Isibonelo sokuhlelwa kweziphethu okuhambisana nochungechunge

Izibonelo ezi-4 zokuhlelwa kwentwasahlobo okuhambisana nochungechunge

1. Iziphethu ezintathu ezifanayo, ngasinye esinokuqina okunwebeka okungu-200 N/m, zihlelwe ngokulandelana futhi zihambisana njengoba kuboniswe esithombeni esingezansi. Isisindo u-w silenga engxenyeni engezansi yenhlangano yentwasahlobo, okwandisa ubude benhlangano yentwasahlobo ngo-1 cm. Isisindo sesisindo u-w…
Ingxoxo
Kuyaziwa ukuthi:
I-constant yentwasahlobo ngayinye (k)₁ = k₂ = k₃) = 200 N/m
Ukwanda kobude besistimu yentwasahlobo (x) = 1 cm = 0,01 amamitha
Kubuziwe: isisindo somthwalo (w)
Impendulo:
Ukubala kokuqala i-spring constant inhlanganisela.
Intwasahlobo 1 kanye nentwasahlobo 2 zihlelwe ngokulingana. I-spring constant efanayo yile:
k_p = k₁ +k₂ = 200 + 200 = 400 Newtons/meter

Iziphethu zokufaka esikhundleni selungiselelo elifanayo (k)_p) kanye nentwasahlobo 3 (k₃) ihlelwe ngokulandelana. I-spring constant ethatha indawo yile:
1/k = 1/k_p + 1/k₃ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400
k = 400/3 iNewton/imitha
Bala isisindo somthwalo usebenzisa ifomula Umthetho kaHooke.
F = w = kx
w = (400/3)(0,01) = 4/3 amaNewton
Ubunzima bomthwalo buyi-4/3 Newtons

2. Iziphethu ezine ezifanayo ngasinye sinokuqina okungu-500 N/m, okuhlelwe ngokulandelana nangokuhambisana. Thola ukwanda kobude besistimu yesiphethu uma unikezwe umthwalo wama-Newton angu-20.
Ingxoxo
Kuyaziwa ukuthi:
I-constant yentwasahlobo ngayinye (k)₁ = k₂ = k₃ = k₄) = 500 N/m
Amandla esisindo (w) = amaNewton angu-20
Umbuzo: ukwanda kobude besistimu yentwasahlobo (x)
Impendulo:
Okokuqala bala i-constant yasentwasahlobo ehlanganisiwe.
Intwasahlobo 1, intwasahlobo 2 kanye nentwasahlobo 3 zihlelwe ngokulingana. Isilinganiso esilinganayo sentwasahlobo yilesi:
k_p = k₁ +k₂ +k₃ = 500 + 500 + 500 = 1500 Newtons/meter

Iziphethu zokufaka esikhundleni selungiselelo elifanayo (k)_p) kanye nentwasahlobo 4 (k₄) ihlelwe ngokulandelana. I-spring constant ethatha indawo yile:
1/k = 1/k_p + 1/k₃ = 1/1500 + 1/500 = 1/1500 + 3/1500 = 4/1500
k = 1500/4 = 375 Newton/imitha
Sebenzisa umthetho kaHooke ukuze unqume ukwanda kobude besistimu yentwasahlobo. Ukwanda kobude besistimu yentwasahlobo yilokhu:
x = F / k = w / k
x = 20/375
x = amamitha angu-0,05
x = 5cm

3. Iziphethu ezine ezifanayo zihlelwe ngokulandelana futhi zihambisana njengoba kuboniswe esithombeni esingezansi. Uma zinikezwe umthwalo wamaNewton angu-20, uhlelo lwesiphethu lukhula ngobude ngamasentimitha angu-4. Thola (a) i-constant ehlanganisiwe yesistimu. iziphethu ezihambisana nochungechunge (b) ukungaguquguquki kwentwasahlobo ngayinye.
Ingxoxo
Kuyaziwa ukuthi:
Amandla esisindo (w) = amaNewton angu-20
Ukwanda kobude besistimu yentwasahlobo (x) = 4 cm = 0,04 amamitha
Impendulo:
(A) i-constant ehlanganisiwe yesistimu yentwasahlobo
k = F / x = w / x
k = 20 / 0,04 = 500 Newtons/meter
(B) okungaguquki kwentwasahlobo ngayinye
Iziphethu ezine ziyafana ukuze zonke iziphethu ezine zibe nokuqina okufanayo. Uma iziphethu 1, 2, kanye no-3 zithathelwa indawo yisiphethu esisodwa, kuzoba neziphethu ezimbili, okungukuthi iziphethu ezithatha indawo efanayo (k)._p) kanye nentwasahlobo 4 (k₄). Lezi zintwasahlobo ezimbili zihlelwe ngochungechunge. Ifomula yokunquma ukungaguquguquki kochungechunge yile:
1/k = 1/k_p + 1/k₄  
1/500 = 1/k_p + 1/k₄  —- isibalo 1
k_p yi-spring constant yokufaka esikhundleni seziphethu 1, 2, kanye no-3 ehlelwe ngokuhambisana. Njengoba iziphethu ezintathu zifana, i-spring constant yephethu ngayinye inobukhulu obufanayo futhi ingamelwa uhlamvu u-k.
k_p = k₁ +k₂ +k₃
k_p = k + k + k
k_p = 3k —- isibalo 2
Shintsha u-k_p ku-equation 1 no-k_p ku-equation 2. Faka futhi u-k esikhundleni₄ no-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 (umphumela ojikeleziwe)
Ngakho-ke i-constant yentwasahlobo ngayinye ingu-k₁ = k₂ = k₃ = k₄ = 667 amaNewton/imitha.

4. Iziphethu ezintathu zihlelwe njengoba kuboniswe esithombeni esingezansi. I-constant yephethu ngayinye ingu-k.₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m. Isisindo silenga phansi kwentwasahlobo ukuze ukuhlangana kwentwasahlobo kuthole ukwanda kobude obuyi-10 cm. Uma ukusheshisa ngenxa yamandla adonsela phansi kungu-10 m/s² khona-ke isisindo somthwalo…
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg

Ingxoxo:
I-Diketahui :
k₁= 100 N/m, k₂ = 100 N/m, k₃ = 200 N/m
x = 10 cm = 0,1 amamitha
g = 10 m/s²
Kubuziwe :
Isisindo somthwalo (m) ?
Jawab :
Ifomula Yomthetho KaHooke :
F = kx
w = kx
mg = kx
Incazelo: F = amandla, w = amandla adonsela phansi, m = isisindo somthwalo, g = ukusheshisa ngenxa yamandla adonsela phansi, k = ukungaguquguquki kwentwasahlobo, x = ukwanda kobude bokuhlanganiswa kwentwasahlobo
Bala i-constant yasentwasahlobo ehlanganisiwe :
Intwasahlobo 1 kanye nentwasahlobo 2 zihlelwe ngokulingana. I-spring constant efanayo yile:
k_p = k₁ +k₂ = 100 + 100 = 200 N/m
Intwasahlobo eshintshayo kanye nentwasahlobo 3 zihlelwe ngokulandelana. I-constant yentwasahlobo eshintshayo yile:
1/k = 1/k_p + 1/k₃ = 1/200 + 1/200 = 2/200
k = 200/2 = 100 N/m
Bala isisindo somthwalo :
mg = kx
m (10) = (100)(0,1)
m (10) = 10
m = 10/10
m = 1 kg
Impendulo efanele ngu-A.