Sharciga Hooke iyo dabacsanaanta - dhibaatooyinka iyo xalalka

Sharciga Hooke iyo dabacsanaanta - dhibaatooyinka iyo xalalka

Isbeddelka dhererka

1. Ul waxay leedahay dherer L ah, oo ay jiidato xoog F ah. Cadadka dheereynta waa ∆L. Waa maxay baaxadda xoogga haddii isbeddelka dhererku yahay 4∆L.

La yaqaan:

Xoogga 1 (F ₁ ) = F

Isbeddelka dhererka 1 (∆L ₁ ) = ∆L

Isbeddelka dhererka 2 (∆L ₂ ) = 4 ∆L

La Raadinayo: Xoogga 2 (F ₂ )

Xalka:

Isle'egta sharciga Hooke

k = F / ΔL

k = dabacsanaan joogto ah, F = xoogga F, ΔL = isbeddelka dhererka

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. Guga waxaa ku xiran yihiin taxane is barbar socda, sida ka muuqata sawirka hoose. Guga 1 wuxuu leeyahay joogto ah 200 N/m, guga 2 wuxuu leeyahay joogto ah 200 N/m iyo guga 3 wuxuu leeyahay joogto ah 200 N/m. Cufka shaygu waa 100 garaam iyo dardargelinta cuf-isjiidadka awgeed waa 10 m/s²Waa maxay isbeddelka dhererka ka u dhiganta guga.

La yaqaan:

Cufka walaxda (m) = 100 garaam = 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

La Doonayo: Isbeddelka dhererka guga u dhigma.

Xalka:

Go'aami u dhigma joogto ah guga:

Gu'ga 2 (k2 ₎ iyo gu'ga 3 (k3 ₎ ayaa isku xiran si is barbar socda. Joogtada guga ee u dhiganta:

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

Gu'ga 1 (k ₁ ) iyo gu'ga p (k _P ) waxay ku xiran yihiin taxane. Joogtada guga ee u dhiganta:

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

ks ₌ 400/3 Nm ⁻¹

Joogtada guga ee u dhiganta waa 400/3 Nm ^-1

Go'aami isbeddelka dhererka guga u dhigma :

Isle'egta sharciga Hooke:

∆x = F / k = w / k

Isbeddelka dhererka guga u dhigma :

∆x = w / k

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

Joogtada ah ee gu'ga

3. Waa maxay joogtada gu'ga sida ku cad xogta ku jirta jadwalka hoose.

Xalka:

Isle'egta sharciga Hooke:

k = F / Δx

Joogtada ah ee gu'ga:

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

4. Saddex gu' ayaa isku xiran taxane-isbarbar socda sida ku cad jaantuska hoose. Joogtada gu'ga k ₁ = k ₂ = 3 Nm ⁻¹ iyo k ₃ = 6 Nm ⁻¹ . Waa maxay joogsiga u dhigma gu'ga.

La yaqaan:

Joogtada guga 1 (k1 ₎ = joogto ah guga 2 (k2 ₎ = 3 Nm ⁻¹

Joogtada guga 3 (k3 ₎ = 6 Nm ⁻¹

La rabay: joogto ah oo ah guga u dhigma (k)

Xalka:

Gu'ga 1 (k ₁ ) iyo gu'ga 2 (k ₂ ) ayaa isku xiran si is barbar socda. Joogtada guga u dhigma:

k _p = k ₁ + k ₂ = 3 + 3 = 6 Nm ⁻¹

Gu'ga p (k _P ) iyo gu'ga 3 (k ₃ ) waxay ku xiran yihiin taxane. Joogtada gu'ga u dhigma:

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

k _s = 6/2 = 3 Nm ⁻¹

Joogtada u dhiganta gu'ga = 3 Nm ⁻¹.

