Mutemo waHooke uye kusimba kwesimba - matambudziko nemhinduro

Mutemo waHooke uye kusimba kwesimba - matambudziko nemhinduro

Kuchinja kwehurefu

1. Chimuti chine hurefu hweL, chinodhonzwa nesimba reF. Huwandu hwekureba i∆L. Hukuru hwesimba chii kana shanduko muhurefu iri 4∆L?

Zvinozivikanwa:

Simba 1 (F)₁) = F

Kuchinja kwehurefu 1 (∆L)₁) = ∆L

Kuchinja kwehurefu 2 (∆L)₂) = 4 ΔL

Zvaidiwa: Simba 2 (F)₂)

Solution:

Kuenzanisa kwe Mutemo waHooke

k = F / ΔL

k = kusagadzikana kwekusimba, F = simba raF, ΔL = kuchinja kwehurefu

k₁ = k₂

F₁ / ΔL₁ =F₂ / ΔL₂

F / ΔL = F₂ / 4ΔL

F / 1 = F₂ / 4

F = F₂ / 4

F₂ = 4F

2. Zvitubu zvakabatana muchikamu-chinofanana, sezvakaratidzwa mumufananidzo uri pazasi. Chitubu 1 chine 200 N/m isingachinji, chitubu 2 chine 200 N/m isingachinji uye chitubu 3 chine 200 N/m isingachinji. Huremu hwechinhu i100 magiramu uye kukurumidza nekuda kwegiravhiti iri 10 m/s²Chii chinonzi kuchinja kwehurefu hwe ari zvakaenzana chitubu.

Zvinozivikanwa:

Chinhu uremu (m) = magiramu 100 = 0.1 kg

k₁ = k₂ = k₃ = 200 N/m

w = mg = (0.1 kg)(10 m/s²) = 1 kg m/s² = 1 Newton

Zvaidiwa: Kuchinja kwehurefu hwe zvakaenzana chitubu.

Solution:

Sarudza zvakaenzana nguva dzose yechirimo:

Chitubu 2 (k)₂) uye chitubu 3 (k₃) zvakabatana zvakafanana. Zvakafanana nguva dzose yechirimo:

k_p = k₂ +k₃ = 200 + 200 = 400 Nm^-1

Chitubu 1 (k)₁) uye chitubu p (k_P) dzakabatana dzakatevedzana. Chimiro chechirimo chakaenzana:

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

k_s = 400/3 Nm^-1

The yakaenzana chitubu chisingaperi 400 / 3 Nm^-1

Sarudza shanduko muhurefu hwe ari zvakaenzana chitubu:

Kuenzanisa kwemutemo waHooke:

∆x = F / k = w / k

Kuchinja kwehurefu hwe ari zvakaenzana chitubu:

∆x = w / k

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

Chitubu chisingachinji

3. Chii chinonzi chitubu chisingaperi zvichienderana nedata riri patafura iri pazasi?

Solution:

Kuenzanisa kwemutemo waHooke:

k = F / Δx

Nguva dzose yechirimo:

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

4. Masipiringi matatu akabatana muzvikamu zvakafanana sezvakaratidzwa mumufananidzo uri pazasi. Chimiro chemasipiringi k₁ = k₂ = 3 Nm^-1 uye k₃ = 6 Nm^-1Chii chinonzi "constant" che "equivalent" yechirimo?

Zvinozivikanwa:

Nguva dzose yechirimo 1 (k)₁) = chisingaperi chechirimo 2 (k)₂) = 3 Nm^-1

Nguva dzose yechirimo 3 (k)₃) = 6 Nm^-1

Zvaidiwa: chisingaperi chechitubu chakaenzana (k)

Solution:

Chitubu 1 (k)₁) uye chitubu 2 (k₂) dzakabatana zvakafanana. Chimiro che "constant" chechirimo chakaenzana:

k_p = k₁ +k₂ = 3 + 3 = 6 Nm^-1

Chitubu p (k)_P) uye chitubu 3 (k₃ ) dzakabatana dzakatevedzana. Chimiro chechikamu chechirimo chakaenzana:

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

Chimiro chechinhu chakaenzana nechitubu = 3 Nm^-1.

