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 ∆L

Zvinodiwa: Simba 2 (F ₂ )

Solution:

Kuenzanisa kwemutemo waHooke

k = F / ΔL

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

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. 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:

Huremu hwechinhu (m) = 100 magiramu = 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

Zvinodiwa: Kuchinja kwehurefu hwechitubu chakaenzana.

Solution:

Sarudza zvakaenzana nguva dzose yechirimo:

Chitubu 2 (k ₂ ) nechitubu 3 (k ₃ ) zvakabatana zvakafanana. Chitubu chakafanana:

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

Chitubu 1 (k ₁ ) nechitubu p (k _P ) zvakabatana zvakatevedzana. Chitubu chakafanana:

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

k = 400/3 _Nm ⁻¹

Chimiro chakaenzana chechirimo i400/3 Nm ^-1

Sarudza shanduko muhurefu hwechitubu chakaenzana :

Kuenzanisa kwemutemo waHooke:

∆x = F / k = w / k

Kuchinja kwehurefu hwechitubu chakaenzana :

∆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. Zvitubu zvitatu zvakabatana muzvikamu zvakafanana sezvakaratidzwa mumufananidzo uri pazasi. Zvimisikidzo zvechitubu k ₁ = k ₂ = 3 Nm ⁻¹ uye k ₃ = 6 Nm ⁻¹ . Chii chinonzi chimisikidzo cheyakaenzana nechitubu?

Zvinozivikanwa:

Chisingaperi chechirimo 1 (k ₁ ) = chisingaperi chechirimo 2 (k ₂ ) = 3 Nm ⁻¹

Chimiro chenguva dzose chechirimo 3 (k ₃ ) = 6 Nm ⁻¹

Zvinodiwa: chisingaperi chechirimo chakaenzana (k)

Solution:

Chitubu 1 (k ₁ ) nechitubu 2 (k ₂ ) zvakabatana zvakafanana. Chimiro chechitubu chakaenzana:

k _p = k ₁ + k ₂ = 3 + 3 = 6 Nm ⁻¹

Chitubu p (k _P ) nechitubu 3 (k ₃ ) zvakabatana zvakatevedzana. Chimiro chechitubu chakaenzana:

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

k = 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 / Δx

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 / Δx = w / Δx = mg / Δx

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

k = 4k/ ₃

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

Solution:

Kuenzanisa kwemutemo waHooke:

k = F / Δ L

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

Chisingachinji 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 elasticity.

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. Ndeipi girafu h ine ma "elastic constant" makuru?

Solution:

Kugara kwekusagadzikana :

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 nekuchinja kwehurefu hwechitubu. Chii chinonzi simba rinogona kushandiswa muchitubu, zvichienderana negirafu iri pazasi.

Zvinozivikanwa:

F = 40N

x = 0.08 mamita

Zvinodiwa : Simba rinogona kuwanikwa muchirimo

Solution:

Nguva dzose yechirimo:

k = F / Δx = 40 / 0.08 = 500 N/m

Simba rinogona kuwanikwa muchirimo:

PE = 1/2 kx ² = 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 kwesimba rinokwevera pasi kuri 10 m/s ² , simba ripi rinogona kushandiswa muchirimo?

Zvinozivikanwa:

Kuwedzera kwehurefu (Δx) = 5 cm = 0.05 metres

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Huremu hwebhuroko (m) = 2 kg

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

Zvinodiwa: 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 Δx ² = 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

Zvinodiwa : 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 Δx ² = 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:

k ₁ = k ₂ = k ₃ = k ₄ = 800 N m ⁻¹

Δx = 5 cm = 0.05 m

Zvinodiwa: 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 = k ₁ + k ₂ + k ₃ = 800 + 800 + 800 = 2400 Nm ⁻¹

Chitubu p (k _P ) nechitubu 4 (k ₄ ) zvakabatana zvakatevedzana. Chimiro chechitubu chakaenzana:

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

k = 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 Newtons

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:

k ₁ = k ₂ = k ₃ = k ₄ = 1600 N m ⁻¹

Δx = 5 cm = 0.05 m

Zvinodiwa: 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 = k ₁ + k ₂ + k ₃ = 1600 + 1600 + 1600 = 4800 Nm ⁻¹

Chitubu p (k _P ) nechitubu 4 (k ₄ ) zvakabatana zvakatevedzana. Chimiro chechitubu chakaenzana:

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

k = 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 Newtons

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.