Umthetho kaHooke kanye nokunwebeka – izinkinga nezixazululo

Umthetho kaHooke kanye nokunwebeka – izinkinga nezixazululo

Ushintsho lobude

1. Induku inobude obungu-L, idonswa ngamandla ka-F. Inani lokunwebeka lingu-∆L. Ubukhulu bamandla buyini uma ushintsho lobude lungu-4∆L?

Kwaziwa:

Amandla 1 (F ₁ ) = F

Ushintsho lobude 1 (∆L ₁ ) = ∆L

Ushintsho lobude 2 (∆L ₂ ) = 4 ∆L

Kufunwa: Amandla 2 (F ₂ )

Isixazululo:

Isilinganiso somthetho kaHooke

k = F / ΔL

k = ukungaguquguquki kokuguquguquka, F = amandla ka-F, ΔL = ushintsho lobude

k ₁ = k ₂

F ₁ / ∆L ₁ = F ₂ / ∆L ₂

F / ΔL = F ₂ / 4ΔL

F / 1 = F ₂ / 4

F = F _2/4

F ₂ = 4F

2. Kukhona iziphethu ezixhunywe ngochungechunge oluhambisanayo, njengoba kuboniswe esithombeni esingezansi. Intwasahlobo 1 ine-constant engu-200 N/m, intwasahlobo 2 ine-constant engu-200 N/m kanti intwasahlobo 3 ine-constant engu-200 N/m. Isisindo sento singamagremu ayi-100 futhi ukusheshisa ngenxa yamandla adonsela phansi ingu-10 m/s². Luyini ushintsho lobude besikhathi the okulinganayo intwasahlobo.

Kwaziwa:

Isisindo sento ( m) = 100 amagremu = 0.1 kg

k ₁ = k ₂ = k ₃ = 200 N/m

w = mg = (0.1 kg)(10 m/s ² ) = 1 kg m/s ² = 1 Newton

Okufunwayo: Ushintsho lobude besiphethu esilinganayo.

Isixazululo:

Nquma okulingana i-spring constant:

Intwasahlobo 2 (k ₂ ) kanye nentwasahlobo 3 (k ₃ ) zixhunywe ngokulingana. I -spring constant efanayo:

k _p = k ₂ + k ₃ = 200 + 200 = 400 Nm ⁻¹

Intwasahlobo 1 (k ₁ ) kanye nentwasahlobo p (k _P ) zixhunywe ochungechungeni. I-spring constant efanayo:

1/k _s = 1/k _p + 1/k ₁ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400

ks = 400/3 ^Nm ₋₁

Isilinganiso esilinganayo sentwasahlobo yi -400/3 Nm ^-1

Nquma ushintsho lobude besiphethu esilinganayo :

Isilinganiso somthetho kaHooke:

∆x = F / k = w / k

Ushintsho lobude besiphethu esilinganayo :

∆x = w / k

∆x = 1 : 400/3 = 1 x 3/400 = 3/400 = 0.0075 m = 0.75 cm

I-constant yentwasahlobo

3. Iyini i-constant yentwasahlobo ngokwemininingwane esethebula elingezansi.

Isixazululo:

Isilinganiso somthetho kaHooke:

k = F / Δx

I-Constant yentwasahlobo:

k = 0.98 / 0.0008 = 1.96 / 0.0016 = 2.94 / 0.0024 = 3.92 / 0.0032 = 1.225 N/m

4. Iziphethu ezintathu zixhunywe ngochungechunge-ngokufana njengoba kuboniswe esithombeni esingezansi. Ama-constant entwasahlobo k ₁ = k ₂ = 3 Nm ⁻¹ kanye ne-k ₃ = 6 Nm ⁻¹ . Iyini i-constant ye-constant ye-spring elingana nentwasahlobo.