5. Chitubu chine hurefu hweL, chakadhonzwa nehuremu hwew. Zvichienderana nedata riri patafura iri pazasi, chii chinonzi constant yechitubu chakaenzana:

Solution:

k = F / .X

Nguva dzose yechirimo:

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

6. Zvichienderana nedata riri patafura iri pazasi, chii chinonzi constant yechitubu chakaenzana:

Solution:

k = F / .X = w / .X = mg / .X

k = kusagadzikana kwekusimba, w = uremu, m ​​= uremu, g = kukurumidza nekuda kwegiravhiti, Δx = shanduko muhurefu

Chirimo chinogara kwenguva refu:

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

7. Kana k₁ = 4k, chii chinonzi constant yechitubu chakaenzana.

Solution:

Zvitubu zviviri zvakabatana zvakaenzana. Chimiro chezvitubu zvakafanana:

k_p = k + k = 2k

Masipiresi maviri akabatana akatevedzana. Chinogadzika chechitubu chakaenzana

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

k_s = 4k/3

8. Zvichienderana nedata riri patafura iri pazasi, chii chinonzi constant yechitubu chakaenzana:

Solution:

Kuenzanisa kwemutemo waHooke:

k = F / ΔL

Nguva dzose yechirimo:

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

9. Chinhu chidiki chisingaperi ndeche…

mhinduro

Kuenzanisa kwemutemo waHooke:

k = F / Δx

k = kusagadzikana kwekusimba, F = simba, Δx = kuchinja kwehurefu

Kugara kwenguva refu kwe 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. Ndeipi constant yakakura zvikuru zvichienderana nedata riri patafura iri pazasi.

Solution:

Kuenzanisa kwemutemo waHooke:

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

Chisingachinjiki chikuru i320 Nm^-1.

11. Girafu iri pazasi rinoratidza hukama huripo pakati pekuchinja kwesimba (ΔF) nekuwedzera kwehurefu (Δx). Chii chinonzi girafu inoratidza kusagadzikana kudiki kwe elasticityy.

mhinduro

Kuenzanisa kwemutemo waHooke:

k = F / Δx

Δx = kuchinja kwehurefu, F = simba, k = kusagadzikana kwekusimba

Kugara kwenguva refu kwe 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. Girafu ipih ine ma constant elastic akakura kupfuura mamwe ese?

Solution:

Nguva dzose ye kusimba :

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

Simba rinogona kuwanikwa muchirimo:

13.Girafu iri pazasi rinoratidza hukama huripo pakati pesimba ne shanduko mu kureba kwechitubu. Chii chingangoitika kuti chitubu chishande nesimba, zvichienderana negirafu iri pazasi.

Zvinozivikanwa:

F = 40N

x = 0.08 mamita

Wanted : The simba rinogona kuwanikwa rechirimo

Solution:

Nguva dzose yechirimo:

k = F / Δx = 40 / 0.08 = 500 N/m

Simba rinogona kuwanikwa muchirimo:

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

14. Bhokisi re2-kg rinosungirirwa muchirimo. Kana kuwedzera kwehurefu hwechirimo kuri 5 cm uye kumhanyisa nekuda kwegiravhiti kuri 10 m/s², chii chingangoitika kuti chitubu chive nesimba rei.

Zvinozivikanwa:

Kuwedzera kwehurefu (Δx) = 5 cm = 0.05 metres

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

Huremu hwebhuroko (m) = 2 kg

Kurema kwebhuroko (w) = mg = (2)(10) = 20 Newtons

Zvaidiwa: simba rinogona kuwanikwa muchirimo

Solution:

Kugara kwenguva refu kwe elasticity:

k = w / Δx = 20 / 0.05 = 400 N/m

Simba rinogona kuwanikwa muchirimo:

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

PE = 0.5 Joule

15. Kuchinja kwehurefu hwechitubu i5 cm kana ichidhonzwa nesimba re20-N. Ndeipi simba rinogona kushandiswa muchitubu kana kuchinja kwehurefu hwechitubu kuri 10 cm.

