Muenzaniso wekurongeka kwemasipiresi akafanana neakatevedzana

Mienzaniso mina yezvirongwa zvechitubu zvakafanana nezvinotevedzana

1. Masipiringi matatu akafanana, rimwe nerimwe rine elastic constant ye200 N/m, akarongwa akatevedzana uye akafanana sezvakaratidzwa mumufananidzo uri pazasi. Huremu w hwakasungirirwa kubva kumucheto wezasi wemasipiringi, zvichiwedzera hurefu hwemasipiringi ne1 cm. Huremu hwehuremu w ndi…
Kukurukurirana
Zvinozivikanwa kuti:
Chimiro chenguva dzose chechirimo (k)₁ = k₂ = k₃) = 200 N/m
Kuwedzera kwehurefu hwechitubu (x) = 1 cm = 0,01 metres
Akabvunzwa: huremu hwemutoro (w)
Mhinduro:
Kuverengwa kwekutanga chitubu chisingachinji musanganiswa.
Chitubu 1 nechitubu 2 zvakarongwa zvakaenzana. Chitubu chakafanana ndeichi:
k_p = k₁ +k₂ = 200 + 200 = 400 Newtons/mita

Zvitubu zvinotsiva zvakarongwa zvakafanana (k)_p) uye chitubu 3 (k₃) dzakarongwa zvakatevedzana. Chitubu chinotsiva chinogara chiripo ndeichi:
1/k = 1/k_p + 1/k₃ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400
k = 400/3 Newton/mita
Verenga huremu hwemutoro uchishandisa fomura Mutemo waHooke.
F = w = kx
w = (400/3)(0,01) = 4/3 Newtons
Huremu hwemutoro i4/3 Newtons

2. Masipiringi mana akafanana chimwe nechimwe chine constant ye500 N/m, yakarongwa zvakatevedzana uye yakafanana. Sarudza kuwedzera kwehurefu hwesisitiringi kana ukapihwa mutoro we20 Newtons.
Kukurukurirana
Zvinozivikanwa kuti:
Chimiro chenguva dzose chechirimo (k)₁ = k₂ = k₃ = k₄) = 500 N/m
Kurema kwemutoro (w) = 20 Newtons
Mubvunzo: kuwedzera kwehurefu hwechitubu (x)
Mhinduro:
Kutanga verenga chisipiti chakabatana.
Chitubu 1, chitubu 2 nechitubu 3 zvakarongwa zvakaenzana. Chitubu chakafanana ndeichi:
k_p = k₁ +k₂ +k₃ = 500 + 500 + 500 = 1500 Newtons/mita

Zvitubu zvinotsiva zvakarongwa zvakafanana (k)_p) uye chitubu 4 (k₄) dzakarongwa zvakatevedzana. Chitubu chinotsiva chinogara chiripo ndeichi:
1/k = 1/k_p + 1/k₃ = 1/1500 + 1/500 = 1/1500 + 3/1500 = 4/1500
k = 1500/4 = 375 Newton/mita
Shandisa mutemo waHooke kuti uone kuwedzera kwehurefu hwesystem yechitubu. Kuwedzera kwehurefu hwesystem yechitubu ndekwekuti:
x = F / k = w / k
x = 20 / 375
x = 0,05 mamita
x = 5cm

3. Masipiringi mana akafanana akarongwa akatevedzana uye akafanana sezvakaratidzwa mumufananidzo uri pazasi. Kana akapihwa mutoro wemaNewton makumi maviri, sisitimu yechitubu inowedzera kureba nemasendimita mana. Sarudza (a) chisimbiso chakabatanidzwa chesisitimu. zvitubu zvakafanana-zvakatevedzana (b) chisingaperi chechirimo chega chega.
Kukurukurirana
Zvinozivikanwa kuti:
Kurema kwemutoro (w) = 20 Newtons
Kuwedzera kwehurefu hwechitubu (x) = 4 cm = 0,04 metres
Mhinduro:
(A) chisimbiso chemusanganiswa chesystem yechitubu
k = F / x = w / x
k = 20 / 0,04 = 500 Newtons/mita
(B) nguva dzose yechirimo chega chega
Zvitubu zvina zvakafanana zvekuti zvitubu zvese zvina zvine chimiro chakafanana. Kana zvitubu 1, 2, uye 3 zvikatsiviwa nechitubu chimwe chete, pachava nezvitubu zviviri, zvinoti zvitubu zvinotsiva zvakafanana (k)._p) uye chitubu 4 (k₄). Masipiringi maviri aya akarongwa munhevedzano. Nzira yekuona kuti series constant ndeye:
1/k = 1/k_p + 1/k₄  
1/500 = 1/k_p + 1/k₄  —- muyero 1
k_p ndiyo chisimbiso chechitubu chinotsiva zvitubu 1, 2, uye 3 zvakarongwa zvakafanana. Sezvo zvitubu zvitatu zvakafanana, chisimbiso chechitubu chimwe nechimwe chine hukuru hwakafanana uye chinogona kumiririrwa nebhii k.
k_p = k₁ +k₂ +k₃
k_p = k + k + k
k_p = 3k —- equation 2
Tsiva k_p muequation 1 na k_p muequation 2. Chitsivawo k₄ na 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 (mhedzisiro yakatenderera)
Saka chisingaperi chechirimo chega chega ndi k₁ = k₂ = k₃ = k₄ = 667 Newtons/mita.

4. Masipiringi matatu akarongwa sezvakaratidzwa mumufananidzo uri pazasi. Chimiro chechipringi chimwe nechimwe ndi k.₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m. Huremu hunosungirirwa pasi pechitubu kuitira kuti chitubu chiunganidzwe chiwedzere kureba kwe10 cm. Kana kukurumidza kunokonzerwa negiravhiti kuri 10 m/s² ipapo huremu hwemutoro hwacho…
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg

Kukurukurirana:
Zvinozivikanwa :
k₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m
x = 10 cm = 0,1 mamita
g = 10 m/s²
Akabvunzwa :
Huremu hwemutoro (m)?
Jawab :
Fomura yeMutemo waHooke :
F = kx
w = kx
mg = kx
Tsananguro: F = simba, w = simba rinokwevera pasi, m = uremu hwemutoro, g = kukurumidza nekuda kwesimba rinokwevera pasi, k = nguva dzose yechitubu, x = kuwedzera kwehurefu hwechikamu chechitubu
Verenga huwandu hwechitubu hwakabatana :
Chitubu 1 nechitubu 2 zvakarongwa zvakaenzana. Chitubu chakafanana ndeichi:
k_p = k₁ +k₂ = 100 + 100 = 200 N/m
Chitubu chinotsiva nechitubu 3 zvakarongwa zvakatevedzana. Chitubu chinotsiva chinogara chiripo ndeichi:
1/k = 1/k_p + 1/k₃ = 1/200 + 1/200 = 2/200
k = 200/2 = 100 N/m
Verenga huremu hwemutoro :
mg = kx
m (10) = (100)(0,1)
m (10) = 10
m = 10 / 10
m = 1 kg
Mhinduro chaiyo ndiA.