Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho

Kusintha kwa kutalika

1. Ndodo ili ndi kutalika kwa L, komwe kumakokedwa ndi mphamvu ya F. Kuchuluka kwa kutalika ndi ∆L. Kodi kukula kwa mphamvuyo ndi kotani ngati kusintha kwa kutalika ndi 4∆L?

Zodziwika:

Mphamvu 1 (F ₁ ) = F

Kusintha kwa kutalika 1 (∆L ₁ ) = ∆L

Kusintha kwa kutalika 2 (∆L ₂ ) = 4 ∆L

Akufuna: Mphamvu 2 (F ₂ )

Yankho:

Kuyerekeza kwa lamulo la Hooke

k = F / ΔL

k = kusinthasintha kosalekeza, F = mphamvu ya F, ΔL = kusintha kwa kutalika

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. Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 1 Masipu a masikawa amalumikizidwa motsatizana, monga momwe chithunzi chili pansipa chikusonyezera. Kasupe 1 ali ndi 200 N/m yosasinthika, kasupe 2 ali ndi 200 N/m yosasinthika ndipo kasupe 3 ali ndi 200 N/m yosasinthika. Kulemera kwa chinthucho ndi magalamu 100 ndipo kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s²Kodi kusintha kwa kutalika kwa ndi Zofanana kasupe.

Zodziwika:

Kulemera kwa chinthu (m) = magalamu 100 = 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

Kufunidwa: Kusintha kwa kutalika kwa kasupe wofanana.

Yankho:

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 2 Dziwani chofanana nthawi zonse ya masika:

Kasupe 2 (k ₂ ) ndi kasupe 3 (k ₃ ) zimalumikizidwa motsatizana. Chokhazikika chofanana cha kasupe:

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

Kasupe 1 (k ₁ ) ndi kasupe p (k _P ) zimalumikizidwa motsatizana. Chofanana ndi chokhazikika cha kasupe:

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

k _s = 400/3 Nm ⁻¹

Chofanana ndi masika ndi 400/3 Nm ^-1

Dziwani kusintha kwa kutalika kwa kasupe wofanana :

Kuyerekeza kwa lamulo la Hooke:

∆x = F / k = w / k

Kusintha kwa kutalika kwa kasupe wofanana :

∆x = w / k

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

Chokhazikika cha masika

3. Kodi nthawi yokhazikika ya masika ndi yotani malinga ndi zomwe zili mu tebulo ili m'munsimu?

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 3

Yankho:

Kuyerekeza kwa lamulo la Hooke:

k = F / Δx

Chokhazikika cha masika:

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

4. Masipu ang'onoang'ono atatu alumikizidwa motsatizana monga momwe chithunzi chili pansipa chikusonyezera. Zosasinthika za kasupe k ₁ = k ₂ = 3 Nm ⁻¹ ndi k ₃ = 6 Nm ⁻¹ . Kodi chosinthika cha chofanana ndi kasupe n'chiyani?

Zodziwika: Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 4

Chokhazikika cha kasupe 1 (k ₁ ) = chokhazikika cha kasupe 2 (k ₂ ) = 3 Nm ⁻¹

Chokhazikika cha kasupe 3 (k ₃ ) = 6 Nm ⁻¹

Kufunidwa: kokhazikika kwa kasupe wofanana (k)

Yankho:

Kasupe 1 (k ₁ ) ndi kasupe 2 (k ₂ ) zimalumikizidwa motsatizana. Chokhazikika cha kasupe wofanana:

k _p = k ₁ + k ₂ = 3 + 3 = 6 Nm ⁻¹

Kasupe p (k _P ) ndi kasupe 3 (k ₃ ) zimalumikizidwa motsatizana. Chokhazikika cha kasupe wofanana:

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

Chokhazikika cha chofanana ndi kasupe = 3 Nm ⁻¹.

