Chitsanzo cha makonzedwe ofanana a masipuleti

Zitsanzo 4 za makonzedwe a masika ofanana ndi mndandanda

1. Masipule atatu ofanana, aliwonse okhala ndi chokhazikika chotanuka cha 200 N/m, amakonzedwa motsatizana komanso motsatizana monga momwe chithunzi chili pansipa chikusonyezera. Kulemera w kumapachikidwa kumapeto kwa gawo la kasupe, zomwe zimawonjezera kutalika kwa gawo la kasupe ndi 1 cm. Kulemera kwa kulemera w ndi…
Zokambirana
Amadziwika kuti:
Chokhazikika cha masika aliwonse (k)₁ = k₂ = k₃) = 200 N/m
Kuwonjezeka kwa kutalika kwa dongosolo la kasupe (x) = 1 cm = 0,01 mamita
Anafunsa: kulemera kwa katundu (w)
Yankho:
Kuwerengera koyamba nthawi zonse ya masika kuphatikiza.
Kasupe 1 ndi kasupe 2 zakonzedwa motsatizana. Chofanana ndi chokhazikika cha kasupe ndi:
k_p = k₁ +k₂ = 200 + 200 = 400 Newtons/mita

Makonzedwe ofanana a akasupe olowa m'malo (k)_p) ndi kasupe 3 (k₃) yokonzedwa motsatizana. Chokhazikika cha masika cholowa m'malo ndi:
1/k = 1/k_p + 1/k₃ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400
k = 400/3 Newton/mita
Werengerani kulemera kwa katundu pogwiritsa ntchito fomula Lamulo la Hooke.
F = w = kx
w = (400/3)(0,01) = 4/3 Newtons
Kulemera kwa katundu ndi 4/3 Newtons

2. Masipuri anayi ofanana aliyense ali ndi nthawi yokhazikika ya 500 N/m, yokonzedwa motsatizana komanso yofanana. Dziwani kutalika kwa dongosolo la masipuri pamene mupatsidwa katundu wa ma Newton 20.
Zokambirana
Amadziwika kuti:
Chokhazikika cha masika aliwonse (k)₁ = k₂ = k₃ = k₄) = 500 N/m
Mphamvu yolemera (w) = 20 Newtons
Funso: kuwonjezeka kwa kutalika kwa dongosolo la masika (x)
Yankho:
Choyamba werengani nthawi yokhazikika ya masika.
Masika 1, masika 2 ndi masika 3 zakonzedwa motsatizana. Chilinganizo chofanana cha masika ndi:
k_p = k₁ +k₂ +k₃ = 500 + 500 + 500 = 1500 Newtons/mita

Makonzedwe ofanana a akasupe olowa m'malo (k)_p) ndi kasupe 4 (k₄) yokonzedwa motsatizana. Chokhazikika cha masika cholowa m'malo ndi:
1/k = 1/k_p + 1/k₃ = 1/1500 + 1/500 = 1/1500 + 3/1500 = 4/1500
k = 1500/4 = 375 Newton/mita
Gwiritsani ntchito lamulo la Hooke kuti mudziwe kuchuluka kwa kutalika kwa makina a kasupe. Kuwonjezeka kwa kutalika kwa makina a kasupe ndi:
x = F / k = w / k
x = 20 / 375
x = mamita 0,05
x = 5 cm

3. Masipu ang'onoang'ono anayi ofanana akonzedwa motsatizana komanso mofanana monga momwe zasonyezedwera pachithunzi chili pansipa. Akapatsidwa katundu wa ma Newton 20, makina ang'onoang'ono amawonjezeka kutalika ndi masentimita 4. Dziwani (a) chokhazikika chophatikizana cha makinawo. akasupe ofanana ndi mndandanda (b) chokhazikika cha masika aliwonse.
Zokambirana
Amadziwika kuti:
Mphamvu yolemera (w) = 20 Newtons
Kuwonjezeka kwa kutalika kwa dongosolo la kasupe (x) = 4 cm = 0,04 mamita
Yankho:
(a) kuphatikiza kokhazikika kwa dongosolo la masika
k = F / x = w / x
k = 20 / 0,04 = 500 Newtons/mita
(b) nthawi zonse za masika aliwonse
Akasupe anayiwa ndi ofanana kotero kuti akasupe onse anayi ali ndi mawonekedwe ofanana. Ngati akasupe 1, 2, ndi 3 alowedwa m'malo ndi kasupe mmodzi, padzakhala akasupe awiri, omwe ndi akasupe olowa m'malo ofanana (k)._p) ndi kasupe 4 (k₄). Masipu awiriwa amakonzedwa motsatizana. Njira yodziwira nthawi zonse ya mndandanda ndi iyi:
1/k = 1/k_p + 1/k₄  
1/500 = 1/k_p + 1/k₄  —- equation 1
k_p ndi kasupe wokhazikika wolowa m'malo mwa akasupe 1, 2, ndi 3 wokonzedwa motsatizana. Popeza akasupe atatuwa ndi ofanana, kasupe wokhazikika wa kasupe aliyense uli ndi kukula kofanana ndipo ukhoza kuimiridwa ndi chilembo k.
k_p = k₁ +k₂ +k₃
k_p = k + k + k
k_p = 3k —- equation 2
Sinthani k_p mu equation 1 ndi k_p mu equation 2. Komanso m'malo mwa k₄ ndi 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 (zotsatira zozungulira)
Kotero nthawi zonse ya kasupe uliwonse ndi k₁ = k₂ = k₃ = k₄ = 667 Newton/mita.

4. Masipu a katatu akonzedwa monga momwe zasonyezedwera pachithunzi chili pansipa. Chokhazikika cha masipu a kasupe aliyense ndi k.₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m. Chidutswa chimapachikidwa pansi pa kasupe kuti masika apangidwe kutalika kwa 10 cm. Ngati kuthamanga chifukwa cha mphamvu yokoka kuli 10 m/s² ndiye kulemera kwa katundu ndi…
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg

Kukambirana:
Ndizodziwika kuti :
k₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m
x = 10 cm = 0,1 mamita
g = 10 m/s²
Anafunsa :
Kulemera kwa katundu (m) ?
Yankhani :
Fomula ya Malamulo a Hooke :
F = kx
w = kx
mg = kx
Kufotokozera: F = mphamvu, w = mphamvu yokoka, m = kulemera kwa katundu, g = kuthamanga chifukwa cha mphamvu yokoka, k = nthawi zonse ya masika, x = kuwonjezeka kwa kutalika kwa msonkhano wa masika
Werengerani nthawi yokhazikika ya masika :
Kasupe 1 ndi kasupe 2 zakonzedwa motsatizana. Chofanana ndi chokhazikika cha kasupe ndi:
k_p = k₁ +k₂ = 100 + 100 = 200 N/m
Kasupe wolowa m'malo ndi kasupe 3 amakonzedwa motsatizana. Chokhazikika cha kasupe wolowa m'malo ndi:
1/k = 1/k_p + 1/k₃ = 1/200 + 1/200 = 2/200
k = 200/2 = 100 N/m
Werengerani kulemera kwa katundu :
mg = kx
m (10) = (100)(0,1)
m (10) = 10
m = 10 / 10
m = 1 makilogalamu
Yankho lolondola ndi A.