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Kalkulator syly pruzhyny

Kalkulator syly pruzhyny zastosovuye zakon Huka dlya obchyslennya syly pruzhnosti F = k * x ta potentsiynoyi energiyi pruzhnosti E = 0.5 * k * x^2. Pislya vvedennya masy navantazhennya kalkulator dodatkovo vyznachaye statychnu deformatsiyu x = m * g / k ta period harmoniynykh kolyvan T = 2 * PI * sqrt(m / k).

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Formuly zakonu Huka

Syla pruzhnosti: F = k * x Potentsiyna energiya pruzhnosti: E = 0.5 * k * x^2 Statychna deformatsiya vid masy: x = m * g / k (g = 9.81 m/s^2) Period harmoniynykh kolyvan: T = 2 * PI * sqrt(m / k) k — koefitsiyent pruzhnosti [N/m], x — deformatsiya [m], m — masa navantazhennya [kg]. Syla napravlena protylezhno deformatsiyi (vidnovlyuyucha); tut navodymo yiyi chyslove znachennya.

Pryklad: pruzhyna k = 200 N/m, x = 0.1 m

Dlya koefitsiyenta pruzhnosti k = 200 N/m i podovzhennya x = 0.1 m syla pruzhnosti dorivnyuye F = 200 * 0.1 = 20 N, a potentsiyna energiya E = 0.5 * 200 * 0.1^2 = 1 J. Pislya pidvishuvannya masy m = 1 kg statychna deformatsiya x = 1 * 9.81 / 200 priblyzno 0.049 m.

Chasto zadavani pytannya

Shcho take zakon Huka?

Zakon Huka stverdzhuye, shcho syla pruzhnosti pryamo proportsiyna deformatsiyi: F = k * x. Stala k (koefitsiyent pruzhnosti) opysuye zhorstkist pruzhyny v nyutonakh na metr (N/m). Zakon diye v mezhakh pruzhnosti, poky material povertayetsya do pochatkovoyi formy.

Yak obchyslyty sylu pruzhnosti?

Sylu pruzhnosti obchyslyuyemo za formuloyu F = k * x, de k — koefitsiyent pruzhnosti [N/m], a x — deformatsiya v metrakh. Pryklad: dlya k = 500 N/m i x = 0.04 m syla dorivnyuye F = 500 * 0.04 = 20 N.

Shcho oznachaye koefitsiyent pruzhnosti k?

Koefitsiyent pruzhnosti k pokazuye, naskilky zhorstka pruzhyna — skilky nyutoniv potribno, shchob roztyahnuty yiyi na odyn metr. Chym bilshe k, tym zhorstkisha pruzhyna. Odynytsya — N/m; pruzhyna z k = 1000 N/m u desyat raziv zhorstkisha za pruzhynu z k = 100 N/m.

Potentsiynu energiyu pruzhnosti obchyslyuyemo za formuloyu E = 0.5 * k * x^2. Tse robota pry deformatsiyi pruzhyny ta energiya, nakopychena v niy. Pryklad: k = 200 N/m, x = 0.1 m daye E = 0.5 * 200 * 0.01 = 1 J.

U formuli E = 0.5 * k * x^2 deformatsiya v kvadrati, bo syla zrostaye liniyno z x, a energiya — tse ploshcha pid grafikom syly vid shlyakhu (trykutnyk). Podviyennya deformatsiyi zbilshuye energiyu vchetvero, a ne vdvichi.

Pidvisheny vantazh rozteyaguye pruzhynu, doky syla pruzhnosti ne zrivnovazhyt vagu: k * x = m * g. Zvidsy statychna deformatsiya x = m * g / k, de g = 9.81 m/s^2. Chym bilsha masa abo mensha stala k, tym bilshe podovzhennya.

Dlya masy m na pruzhyni zhorstkosti k period harmoniynykh kolyvan dorivnyuye T = 2 * PI * sqrt(m / k). Pryklad: m = 1 kg, k = 100 N/m daye T = 2 * PI * sqrt(0.01) priblyzno 0.628 s. Bilsha masa podovzhuye period, bilsha zhorstkist yoho skorochuye.

Syla pruzhnosti — tse vidnovlyuyucha syla, zavzhdy napravlena protylezhno deformatsiyi. Pry stysnenni (x vidyemne) syla vykhodyt vidyemnoyu v tsiy systemi znakiv. Kalkulator pokazuye chyslove znachennya zi znakom; napryamok zavzhdy — povernennya do polozhennya rivnovagy.

Zakon Huka diye lyshe v mezhakh pruzhnosti materialu. Pislya perevyshchennya mezhi pruzhnosti zalezhnist syly vid deformatsiyi staye neliniynoyu, a pislya mezhi plastychnosti material deformuyetsya nazavzhdy i ne povertayetsya do pochatkovoyi formy.

Koefitsiyent pruzhnosti k vvodyt u N/m, deformatsiyu x — u metrakh (napr. 0.05 m zamist 5 sm), a optsionalnu masu m — u kilogramakh. Sylu otrymayete v nyutonakh (N), energiyu — v dzhoulakh (J), a period kolyvan — u sekundakh (s).

Kalkulator pryputskaye idealnu pruzhynu zgidno zakonu Huka (liniyna zalezhnist syly vid deformatsiyi) ta nekhtuye masoyu samoyi pruzhyny i tertyam. Dlya velykykh deformatsiy abo neliniynykh pruzhyn rezultaty maut nablyzhenyy kharakter.

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