Kwaziwa:

I-Constant yentwasahlobo 1 (k ₁ ) = i-constant yentwasahlobo 2 (k ₂ ) = 3 Nm ⁻¹

I-Constant yentwasahlobo 3 (k ₃ ) = 6 Nm ⁻¹

Okufunwayo: okungaguquki kwentwasahlobo efanayo (k)

Isixazululo:

Intwasahlobo 1 (k ₁ ) kanye nentwasahlobo 2 (k ₂ ) zixhunywe ngokulingana. I-Constant yentwasahlobo efanayo:

k _p = k ₁ + k ₂ = 3 + 3 = 6 Nm ⁻¹

Intwasahlobo p (k _P ) kanye nentwasahlobo 3 (k ₃ ) zixhunywe ngochungechunge. I-constant yentwasahlobo efanayo:

1/k _s = 1/k _p + 1/k ₃ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6

ks = 6/2 = 3 ^Nm ₋₁

I-constant yesilinganiso sentwasahlobo = 3 Nm ⁻¹.

5. Isiphethu esinobude obungu-L, sidonswa ngesisindo esingu-w. Ngokusho kwedatha ethebuleni elingezansi, iyini i-constant yesiphethu esilinganayo:

Isixazululo:

k = F / Δx

I-Constant yentwasahlobo:

k = 10 / 0.02 = 20 / 0.04 = 30 / 0.06 = 40 / 0.08 = 500 N/m

6. Ngokusho kwedatha ethebuleni elingezansi, iyini i-constant yentwasahlobo efanayo:

Isixazululo:

k = F / Δx = w / Δx = mg / Δx

k = ukungaguquguquki kokuguquguquka, w = isisindo, m ​​= isisindo, g = ukusheshisa ngenxa yamandla adonsela phansi, Δx = ushintsho lobude

I-constant yasentwasahlobo:

k = 2 / 0.05 = 4 / 0.1 = 6 / 0.15 = 8 / 0.20 = 10 / 0.25 = 40 N/m

7. Uma _u- k = 4k, iyini i-constant yesiphethu esilinganayo.

Isixazululo:

Iziphethu ezimbili zixhunywe ngokulingana. I-constant yephethu elilinganayo:

k _p = k + k = 2k

Iziphethu ezimbili zixhunywe ngokulandelana. I-constant yephethu elilinganayo

1/k _s = 1/k _p + 1/k ₁ = 1 / 2k + 1 / 4k = 2 / 4k + 1 / 4k = 3 / 4k

k _s = 4k/3

8. Ngokusho kwedatha ethebuleni elingezansi, iyini i-constant yentwasahlobo efanayo:

Isixazululo:

Isilinganiso somthetho kaHooke:

k = F / Δ L

I-Constant yentwasahlobo:

k = 2 / 0.0050 = 3 / 0.0075 = 4 / 0.01 = 400 Nm ^-1

9. Okungaguquki okuncane kakhulu…

Isixazululo

Isilinganiso somthetho kaHooke:

k = F / Δx

k = ukungaguquguquki kokuguquguquka, F = amandla, Δx = ushintsho lobude

Ukunwebeka okuhlala njalo:

k _A = F / Δx = 1 / 0.05 = 20 N/m

k _B = F / Δx = 2 / 0.025 = 80 N/m

k _C = F / Δx = 1 / 0.025 = 40 N/m

k _D = F / Δx = 2 / 0.05 = 40 N/m

k _E = F / Δx = 2 / 0.25 = 8 N/m

10. Yisiphi isici esivamile esikhulu ngokwedatha ethebula elingezansi.

Isixazululo:

Isilinganiso somthetho kaHooke:

k = F / Δx

k _A = 7 / 0.035 = 200 Nm ^-1

k _B = 8 / 0.025 = 320 Nm ^-1

k _C = 6 / 0.020 = 300 Nm ^-1

k _D = 9 / 0.045 = 200 Nm ^-1

k _E = 10 / 0.033 = 303 Nm ^-1

I-constant enkulu kunazo zonke yi-320 Nm ^-1.

