Txoj Cai Hooke thiab Elasticity - Teeb Meem thiab Kev Dais Teeb Meem

Txoj Cai Hooke thiab Elasticity - Teeb Meem thiab Kev Dais Teeb Meem

Qhov kev hloov pauv ntawm qhov ntev

1. Ib tug pas nrig muaj qhov ntev L, rub los ntawm lub zog F. Qhov ntev ntawm qhov ntev yog ∆L. Yog tias qhov kev hloov pauv ntawm qhov ntev yog 4∆L, qhov loj ntawm lub zog yog dab tsi.

Paub:

Lub zog 1 (F₁) = F

Qhov kev hloov pauv ntawm qhov ntev 1 (∆L₁) = ∆L

Qhov kev hloov pauv ntawm qhov ntev 2 (∆L₂) = 4 ΔL

Xav tau: Lub zog 2 (F₂)

Tshuaj:

Tus qauv ntawm Txoj cai ntawm Hooke

k = F / ΔL

k = qhov tsis hloov pauv ntawm elasticity, F = lub zog ntawm F, ΔL = qhov hloov pauv ntawm qhov ntev

k₁ = k₂

F₁ / ΔL₁ =F₂ / ΔL₂

F / ΔL = F₂ / 4ΔL

F / 1 = F₂ / 4

F = F₂ / 4

F₂ = 4F

2. Cov caij nplooj ntoos hlav no txuas ua ke ua kab sib luag, raws li pom hauv daim duab hauv qab no. Caij nplooj ntoos hlav 1 muaj qhov ruaj khov 200 N/m, caij nplooj ntoos hlav 2 muaj qhov ruaj khov 200 N/m thiab caij nplooj ntoos hlav 3 muaj qhov ruaj khov 200 N/m. Qhov hnyav ntawm yam khoom yog 100 grams thiab acceleration vim lub ntiajteb txawj nqus yog 10 m/s²Qhov kev hloov pauv ntawm qhov ntev yog dab tsi? lub sib npaug caij nplooj ntoo hlav.

Paub:

Cov khoom loj (m) = 100 grams = 0.1 kg

k₁ = k₂ = k₃ = 200 N/m2

w = mg = (0.1 kg)(10 m/s)²) = 1 kg m/s² = 1 Newtons

Xav tau: Qhov kev hloov pauv ntawm qhov ntev ntawm sib npaug caij nplooj ntoo hlav.

Tshuaj:

Txheeb xyuas qhov sib npaug lub caij nplooj ntoos hlav tas li:

Caij nplooj ntoos hlav 2 (k₂) thiab lub caij nplooj ntoos hlav 3 (k₃) txuas nrog ua ke. Qhov sib npaug lub caij nplooj ntoos hlav tas li:

k_p = k₂ +k₃ = 200 + 200 = 400 Nm^-1

Caij nplooj ntoos hlav 1 (k₁) thiab lub caij nplooj ntoos hlav p (k_P) txuas ua ke. Lub caij nplooj ntoos hlav sib npaug tas li:

1/k_s = 1/k_p + 1/k₁ = 1/400 + 1/200 = 1/400 + 2/400 = 3/400

k_s = 400/3 Nm^-1

Qhov sib npaug lub caij nplooj ntoos hlav tas li yog 400 / 3 Nm^-1

Txheeb xyuas qhov kev hloov pauv ntawm qhov ntev ntawm lub sib npaug caij nplooj ntoos hlav:

Cov qauv ntawm Hooke txoj cai lij choj:

∆x = F / k = w / k

Qhov kev hloov pauv ntawm qhov ntev ntawm lub sib npaug caij nplooj ntoos hlav:

∆x = w / k

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

Qhov tsis tu ncua ntawm lub caij nplooj ntoos hlav

3. Tus nqi tsis hloov pauv ntawm lub caij nplooj ntoos hlav raws li cov ntaub ntawv hauv lub rooj hauv qab no yog dab tsi.