Zvinozivikanwa:

Kuchinja kwehurefu (Δx) = 5 cm = 0.05 metres

Simba (F) = 20 Newton

Wanted : Simba rinogona kuwanikwa muchirimo

Solution:

Chisingaperi chechirimo:

k = F / Δx = 20 / 0.05 = 400 N/m

Simba rinogona kuwanikwa muchirimo kana Δx = 10 cm = 0.1 m:

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

PE = 2 Joule

Kurema kwechinhu

16. Masipiya mana apo chisimbiso chechisipiti chimwe nechimwe chiri 800 N/m, chakabatana muchikamu-chakafanana, sezvakaratidzwa mumufananidzo. Bhokisi rakabatanidzwa pachisipiti. Kuchinja kwehurefu hwemasipiya ese i5 cm. Huremu hwemabhuroko chii?

Zvinozivikanwa:

k₁ = k₂ = k₃ = k₄ = 800 N m^-1

Δx = 5 cm = 0.05 m

Zvaidiwa: huremu hwebhuroko (w)

Solution:

Sarudza chisingaperi chechitubu chakaenzana

Chitubu 1 (k)₁), chitubu 2 (k₂) uye chitubu 3 (k₃) zvakabatana zvakafanana. Chimiro chechikamu chechitubu chakaenzana:

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

Chitubu p (k)_P) uye chitubu 4 (k₄) dzakabatana dzakatevedzana. Chimiro chechikamu chechirimo chakaenzana:

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

Chimiro chemuchina wakaenzana wechitubu i600 Nm^-1

Sarudza huremu hwechinhu:

Kuenzanisa kwemutemo waHooke:

F = k Δx kana w = k Δx

Kurema kwechinhu:

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

17. Masipiringi mana akabatana muchikamu-chakafanana. Chinochinjika chechirimo chimwe nechimwe i1600 N/m. Bhokisi rakabatanidzwa pakupera kwechirimo, sezvakaratidzwa mumufananidzo. Kuwedzera kwehurefu hwemasipiringi ese i5 cm. Huremu hwemabhuriki chii?

Zvinozivikanwa:

k₁ = k₂ = k₃ = k₄ = 1600 N m^-1

Δx = 5 cm = 0.05 m

Zvaidiwa: huremu hwebhuroko

Solution:

Sarudza chisingaperi chechitubu chakaenzana

Chitubu 1 (k)₁), chitubu 2 (k₂) uye chitubu 3 (k₃) zvakabatana zvakafanana. Chimiro chechikamu chechitubu chakaenzana:

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

Chitubu p (k)_P) uye chitubu 4 (k₄) dzakabatana dzakatevedzana. Chimiro chechikamu chechirimo chakaenzana:

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

Chimiro chemuchina wakaenzana wechitubu i1200 Nm^-1

Sarudza huremu hwechinhu:

Kuenzanisa kwemutemo waHooke:

F = k Δx kana w = k Δx

Kurema kwechinhu:

