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Fizika

Course: Fizika > Unit 3

Lesson 6: Taranglik

Taranglik nima?

Zanjirlar jismlarni koʻtaradi! Shu kabi kuchlar bilan ishlashni oʻrganing.

Taranglik nima?

Bir-biriga tegib turgan ixtiyoriy fizik jismlar orasida taʼsir kuchlari boʻlishi mumkin. Biz bu kuchlarni oʻzaro taʼsir kuchlari deb ataymiz. Agar kuch taʼsir qilayotgan jismlardan biri prujina, rezina, zanjir, ip, arqon, kabel boʻlsa, biz unga taʼsir qilayotgan kuchni taranglik deb ataymiz.

[Qanday qilib arqon kuch hosil qilishi mumkin?]

Arqonlar va kabellar kuchlar taʼsirini yetkazish uchun foydalidir, chunki ular kuch taʼsirini sezilarli masofaga (yaʼni arqon uzunligi) samarali ravishda uzata oladi. Masalan, Sibir changʻichilari jamosi chanani arqonlar yordamida itlarga bogʻlashadi bu esa itlarga harakatlanish uchun kattaroq oraliq yaratadi va itlar chanani tortadi, ushbu holat itlar chanani itarganiga qaraganda ancha (bu juda achinarli jamoa boʻlar edi) unumli.

Yodda tuting, taranglik bu tortish kuchi, chunki arqonlar itara olmasligi aniq va ravshan. Arqon bilan itarishga boʻlgan urinish uning tortishda yuzaga kelgan tarangligini yoʻqotishiga sabab boʻladi. Bu juda sodda va ravshan tuyulishi mumkin, ammo koʻp odamlar chizmalarda taranglik kuchining yoʻnalishini notoʻgʻri chizishadi, yodda tuting, taranglik faqat jismni tortishi mumkin.

Taranglik kuchini qanday topamiz?

Afsuski, taranglik kuchini topish uchun maxsus formula yoʻq. Taranglik kuchini topish yoʻli xuddi normal reaksiya kuchini topish usuliga oʻxshaydi. Yaʼni biz jismning harakatini unga taʼsir etuvchi kuchlarga Nyutonning ikkinchi qonuni yordamida bogʻlaymiz. Aniqroq aytganda biz, quyidagi ishlarni bajaramiz:

Jismga taʼsir qilayotgan kuchlarni chizing.
Taranglik hosil boʻlgan yoʻnalish uchun Nyutonning ikkinchi qonuni formulasi left parenthesis, a, equals, start fraction, \Sigma, F, divided by, m, end fraction, right parenthesis ni yozing.
Nyutonning ikkinchi qonuni formulasidan a, equals, start fraction, \Sigma, F, divided by, m, end fraction taranglikni toping.

Biz bu yoʻl orqali quyidagi masalalarni yechamiz.

Taranglik kuchi ishtirok etgan masalalar qanday yechiladi?

1-masala: Ip burchak ostida qutini tortmoqda

Silliq stolda ichiga 2, point, 0, start text, space, k, g, end text bodring solingan quti gorizontga theta, equals, 60, start superscript, o, end superscript burchak ostida yoʻnalgan ip bilan tortilmoqda. Ipning tarangligi sababli quti oʻngga qarab 3, point, 0, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction tezlanish bilan harakatlanmoqda.

Ipning taranglik kuchi nimaga teng?

Avval, biz qutiga taʼsir qilayotgan barcha kuchlarni chizib olamiz.

Endi Nyutonning ikkinchi qonunidan foydalanamiz. Taranglik ham vertikal ham gorizontal yoʻnalgani sababli qaysi yoʻnalishni tanlash biroz noaniq. Ammo bizga tezlanish gorizontal ekani maʼlum va taranglik gorizontal proyeksiyaga ega boʻlgan yagona kuch boʻlgani sababli biz Nyutonning ikkinchi qonunidan gorizontal yoʻnalish uchun foydalanamiz.