5. Gu' dhererkiisu yahay L, oo ​​lagu jiiday miisaanka w. Sida ku cad xogta ku jirta jadwalka hoose, waa maxay joogtada gu'ga u dhigma:

Xalka:

k = F / Δx

Joogtada ah ee gu'ga:

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

6. Sida ku cad xogta ku jirta jadwalka hoose, waa maxay joogtada gu'ga u dhigma:

Xalka:

k = F / Δx = w / Δx = mg / Δx

k = dabacsanaan joogto ah, w = miisaan, m = cufnaan, g = dardargelin cufisjiidadka awgeed, Δx = isbeddelka dhererka

Joogtada guga:

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

7. Haddii k ₁ = 4k, waa maxay joogtada gu'ga u dhigma.

Xalka:

Laba ilo ayaa isku xiran iyagoo is barbar socda. Joogtada guga u dhigma:

k _p = k + k = 2k

Laba gu' ayaa isku xiran taxane ahaan. Joogtada guga u dhigma.

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

k _s = 4k/3

8. Sida ku cad xogta ku jirta jadwalka hoose, waa maxay joogtada gu'ga u dhigma:

Xalka:

Isle'egta sharciga Hooke:

k = F / Δ L

Joogtada ah ee gu'ga:

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

9. Joogtada ugu yar waa…

Solution

Isle'egta sharciga Hooke:

k = F / Δx

k = dabacsanaan joogto ah, F = xoog, Δx = isbeddelka dhererka

Joogtada ah ee dabacsanaanta:

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. Waa maxay joogtada ugu weyn sida ku cad xogta ku jirta jadwalka hoose.

Xalka:

Isle'egta sharciga Hooke:

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

Joogtada ugu weyn waa 320 Nm ^-1.

11. Jaantuska hoose wuxuu muujinayaa xiriirka ka dhexeeya isbeddelka xoogga (ΔF) iyo kororka dhererka (Δx). Waa maxay garaafka muujinaya joogtada ugu yar ee dabacsanaanta.

Solution

Isle'egta sharciga Hooke:

k = F / Δx

Δx = isbeddelka dhererka, F = xoog, k = joogtaynta dabacsanaanta

Joogtada ah ee dabacsanaanta:

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. Garaafkee h ayaa leh joogtada ugu weyn ee laastikada ah?

Xalka:

Joogtada ah ee dabacsanaanta :

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

Tamarta suurtagalka ah ee gu'ga:

13. Jaantuska hoose wuxuu muujinayaa xiriirka ka dhexeeya xoogga iyo isbeddelka dhererka gu'ga. Waa maxay tamarta suurtagalka ah ee gu'ga, sida ku cad jaantuska hoose.

La yaqaan:

F = 40N

x = 0.08 mitir

La Doonayo : Tamarta suurtagalka ah ee guga

Xalka:

Joogtada ah ee gu'ga:

k = F / Δx = 40 / 0.08 = 500 N/m

Tamarta suurtagalka ah ee gu'ga:

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

14. Baloog 2-kg ah ayaa lagu xiraa guga. Haddii kororka dhererka gu'gu uu yahay 5 cm oo dardargelinta cufisjiidadka awgeed ay tahay 10 m/s ² , waa maxay tamarta suurtagalka ah ee gu'ga.

La yaqaan:

Kordhinta dhererka (Δx) = 5 cm = 0.05 mitir

Dardargelinta cufisjiidadka awgeed (g) = 10 m/s ²

Cufka baloogga (m) = 2 kg

Miisaanka baloogga (w) = mg = (2)(10) = 20 Newtons

La Doonayo: tamarta suurtagalka ah ee guga

Xalka:

Joogtada ah ee dabacsanaanta:

k = w / Δx = 20 / 0.05 = 400 N/m

Tamarta suurtagalka ah ee gu'ga:

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

PE = 0.5 Joule

15. Isbeddelka dhererka gu'ga waa 5 cm marka lagu jiido xoog 20-N ah. Waa maxay tamarta suurtagalka ah ee gu'ga marka isbeddelka dhererka gu'gu uu yahay 10 cm.