5. Kasupe wokhala ndi kutalika kwa L, wokokedwa ndi kulemera kwa w. Malinga ndi deta yomwe ili patebulo pansipa, kodi chokhazikika cha kasupe wofanana ndi chiyani:

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 5

Yankho:

k = F / Δx

Chokhazikika cha masika:

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

6. Malinga ndi deta yomwe ili patebulo ili pansipa, kodi chokhazikika cha kasupe wofanana ndi chiyani:

Onaninso Kuthamanga chifukwa cha mphamvu yokoka - mavuto ndi mayankho

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 6

Yankho:

k = F / Δx = w / Δx = mg / Δx

k = kusinthasintha kosalekeza, w = kulemera, m = kulemera, g = kuthamanga chifukwa cha mphamvu yokoka, Δx = kusintha kwa kutalika

Chokhazikika cha masika:

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

7. Ngati k ₁ = 4k, kodi nthawi zonse ya kasupe wofanana ndi iti?

Yankho: Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 7

Masipu aŵiri alumikizidwa motsatizana. Chokhazikika cha masipu olingana:

k _p = k + k = 2k

Masipu aŵiri alumikizidwa motsatizana. Chokhazikika cha masipu ofanana

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

k ₌ 4k/3

8. Malinga ndi deta yomwe ili patebulo ili pansipa, kodi chokhazikika cha kasupe wofanana ndi chiyani:

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 8

Yankho:

Kuyerekeza kwa lamulo la Hooke:

k = F / Δ L

Chokhazikika cha masika:

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

9. Chosasinthika chaching'ono kwambiri ndi…

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 9

Anakonza

Kuyerekeza kwa lamulo la Hooke:

k = F / Δx

k = kusinthasintha kosalekeza, F = mphamvu, Δx = kusintha kwa kutalika

Kukhazikika kwa 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. Kodi chokhazikika chachikulu kwambiri ndi chiti malinga ndi deta yomwe ili patebulo ili pansipa?

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 10

Yankho:

Kuyerekeza kwa lamulo la 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

Chosasinthika chachikulu kwambiri ndi 320 Nm ^-1.

11. Chithunzi chomwe chili pansipa chikuwonetsa kulumikizana pakati pa kusintha kwa mphamvu (ΔF) ndi kuwonjezeka kwa kutalika (Δx). Kodi graph yomwe ikuwonetsa kusinthasintha kochepa kwambiri ndi chiyani?

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 11

Anakonza

Kuyerekeza kwa lamulo la Hooke:

k = F / Δx

Δx = kusintha kwa kutalika, F = mphamvu, k = kusinthasintha kosalekeza

Kukhazikika kwa 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. Ndi graph iti h yomwe ili ndi ma elastic constants akuluakulu kwambiri?

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 12

Yankho:

Kukhazikika kwa kusinthasintha :

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

Mphamvu yomwe ingakhalepo ya masika:

13. Chithunzi chili pansipa chikuwonetsa ubale pakati pa mphamvu ndi kusintha kwa kutalika kwa kasupe. Kodi mphamvu yomwe ingakhalepo ya kasupe ndi yotani, malinga ndi chithunzi chili pansipa?

Zodziwika: Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 13

F = 40N

x = mamita 0.08

Kufunidwa : Mphamvu yomwe ingakhalepo ya masika

Yankho:

Chokhazikika cha masika:

k = F / Δx = 40 / 0.08 = 500 N/m

Mphamvu yomwe ingakhalepo ya masika:

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

14. Chipolopolo cha makilogalamu awiri chimamangiriridwa nthawi ya masika. Ngati kutalika kwa masika kuli 5 cm ndipo kuthamanga chifukwa cha mphamvu yokoka kuli 10 m/s ² , kodi mphamvu ya masika ndi yotani?

Zodziwika: Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 14

Kuwonjezeka kwa kutalika (Δx) = 5 cm = 0.05 mamita

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera kwa Block (m) = 2 kg

Kulemera kwa chipika (w) = mg = (2)(10) = 20 Newtons

Kufunidwa: mphamvu yomwe ingakhalepo ya masika

Yankho:

Kukhazikika kwa elasticity:

k = w / Δx = 20 / 0.05 = 400 N/m

Mphamvu yomwe ingakhalepo ya masika:

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

PE = 0.5 Joule

15. Kusintha kwa kutalika kwa kasupe ndi 5 cm pamene mphamvu ya 20-N ikukokedwa. Kodi mphamvu ya kasupe ndi yotani pamene kusintha kwa kutalika kwa kasupe ndi 10 cm?