Tshuaj:

Cov qauv ntawm Hooke txoj cai lij choj:

k = F / Δx

Qhov tsis hloov ntawm lub caij nplooj ntoos hlav:

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

4. Peb lub caij nplooj ntoos hlav txuas ua ke raws li qhia hauv daim duab hauv qab no. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav k₁ = k₂ = 3 Nm^-1 thiab k₃ = 6 Nm^-1Qhov tsis hloov pauv ntawm qhov sib npaug ntawm lub caij nplooj ntoos hlav yog dab tsi.

Paub:

Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav 1 (k)₁) = qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav 2 (k₂) = 3 Nm^-1

Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav 3 (k)₃) = 6 Nm^-1

Xav tau: qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug (k)

Tshuaj:

Caij nplooj ntoos hlav 1 (k₁) thiab lub caij nplooj ntoos hlav 2 (k₂) txuas nrog ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

k_p = k₁ +k₂ = 3 + 3 = 6 Nm^-1

Caij nplooj ntoos hlav p (k_P) thiab lub caij nplooj ntoos hlav 3 (k₃ ) txuas ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

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

Qhov tsis hloov pauv ntawm qhov sib npaug ntawm lub caij nplooj ntoos hlav = 3 Nm^-1.

5. Ib lub caij nplooj ntoos hlav uas ntev li L, rub los ntawm qhov hnyav li w. Raws li cov ntaub ntawv hauv lub rooj hauv qab no, qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug yog dab tsi:

Tshuaj:

k = F / Δx

Qhov tsis hloov ntawm lub caij nplooj ntoos hlav:

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

6. Raws li cov ntaub ntawv hauv lub rooj hauv qab no, qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug yog dab tsi:

Tshuaj:

k = F / Δx = w / Δx = mg / Δx

k = qhov tsis hloov pauv ntawm elasticity, w = qhov hnyav, m = pawg, g = kev nrawm vim yog lub ntiajteb txawj nqus, Δx = qhov hloov pauv ntawm qhov ntev

Caij nplooj ntoos hlav tas li:

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

7. Yog tias k₁ = 4k, qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug yog dab tsi.

Tshuaj:

Ob lub caij nplooj ntoos hlav txuas ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

k_p = k + k = 2k

Ob lub caij nplooj ntoos hlav txuas ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug

1/k_s = 1/k_p + 1/k₁ = 1 / 2k + 1 / 4k = 2 / 4k + 1 / 4k = 3 / 4k

k_s = 4k/3

8. Raws li cov ntaub ntawv hauv lub rooj hauv qab no, qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug yog dab tsi:

Tshuaj:

Cov qauv ntawm Hooke txoj cai lij choj:

k = F / ΔL

Qhov tsis hloov ntawm lub caij nplooj ntoos hlav:

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

9. Tus nqi tsawg tshaj plaws yog ...

tshuaj

Cov qauv ntawm Hooke txoj cai lij choj:

k = F / Δx

k = qhov tsis hloov pauv ntawm elasticity, F = lub zog, Δx = qhov hloov pauv ntawm qhov ntev

Qhov tsis hloov pauv ntawm elasticity:

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. Tus nqi tsis hloov pauv loj tshaj plaws raws li cov ntaub ntawv hauv qab no yog dab tsi.

Tshuaj:

Cov qauv ntawm Hooke txoj cai lij choj:

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

Qhov siab tshaj plaws yog 320 Nm^-1.

11. Daim duab hauv qab no qhia txog kev sib txuas ntawm kev hloov pauv ntawm lub zog (ΔF) thiab kev nce ntxiv ntawm qhov ntev (Δx). Dab tsi yog daim duab qhia qhov tsawg tshaj plaws ntawm elasticityy.

tshuaj

Cov qauv ntawm Hooke txoj cai lij choj:

k = F / Δx

Δx = qhov kev hloov pauv ntawm qhov ntev, F = lub zog, k = qhov tsis hloov pauv ntawm elasticity

Qhov tsis hloov pauv ntawm elasticity:

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. Daim duab twgh muaj cov elastic constants loj tshaj plaws?