La yaqaan:

Isbeddelka dhererka (Δx) = 5 cm = 0.05 mitir

Xoogga (F) = 20 Newton

La Doonayo : Tamarta suurtagalka ah ee guga

Xalka:

Joogtada ah ee gu'ga:

k = F / Δx = 20 / 0.05 = 400 N/m

Tamarta suurtagalka ah ee gu'ga marka Δx = 10 cm = 0.1 m:

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

PE = 2 Joule

Miisaanka walaxda

16. Afar ilbiriqood oo joogto ah oo gu' kasta ah uu yahay 800 N/m, oo isku xiran taxane-isbarbardhig ah, sida ku cad sawirka. Baloog ayaa ku xiran gu'ga. Isbeddelka dhererka dhammaan ilbiriquhu waa 5 cm. Waa maxay miisaanka baloogyada.

La yaqaan:

k ₁ = k ₂ = k ₃ = k ₄ = 800 N m ⁻¹

Δx = 5 cm = 0.05 m

La Rabay: miisaanka baloogga (w)

Xalka:

Go'aami joogtada ah ee guga u dhigma

Gu'ga 1 (k)₁), guga 2 (k₂) iyo guga 3 (k₃) waxay ku xiran yihiin is barbar socda. Joogtada guga u dhigma:

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

Gu'ga p (k _P ) iyo gu'ga 4 (k ₄ ) waxay ku xiran yihiin taxane. Joogtada gu'ga u dhigma:

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

k _s = 2400/4 = 600 Nm ⁻¹

Joogtada guga u dhiganta waa 600 Nm ^-1

Go'aami miisaanka shayga:

Isle'egta sharciga Hooke:

F = k Δx ama w = k Δx

Miisaanka shayga:

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

17. Afar ilbiriqood ayaa isku xiran taxane ahaan. Joogtada guga kasta waa 1600 N/m. Baloog ayaa ku xiran dhammaadka guga, sida ku cad sawirka. Kordhinta dhererka dhammaan ilbiriqoodyadu waa 5 cm. Waa maxay miisaanka baloogyada.

La yaqaan:

k ₁ = k ₂ = k ₃ = k ₄ = 1600 N m ⁻¹

Δx = 5 cm = 0.05 m

La Doonayo: miisaanka baloogga

Xalka:

Go'aami joogtada ah ee guga u dhigma

Gu'ga 1 (k)₁), guga 2 (k₂) iyo guga 3 (k₃) waxay ku xiran yihiin is barbar socda. Joogtada guga u dhigma:

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

Gu'ga p (k _P ) iyo gu'ga 4 (k ₄ ) waxay ku xiran yihiin taxane. Joogtada gu'ga u dhigma:

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

k _s = 4800/4 = 1200 Nm ⁻¹

Joogtada guga u dhiganta waa 1200 Nm ^-1

Go'aami miisaanka shayga:

Isle'egta sharciga Hooke:

F = k Δx ama w = k Δx

Miisaanka walaxda:

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

1. Waa maxay Sharciga Hooke?
   • Jawaab: Sharciga Hooke wuxuu qeexayaa xiriirka ka dhexeeya xoogga lagu dabaqay shay laastikada ah iyo isbeddelka ka dhasha (badanaa dheereynta ama cadaadiska). gaar ahaan, wuxuu sheegayaa in xoogga loo baahan yahay in lagu cadaadiyo ama lagu kordhiyo guga uu si toos ah ugu dhigmayo masaafada la fidiyay ama la cadaadiyay, haddii xadka laastikada aan la dhaafin.
2. Maxay ka dhigan tahay marka aan nidhaahno walax ayaa gaartay xadka laastikada?
   • Jawaab: Marka walaxdu gaarto xadka laastikada, waxay la macno tahay inaysan dib ugu soo laaban doonin qaabkeedii ama cabbirkeedii asalka ahaa ka dib marka laga saaro xoogga beddelka. Wixii ka dambeeya qodobkan, walaxdu waxay u dhaqantaa si balaastig ah waxayna si joogto ah u qalloocan kartaa.
3. Sidee ayuu joogtada gu'ga (k) ula xiriiraa adkaanta gu'ga?
   • Jawaab: Joogtada guga (k) waa cabbir lagu cabbiro adkaanta gu'ga. Qiimaha weyn ee k wuxuu tilmaamayaa gu' adag, taasoo la macno ah in loo baahan yahay xoog badan si loo beddelo xaddi la bixiyay, halka k yar uu tilmaamayo gu' aad u hoggaansan ama jilicsan.
4. Waa maxay cutubyada joogtada guga ee nidaamka SI?
   • Jawaab: Nidaamka SI, cutubyada joogtada guga (k) waa Newtons halkii mitir (N/m).
5. Maxaa dhaqanka lagu sharraxay Sharciga Hooke loogu arkaa mid toosan?
   • Jawaab: Dhaqanka waxaa loo arkaa mid toosan sababtoo ah xiriirka ka dhexeeya xoogga la adeegsaday (F) iyo barokaca (x) waa xariiq toosan, iyadoo xiriirka la bixiyay sida $F=kx$, halkaas oo k uu yahay joogto ah oo loogu talagalay walxo ama gu' la bixiyay.
6. Sharciga Hooke ma khuseeyaa oo keliya ilaha biyaha?
   • Jawaab: Maya, Sharciga Hooke wuxuu khuseeyaa walxo kasta oo laastikada ah oo si toosan u beddesha xoogga la mariyey, ilaa xadka laastikada. In kasta oo ilo-biyoodku ay yihiin tusaale caadi ah, haddana walxaha kale sida xargaha caagga ah, biraha hoos yimaada isbeddellada yaryar, iyo qaar ka mid ah unugyada bayoolojiga ayaa sidoo kale muujin kara hab-dhaqanka lagu sharraxay Sharciga Hooke.
7. Maxaa dhacaya haddii walax la fidiyo oo ka baxsan xadka laastikada laakiin aan ku filnayn inay jabto?
   • Jawaab: Haddii walax la fidiyo oo ka baxsan xadka laastikada laakiin aan la gaarin heer ay jabto, waxay mari doontaa isbeddel balaastig ah. Taas macnaheedu waa marka xoogga la saaro, walaxdu si buuxda uma soo noqon doonto qaabkeedii asalka ahaa, oo isbeddel joogto ah ayaa sii jiri doona.
8. Sidee bay fikradaha walbahaarka iyo cadaadiska ula xiriiraan Sharciga Hooke?
   • Jawaab: Cadaadisku waa xoogga la isticmaalo halkii cutubba, cadaadiskuna waa isbeddelka qaraabada ah ee walaxda. Sharciga Hooke marka la eego cadaadiska iyo cadaadiska wuxuu sheegayaa in walbahaarka uu si toos ah ugu dhigmayo cadaadiska, iyadoo joogtada saamiga uu yahay habka Young's ee walaxda. Tani waa hab kale oo lagu muujiyo xiriirka toosan ee u dhexeeya xoogga iyo isbeddelka, laakiin walxaha badan halkii laga isticmaali lahaa kaliya ilo.
9. Waa maxay Modulus-ka Young, sideese ula xiriirtaa dabacsanaanta?
   • Jawaab: Modulus-ka Young, oo badanaa lagu matalo xarafka $E$, waa cabbir lagu cabbiro adkaanta walaxda marka la eego xiisadda ama cadaadiska. Waxay qeexaysaa awoodda walaxda ee ay u leedahay inay iska caabiso isbeddelka iyadoo la adeegsanayo xoog la adeegsanayo. Modulus-ka Young ee sare wuxuu tilmaamayaa walax adag, waxaana lagu qeexaa saamiga walbahaarka iyo cadaadiska.
10. Dhammaan agabka ma lagu sharxi karaa Sharciga Hooke?

• Jawaab: Maya, dhammaan agabku ma dhaqmaan sida waafaqsan Sharciga Hooke. Agab badan, gaar ahaan kuwa aan tooska ahayn, viscoelastic, ama balaastig, ma muujiyaan xiriir toosan oo u dhexeeya walbahaarka iyo cadaadiska. Sharciga Hooke waa sharraxaad ku habboon waana midka ugu saxsan ee isbeddellada yaryar ee agabka laastikada.