Onaninso Kupanikizika kwa zinthu zolimba - mavuto ndi mayankho

Zodziwika:

Kusintha kwa kutalika (Δx) = 5 cm = 0.05 mamita

Mphamvu (F) = 20 Newton

Kufunidwa : Mphamvu yomwe ingakhalepo ya masika

Yankho:

Chokhazikika cha masika:

k = F / Δx = 20 / 0.05 = 400 N/m

Mphamvu yomwe ingakhalepo ya masika pamene Δx = 10 cm = 0.1 m :

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

PE = 2 Joule

Kulemera kwa chinthucho

16. Masipu ang'onoang'ono anayi omwe chiŵerengero cha kasupe aliyense ndi 800 N/m, cholumikizidwa motsatizana, monga momwe chithunzi chikusonyezera. Chipika chalumikizidwa pa kasupe. Kusintha kwa kutalika kwa masipupe onse ndi 5 cm. Kodi kulemera kwa masipupe ndi kotani?

Zodziwika: Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 15

k ₁ = k ₂ = k ₃ = k ₄ = 800 N m ⁻¹

Δx = 5 cm = 0.05 m

Kufunidwa: kulemera kwa chipika (w)

Yankho:

Dziwani nthawi zonse ya kasupe wofanana

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 16 Kasupe 1 (k₁), kasupe 2 (k₂) ndi kasupe 3 (k₃) zimalumikizidwa motsatizana. Chosasintha cha kasupe wofanana :

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

Kasupe p (k _P ) ndi kasupe 4 (k ₄ ) zimalumikizidwa motsatizana. Chokhazikika cha kasupe wofanana:

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

Chokhazikika cha kasupe wofanana ndi 600 Nm ^-1

Dziwani kulemera kwa chinthu:

Kuyerekeza kwa lamulo la Hooke:

F = k Δx kapena w = k Δx

Kulemera kwa chinthu:

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

17. Masipu ang'onoang'ono anayi alumikizidwa motsatizana. Chokhazikika cha masipu ang'onoang'ono aliwonse ndi 1600 N/m. Chipika chimamangiriridwa kumapeto kwa masika, monga momwe chithunzi chikusonyezera. Kutalika kwa masipu ang'onoang'ono onse ndi 5 cm. Kodi kulemera kwa masipu ang'onoang'ono ndi kotani?

Zodziwika: Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 17

k ₁ = k ₂ = k ₃ = k ₄ = 1600 N m ⁻¹

Δx = 5 cm = 0.05 m

Kufunidwa: kulemera kwa chipika

Yankho:

Dziwani nthawi zonse ya kasupe wofanana

Lamulo la Hooke ndi kusinthasintha kwake - mavuto ndi mayankho 18 Kasupe 1 (k₁), kasupe 2 (k₂) ndi kasupe 3 (k₃) zimalumikizidwa motsatizana. Chosasintha cha kasupe wofanana :

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

Kasupe p (k _P ) ndi kasupe 4 (k ₄ ) zimalumikizidwa motsatizana. Chokhazikika cha kasupe wofanana:

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

Chokhazikika cha kasupe wofanana ndi 1200 Nm ^-1

Dziwani kulemera kwa chinthu:

Kuyerekeza kwa lamulo la Hooke:

F = k Δx kapena w = k Δx

Kulemera kwa chinthucho:

