini hope loa (EM)_t) = ikehu kinetic (EK)
EM_t = EK
ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu mechanical hope loa.
EM_o = EM_t
200 = EK
ʻO ka ikehu kinetic o kahi mea ma ke kiʻekiʻe o 5 mika ma luna o ka honua he 200 Joules.

(b) Ka wikiwiki o ka mea ma ke kiʻekiʻe o 5 mika
Ikehu mīkini mua (EM)_o) = ikehu mīkini hope loa (EM)_t)
EP = EK
200 = ½ mv²
2(200) / 4 = v²
100 = v²
v = √100
v = 10 mika/kekona
ʻO ka wikiwiki o ka mea he 10 mika/kekona

5. Hāʻule kūʻokoʻa kahi hua mango mai ke kiʻekiʻe o 2 mika. Inā g = 10 ms^-2, e helu i ka wikiwiki o ka mango ma mua pono o kona pā ʻana i ka honua me ka hoʻohana ʻana i ke kānāwai o ka ikehu mechanical.
Pahana
Ua ʻike ʻia :
Kiʻekiʻe (h) = 2 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ka wikiwiki o ka mango ma mua pono o kona kuʻi ʻana i ka honua (v)
Pane :
Ikehu mīkini mua (EM)_o) = ikehu hiki ke hoʻonui ʻia ka umekaumaha (EP)
EM_o = EP = mgh = m (10)(2) = 20 m
Ikehu mīkini hope loa (EM)_t) = ikehu kinetic (EK)
EM_t = EK = ½ mv²
ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu mechanical hope loa.
EM_o = EM_t
20 m = ½ mv²
20 = ½ v²
2(20) = v²
40 = v²
v = √40 = √(4)(10) = 2√10 mika/kekona
ʻO ka wikiwiki o ka mango ma mua pono o kona pā ʻana i ka honua he 2√10 mika/kekona.
He mea nui e hoʻomaopopo i kā mākou mau helu ʻana, hoʻowahāwahā mākou i ka haʻalulu ea. ʻO ka ʻoiaʻiʻo, inā hāʻule wale kekahi mea ma luna o ka ʻili o ka Honua, hoʻopilikia pū ka haʻalulu ea i kona neʻe ʻana, e hopena ana i ka wikiwiki haʻahaʻa ma mua o ka helu ʻana ma luna.

ʻO ke kānāwai o ka mālama ʻana i ka ikehu mechanical i ka neʻe ʻana i luna a i lalo

6. Ua kiola ʻia kekahi mea me ke kaumaha o 1 kg i lalo me ka wikiwiki mua o 2 m/s mai ka lihi o kahi hale he 40 mika ke kiʻekiʻe. ʻO ka ikehu kinetic o ka mea ke kiʻekiʻe ia he 10 mika ma luna o ka honua he… g = 10 m/s ²

Pahana
Ua ʻike ʻia :
Ka nuipa o ka mea (m) = 1 kg
Ka wikiwiki mua (v_o) = 2 m/s
Ka loli o ke kiʻekiʻe = 40 – 10 = 30 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic o kahi mea ma ke kiʻekiʻe o 10 mika ma luna o ka ʻilikai honua
Pane :

Ikehu mīkini mua
I ka wā mua, loaʻa i ka mea ka ikehu hiki ke umekaumaha a me ka ikehu kinetic.
Ka ikehu hiki ke hoʻomaka ʻia o ka umekaumaha (EP) = mgh = (1)(10)(30) = 300 Joules
Ikehu kinetic mua (EK) = ½ mv_o² = ½ (1)(2)² = ½ (4) = 2 Joule
No laila, ʻo ka ikehu mechanical mua = ka ikehu hiki ke umekaumaha mua + ka ikehu kinetic mua = 300 + 2 = 302 Joules.

Ikehu mīkini hope loa
I ka neʻe ʻana o kahi mea i lalo, e emi ana kona kiʻekiʻe, a pēlā e hōʻemi ai i kona ikehu hiki ke hoʻopaʻa ʻia. Hoʻololi ʻia kēia ikehu hiki ke hoʻopaʻa ʻia i ikehu kinetic. Ma hope o ka neʻe ʻana i 30 mika, a i ʻole ke kiʻekiʻe o ka mea he 10 mika ma luna o ka honua, hoʻololi ʻia kona ikehu hiki ke hoʻopaʻa ʻia a pau i ikehu kinetic.
No laila, ka ikehu mechanical hope loa = ka ikehu kinetic hope loa = ka ikehu hiki ke umekaumaha mua + ka ikehu kinetic mua = 300 + 2 = 302 Joules.

