4 mau laʻana o nā hoʻonohonoho pūnāwai moʻo-parallel
1. ʻEkolu mau pūnāwai like, kēlā me kēia me kahi kūpaʻa elastic o 200 N/m, ua hoʻonohonoho ʻia ma ke ʻano moʻo a me ke ʻano like e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. Ua kau ʻia kahi kaumaha w mai ka ʻaoʻao haʻahaʻa o ka hui pūnāwai, e hoʻonui ana i ka lōʻihi o ka hui pūnāwai ma 1 cm. ʻO ke kaumaha o ke kaumaha w…
Pahana
Ua ʻike ʻia:
ʻO ke kūpaʻa o kēlā me kēia pūnāwai (k1 = k2 = k3) = 200 N/m
ʻO ka hoʻonui ʻia o ka lōʻihi o ka ʻōnaehana puna (x) = 1 cm = 0,01 mika
Nīnau ʻia: ke kaumaha o ka ukana (w)
Pane:
Helu mua mau puna hui pū ʻana.
Ua hoʻonohonoho like ʻia ka puna 1 a me ka puna 2. ʻO ke kūpaʻa puna like:
kp = k1 +k2 = 200 + 200 = 400 Newtons/mika
Nā pūnāwai pani hoʻonohonoho like (kp) a me ka pūnāwai 3 (k3) i hoʻonohonoho ʻia ma ke ʻano moʻo. ʻO ke kūpaʻa puna pani:
1/k = 1/kp + 1/k3 = 1/400 + 1/200 = 1/400 + 2/400 = 3/400
k = 400/3 Newton/mika
E helu i ke kaumaha o ka ukana me ka hoʻohana ʻana i ke ʻano hana Ke kānāwai o Hooke.
F = w = kx
w = (400/3)(0,01) = 4/3 Newtons
ʻO ke kaumaha o ka ukana he 4/3 Newtons
2. ʻEhā mau pūnāwai like me kēlā me kēia he 500 N/m mau, i hoʻonohonoho ʻia ma ke ʻano moʻo a me ke ʻano like. E hoʻoholo i ka hoʻonui ʻia o ka lōʻihi o ka ʻōnaehana pūnāwai ke hāʻawi ʻia kahi ukana o 20 Newtons.
Pahana
Ua ʻike ʻia:
ʻO ke kūpaʻa o kēlā me kēia pūnāwai (k1 = k2 = k3 = k4) = 500 N/m
Ka ikaika kaumaha (w) = 20 Newtons
Nīnau: hoʻonui ʻia ka lōʻihi o ka ʻōnaehana puna (x)
Pane:
E helu mua i ke kūpaʻa puna i hui pū ʻia.
Ua hoʻonohonoho like ʻia ka puna 1, ka puna 2 a me ka puna 3. ʻO ke kūpaʻa puna like:
kp = k1 +k2 +k3 = 500 + 500 + 500 = 1500 Newtons/mika
Nā pūnāwai pani hoʻonohonoho like (kp) a me ka pūnāwai 4 (k4) i hoʻonohonoho ʻia ma ke ʻano moʻo. ʻO ke kūpaʻa puna pani:
1/k = 1/kp + 1/k3 = 1/1500 + 1/500 = 1/1500 + 3/1500 = 4/1500
k = 1500/4 = 375 Newton/mika
E hoʻohana i ke kānāwai o Hooke e hoʻoholo ai i ka piʻi ʻana o ka lōʻihi o ka ʻōnaehana puna. ʻO ka piʻi ʻana o ka lōʻihi o ka ʻōnaehana puna:
x = F / k = w / k
x = 20 / 375
x = 0,05 mika
x = 5 kenimika
3. Ua hoʻonohonoho ʻia nā pūnāwai like ʻehā ma ke ʻano moʻo a me ke ʻano like e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. Ke hāʻawi ʻia kahi ukana o 20 Newtons, hoʻonui ka ʻōnaehana pūnāwai i ka lōʻihi ma 4 cm. E hoʻoholo (a) i ka hui mau o ka ʻōnaehana. nā pūnāwai moʻo-like (b) ke kūpaʻa o kēlā me kēia pūnāwai.
