Izinkinga nezixazululo ze-Springs ezilandelanayo nezihambisanayo

1. Into engamagremu angu-160 inamathela kolunye uhlangothi lwesipilingi kanti ushintsho lobude besipilingi luyi-4 cm. Luyini ushintsho lobude bezintathu iziphethu ezixhunywe ngochungechunge nangokuhambisana, njengoba kuboniswe esithombeni esingezansi?

Kwaziwa:

Ushintsho lobude besiphethu (Δx) = 4 cm = 0.04 m Izinhlobo ze-Springs ezilandelanayo kanye nezihambisanayo – izinkinga nezixazululo 1

Imisa (m) = amagremu angu-160 = 0.16 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

Isisindo (w) = mg = (0.16)(10) = 1.6 AmaNewton

Kufunwa: Ushintsho lobude beziphethu ezintathu (Δx)

Isixazululo:

Isibalo se Umthetho kaHooke :

k = w / Δx = 1.6 / 0.04 = 40 N/m

Iziphethu ezintathu zinokuqina okufanayo, k = 40 N/m.

Nquma i-constant efanayo :

Intwasahlobo 2 (k₂) kanye nentwasahlobo 3 (k₃) i-tare ixhunywe ngokulingana. I-constant efanayo :

k₂₃ = k₂ +k₃ = 40 + 40 = 80 N/m

Intwasahlobo 1 (k₁) kanye nentwasahlobo 23 (k₂₃) zixhunywe ochungechungeni. I-constant efanayo :

1/k = 1/k₁ + 1/k₂₃ = 1/40 + 1/80 = 2/80 + 1/80 = 3/80

k = 80/3

Nquma ushintsho lobude beziphethu ezintathu:

Δx = w / k = 1.6 : 80/3 = (1.6)(3/80) = 4.8 / 80 = 0.06 m = 6 cm

2. Iziphethu ezintathu ezine-constant efanayo exhunywe ochungechungeni futhi ehambisanayo, kanye nento engamakhilogremu angu-2 enamathiselwe kolunye uhlangothi lwesipilingi, njengoba kuboniswe esithombeni esingezansi. I-Spring constant ingu-k₁= k₂ = k₃= 300 N/m. Luyini ushintsho lobude beziphethu ezintathu. Ukusheshisa ngenxa yamandla adonsela phansi kungu-g = 10 ms^-2.

Kwaziwa:

I-k engaguquki yasentwasahlobo₁= k₂ = k₃= 300 Nm^-1

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 ms^-2

Isisindo sento (m) = 2 kg

Isisindo sento (w) = mg = (2)(10) = 20 Newtons

Bhekafuthi Umthetho waseKirchhoff - izinkinga nezixazululo

Kufunwa: Ushintsho lobude beziphethu ezintathu (Δx)

Isixazululo:

Nquma i-constant efanayo :

Intwasahlobo 1 (k₁) kanye nentwasahlobo 2 (k₂) zixhunywe ngokulingana. I-constant efanayo :

k₁₂ = k₁ +k₂ = 300 + 300 = 600 N/m

Intwasahlobo 3 (k₃) kanye nentwasahlobo 12 (k₁₂) zixhunywe ochungechungeni. I-constant efanayo :

1/k = 1/k₃ + 1/k₁₂ = 1/300 + 1/600 = 2/600 + 1/600 = 3/600

k = 600/3 = 200 N/m

Nquma ushintsho lobude beziphethu ezintathu:

Δx = w / k = 20/200 = 2/20 = 1/10 = 0.1 m

3. Iziphethu ezintathu zixhunywe ngochungechunge nangokuhambisana, njengoba kuboniswe esithombeni esingezansi. Uma i-spring constant k = 50 Nm^-1 kanye nesisindo esingamagremu angu-400 esinamathiselwe kolunye uhlangothi lwesiphethu. Luyini ushintsho lobude beziphethu ezintathu?

Kwaziwa:

I-Spring constant 1 (k)₁) = k = 50 Nm^-1

I-Spring constant 2 (k)₂) = k = 50 Nm^-1

I-Spring constant 3 (k)₃) = 2k = 2 (50 Nm^-1) = 100 Nm^-1

Isisindo sento (m) = 400 amagremu = 0.4 kg

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²

Isisindo sento (w) = mg = (0.4)(10) = 4 Newtons

Kufunwa: Ushintsho lobude (Δx)

Isixazululo:

Nquma i-constant efanayo :

Intwasahlobo 1 (k₁) kanye nentwasahlobo 2 (k₂) zixhunywe ngokulingana. I-constant efanayo :

k₁₂ = k₁ +k₂ = 50 + 50 = 100 N/m

Intwasahlobo 3 (k₃) kanye nentwasahlobo 12 (k₁₂) zixhunywe ochungechungeni. I-constant efanayo :