Tshuaj:

Tsis tu ncua ntawm elasticity :

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

Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav:

13.Daim duab hauv qab no qhia txog kev sib raug zoo ntawm lub zog thiab qhov kev hloov pauv hauv lub caij nplooj ntoos hlav ntev. Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav yog dab tsi, raws li daim duab hauv qab no.

Paub:

F = 40 N

x = 0.08 meters

xav : cov lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav

Tshuaj:

Qhov tsis hloov ntawm lub caij nplooj ntoos hlav:

k = F / Δx = 40 / 0.08 = 500 N/m

Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav:

PE = 1/2 kx² = 1/2 (500)(0.08) = (250)(0.08) = 20 Joules

14. Muaj ib lub thaiv 2-kg txuas rau ntawm lub caij nplooj ntoos hlav. Yog tias qhov ntev ntawm lub caij nplooj ntoos hlav nce ntxiv 5 cm thiab qhov kev nrawm vim lub ntiajteb txawj nqus yog 10 m/s², lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav yog dab tsi.

Paub:

Qhov nce ntawm qhov ntev (Δx) = 5 cm = 0.05 meters

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s²

Qhov hnyav ntawm lub thaiv (m) = 2 kg

Qhov hnyav ntawm lub thaiv (w) = mg = (2)(10) = 20 Newtons

Xav tau: lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav

Tshuaj:

Tus nqi ntawm elasticity:

k = w / Δx = 20 / 0.05 = 400 N/m

Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav:

PE = ½ k Δx² = ½ (400)(0.05)² = (200)(0.0025)

PE = 0.5 Joule

15. Qhov kev hloov ntawm qhov ntev ntawm lub caij nplooj ntoos hlav yog 5 cm thaum rub los ntawm lub zog 20-N. Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav yog dab tsi thaum qhov kev hloov ntawm qhov ntev ntawm lub caij nplooj ntoos hlav yog 10 cm.

Paub:

Qhov kev hloov pauv ntawm qhov ntev (Δx) = 5 cm = 0.05 meters

Lub zog (F) = 20 Newton

xav : Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav

Tshuaj:

Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav:

k = F / Δx = 20 / 0.05 = 400 N/m

Lub zog muaj peev xwm ntawm lub caij nplooj ntoos hlav thaum Δx = 10 cm = 0.1 m:

PE = ½ k Δx² = ½ (400)(0.1)² = (200)(0.01)

PE = 2 Joule

Qhov hnyav ntawm yam khoom

16. Plaub lub caij nplooj ntoos hlav uas qhov tsis hloov pauv ntawm txhua lub caij nplooj ntoos hlav yog 800 N/m, txuas ua ke ua kab sib luag, raws li pom hauv daim duab. Ib lub thaiv raug txuas rau ntawm lub caij nplooj ntoos hlav. Qhov kev hloov pauv ntawm qhov ntev ntawm txhua lub caij nplooj ntoos hlav yog 5 cm. Qhov hnyav ntawm cov thaiv yog dab tsi.

Paub:

k₁ = k₂ = k₃ = k₄ = 800 N m^-1

Δx = 5 cm = 0.05 m

Xav tau: qhov hnyav ntawm lub thaiv (w)

Tshuaj:

Txheeb xyuas qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug

Caij nplooj ntoos hlav 1 (k₁), lub caij nplooj ntoos hlav 2 (k₂) thiab lub caij nplooj ntoos hlav 3 (k₃) txuas nrog ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

k_p = k₁ +k₂ +k₃ = 800 + 800 + 800 = 2400 Nm^-1

Caij nplooj ntoos hlav p (k_P) thiab lub caij nplooj ntoos hlav 4 (k₄) txuas ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

