Tusaale ah isku-dubarid taxane ah oo is barbar socda oo ah ilo

4 tusaale oo ah qabanqaabada guga ee taxanaha ah

1. Saddex ilo oo isku mid ah, mid walbana leh joogto laastikada ah oo ah 200 N/m, ayaa loo habeeyay si taxane ah oo is barbar socda sida ku cad sawirka hoose. Miisaan w ayaa laga laalaaday dhammaadka hoose ee isu-imaatinka gu'ga, taasoo kordhinaysa dhererka isu-imaatinka gu'ga 1 cm. Miisaanka w waa…
Dood
Waa la ogyahay in:
Joogtada ah ee gu' kasta (k)₁ = k₂ = k₃) = 200 N/m
Kordhinta dhererka nidaamka guga (x) = 1 cm = 0,01 mitir
La weydiiyay: miisaanka culayska (w)
Jawaab:
Tirada koowaad joogto ah guga isku darka.
Gu'ga 1aad iyo gu'ga 2aad si is barbar socda ayaa loo habeeyey. Joogtada guga ee u dhiganta waa:
k_p = k₁ +k₂ = 200 + 200 = 400 Newtons/mitir

ilo beddelka nidaamka is barbar socda (k)_p) iyo guga 3 (k₃) oo loo habeeyay taxane. Joogtada guga ee beddelka ah waa:
1/k = 1/k_p + 1/k₃ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400
k = 400/3 Newton/mitir
Xisaabi miisaanka culayska adoo isticmaalaya qaacidada Sharciga Hooke.
F = w = kx
w = (400/3)(0,01) = 4/3 Newtons
Cufnaanta culaysku waa 4/3 Newtons

2. Afar ilo oo isku mid ah midkiiba wuxuu leeyahay joogto ah oo ah 500 N/m, oo loo habeeyay taxane iyo is barbar socda. Go'aami kororka dhererka nidaamka guga marka la siiyo culays dhan 20 Newtons.
Dood
Waa la ogyahay in:
Joogtada ah ee gu' kasta (k)₁ = k₂ = k₃ = k₄) = 500 N/m
Miisaanka culayska (w) = 20 Newtons
Su'aal: kordhinta dhererka nidaamka gu'ga (x)
Jawaab:
Marka hore xisaabi joogtada guga ee isku dhafan.
Gu'ga 1aad, gu'ga 2aad iyo gu'ga 3aad ayaa si is barbar socda loo habeeyey. Joogtada guga ee u dhiganta waa:
k_p = k₁ +k₂ +k₃ = 500 + 500 + 500 = 1500 Newtons/mitir

ilo beddelka nidaamka is barbar socda (k)_p) iyo guga 4 (k₄) oo loo habeeyay taxane. Joogtada guga ee beddelka ah waa:
1/k = 1/k_p + 1/k₃ = 1/1500 + 1/500 = 1/1500 + 3/1500 = 4/1500
k = 1500/4 = 375 Newton/mitir
Adeegso sharciga Hooke si aad u go'aamiso kororka dhererka nidaamka gu'ga. Kordhinta dhererka nidaamka gu'ga waa:
x = F / k = w / k
x = 20/375
x = 0,05 mitir
x = 5cm

3. Afar ilo oo isku mid ah ayaa loo habeeyay si taxane ah oo is barbar socda sida ku cad sawirka hoose. Marka la siiyo culays dhan 20 Newtons, nidaamka guga wuxuu dhererkiisu kordhaa 4 cm. Go'aami (a) isku-darka joogtada ah ee nidaamka. ilo taxane ah oo is barbar socda (b) joogtada ah ee gu' kasta.
Dood
Waa la ogyahay in:
Miisaanka culayska (w) = 20 Newtons
Kordhinta dhererka nidaamka guga (x) = 4 cm = 0,04 mitir
Jawaab:
(A) isku-darka joogtada ah ee nidaamka guga
k = F / x = w / x
k = 20 / 0,04 = 500 Newtons/mitir
(B) joogto ah guga kasta
Afarta ilbiriqood waa isku mid si afarta ilbiriqoodba ay u yeeshaan isku joogto ah. Haddii ilbiriqoodyada 1, 2, iyo 3 lagu beddelo hal ilbiriqood, waxaa jiri doona laba ilbiriqood, kuwaas oo ah ilbiriqoodyada beddelka ah ee isbarbar socda (k)._p) iyo guga 4 (k₄Labadan gu' waxaa loo habeeyay si taxane ah. Qaacidada lagu go'aaminayo joogtada taxanaha waa:
1/k = 1/k_p + 1/k₄  
1/500 = 1/k_p + 1/k₄  —- isla'egta 1aad
k_p waa isbeddelka joogtada ah ee guga ee loogu talagalay gu'yada 1, 2, iyo 3 ee isku midka ah. Maadaama saddexda gu' ay isku mid yihiin, joogtada guga ee gu' kasta waxay leedahay isla cabbirka waxaana lagu matali karaa xarafka k.
k_p = k₁ +k₂ +k₃
k_p = k + k + k
k_p = 3k —- isle'egta 2
Ku beddel k_p isle'egta 1aad ee k_p isle'egta 2. Sidoo kale beddel k₄ oo leh 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 (natiijo wareegsan)
Markaa joogtada gu' kasta waa k₁ = k₂ = k₃ = k₄ = 667 Newtons/mitir.

4. Saddex ilbiriqood ayaa loo habeeyey sida ku cad sawirka hoose. Joogtada gu' kasta waa k.₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m. Cuf ayaa lagu laalaadaa salka gu'ga si isu-ururinta gu'gu ay u yeelato koror dhererkeedu yahay 10 cm. Haddii dardargelinta cufisjiidadka awgeed ay tahay 10 m/s² markaa cufka culaysku waa…
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg

Dood:
Waa la garanayaa :
k₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m
x = 10 cm = 0,1 mitir
g = 10 m/s²
La weydiiyay :
Cufka culayska (m)?
Jawab :
Qaaciddada Sharciga Hooke :
F = kx
w = kx
mg = kx
Sharaxaad: F = xoog, w = cuf-isjiidadka, m = cuf-isjiidadka culayska, g = dardar-gelin ay sabab u tahay cuf-isjiidadka, k = joogtada guga, x = kordhinta dhererka isu-imaatinka guga
Xisaabi joogtada guga ee la isku daray :
Gu'ga 1aad iyo gu'ga 2aad si is barbar socda ayaa loo habeeyey. Joogtada guga ee u dhiganta waa:
k_p = k₁ +k₂ = 100 + 100 = 200 N/m
Gu'ga beddelka ah iyo gu'ga 3aad waxaa loo diyaariyey taxane. Joogtada gu'ga beddelka ah waa:
1/k = 1/k_p + 1/k₃ = 1/200 + 1/200 = 2/200
k = 200/2 = 100 N/m
Xisaabi miisaanka culayska :
mg = kx
m (10) = (100)(0,1)
m (10) = 10
m = 10 / 10
m = 1 kg
Jawaabta saxda ah waa A.