7. Ua kiola ʻia kahi mea me ke kaumaha o 1 kg i luna me ka wikiwiki mua o 10 m/s. E hoʻoholo (a) ka ikehu hiki ke hoʻopaʻa ʻia ma ke kiko kiʻekiʻe loa (b) ke kiko kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa i hiki i ka mea… g = 10 m/s²
Pahana
Ua ʻike ʻia :
Ka nuipa o ka mea (m) = 1 kg
Ka wikiwiki mua (v_o) = 10 m/s
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ka ikehu hiki ke hoʻouluulu ʻia ma ke kiko kiʻekiʻe loa a me ke kiko haʻahaʻa loa
Pane :
(a) Ka ikehu hiki ke hoʻouluulu ʻia ma kahi kiʻekiʻe loa
Ikehu mīkini mua
I ka wā mua, loaʻa i ka mea ka ikehu kinetic akā ʻaʻohe ona ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha. Ikehu mechanical mua = ikehu kinetic mua (EK) = ½ mv_o² = ½ (1)(10)² = ½ (100) = 50 Joules.
 
Ikehu mīkini hope loa
Ma hope o ka neʻe ʻana i luna, piʻi aʻe ke kiʻekiʻe o ka mea, a laila e hoʻonui ai i kona ikehu hiki ke umekaumaha. ʻAʻole kū koke mai kēia ikehu hiki ke umekaumaha akā ua loaʻa mai ia mai ka ikehu kinetic. Ma kona kiʻekiʻe loa a i ʻole ke kiko kiʻekiʻe loa, ua hoʻomaha ka mea no kekahi manawa ma mua o ka hoʻohuli ʻana i ke kuhikuhi. No ka mea ua hoʻomaha no kekahi manawa, ʻo kona wikiwiki he ʻole, a ʻo kona ikehu kinetic he ʻole nō hoʻi. Hoʻololi ʻia nā ikehu kinetic a pau i ikehu hiki ke umekaumaha.
Ikehu mīkini hope loa = ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha (EP)

Ke kānāwai o ka mālama ʻana i ka ikehu mechanical:
Ikehu mīkini mua = ikehu mīkini hope loa
EK = EP
50 = EP
ʻO ka ikehu hiki ke hoʻoulu ʻia e ka umekaumaha he 50 Joules.

(b) Kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa
EP = mgh
50 = (1)(10) hola
50 = 10 hola
h = 50 / 10 = 5 mika
ʻO ke kiko kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa i hiki i kahi mea he 5 mika mai ka ʻili honua.

 

ʻO ke kānāwai o ka mālama ʻana i ka ikehu mechanical i ka neʻe ʻana ma kahi mokulele inclined

8. Mai kahi kūlana hoʻomaha, heʻe kahi poloka me ka ʻole o ka friction ma kahi mokulele hilig. ʻO ka wikiwiki o ka poloka i kona hiki ʻana i ka lalo o ka mokulele hilig he… g = 10 m/s²
Pahana
Ua ʻike ʻia :
Kiʻekiʻe (h) = 8 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ka wikiwiki (v) o ka poloka i kona hiki ʻana i ka lalo o ka mokulele inclined
Pane :
Ke kiʻekiʻe o 8 mika, loaʻa i ka poloka ka ikehu hiki ke hoʻopaʻa ʻia akā ʻaʻohe ikehu kinetic no ka mea ʻaʻole i neʻe. No laila, ʻo ka ikehu mechanical mua o ka poloka ka ikehu hiki ke hoʻopaʻa ʻia.
Ikehu mīkini mua (EM)_o) = ikehu hiki ke hoʻonui ʻia ka umekaumaha (EP)
EM_o = EP = mgh = m (10)(8) = 80 m
I ka hoʻomaka ʻana o ka poloka e neʻe i lalo, hoʻomaka kona ikehu hiki ke umekaumaha e hoʻololi i ka ikehu kinetic. Ke hiki i ka lalo o ke kiʻekiʻe, hoʻololi kona ikehu hiki ke umekaumaha a pau i ka ikehu kinetic. No laila, ʻo ka ikehu mechanical hope loa o ka poloka he ikehu kinetic.
Ikehu mīkini hope loa (EM)_t) = ikehu kinetic (EK)
EM_t = EK = ½ mv²
ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu mechanical hope loa.
EM_o = EM_t
80 m = ½ mv²
80 = ½ v²
160 = v²
v = √160 = √(16)(10) = 4√10 m/s
ʻO ka wikiwiki o ka poloka ma ka lalo o ka mokulele hilig he 4√10 mika/kekona.