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

Kodi Lamulo la Hooke n’chiyani?
- Yankho: Lamulo la Hooke limafotokoza ubale pakati pa mphamvu yomwe imagwiritsidwa ntchito pa chinthu chotanuka ndi kusintha komwe kumachitika (nthawi zambiri kumatalikirana kapena kupsinjika). Makamaka, limanena kuti mphamvu yomwe imafunika kuti ikanikize kapena kukulitsa kasupe imagwirizana mwachindunji ndi mtunda womwe yatambasulidwa kapena kukakamizidwa, bola ngati malire a elastic sadutsa.
Kodi zikutanthauza chiyani tikamanena kuti chinthu chafika pamlingo wake wotanuka?
- Yankho: Chida chikafika pamlingo wake wotanuka, zikutanthauza kuti sichidzabwerera ku mawonekedwe ake oyambirira kapena kukula kwake pambuyo poti mphamvu yosintha yachotsedwa. Kupitirira apo, chidacho chimachita zinthu ngati pulasitiki ndipo chikhoza kusinthika kosatha.
Kodi kasupe wosasintha (k) umagwirizana bwanji ndi kuuma kwa kasupe?
- Yankho: Kasinthasintha ka kasupe (k) ndi muyeso wa kuuma kwa kasupe. Mtengo waukulu wa k umasonyeza kasupe wolimba, kutanthauza kuti mphamvu yochulukirapo imafunika kuti isinthe kuchuluka kwake, pomwe k wocheperako akusonyeza kasupe womvera bwino kapena wofewa.
Kodi mayunitsi a masika osasinthika mu dongosolo la SI ndi ati?
- Yankho: Mu dongosolo la SI, mayunitsi a nthawi yokhazikika ya masika (k) ndi ma Newton pa mita (N/m).
N’chifukwa chiyani khalidwe lofotokozedwa ndi Lamulo la Hooke limaonedwa kuti ndi lolunjika?
- Yankho: Khalidweli limaonedwa kuti ndi lolunjika chifukwa ubale pakati pa mphamvu yogwiritsidwa ntchito (F) ndi kusamuka (x) ndi mzere wowongoka, ndipo ubalewu waperekedwa ngati $F = k x$ , kumene k ndi chinthu chosasintha cha chinthu kapena kasupe woperekedwa.
Kodi Lamulo la Hooke limagwira ntchito pa akasupe okha?
- Yankho: Ayi, Lamulo la Hooke limagwira ntchito pa zinthu zilizonse zotanuka zomwe zimasinthasintha molingana ndi mphamvu yogwiritsidwa ntchito, mpaka malire ake otanuka. Ngakhale kuti masika ndi chitsanzo chofala, zinthu zina monga mipiringidzo ya rabara, zitsulo zomwe zili ndi masinthidwe ang'onoang'ono, ndi minofu ina ya zamoyo zimatha kusonyeza khalidwe lomwe lafotokozedwa ndi Lamulo la Hooke.
Nanga chimachitika n’chiyani ngati chinthu chatambasulidwa kupitirira malire ake otanuka koma chosakwanira kusweka?
- Yankho: Ngati chinthu chatambasulidwa kupitirira malire ake otanuka koma osasweka, chidzasintha pulasitiki. Izi zikutanthauza kuti mphamvu ikachotsedwa, chinthucho sichidzabwerera kwathunthu ku mawonekedwe ake oyambirira, ndipo kusintha kwina kosatha kudzatsala.
Kodi mfundo za kupsinjika maganizo ndi kupsinjika maganizo zimagwirizana bwanji ndi lamulo la Hooke?
- Yankho: Kupsinjika maganizo ndi mphamvu yomwe imagwiritsidwa ntchito pa gawo lililonse, ndipo kupsinjika ndiko kusintha kwa zinthu. Lamulo la Hooke pankhani ya kupsinjika ndi kupsinjika limati kupsinjikako kumagwirizana mwachindunji ndi kupsinjikako, ndipo kusinthasintha kofananako ndiko modulus ya zinthu ya Young. Iyi ndi njira ina yowonetsera ubale wolunjika pakati pa mphamvu ndi kusinthika, koma pazinthu zazikulu osati ma spring okha.
Kodi Young's Modulus ndi chiyani ndipo imagwirizana bwanji ndi kusinthasintha?
- Yankho: Young's Modulus, yomwe nthawi zambiri imaimiridwa ndi kalata $E$ , ndi muyeso wa kuuma kwa chinthu malinga ndi kupsinjika kapena kupsinjika. Chimafotokoza kuthekera kwa chinthucho kukana kusintha pogwiritsa ntchito mphamvu yogwiritsidwa ntchito. Modulus yapamwamba ya Young imasonyeza chinthu cholimba, ndipo imafotokozedwa ngati chiŵerengero cha kupsinjika ndi kupsinjika.
Kodi zinthu zonse zingathe kufotokozedwa ndi lamulo la Hooke?

Yankho: Ayi, si zinthu zonse zomwe zimagwira ntchito motsatira lamulo la Hooke. Zinthu zambiri, makamaka zomwe sizili zolunjika, zooneka ngati pulasitiki, siziwonetsa ubale wolunjika pakati pa kupsinjika ndi kupsinjika. Lamulo la Hooke ndi lolondola kwambiri ndipo ndi lolondola kwambiri pakusintha pang'ono kwa zinthu zotanuka.