Pahana
Ua ʻike ʻia:
Ka ikaika kaumaha (w) = 20 Newtons
ʻO ka hoʻonui ʻia o ka lōʻihi o ka ʻōnaehana puna (x) = 4 cm = 0,04 mika
Pane:
(a) kūpaʻa i hui pū ʻia o ka ʻōnaehana puna
k = F / x = w / x
k = 20 / 0,04 = 500 Newtons/mika
(B) mau o kēlā me kēia pūnāwai
Ua like nā pūnāwai ʻehā i loaʻa i nā pūnāwai ʻehā ke kūpaʻa like. Inā pani ʻia nā pūnāwai 1, 2, a me 3 e hoʻokahi pūnāwai, e loaʻa nā pūnāwai ʻelua, ʻo ia hoʻi nā pūnāwai pani like (kp) a me ka pūnāwai 4 (k4). Ua hoʻonohonoho ʻia kēia mau pūnāwai ʻelua ma ke ʻano moʻo. ʻO ke ʻano hana no ka hoʻoholo ʻana i ke kūpaʻa moʻo:
1/k = 1/kp + 1/k4
1/500 = 1/kp + 1/k4 —- hoʻohālikelike 1
kp ʻo ia ke kūpaʻa puna pani no nā puna 1, 2, a me 3 i hoʻonohonoho like ʻia. No ka mea ua like nā puna ʻekolu, ua like ka nui o ke kūpaʻa o kēlā me kēia puna a hiki ke hōʻike ʻia e ka leka k.
kp = k1 +k2 +k3
kp = k + k + k
kp = 3k —- hoʻohālikelike 2
E pani iā kp ma ka hoohalike 1 me kp ma ka hoʻohālikelike 2. E pani pū iā k4 me k
1/500 = 1/3k + 1/k
1/500 = 1/3k + 3/3k
1/500 = 4/3k
3k = (4)(500)
3k = 2000
k = 2000 / 3
k = 667 N/m (hopena i hoʻopuni ʻia)
No laila, ʻo ke kūpaʻa o kēlā me kēia pūnāwai he k1 = k2 = k3 = k4 = 667 Newton/mika.
4. Ua hoʻonohonoho ʻia ʻekolu mau pūnāwai e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ke kūpaʻa o kēlā me kēia pūnāwai ʻo k.1= 100 N/m, k2 = 100 N/m, k3 = 200 N/m. Ua kau ʻia kekahi nuipa ma lalo o ka pūnāwai i mea e ʻike ai ka ʻākoakoa pūnāwai i ka hoʻonui ʻia o ka lōʻihi o 10 cm. Inā ʻo ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s2 a laila ʻo ke kaumaha o ka ukana…
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg
Kūkākūkā:
Ua ʻike ʻia :
k1= 100 N/m, k2 = 100 N/m, k3 = 200 N/m
x = 10 kenimika = 0,1 mika
g = 10 m/s2
Ua nīnau ʻia :
Ka nui o ka ukana (m) ?
Pane :
Ke Kumukānāwai o Hooke :
F = kx
w = kx
mg = kx
Wehewehe: F = ikaika, w = umekaumaha, m = nuipa o ka ukana, g = wikiwiki ma muli o ke umekaumaha, k = kūpaʻa puna, x = hoʻonui ʻia ka lōʻihi o ka ʻākoakoa puna
E helu i ke kūpaʻa puna i hui pū ʻia :
Ua hoʻonohonoho like ʻia ka puna 1 a me ka puna 2. ʻO ke kūpaʻa puna like:
kp = k1 +k2 = 100 + 100 = 200 N/m
Ua hoʻonohonoho ʻia ka pūnāwai pani a me ka pūnāwai 3 ma ke ʻano moʻo. ʻO ke kūpaʻa pūnāwai pani:
1/k = 1/kp + 1/k3 = 1/200 + 1/200 = 2/200
k = 200/2 = 100 N/m
E helu i ka nuipa o ka ukana :
mg = kx
m (10) = (100)(0,1)
m (10) = 10
m = 10 / 10
m = 1 kg
ʻO A ka pane pololei.