9. Ua hoʻokuʻu ʻia kahi mea me ke kaumaha o 1 kg, i ka wā hoʻomaha mua, mai luna mai o kahi mokulele hilig laumania he 8 mika ka lōʻihi. E hoʻoholo i ka ikehu kinetic ma hope o ka paheʻe ʻana o ka mea ma luna o ka mokulele hilig no 5 mika…. (g = 10 m/s²)
Pahana
Ua ʻike ʻia :
Ka nuipa o ka mea (m) = 0,2 kg
ʻO ka lōʻihi o ke hypotenuse a ka mea e hele ai = 5 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic (EK) o kahi mea ma hope o ka paheʻe ʻana he 5 mika
Pane :
ʻO ka hana mua i ka hoʻoponopono ʻana i kēia pilikia, ʻo ia ka helu ʻana i ka loli o ke kiʻekiʻe o ka mea ma hope o ka paheʻe ʻana o ka mea ma luna o kahi mokulele hilig no 5 mika.
hewa 30^o = ka lōʻihi o ka ʻaoʻao kū pololei / ka lōʻihi o ka hypotenuse
0,5 = ka lōʻihi o ka ʻaoʻao kū pololei / 5
ʻO ka lōʻihi o ka ʻaoʻao kū pololei = (0,5)(5) = 2,5 mika
ʻO ka loli o ke kiʻekiʻe o ka mea he 2,5 mika.

Ikehu mīkini mua (EM)_o) = ikehu hiki ke hoʻonui ʻia ka umekaumaha (EP)
EM_o = EP = mgh = (1)(10)(2,5) = 25 Joules
Ikehu mīkini hope loa (EM)_t) = ikehu kinetic (EK)
EM_t = EK
ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu mechanical hope loa.
EM_o = EM_t
25 = EK
ʻO ka ikehu kinetic o ka mea ma hope o ka paheʻe ʻana o ka mea i 5 mika he 25 Joules.

 

ʻO ke kānāwai o ka mālama ʻana i ka ikehu mechanical i ka neʻe ʻana i loko o kahi mokulele piʻo

10. Heheʻe kahi mea me ke kaumaha o 1 kg me ka ʻole o ka friction mai ke kiʻekiʻe o 5 mika me ka ʻole o ka wikiwiki mua. ʻO ka ikehu kinetic a me ka wikiwiki o ka mea ma ke kiko haʻahaʻa loa he… g = 10 m/s²
Pahana
Ua ʻike ʻia :
Ka nuipa o ka mea (m) = 1 kg
Ka loli o ke kiʻekiʻe (h) = 5 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic (EK) a me ka wikiwiki (v) o ka mea ma ke kiko haʻahaʻa loa
Pane :

(a) Ikehu kinetic o kahi mea ma kona wahi haʻahaʻa loa
I ke kiʻekiʻe o 5 mika a ʻaʻole i hoʻomaka e neʻe, loaʻa i ka mea ka ikehu hiki ke umekaumaha akā ʻaʻohe ikehu kinetic no ka mea e hoʻomaha ana. No laila, ʻo ka ikehu mechanical mua ma mua o ka hoʻomaka ʻana o ka mea e neʻe, ʻo ia ka ikehu hiki ke umekaumaha. Ke hoʻomaka ka mea e neʻe i lalo, hoʻomaka ka ikehu hiki ke umekaumaha e hoʻololi i ka ikehu kinetic. Ke hiki i ka wahi haʻahaʻa loa, hoʻololi nā ikehu hiki ke umekaumaha āpau i ka ikehu kinetic. No laila, ʻo ka ikehu mechanical hope loa, ʻo ia ka ikehu kinetic.
Ikehu mechanical mua = ikehu hiki ke hoʻopaʻa ʻia
EM_o = EP = mgh = (1)(10)(5) = 50 Joules
Ikehu mīkini hope loa = ikehu kinetic
EM_t = EK = ½ mv_t²
ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu mechanical hope loa..
EM_o = EM_t
EP = EK
50 = EK
ʻO ka ikehu kinetic (EK) ma ke kiko haʻahaʻa loa he 50 Joules.