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

1. Mutemo waHooke chii?
   • Pindura: Mutemo waHooke unotsanangura hukama huripo pakati pesimba rinoshandiswa pachinhu chinopfava uye kuchinja kunokonzerwa nako (kazhinji kurebesa kana kudzvanywa). Zvikuru sei, unotaura kuti simba rinodiwa kuti ridzvanye kana kuwedzera chitubu rinoenderana zvakananga nedaro rayo rakatambanudzwa kana kudzvanywa, chero bedzi muganho wepfava usina kudarika.
2. Zvinorevei kana tichiti chinhu chasvika pamuganho wacho wekupfava?
   • Pindura: Kana chinhu chasvika pamuganho wacho wekupfava, zvinoreva kuti hachizodzokeri kuchimiro chacho chepakutanga kana saizi mushure mekunge simba rekupfava rabviswa. Pamusoro peizvi, chinhu chacho chinoita sepurasitiki uye chinogona kupfava zvachose.
3. Chinogadzika chemuchirimo (k) chine hukama hwakadii nekuoma kwechiprimo?
   • Pindura: Chinoganhurirwa chechitubu (k) chinoratidza kuomarara kwechitubu. Kukosha kukuru kwek kunoratidza chitubu chakasimba, zvichireva kuti simba rakawanda rinodiwa kuti chigadziriswe nehuwandu hwakatarwa, nepo k diki ichiratidza chitubu chakanyatsoenderana kana kuti chakapfava.
4. Ndezvipi zvikamu zvechitubu chisingaperi muSI system?
   • Pindura: Muchirongwa cheSI, mayuniti echitubu (k) ndiwo maNewtons pamita (N/m).
5. Sei maitiro anotsanangurwa neMutemo waHooke achionekwa seakafanana?
   • Pindura: Maitiro aya anoonekwa seakarongeka nekuti hukama huripo pakati pesimba rinoshandiswa (F) uye kutama (x) mutsetse wakatwasuka, hukama hwacho huchipiwa se $F=kx$, apo k iri chinhu chisingachinji chechinhu chakapihwa kana chitubu.
6. Mutemo waHooke unoshanda chete kumatsime emvura here?
   • Pindura: Kwete, Mutemo waHooke unoshanda kune chero chinhu chinonamira chinoshanduka-shanduka zvichienderana nesimba rinoshandiswa, kusvika pamuganho waro wekunamira. Kunyange zvazvo maspring ari muenzaniso wakajairika, zvimwe zvinhu zvakaita semabhandi erabha, simbi dzine madiki madiki, uye mamwe matishu ehupenyu zvinogonawo kuratidza maitiro anotsanangurwa neMutemo waHooke.
7. Chii chinoitika kana chinhu chikatambanudzwa kupfuura muganho wacho we elastic asi chisina kukwana kuti chityoke?
   • Pindura: Kana chinhu chikatambanudzwa kupfuura muganho wacho wekupfava asi chikasasvika pakutyoka, chichashanduka kuita purasitiki. Izvi zvinoreva kuti kana simba rabviswa, chinhu chacho hachizodzokeri zvachose kuchimiro chacho chepakutanga, uye chimwe chinhu chichashanduka zvachose.
8. Pfungwa dzekushushikana uye kushushikana dzinobatana sei neMutemo waHooke?
   • Pindura: Kushushikana isimba rinoshandiswa pachikamu chimwe nechimwe, uye kumanikidzwa ndiko kuchinja kwezvinhu. Mutemo waHooke panyaya yekushushikana nekumanikidzwa unoti kushushikana kwacho kwakanangana nekumanikidzwa, nepo kuenzana kuri modulus yechinhu ichi yeYoung. Iyi imwe nzira yekuratidza hukama huripo pakati pesimba nekusagadzikana, asi kune zvinhu zvakawanda kwete maspring chete.
9. Chii chinonzi Young's Modulus uye chinoenderana sei nekusimba kwemuviri?
   • Pindura: Modulus yaYoung, inowanzomiririrwa nebhii $E$, chiyero chekuomarara kwechigadzirwa maererano nekumanikidzwa kana kumanikidzwa. Chinotsanangura kugona kwechigadzirwa kuramba kushanduka pasi pesimba rinoshandiswa. Modulus yeYoung yepamusoro inoratidza chinhu chakasimba, uye inotsanangurwa sechiyero chekumanikidzwa nekumanikidzwa.
10. Zvinhu zvose zvinogona kutsanangurwa neMutemo waHooke here?

• Pindura: Kwete, hazvisi zvese zvinhu zvinotevedzera Mutemo waHooke. Zvinhu zvakawanda, kunyanya izvo zvisina kuenzana, zvakapfava, kana kuti zvepurasitiki, hazviratidzi hukama hwakaenzana pakati pekushushikana nekumanikidzwa. Mutemo waHooke itsananguro yakakodzera uye inonyanya kurongeka pakuchinja kudiki kwezvinhu zvinonamira.