[Agar biz tasodifan Nyutonning ikkinchi qonunini vertikal yoʻnalish uchun qoʻllasak-chi?]

a, start subscript, x, end subscript, equals, start fraction, \Sigma, F, start subscript, x, end subscript, divided by, m, end fraction, start text, left parenthesis, G, o, r, i, z, o, n, t, a, l, space, y, o, ʻ, n, a, l, i, s, h, space, u, c, h, u, n, space, N, y, u, t, o, n, n, i, n, g, space, i, k, k, i, n, c, h, i, space, q, o, n, u, n, i, d, a, n, space, f, o, y, d, a, l, a, n, i, n, g, point, right parenthesis, end text

3, point, 0, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction, equals, start fraction, start color #7854ab, T, end color #7854ab, start text, c, o, s, end text, 60, start superscript, o, end superscript, divided by, 2, point, 0, start text, space, k, g, end text, end fraction, start text, left parenthesis, G, o, r, i, z, o, n, t, a, l, space, t, e, z, l, a, n, i, s, h, comma, space, m, a, s, s, a, space, v, a, space, g, o, r, i, z, o, n, t, a, l, space, k, u, c, h, l, a, r, n, i, space, k, e, l, t, i, r, i, b, space, q, o, ʻ, y, i, n, g, point, right parenthesis, end text

[Tcos60 birhad qanday hosil qilindi?]

start color #7854ab, T, end color #7854ab, start text, c, o, s, end text, 60, start superscript, o, end superscript, equals, left parenthesis, 3, point, 0, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, left parenthesis, 2, point, 0, start text, space, k, g, end text, right parenthesis, start text, left parenthesis, end text, start color #7854ab, T, end color #7854ab, start text, space, n, i, space, b, i, r, space, t, o, m, o, n, g, a, space, o, ʻ, t, k, a, z, i, n, g, point, end text, right parenthesis

start color #7854ab, T, end color #7854ab, equals, start fraction, left parenthesis, 3, point, 0, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, left parenthesis, 2, point, 0, start text, space, k, g, end text, right parenthesis, divided by, start text, c, o, s, end text, 60, start superscript, o, end superscript, end fraction, start text, left parenthesis, Q, u, y, i, d, a, g, i, n, i, space, t, o, p, a, m, i, z, colon, space, end text, start color #7854ab, T, end color #7854ab, right parenthesis

start color #7854ab, T, end color #7854ab, equals, 12, start text, space, N, end text, start text, left parenthesis, H, i, s, o, b, l, a, n, g, space, v, a, space, n, i, s, h, o, n, l, a, n, g, point, end text, right parenthesis

2-masala: Ikki ipga osilgan quti

Quritilgan shirinliklar toʻldirilgan quti umumiy 0, point, 25, start text, space, k, g, end text massaga ega va u biri devorga, biri uy tomiga mahkamlangan ikkita ipda muvozanatda turibdi. Gorizontga theta, equals, 30, start superscript, o, end superscript burchak ostida turgan ipda taranglik kuchi T, start subscript, 2, end subscript ga teng.

Iplarda taranglik left parenthesis, T, start subscript, 1, end subscript va T, start subscript, 2, end subscript, right parenthesis nimaga teng?

Avval biz qutiga taʼsir qiluvchi barcha kuchlarni chizib olamiz.

Endi Nyutonning ikkinchi qonunidan foydalanamiz. Bu yerda ham gorizontal ham vertikal yoʻnalgan taranglik kuchari boʻlgani sababli qaysi yoʻnalishni tanlash biroz mavhum. Ammo ogʻirlik kuchi vertikal yoʻnalgan ekani bizga maʼlum, shu sababli Nyutonning ikkinchi qonunini vertikal yoʻnalish uchun qoʻllaymiz.

a, start subscript, y, end subscript, equals, start fraction, \Sigma, F, start subscript, y, end subscript, divided by, m, end fraction, start text, left parenthesis, V, e, r, t, i, k, a, l, space, y, o, ʻ, n, a, l, i, s, h, space, u, c, h, u, n, space, N, y, u, t, o, n, n, i, n, g, space, i, k, k, i, n, c, h, i, space, q, o, n, u, n, i, n, i, space, q, o, ʻ, l, l, a, n, g, point, right parenthesis, end text