(b) Ka wikiwiki o ka mea ma kahi haʻahaʻa loa
ʻO ke ala mua:
Ke kānāwai o ka mālama ʻana i ka ikehu mechanical:
Ikehu mīkini mua (EM)_o) = ikehu mīkini hope loa (EM)_t)
Ikehu hiki ke hoʻouluulu ʻia (EP) = ikehu kinetic (EK)
50 = ½ mv²
2(50) / m = v²
100 / 1 = v²
100 = v²
v = √100
v = 10 mika/kekona
 
ʻO ke ala ʻelua:
Ke kānāwai o ka mālama ʻana i ka ikehu mechanical :
Ikehu mīkini mua (EM)_o) = ikehu mīkini hope loa (EM)_t)
Ikehu hiki ke hoʻouluulu ʻia (EP) = ikehu kinetic (EK)
mgh = ½ mv²
gh = ½ v²
2 gh = v²
2(10)(5) = v²
100 = v²
v = √100
v = 10 mika/kekona
ʻO ka wikiwiki o ka mea ma kahi haʻahaʻa loa he 10 m/s.

11. He mea me ke kaumaha o 2 kg i hoʻomaha mua ʻia, e paheʻe ana me ka ʻole o ka friction mai ke kiʻekiʻe o 10 mika ma luna o ka honua. ʻO ka ikehu kinetic a me ka wikiwiki o ka mea ma ke kiʻekiʻe o 2 mika ma luna o ka honua he… g = 10 m/s²
Pahana
Ua ʻike ʻia :
Ka nuipa o ka mea (m) = 2 kg
Ka loli o ke kiʻekiʻe (h) = 10 – 2 = 8 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ka ikehu kinetic (EK) a me ka wikiwiki (v) o ka mea ma ke kiʻekiʻe o 2 mika ma luna o ka ʻili honua.
Pane :
Ua like ke ʻano o ka hoʻonā ʻana i kēia pilikia me ka hoʻonā ʻana i ka pilikia ma mua.

(a) Ka ikehu kinetic o kahi mea ma ke kiʻekiʻe o 2 mika
Ikehu mechanical mua = ikehu hiki ke hoʻopaʻa ʻia
EM_o = EP = mgh = (2)(10)(8) = 160 Joules
Ikehu mīkini hope loa = ikehu kinetic
EM_t = EK = ½ mv_t²
ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical mua me ka ikehu mechanical hope loa..
EM_o = EM_t
EP = EK
160 = EK
ʻO ka ikehu kinetic (EK) ma ke kiʻekiʻe o 2 mika he 160 Joules.

(b) Ka wikiwiki o ka mea ma kahi haʻahaʻa loa
ʻO ke ala mua:
Ke kānāwai o ka mālama ʻana i ka ikehu mechanical:
Ikehu mīkini mua (EM)_o) = ikehu mīkini hope loa (EM)_t)
Ikehu hiki ke hoʻouluulu ʻia (EP) = ikehu kinetic (EK)
160 = ½ mv²
160 = ½ (2) v²
160 = v²
v = √160 = √(16)(10) = 4√10 mika/kekona

ʻO ke ala ʻelua:
Ke kānāwai o ka mālama ʻana i ka ikehu mechanical :
Ikehu mīkini mua (EM)_o) = ikehu mīkini hope loa (EM)_t)
Ikehu hiki ke hoʻouluulu ʻia (EP) = ikehu kinetic (EK)
mgh = ½ mv²
gh = ½ v²
2 gh = v²
2(10)(8) = v²
160 = v²
v = √160 = √(16)(10) = 4√10 mika/kekona
ʻO ka wikiwiki o kahi mea ma ke kiʻekiʻe o 2 mika he 4√10 mika/kekona.

12. I ka hoʻoilo, ma Suedena, mālama ʻia nā hoʻokūkū heʻe hau ma nā mauna. Paheʻe nā mea heʻe hau mai ke kiʻekiʻe A e like me ka mea i hōʻike ʻia ma ke kiʻi 2.

