Zvitubu zvakatevedzana uye zvakafanana - matambudziko nemhinduro

1. Chinhu che 160-gram chinonamira pamucheto wechitubu uye kuchinja kwehurefu hwechitubu i4 cm. Chii chinonzi kuchinja kwehurefu hwezvitubu zvitatu zvakabatana zvakatevedzana uye zvakafanana , sezvakaratidzwa mumufananidzo uri pazasi?

Zvinozivikanwa:

Kuchinja kwehurefu hwechitubu (Δx) = 4 cm = 0.04 m Zvitubu zvakatevedzana uye zvakafanana - matambudziko nemhinduro 1

Huremu (m) = magiramu makumi mana = 0.16 kg

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

Huremu (w) = mg = (0.16)(10) = 1.6 Newtons

Zvinodiwa: Kuchinja kwehurefu hwematsime matatu (Δx)

Solution:

Kuenzanisa kwemutemo waHooke :

k = w / Δx = 1.6 / 0.04 = 40 N/m

Masipiringi matatu ane chimiro chakafanana, k = 40 N/m.

Sarudza iyo yakafanana constant :

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

k ₂₃ = k ₂ + k ₃ = 40 + 40 = 80 N/m

Chitubu 1 (k ₁ ) nechitubu 23 (k ₂₃ ) zvakabatana zvakatevedzana. Chimiro chakafanana:

1/k = 1/k ₁ + 1/k ₂₃ = 1/40 + 1/80 = 2/80 + 1/80 = 3/80

k = 80/3

Sarudza shanduko muhurefu hwematsime matatu:

Δx = w / k = 1.6 : 80/3 = (1.6)(3/80) = 4.8 / 80 = 0.06 m = 6 cm

2. Masipiringi matatu ane chinoramba chimwe chete chakabatana mu series uye parallel , uye chinhu chinorema 2-kg chakabatanidzwa kune rimwe divi rechitubu, sezvakaratidzwa mumufananidzo uri pazasi. Chiramba chechitubu i k ₁ = k ₂ = k ₃ = 300 N/m. Chii chinonzi shanduko muhurefu hwemasipiringi matatu? Kukurumidza kunokonzerwa negiravhiti g = 10 ms ^-2.

Zvinozivikanwa:

Chitubu chisingachinji k₁= k₂ = k₃= 300 Nm^-1

Kukurumidza kunokonzerwa negiravhiti (g) = 10 ms ^-2

Huremu hwechinhu (m) = 2 kg

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

onawo Kumanikidzwa kwemvura - matambudziko nemhinduro

Zvinodiwa: Kuchinja kwehurefu hwematsime matatu (Δx)

Solution:

Sarudza iyo yakafanana constant :

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

k ₁₂ = k ₁ + k ₂ = 300 + 300 = 600 N/m

Chitubu 3 (k ₃ ) nechitubu 12 (k ₁₂ ) zvakabatana zvakatevedzana. Chimiro chakafanana:

1/k = 1/k ₃ + 1/k ₁₂ = 1/300 + 1/600 = 2/600 + 1/600 = 3/600

k = 600/3 = 200 N/m

Sarudza shanduko muhurefu hwematsime matatu:

Δx = w / k = 20/200 = 2/20 = 1/10 = 0.1 m

3. Zvitubu zvitatu zvakabatana zvakatevedzana uye zvakafanana, sezvakaratidzwa mumufananidzo uri pazasi. Kana chitubu chisingachinji k = 50 Nm ^-1 uye huremu hwemagiramu mazana mana zvakabatanidzwa pamucheto wechitubu. Chii chinonzi shanduko pakureba kwezvitubu zvitatu?

Zvinozivikanwa:

Chitubu chinogara kwenguva refu 1 (k)₁) = k = 50 Nm^-1

Chitubu chinogara kwenguva refu 2 (k ₂ ) = k = 50 Nm ^-1

Chitubu chinogara kwenguva refu 3 (k ₃ ) = 2k = 2 (50 Nm ^-1 ) = 100 Nm ^-1

Huremu hwechinhu (m) = 400 magiramu = 0.4 kg

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

Kurema kwechinhu (w) = mg = (0.4)(10) = 4 Newtons

Zvinodiwa: Kuchinja kwehurefu (Δx)

Solution:

Sarudza iyo yakafanana constant :

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

k ₁₂ = k ₁ + k ₂ = 50 + 50 = 100 N/m

Chitubu 3 (k ₃ ) nechitubu 12 (k ₁₂ ) zvakabatana zvakatevedzana. Chimiro chakafanana:

