Dokar Newton ta biyu kan motsi na juyawa

Labarin game da dokar Newton ta biyu kan motsi na juyawa

4.1 Alaƙar da ke tsakanin lokacin ƙarfi, lokacin inertia, da kuma saurin kusurwa

Idan akwai ƙarfin sakamako (ΣF) da ke aiki akan abu mai taro (m) to abin yana tafiya a layi tare da wani hanzari (a). Alaƙar da ke tsakanin ƙarfin sakamako, taro, da hanzari ana bayyana ta hanyar lissafi:

Σ F = ma

Wannan shine daidaiton dokar Newton ta biyu.

Adadin motsin juyawa wanda yayi daidai da ƙarfin sakamako (ΣF) a cikin motsi na layi shine lokacin ƙarfi da aka samu (Στ). Adadin motsin juyawa wanda yayi daidai da taro (m) a cikin motsi na layi sune lokutan inertia (I). Adadin motsin juyawa wanda yayi daidai da hanzari (a) a cikin motsi na layi shine hanzarin kusurwa (α).

Idan akwai lokacin ƙarfi (Στ) da ke aiki akan wani abu wanda ke da takamaiman lokacin inertia (I) to abin yana juyawa da wani takamaiman hanzarin kusurwa (α). Alaƙar da ke tsakanin ƙarfin lokacin da aka samu, lokacin inertia, da saurin kusurwa ana bayyana ta ta hanyar lissafi:

Στ = I α

Wannan lissafin yana kama da na juyi na dokar Newton ta biyu.

4.2 Misalan matsalolin dokar Newton ta biyu kan motsi na juyawa

Misalin matsalar 1.

Pulley mai ƙarfi mai nauyin kilogiram 1 da radius na santimita 10, a gefuna, igiya da aka naɗe, ƙarshen igiyar ɗaya an rataye shi da nauyin kilogiram 1. Ka yi tunanin igiyar ba ta da nauyi. Ka ƙayyade girman hanzarin kayan lokacin da aka sauke ƙasa. (g = 10 m/s²)

Magani:

Wanda aka sani:

F = w = mg = (1 kg)(10 m/s ² ) = 10 N

r = 0.1 m

Ana so: Haɓaka kaya

Magani:

Da farko, ƙididdige lokacin inertia da lokacin ƙarfi.

Lokacin inertia na pulley mai ƙarfi:

I = 1⁄2 mr ² = 1⁄2 (1 kg)(0.1 m) ²

I = (0.5 kg)(0.01 m ² ) = 0.005 kg m ²

Lokacin ƙarfi:

τ = F l = (10 N)(0.1 m) = 1 N m

Haɓaka kusurwa:

Haɓaka kaya:

a = r α = (0.1) (200) = 20 m/s ²

Misalin matsalar 2.

Pulley mai ƙarfi mai nauyin 2M da radius na R, a gefen, ya naɗe igiya, ƙarshen igiyar ɗaya ya rataye da kaya mai nauyin m. Lokacin da aka cire kayan, pulley ɗin yana juyawa da hanzarin kusurwa. Idan pulley ɗin an haɗa shi da wani abu mai nauyin M, don haka pulley ɗin ya juya tare da saurin kusurwa iri ɗaya, a ƙayyade nauyin kayan. (I pulley = 1⁄2 MR ² ).

Magani:

Wanda aka sani:

Nauyin injin jan ƙarfe mai ƙarfi: 2M

Radius na ƙarfin pulley: R

Nauyin kaya: m

Ana so: Nauyin kaya

Magani:

Lissafa lokacin inertia na pulley mai ƙarfi, kafin da bayan haɗa abubuwa da taro M:

Lokacin rashin kuzari 1 : I = 1⁄2 mr ² = 1⁄2

(2M)(R) ² = MR ²

Lokacin rashin kuzari 2 : I = 1⁄2 mr ² = 1⁄2

(2M + M) (R) ² = 1⁄2 (3M) (R) ² = 1.5 MR ²

Lokacin ƙarfin da kayan da ke kan kura ke yi:

τ = F l = (m)(g)(R)

Haɓaka kusurwar pulley iri ɗaya ne, duka kafin da kuma bayan haɗa abubuwa da taro M.

Nauyin kaya = sau 1.5 na nauyin kayan da aka ɗora.