11. Igrafu engezansi ikhombisa ukuxhumana phakathi koshintsho lwamandla (ΔF) kanye nokwanda kobude (Δx). Iyini igrafu ekhombisa ukuqina okuncane kakhulu kokuqina.

Isixazululo

Isilinganiso somthetho kaHooke:

k = F / Δx

Δx = ushintsho lobude, F = amandla, k = ukungaguquguquki kokuguquguquka

Ukunwebeka okuhlala njalo:

k _A = F / Δx = 1 / 8 = 0.125

k _B = F / Δx = 8 / 3 = 2.7

k _C = F / Δx = 6 / 6 = 1

k _D = F / Δx = 3 / 5 = 0.6

k _E = F / Δx = 2 / 4 = 0.5

12. Yiliphi igrafu u-h enezingqimba ezinkulu kakhulu ze-elastic?

Isixazululo:

Ukunwebeka okuhlala njalo :

k _A = F / Δx = 50 / 10 = 5

k _B = F / Δx = 50 / 0.1 = 500

k _C = F / Δx = 5 / 0.1 = 50

k _D = F / Δx = 500 / 0.1 = 5000

k _E = F / Δx = 500 / 10 = 50

Amandla angaba khona entwasahlobo:

13. Igrafu engezansi ikhombisa ubudlelwano phakathi kwamandla noshintsho lobude bentwasahlobo. Yimaphi amandla angase abe khona entwasahlobo, ngokusho kwegrafu engezansi.

Kwaziwa:

F = 40N

x = amamitha angu-0.08

Okufunwayo : Amandla angaba khona entwasahlobo

Isixazululo:

I-Constant yentwasahlobo:

k = F / Δx = 40 / 0.08 = 500 N/m

Amandla angaba khona entwasahlobo:

I-PE = 1/2 kx ² = 1/2 (500) (0.08) = (250) (0.08) = 20 Joules

14. Ibhulokhi elingamakhilogremu angu-2 linamathiselwe entwasahlobo. Uma ukwanda kobude bentwasahlobo kungu-5 cm futhi ukusheshisa ngenxa yamandla adonsela phansi kungu-10 m/s ² , yimaphi amandla angaba khona entwasahlobo.

Kwaziwa:

Ukwanda kobude (Δx) = 5 cm = 0.05 amamitha

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Isisindo sebhulokhi (m) = 2 kg

Isisindo sebhulokhi (w) = mg = (2)(10) = 20 amaNewton

Okufunwayo: amandla angaba khona entwasahlobo

Isixazululo:

Ukuqina kokuqina:

k = w / Δx = 20 / 0.05 = 400 N/m

Amandla angaba khona entwasahlobo:

PE = ½ k Δx ² = ½ (400) (0.05) ² = (200) (0.0025)

PE = 0.5 amaJoule

15. Ushintsho lobude bentwasahlobo luyi-5 cm uma ludonswa ngamandla angu-20-N. Yimaphi amandla angaba khona entwasahlobo uma ushintsho lobude bentwasahlobo luyi-10 cm.

Kwaziwa:

Ushintsho lobude (Δx) = 5 cm = 0.05 amamitha

Amandla (F) = 20 Newton

Okufunwayo : Amandla angaba khona entwasahlobo

Isixazululo:

I-constant yentwasahlobo:

k = F / Δx = 20 / 0.05 = 400 N/m

Amandla angase abe khona entwasahlobo lapho i-Δx = 10 cm = 0.1 m:

PE = ½ k Δx ² = ½ (400) (0.1) ² = (200) (0.01)

PE = 2 amaJoule

Isisindo sento

16. Iziphethu ezine lapho i-constant yephethu ngayinye ingu-800 N/m, ixhunywe ngochungechunge-ngokufana, njengoba kuboniswe esithombeni. Ibhulokhi linamathiselwe entwasahlobo. Ushintsho lobude bazo zonke iziphethu lungama-5 cm. Siyini isisindo samabhulokhi.