1/k = 1/k ₃ + 1/k ₁₂ = 1/100 + 1/100 = 2/100

k = 100/2 = 50 N/m

Sarudza shanduko muhurefu hwematsime matatu:

Δx = w / k = 4 / 50 = = 0.08 m = 8 cm

Kusanganisa masprings muzvikamu zvinotevedzana kunokanganisa sei chigarire chemuchirimo chose?
- Pindura: Kana masprings akabatanidzwa muzvikamu zvakatevedzana, huwandu hwese hwespring constant hunodzikira. Kuwirirana kwehuwandu hwespring constant hwakaenzana huwandu hwehuwandu hwemaspring constants ega ega: 1/k $=1/ k ^{1} + 1/ k ^{2}$ .
Kugara kwechitubu kwese kunochinja sei kana chitubu chikabatanidzwa pamwe chete?
- Pindura: Kubatanidza matsime nenzira imwecheteyo kunoguma nechinhu chese chemuchirimo chinova huwandu hwezvinhu zvemuchirimo chimwe nechimwe: k $= k_{1} + k_{2}$ .
Kana matsime maviri akafanana akarongwa akatevedzana, chitubu chakabatana chinoenzaniswa sei nechitubu chakabatana chechitubu chimwe nechimwe?
- Pindura: Chitubu chakabatanidzwa chichava hafu yechitubu chakabatana cheimwe yematsime ega ega.
Chii chinoitika pakuwedzerwa kana kudzvinyirirwa kwemaspiringi akatevedzana kana simba rikashandiswa?
- Pindura: Kune matsime akatevedzana, simba rimwe chete rinoita kuti chitubu chega chega chiwedzere kana kudzvanya, asi kuwedzera kwese (kana kudzvanya) ndiko kuwanda kwekuwedzera (kana kudzvanya) kwematsime ega ega.
Kana matsime ari pamwe chete akabatwa nesimba, simba iroro rinoparadzirwa sei?
- Pindura: Kune matsime ari pamwe chete, simba rinogoverwa pakati pematsime zvichibva pazvigaro zvawo zvechitubu. Matsime ane chigaro chepamusoro chechitubu achatakura chikamu chikuru chesimba kupfuura ane chigaro chepasi chechitubu.
Sei matsime akatevedzana achigona kufungwa nezvawo sechitubu chimwe chete chine hurefu hwakareba?
- Pindura: Masipiringi akatevedzana ane mhedzisiro yakabatana yakafanana nekutambanudza sipiringi imwe chete yakareba. Kuwedzerwa kana kudzvanywa kwemasipiringi ega ega kunowedzera, sezvaingoita muchirimo chimwe chete chakareba.
Simba rinogona kuchengetwa mumasipiringi akatevedzana rinoenzaniswa sei neriri mumasipiringi akatevedzana nesimba rakafanana rinoshandiswa?
- Pindura: Masipiringi ari muzvikamu zvinotevedzana anochengetedza simba rakawanda kupfuura masipiringi ari pamwe chete nekushandiswa kwakafanana nekuti anowedzerwa zvakanyanya kana kumanikidzwa.
Kana imwe yemasprings ari muchimiro chakafanana ikatyoka kana kuti ikasashanda, chii chinoitika kune maitiro ese ehurongwa?
- Pindura: Kana chitubu chimwe chete chakakamurwa panguva imwe chete, matsime asara acharamba achishanda. Zvisinei, chitubu chose chinogara chiripo chinoderera, uye sisitimu haizokwanisi kushandisa simba rakawanda rekudzorera sepakutanga.
Sei masprings akatevedzana achinyanya kukanganiswa nekukanganisika kukuru kupfuura ayo ari pamwe chete nekushandiswa kwesimba rimwe chete?
- Pindura: Pazvitubu zvakatevedzana, simba rimwe chete rinoshanda pachitubu chimwe nechimwe, zvichiita kuti chimwe nechimwe chitambanuke kana kudzvanyirirana. Kushanduka kwese ndiko huwandu hwekushanduka kwega kwega. Panguva imwe chete, simba rinogoverwa pakati pezvitubu, saka chimwe nechimwe chinowana simba rakaderera rinoshanda, zvichikonzera kushanduka kwega kwega.
Mukushandisa kwakakodzera, nei mainjiniya angasarudza kushandisa masipiringi panguva imwe chete kwete mumatanho akatevedzana?

Pindura: Mainjiniya vanogona kusarudza masipiringi panguva imwe chete kuti vawane sipiringi yakakwira, zvichikonzera kuomarara. Kugadzirisa uku kunogona zvakare kupa kudzokorora; kana sipiringi imwe ikakundikana, sisitimu inoramba ichishanda, kunyangwe ne sipiringi yakadzikira.