1/k_s = 1/k_p + 1/k₄ = 1/2400 + 1/800 = 1/2400 + 3/2400 = 4/2400

k_s = 2400/4 = 600 Nm^-1

Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug yog 600 Nm^-1

Txheeb xyuas qhov hnyav ntawm yam khoom:

Cov qauv ntawm Hooke txoj cai lij choj:

F = k Δx los yog w = k Δx

Qhov hnyav ntawm yam khoom:

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

17. Muaj plaub lub caij nplooj ntoos hlav txuas ua ke. Lub zog ntawm txhua lub caij nplooj ntoos hlav yog 1600 N/m. Muaj ib lub thaiv txuas rau thaum kawg ntawm lub caij nplooj ntoos hlav, raws li pom hauv daim duab. Qhov ntev ntawm txhua lub caij nplooj ntoos hlav nce ntxiv yog 5 cm. Qhov hnyav ntawm cov thaiv yog dab tsi.

Paub:

k₁ = k₂ = k₃ = k₄ = 1600 N m^-1

Δx = 5 cm = 0.05 m

Xav tau: qhov hnyav ntawm thaiv

Tshuaj:

Txheeb xyuas qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug

Caij nplooj ntoos hlav 1 (k₁), lub caij nplooj ntoos hlav 2 (k₂) thiab lub caij nplooj ntoos hlav 3 (k₃) txuas nrog ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

k_P = k₁ +k₂ +k₃ = 1600 + 1600 + 1600 = 4800 Nm^-1

Caij nplooj ntoos hlav p (k_P) thiab lub caij nplooj ntoos hlav 4 (k₄) txuas ua ke. Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug:

1/k_s = 1/k_p + 1/k₄ = 1/4800 + 1/1600 = 1/4800 + 3/4800 = 4/4800

k_s = 4800/4 = 1200 Nm^-1

Qhov tsis hloov pauv ntawm lub caij nplooj ntoos hlav sib npaug yog 1200 Nm^-1

Txheeb xyuas qhov hnyav ntawm yam khoom:

Cov qauv ntawm Hooke txoj cai lij choj:

F = k Δx los yog w = k Δx

Qhov hnyav ntawm yam khoom:

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

1. Txoj Cai Hooke yog dab tsi?
   • teb: Txoj Cai Lij Choj Hooke piav qhia txog kev sib raug zoo ntawm lub zog siv rau ib yam khoom elastic thiab qhov deformation (feem ntau yog elongation lossis compression). tshwj xeeb, nws hais tias lub zog uas xav tau los nias lossis ntev lub caij nplooj ntoos hlav yog ncaj qha proportional rau qhov deb uas nws ncab lossis nias, yog tias qhov txwv elastic tsis tshaj.
2. Nws txhais li cas thaum peb hais tias cov khoom siv tau mus txog nws qhov kev txwv elastic?
   • teb: Thaum ib yam khoom siv tau mus txog nws qhov elastic limit, nws txhais tau tias nws yuav tsis rov qab mus rau nws cov duab lossis qhov loj qub tom qab lub zog deformation raug tshem tawm. Dhau ntawm qhov no, cov khoom siv ua plastically thiab tej zaum yuav deformed mus tas li.
3. Tus nqi tas mus li ntawm lub caij nplooj ntoos hlav (k) cuam tshuam li cas rau qhov tawv ntawm lub caij nplooj ntoos hlav?
   • teb: Tus nqi tas mus li ntawm lub caij nplooj ntoos hlav (k) yog qhov ntsuas qhov tawv ntawm lub caij nplooj ntoos hlav. Tus nqi loj dua ntawm k qhia tias lub caij nplooj ntoos hlav tawv dua, txhais tau tias yuav tsum muaj zog ntau dua los ua kom nws hloov pauv raws li qhov tau teev tseg, thaum tus nqi k me dua qhia tias lub caij nplooj ntoos hlav ua haujlwm tau zoo dua lossis mos dua.
4. Cov units ntawm lub caij nplooj ntoos hlav tas li hauv SI system yog dab tsi?
   • teb: Hauv SI system, cov chav rau lub caij nplooj ntoos hlav tas mus li (k) yog Newtons ib 'meter' (N/m).
5. Vim li cas tus cwj pwm piav qhia los ntawm Hooke's Law thiaj suav tias yog linear?
   • teb: Tus cwj pwm no suav hais tias yog linear vim tias kev sib raug zoo ntawm lub zog siv (F) thiab kev hloov chaw (x) yog ib txoj kab ncaj, nrog rau kev sib raug zoo muab ua $F=kx$, qhov twg k yog qhov tsis hloov pauv rau ib yam khoom lossis lub caij nplooj ntoos hlav.
6. Txoj Cai Hooke puas tsuas siv tau rau cov caij nplooj ntoos hlav xwb?
   • teb: Tsis yog, Hooke Txoj Cai siv tau rau txhua yam khoom siv elastic uas deforms linearly nrog lub zog siv, mus txog nws qhov txwv elastic. Thaum cov springs yog ib qho piv txwv, lwm yam khoom siv xws li cov roj hmab bands, cov hlau nyob rau hauv me me deformations, thiab qee cov ntaub so ntswg biological kuj tuaj yeem ua tus cwj pwm piav qhia los ntawm Hooke Txoj Cai.
7. Yuav ua li cas yog tias cov khoom siv raug ncab dhau nws qhov kev txwv elastic tab sis tsis txaus kom tawg?
   • teb: Yog tias ib yam khoom raug ncab dhau nws qhov kev ywj pheej tab sis tsis tau tawg, nws yuav raug hloov pauv yas. Qhov no txhais tau tias thaum lub zog raug tshem tawm, cov khoom yuav tsis rov qab mus rau nws cov duab qub, thiab qee qhov kev hloov pauv mus tas li yuav tseem nyob.
8. Cov tswv yim ntawm kev ntxhov siab thiab kev ntxhov siab muaj feem cuam tshuam li cas rau Hooke's Law?
   • teb: Kev ntxhov siab yog lub zog siv rau ib cheeb tsam, thiab kev ntxhov siab yog qhov kev hloov pauv ntawm cov khoom siv. Txoj Cai Hooke hais txog kev ntxhov siab thiab kev ntxhov siab hais tias kev ntxhov siab yog ncaj qha rau kev ntxhov siab, nrog rau qhov sib piv tas mus li yog cov khoom siv Young's modulus. Qhov no yog lwm txoj hauv kev los qhia txog kev sib raug zoo ntawm lub zog thiab kev hloov pauv, tab sis rau cov khoom siv loj dua li tsuas yog cov caij nplooj ntoos hlav xwb.
9. Young's Modulus yog dab tsi thiab nws cuam tshuam li cas rau elasticity?
   • teb: Young's Modulus, feem ntau yog sawv cev los ntawm tsab ntawv $E$, yog ib qho kev ntsuas ntawm cov khoom siv lub zog ntawm kev nruj lossis kev nias. Nws piav qhia txog cov khoom siv lub peev xwm los tiv taus kev hloov pauv hauv qab lub zog siv. Young's Modulus siab dua qhia txog cov khoom siv uas tawv dua, thiab nws tau txhais tias yog qhov sib piv ntawm kev ntxhov siab rau kev ntxhov siab.
10. Puas piav tau txhua yam khoom siv los ntawm Hooke's Law?

• teb: Tsis yog, tsis yog txhua yam khoom siv ua raws li Hooke's Law. Ntau yam khoom siv, tshwj xeeb tshaj yog cov uas tsis yog linear, viscoelastic, lossis yas, tsis qhia txog kev sib raug zoo ntawm kev ntxhov siab thiab kev ntxhov siab. Hooke's Law yog ib qho kev piav qhia zoo tagnrho thiab yog qhov tseeb tshaj plaws rau kev hloov pauv me me ntawm cov khoom siv elastic.