Inā ʻo ka wikiwiki mua o ka mea heʻe hau = ʻole, a ʻo ka wikiwiki ma muli o ke koʻikoʻi = 10 ms ^-2 , a laila ʻo ka wikiwiki o ka mea heʻe hau ma ke kiʻekiʻe B he…

A. √2 ms ^-1

B. 5 √2 ms ^-1

C. 10 √2 ms ^-1

D. 20 √2 ms ^-1

E. 25 √2 ms ^-1

Pahana

Ua ʻike ʻia:

Ka wikiwiki mua (v _o ) = 0

Ke kiʻekiʻe mua (h _o ) = 50 m – 10 m = 40 m

Kiʻekiʻe hope loa (h _t ) = 0

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

Nīnau: Ka wikiwiki hope loa ( _vt )

Pane:

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:

Δ EP = mg (h _t – h _o ) = m (10)(0-40) = m (10)(-40) = – 400 m

E helu i ka wikiwiki hope loa (vt ₎ me ka hoʻohana ʻana i ke ʻano hana no ke kānāwai o ka mālama ʻana i ka ikehu mechanical:

0 = Δ EK + Δ EP

0 = 1/2 mv _t ² – 400 m

1/2 mv _t ² = 400 m

1/2 v _t ² = 400

v _t ² = 2(400)

vt ₌ √(400)(2)

vt = 20√2 m/ _s

ʻO D ka pane pololei.

13. Ua hoʻokuʻu ʻia kahi pōpō me ke kaumaha o 1 kg a paheʻe mai ke kūlana A a i ke kūlana C ma ke ala ʻōniʻoniʻo e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. Inā ka wikiwiki ma muli o ke koʻikoʻi = 10 ms^-2, a laila ʻo ka ikehu kinetic (Ek) o ka pōpō i kona wā ma ke kiko C ʻo ia….

A. 25,0 joules
B. 22,5 joules
C. 20,0 joules
D. 12,5 joules
E. 7,5 joules

Pahana
Ua ʻike ʻia:
Ka nuipa o ka pōpō (m) = 1 kg
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ka loli ʻana o ke kiʻekiʻe (h) = 0,75 m

Ka ikehu hiki ke hoʻomaka ʻia o ka umekaumaha (EP)_o) = mgh = (1)(10)(0,75) = 7,5 Joules
Ikehu kinetic mua (EK)_o) = ½ mv_o² = ½ m (0²) = 0
Ka ikehu hiki ke hoʻopaʻa ʻia o ka umekaumaha hope loa (EP)_t) = mgh = mg (0) = 0
Nīnau: Ikehu kinetic (EK) o ka pōpō i kona wā ma ke kiko C
Pane:

ʻŌlelo ke kānāwai o ka mālama ʻana i ka ikehu mechanical ua like ka ikehu mechanical o ka pōpō ma kona kūlana mua me kona ikehu mechanical hope loa ma kona kūlana hope loa. Ma kēia pilikia, ʻo ke kūlana mua ke kūlana o ka pōpō ma mua o ka hoʻokuʻu ʻia ʻana, a ʻo ke kūlana hope loa ʻo ia ke kiko C.

Ikehu mīkini mua (EM)_o) = Ikehu mīkini hope loa (EM)_t)
Ka ikehu hiki ke hoʻomaka ʻia o ka umekaumaha (EP)_o) + Ikehu kinetic mua (EK)_o) = Ka ikehu hiki ke hoʻopaʻa ʻia ka umekaumaha hope loa (EP)_t) + Ikehu kinetic hope loa (EK)_t)
7,5 Joules + 0 = 0 + EK_t
7,5 Joules = EK_t
ʻO ka ikehu kinetic (EK) o ka pōpō ma ke kiko C he 7,5 Joules.
ʻO ka pane pololei ʻo E.

14. Hoʻokuʻu ʻia ka pōpō A me ke kaumaha o 2 kg a hele ma ke ala laumania e like me ka mea i hōʻike ʻia ma ke kiʻi. Inā he 10 m/s ka wikiwiki ma muli o ke koʻikoʻi^-2, ka ikehu kinetic o ka pōpō i ka wā ma ka ʻaoʻao B ʻo ia hoʻi….