0, equals, start fraction, start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, start text, s, i, n, end text, 30, start superscript, o, end superscript, minus, start color #11accd, F, start subscript, g, end subscript, end color #11accd, divided by, 0, point, 25, start text, space, k, g, end text, end fraction, start text, left parenthesis, V, e, r, t, i, k, a, l, space, t, e, z, l, a, n, i, s, h, comma, space, m, a, s, s, a, space, v, a, space, v, e, r, t, i, k, a, l, space, k, u, c, h, l, a, r, n, i, space, k, e, l, t, i, r, i, b, space, q, o, ʻ, y, i, n, g, point, right parenthesis, end text

[Tsin30 had qanday hosil qilindi?]

start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, equals, start fraction, start color #11accd, F, start subscript, g, end subscript, end color #11accd, divided by, start text, s, i, n, end text, 30, start superscript, o, end superscript, end fraction, start text, left parenthesis, Q, u, y, i, d, a, g, i, n, i, space, t, o, p, i, n, g, colon, space, end text, start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, right parenthesis

start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, equals, start fraction, start color #11accd, m, g, end color #11accd, divided by, start text, s, i, n, end text, 30, start superscript, o, end superscript, end fraction, start text, left parenthesis, Q, u, y, i, d, a, g, i, d, a, n, space, f, o, y, d, a, l, a, n, i, n, g, colon, space, end text, start color #11accd, F, start subscript, g, end subscript, end color #11accd, equals, start color #11accd, m, g, end color #11accd, right parenthesis

start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, equals, start fraction, left parenthesis, 0, point, 25, start text, space, k, g, end text, right parenthesis, left parenthesis, 9, point, 8, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, divided by, start text, s, i, n, end text, 30, start superscript, o, end superscript, end fraction, equals, 4, point, 9, start text, space, N, end text, start text, left parenthesis, H, i, s, o, b, l, a, n, g, space, v, a, space, n, i, s, h, o, n, l, a, n, g, point, end text, right parenthesis

Biz start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab ni topganimizdan soʻng gorizontal yoʻnalish uchun Nyutonning ikkinchi qonunini qoʻllab start color #1fab54, T, start subscript, 1, end subscript, end color #1fab54 ni topishimiz mumkin.

0, equals, start fraction, start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, start text, c, o, s, end text, 30, start superscript, o, end superscript, minus, start color #1fab54, T, start subscript, 1, end subscript, end color #1fab54, divided by, 0, point, 25, start text, space, k, g, end text, end fraction, start text, left parenthesis, G, o, r, i, z, o, n, t, a, l, space, t, e, z, l, a, n, i, s, h, comma, space, m, a, s, s, a, space, v, a, space, g, o, r, i, z, o, n, t, a, l, space, k, u, c, h, l, a, r, n, i, space, k, e, l, t, i, r, i, b, space, q, o, ʻ, y, i, n, g, point, right parenthesis, end text

[Tcos30 had qanday hosil boʻldi?]

start color #1fab54, T, start subscript, 1, end subscript, end color #1fab54, equals, start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, start text, c, o, s, end text, 30, start superscript, o, end superscript, start text, left parenthesis, Q, u, y, i, d, a, g, i, space, t, a, r, a, n, g, l, i, k, n, i, space, t, o, p, i, n, g, colon, end text, start color #1fab54, T, start subscript, 1, end subscript, end color #1fab54, right parenthesis

start color #1fab54, T, start subscript, 1, end subscript, end color #1fab54, equals, left parenthesis, start color #7854ab, 4, point, 9, start text, space, N, end text, end color #7854ab, right parenthesis, start text, c, o, s, end text, 30, start superscript, o, end superscript, start text, left parenthesis, B, i, z, space, t, o, p, g, a, n, space, s, o, n, space, q, i, y, m, a, t, n, i, space, k, e, l, t, i, r, i, b, space, q, o, ʻ, y, i, n, g, point, space, end text, start color #7854ab, T, start subscript, 2, end subscript, end color #7854ab, equals, start color #7854ab, 4, point, 9, start text, space, N, end text, right parenthesis, end color #7854ab

start color #1fab54, T, start subscript, 1, end subscript, end color #1fab54, equals, 4, point, 2, start text, space, N, end text, start text, left parenthesis, h, i, s, o, b, l, a, n, g, space, v, a, space, n, i, s, h, o, n, l, a, n, g, right parenthesis, end text

[Qoʻshimcha maʼlumotlar va manbalar]

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