Kwaziwa:

k ₁ = k ₂ = k ₃ = k ₄ = 800 N m ⁻¹

Δx = 5 cm = 0.05 m

Okufunwayo: isisindo sebhulokhi (w)

Isixazululo:

Nquma i-constant yentwasahlobo elinganayo

Intwasahlobo 1 (k₁), intwasahlobo 2 (k₂) kanye nentwasahlobo 3 (k₃) zixhunywe ngokulingana. I-constant yentwasahlobo efanayo :

k _p = k ₁ + k ₂ + k ₃ = 800 + 800 + 800 = 2400 Nm ⁻¹

Intwasahlobo p (k _P ) kanye nentwasahlobo 4 (k ₄ ) zixhunywe ngochungechunge. I-constant yentwasahlobo efanayo:

1/k _s = 1/k _p + 1/k ₄ = 1/2400 + 1/800 = 1/2400 + 3/2400 = 4/2400

ks = 2400/4 = 600 ^Nm ₋₁

I-constant yesiphethu esilinganayo ingu-600 Nm ^-1

Nquma isisindo sento:

Isilinganiso somthetho kaHooke:

F = k Δx noma w = k Δx

Isisindo sento:

w = (600 Nm ^-1 )(0.05 m) = 30 Newtons

17. Iziphethu ezine zixhunywe ngochungechunge oluhambisanayo. I-constant yephethu ngayinye ingu-1600 N/m. Ibhulokhi linamathiselwe ekupheleni kwentwasahlobo, njengoba kuboniswe esithombeni. Ukwanda kobude bazo zonke iziphethu kungu-5 cm. Siyini isisindo samabhulokhi.

Kwaziwa:

k ₁ = k ₂ = k ₃ = k ₄ = 1600 N m ⁻¹

Δx = 5 cm = 0.05 m

Kufunwa: isisindo sebhulokhi

Isixazululo:

Nquma i-constant yentwasahlobo elinganayo

Intwasahlobo 1 (k₁), intwasahlobo 2 (k₂) kanye nentwasahlobo 3 (k₃) zixhunywe ngokulingana. I-constant yentwasahlobo efanayo :

k _P = k ₁ + k ₂ + k ₃ = 1600 + 1600 + 1600 = 4800 Nm ⁻¹

Intwasahlobo p (k _P ) kanye nentwasahlobo 4 (k ₄ ) zixhunywe ngochungechunge. I-constant yentwasahlobo efanayo:

1/k _s = 1/k _p + 1/k ₄ = 1/4800 + 1/1600 = 1/4800 + 3/4800 = 4/4800

ks = 4800/4 = 1200 ^Nm ₋₁

I-constant yesiphethu esilinganayo ingu-1200 Nm ^-1

Nquma isisindo sento:

Isilinganiso somthetho kaHooke:

F = k Δx noma w = k Δx

Isisindo sento:

w = (1200 Nm ^-1 )(0.05 m) = 60 Newtons

1. Uyini uMthetho kaHooke?
   • Impendulo: UMthetho kaHooke uchaza ubudlelwano phakathi kwamandla asetshenziswa entweni enwebekayo kanye nokuguquguquka okubangelwa yilokhu (ngokuvamile ukunwebeka noma ukucindezela). Ngokuqondile, uthi amandla adingekayo ukucindezela noma ukwandisa isipilingi alingana ngqo nebanga elinwetshiwe noma elicindezelwe ngalo, uma nje umkhawulo we-elastic ungadluli.
2. Kusho ukuthini uma sithi into ethile isifinyelele umkhawulo wayo wokunwebeka?
   • Impendulo: Uma into isifinyelele umkhawulo wayo wokunwebeka, kusho ukuthi ngeke isabuyela esimweni sayo sokuqala noma usayizi ngemva kokususwa kwamandla okuguqula. Ngale kwaleli phuzu, into iziphatha njengepulasitiki futhi ingase iguqulwe unomphela.
3. I-spring constant (k) ihlobene kanjani nokuqina kwe-spring?
   • Impendulo: I-spring constant (k) iyisilinganiso sokuqina kwentwasahlobo. Inani elikhulu lika-k libonisa intwasahlobo eqinile, okusho ukuthi kudingeka amandla engeziwe ukuze iguqulwe inani elithile, kuyilapho u-k omncane ebonisa intwasahlobo evumelana kakhulu noma ethambile.
4. Yiziphi amayunithi e-spring constant ohlelweni lwe-SI?
   • Impendulo: Kuhlelo lwe-SI, amayunithi e-spring constant (k) angama-Newton ngemitha (N/m).
5. Kungani ukuziphatha okuchazwe uMthetho kaHooke kubhekwa njengokuqondile?
   • Impendulo: Ukuziphatha kubhekwa njengokuqondile ngoba ubudlelwano phakathi kwamandla asetshenziswayo (F) kanye nokufuduka (x) buwumugqa oqondile, kanti ubudlelwano bunikezwe njengo $F=kx$, lapho u-k eyisiguquguquki sento ethile noma isiphethu.
6. Ingabe uMthetho kaHooke usebenza eziphethwini kuphela?
   • Impendulo: Cha, uMthetho kaHooke usebenza kunoma yiziphi izinto ezinwebekayo eziguquka ngendlela eqondile ngamandla asetshenziswayo, kuze kufike emkhawulweni wazo wokunwebeka. Nakuba izipilingi ziyisibonelo esivamile, ezinye izinto ezifana namabhande enjoloba, izinsimbi ezingaphansi kokuguquguquka okuncane, kanye nezinye izicubu eziphilayo nazo zingabonisa ukuziphatha okuchazwe uMthetho kaHooke.
7. Kwenzekani uma into inwetshwa ngaphezu komkhawulo wayo wokunwebeka kodwa inganele ukuphuka?
   • Impendulo: Uma into inwetshwa ngaphezu komkhawulo wayo wokunwebeka kodwa ingaze iphuke, izoguqulwa yipulasitiki. Lokhu kusho ukuthi lapho amandla esuswa, into ngeke ibuyele esimweni sayo sokuqala ngokuphelele, futhi kuzosala ukuguquka okungapheli.
8. Imibono yokucindezeleka nokucindezeleka ihlobene kanjani noMthetho kaHooke?
   • Impendulo: Ukucindezeleka kungamandla asetshenziswa endaweni ngayinye, kanti ukucindezeleka kungukuguquguquka okuhlobene kwezinto. Umthetho kaHooke maqondana nokucindezeleka nokucindezeleka uthi ukucindezeleka kuhambisana ngqo nokucindezeleka, kanti ukulingana okungaguquki kuyi-modulus yezinto ezibonakalayo ze-Young. Lena enye indlela yokuveza ubudlelwano obuqondile phakathi kwamandla nokuguquguquka, kodwa ngezinto ezinkulu hhayi nje ngezipringi.
9. Iyini i-Young's Modulus futhi ihlobene kanjani nokunwebeka?
   • Impendulo: I-Modulus kaYoung, evame ukumelelwa yincwadi $E$, iyisilinganiso sokuqina kwezinto ngokwengcindezi noma ukucindezelwa. Ichaza ikhono lezinto lokumelana nokuguquguquka ngaphansi kwamandla asetshenziswayo. I-Young's Modulus ephezulu ikhombisa izinto eziqinile, futhi ichazwa njengesilinganiso sokucindezeleka nokucindezeleka.
10. Ingabe zonke izinto zingachazwa nguMthetho kaHooke?

• Impendulo: Cha, akuzona zonke izinto ezisebenza ngokoMthetho kaHooke. Izinto eziningi, ikakhulukazi lezo ezingezona eziqondile, ezi-viscoelastic, noma ezipulasitiki, azibonisi ubudlelwano obuqondile phakathi kokucindezeleka nokucindezeleka. UMthetho kaHooke uyincazelo efanelekile futhi unembile kakhulu ekuguquguqukeni okuncane kwezinto ezinwebekayo.