A. 4 joules
B. 8 joules
C. 10 joules
D. 12 joules
E. 24 joules

Pahana
Ua ʻike ʻia:
Ka nuipa o ka pōpō (m) = 2 kg
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ka loli o ke kiʻekiʻe (h) = 120 kenimika = 1,2 mika

Ka ikehu hiki ke hoʻomaka ʻia o ka umekaumaha (EP)_o) = mgh = (2)(10)(1,2) = 24 Joules
Ikehu kinetic mua (EK)_o) = ½ mv_o² = ½ m (0²) = 0
Ka ikehu hiki ke hoʻopaʻa ʻia o ka umekaumaha hope loa (EP)_t) = mgh = mg (0) = 0
Nīnau: ʻO ka ikehu kinetic o ka pōpō ma B
Pane:
Ua like ka ikehu mechanical o ka pōpō ma ke kiko A (ka ikehu mechanical mua) me ka ikehu mechanical o ka pōpō ma ke kiko B (ka ikehu mechanical hope loa).

Ikehu mīkini mua (EM)_o) = Ikehu mīkini hope loa (EM)_t)
Ka ikehu hiki ke hoʻomaka ʻia o ka umekaumaha (EP)_o) + Ikehu kinetic mua (EK)_o) = Ka ikehu hiki ke hoʻopaʻa ʻia ka umekaumaha hope loa (EP)_t) + Ikehu kinetic hope loa (EK)_t)
24 Joules + 0 = 0 + EK_t
EK_t = 24 Joule
ʻO ka ikehu kinetic (EK) o ka pōpō ma ke kiko C he 24 Joules.
ʻO ka pane pololei ʻo E.

 

ʻO ke kānāwai o ka mālama ʻana i ka ikehu mechanical i ka neʻe parabolic

15. Ua kīkē ʻia kahi pōpō me ke kaumaha o 0,1 kg i ka wikiwiki o 10 m/s. Inā he 30 ke kihi o ke kiʻekiʻe^o a ʻo ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s² , e hoʻoholo i (a) ka ikehu hiki ke hoʻopaʻa ʻia o ka pōpō ma ke kiko kiʻekiʻe loa (b) ke kiko kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa.
Pahana
Ua ʻike ʻia :
Ka nuipa o ka pōpō (m) = 0,1 kg
Ka wikiwiki mua (v_o) = 10 m/s
Ke kihi kiʻekiʻe = 30^o
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ua nīnau ʻia : ikehu kinetic (EK) o ka pōpō ma ke kiko kiʻekiʻe loa
Pane :

(a) Ka ikehu hiki ke hoʻopaʻa ʻia o ka pōpō ma kahi kiʻekiʻe loa
He parabola ke ala o ka pōpō e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo.
E helu mua i ka ʻāpana wikiwiki mua ma ke kuhikuhi ʻaoʻao (v_ox) a me ke kū pololei (v_oy).
Inā like ke ala neʻe parabolic me ke kiʻi ma luna, a laila ua kālailai ʻia ka neʻe ʻana ma ke kuhikuhi ākea a i ʻole ka ʻaoʻao pae e like me kēia. neʻe laina like a ua kālailai ʻia ka neʻe ʻana ma ke kuhikuhi kū pololei e like me neʻe kū pololei i luna. I ka neʻe laina like, e mau ana ka wikiwiki i ka neʻe ʻana. I ka ʻaoʻao ʻē aʻe, i ka neʻe kū i luna, ke hiki ka mea i kona kiʻekiʻe loa a i ʻole ke kiko kiʻekiʻe loa, kū ia no kekahi manawa ma mua o ka hoʻohuli ʻana i ke kuhikuhi. No laila, ma ke kiko kiʻekiʻe loa, ʻo ka wikiwiki kū o ka mea he ʻole, akā ma ke kiko kiʻekiʻe loa, he wikiwiki ko ka mea he v._ox.