1/k = 1/k₃ + 1/k₁₂ = 1/100 + 1/100 = 2/100

k = 100/2 = 50 N/m

Nquma ushintsho lobude beziphethu ezintathu:

Δx = w / k = 4 / 50 = = 0.08 m = 8 cm

Ukuhlanganisa izipringi ngokulandelana kuyithinta kanjani i-constant yentwasahlobo iyonke?
- Impendulo: Uma iziphethu zihlanganiswa ngochungechunge, i-spring constant iyonke iyancishiswa. I-reciprocal ye-spring constant efanayo iyisamba se-reciprocals ye-spring constant ngayinye: 1/k $=1/ k ^{1} + 1/ k ^{2}$ .
Ukuguquguquka kwentwasahlobo iyonke kushintsha kanjani lapho iziphethu zihlanganiswa ndawonye?
- Impendulo: Ukuhlanganisa iziphethu ngendlela efanayo kuphumela ku-spring constant iyonke eyisamba seziphethu ngazinye: k $= k_{1} + k_{2}$ .

Uma iziphethu ezimbili ezifanayo zihlelwe ngokulandelana, i-constant yentwasahlobo ehlanganisiwe iqhathaniswa kanjani ne-constant yentwasahlobo yentwasahlobo ngayinye?
- Impendulo: I-spring constant ehlanganisiwe izoba yingxenye ye-spring constant yesinye seziphethu ngazinye.

Kwenzekani ekwandisweni noma ekucindezelweni kwezipilingi ngokulandelana lapho kusetshenziswa amandla?
- Impendulo: Kuma-springs alandelanayo, amandla afanayo abangela ukuthi i-spring ngayinye inwebe noma icindezeleke, kodwa i-extension iyonke (noma i-compression) iyisamba se-extensions (noma i-compression) yama-springs ngamanye.

Uma iziphethu ezihambisanayo zibhekene namandla, lawo mandla asatshalaliswa kanjani?
- Impendulo: Kuma-springs ahambisanayo, amandla asatshalaliswa phakathi kwama-springs ngokusekelwe kuma-spring constant awo. Ama-springs ane-spring constant ephezulu azothwala ingxenye enkulu yamandla kunalawo ane-spring constant ephansi.
Kungani iziphethu ezilandelanayo zingacatshangwa njengesiphethu esisodwa esinobude obude?
- Impendulo: Izipilingi ezilandelanayo zinomphumela ohlangene ofana nokwelula isipilingi esisodwa eside. Izandiso noma ukucindezelwa kwezipilingi ngazinye kuyahlangana, njengoba nje bekungenza esipilingini esisodwa eside.

Amandla angase agcinwe eziphethwini ngokulandelana aqhathaniswa kanjani nalawo aseziphethwini ahambisana namandla afanayo asetshenziswayo?
- Impendulo: Iziphethu ezilandelanayo zigcina amandla amaningi angaba khona kuneziphethu ezihambisanayo zamandla afanayo asetshenziswayo ngoba zidlula ekunwetshweni noma ekucindezelweni okukhulu okuhlangene.
Uma esinye sezipilingi esisesimisweni esifanayo siphuka noma singasebenzi kahle, kwenzekani ekuziphatheni kwesistimu iyonke?
- Impendulo: Uma intwasahlobo eyodwa ekucushweni okufanayo iphuka, intwasahlobo esele izoqhubeka isebenza. Kodwa-ke, isisekelo sentwasahlobo iyonke yesistimu sizoncipha, futhi uhlelo ngeke lukwazi ukusebenzisa amandla okubuyisela amaningi njengakuqala.

Kungani iziphethu ezilandelanayo zisengozini enkulu yokuguquguquka okukhulu kunalezo ezihambisana namandla afanayo asetshenziswayo?
- Impendulo: Kuma-spring alandelanayo, amandla afanayo asebenza entwasahlobo ngayinye, okwenza ngayinye inwebeke noma icindezeleke. Ukuguquguquka okuphelele kuyisamba sokuguquguquka ngakunye. Ngesikhathi esifanayo, amandla asatshalaliswa phakathi kwama-spring, ngakho-ke ngayinye ithola amandla asebenzayo anciphile, okuholela ekuguqukeni okuncane ngakunye.
Ezisetshenzisweni ezisebenzayo, kungani onjiniyela bengakhetha ukusebenzisa iziphethu ezifanayo kunokuba basebenzise uchungechunge?

Impendulo: Onjiniyela bangase bakhethe iziphethu ngesikhathi esifanayo ukuze bafinyelele izinga eliphezulu le-spring constant, okuholela ekuziphatheni okuqinile. Lokhu kusethwa kungaphinde kuhlinzeke ngokuphindaphindeka; uma i-spring eyodwa yehluleka, uhlelo luyaqhubeka nokusebenza, yize luncishisiwe izinga le-spring constant.