Ikehu mīkini mua
Ke hoʻomaka ka neʻe ʻana o ka pōpō, ua like kona kiʻekiʻe me ka papahele a i ʻole ka ʻili honua (h = 0), no laila ʻo kona ikehu hiki ke hoʻopaʻa ʻia he ʻole (h = 0, no laila EP = mgh = 0). I ka ʻaoʻao ʻē aʻe, ke hoʻomaka ka neʻe ʻana, loaʻa i ka pōpō ka wikiwiki mua loa, no laila ʻo kona ikehu kinetic ka nui loa. No laila, ʻo ka ikehu mechanical mua o ka pōpō he ikehu kinetic.
Ikehu mīkini mua (EM)_o) = ikehu kinetic (EK)
EM_o = EK = ½ mv_o² = ½ (0,1)(10)² = ½ (0,1)(100) = ½ (10) = 5 Joules

Ikehu mīkini hope loa
Ma hope o ka hoʻomaka ʻana e neʻe, piʻi aʻe ke kiʻekiʻe o ka pōpō, no laila e piʻi aʻe ana kona ikehu hiki ke hoʻopaʻa ʻia. Ke hiki i kona kiʻekiʻe loa, hiki i kona ikehu hiki ke hoʻopaʻa ʻia i kona waiwai nui loa. Pehea lā e pili ana i ka ikehu kinetic o ka pōpō? Ma kona wahi kiʻekiʻe loa, ʻo ka wikiwiki kū pololei (voy) o ka pōpō he ʻole, akā he wikiwiki ākea nō naʻe (vox).
Ikehu kinetic ma ke kiʻekiʻe loa :
EK = ½ mv_ox² = ½ (0,1)(5√3)² = ½ (0,1)((25)(3)) = ½ (0,1)(75) = 3,75 Joules

Ke kānāwai o ka mālama ʻana i ka ikehu mechanical:
Ikehu mīkini mua (EM)_o) = ikehu mīkini hope loa (EM)_t)
EK = EP + EK
5 = EP + 3,75
EP = 5 – 3,75 = 1,25 Joules
ʻO ka ikehu hiki ke hoʻohana ʻia me ke umekaumaha ma ke kiʻekiʻe loa he 1,25 Joules.
 
(b) Kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa
EP = mgh
1,25 = (0,1)(10) hola
1,25 = h
ʻO ke kiʻekiʻe loa he 1,25 mika.

16. Ua kiola ʻia kahi pōpō me ke kaumaha o 0,1 kg ma ka ʻaoʻao pālahalaha ma ka wikiwiki o 10 m/s mai ka lihi o kahi hale he 10 mika ke kiʻekiʻe. Inā ʻo ka wikiwiki ma muli o ke koʻikoʻi ma ia wahi he 10 m/s², a laila ʻo ka ikehu kinetic o ka pōpō i kona hiki ʻana i ka honua he….
Pahana
Ua ʻike ʻia :
Ka nuipa o ka pōpō (m) = 0,1 kg
Ka wikiwiki mua (v_o) = 10 m/s
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ka loli o ke kiʻekiʻe (h) = 10 – 2 = 8 mika
Ua nīnau ʻia : ikehu kinetic o ka pōpō ma ke kiʻekiʻe o 2 mika
Pane :
Ke kiʻekiʻe ka pōpō i 10 mika, loaʻa iā ia ka ikehu hiki ke umekaumaha. Hoʻomaka ka pōpō e neʻe ma hope o ka hoʻolei ʻia ʻana me ka wikiwiki mua o 10 m/s, no laila he ikehu kinetic nō hoʻi. No laila, ʻo ka ikehu mechanical mua o ka pōpō he ikehu hiki ke umekaumaha + ikehu kinetic.
Ka ikehu hiki ke hoʻomaka ʻia o ka umekaumaha (EP) = mgh = (0,1)(10)(10) = 10 Joules
Ikehu kinetic mua (EK) = ½ mv_o² = ½ (0,1)(10)² = ½ (0,1)(100) = ½ (10) = 5 Joules

I ka neʻe ʻana o ka pōpō i lalo, e emi ana kona kiʻekiʻe, a pēlā e hōʻemi ai i kona ikehu hiki ke hoʻokuʻu ʻia. Ke hiki i ka honua, ua like kona kiʻekiʻe me ke kiʻekiʻe o ka honua (h = 0), no laila ʻo kona ikehu hiki ke hoʻokuʻu ʻia he ʻole (h = 0, no laila EP = mgh = 0). Hoʻololi ʻia nā ikehu hiki ke hoʻokuʻu ʻia a pau i ikehu kinetic.
Ikehu kinetic hope loa = ikehu hiki ke hoʻokele umekaumaha mua + ikehu kinetic mua = 10 + 5 = 15 Joules