Umthetho wesibili kaNewton mayelana nokunyakaza kokujikeleza

Isihloko mayelana nomthetho wesibili kaNewton mayelana nokunyakaza kokujikeleza

4.1 Ubudlelwano phakathi kwesikhathi samandla, isikhathi sokungaqhubeki kahle, kanye nokusheshisa kwe-angular

Uma kukhona amandla aphumayo (ΣF) asebenza entweni enesisindo (m) khona-ke into ihamba ngokuhambisana nokusheshisa okuthile (a). Ubudlelwano phakathi kwamandla aphumayo, isisindo, kanye nokusheshisa buvezwa yi-equation:

Σ F = ma

Lesi yisilinganiso somthetho wesibili kaNewton.

Inani lokunyakaza okujikelezayo okufana namandla aphumayo (ΣF) ekuhambeni okuqondile liyisikhathi samandla esiphumayo (Στ). Inani lokunyakaza okujikelezayo okufana nobunzima (m) ekuhambeni okuqondile yizikhathi ze-inertia (I). Inani lokunyakaza okujikelezayo okufana nokusheshisa (a) ekuhambeni okuqondile yi-angular acceleration (α).

Uma kukhona umzuzu wamandla ophumelayo (Στ) osebenza entweni enomzuzu othile we-inertia (I) khona-ke into ijikeleza nge-angular acceleration ethile (α). Ubudlelwano phakathi kwamandla omzuzu ophumelayo, umzuzu we-inertia, kanye ne-angular acceleration buvezwa nge-equation:

Στ = I α

Lesi sibalo siwumfanekiso ojikelezayo womthetho wesibili kaNewton.

4.2 Izibonelo zezinkinga zomthetho wesibili kaNewton mayelana nokunyakaza kokujikeleza

Inkinga yesampula 1.

I-pulley eqinile enesisindo esingu-1 kg kanye nerediyasi engu-10 cm, emaphethelweni, intambo egoqiwe, umkhawulo owodwa wentambo ulengiswe ngomthwalo ongu-1 kg. Cabanga ukuthi intambo ayinasisindo. Nquma ubukhulu bokusheshisa komthwalo lapho uwela phansi ngokukhululeka. (g = 10 m/s²)

Isixazululo:

Kwaziwa:

F = w = mg = (1 kg)(10 m/s ² ) = 10 N

r = 0.1 m

Okufunwayo: Ukusheshisa umthwalo

Isixazululo:

Okokuqala, bala isikhathi sokungalali kanye nesikhathi samandla.

Isikhathi sokungabi namandla kwe-pulley eqinile:

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

Isikhathi samandla:

τ = F l = (10 N)(0.1 m) = 1 N m

Ukusheshisa kwe-angular:

Ukusheshisa umthwalo:

a = r α = (0.1)(200) = 20 m/s ²

Inkinga yesampula 2.

I-pulley eqinile enesisindo esingu-2M kanye ne-radius ka-R, onqenqemeni, igoqe intambo, umkhawulo owodwa wentambo ulengiswe ngomthwalo onesisindo esingu-m. Lapho umthwalo ususwa, i-pulley ijikeleza ngokusheshisa kwe-angular. Uma i-pulley inamathele entweni enesisindo esingu-M, ukuze i-pulley ijikeleze ngokusheshisa kwe-angular okufanayo, nquma isisindo somthwalo. (I-pulley = 1⁄2 MR ² ).

Isixazululo:

Kwaziwa:

Isisindo se-pulley eqinile: 2M

Irediyasi ye-pulley eqinile: R

Isisindo somthwalo: m

Kufunwa: Isisindo somthwalo

Isixazululo:

Bala isikhathi sokungabi namandla kwe-pulley eqinile, ngaphambi nangemva kokunamathisela izinto ngesisindo M:

Isikhathi sokungakhathali 1: I = 1⁄2 mr ² = 1⁄2

(2M)(R) ² = MR ²

Isikhathi sokungakhathali 2: I = 1⁄2 mr ² = 1⁄2

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

Isikhathi samandla asetshenziswa umthwalo osesipijini:

τ = F l = (m)(g)(R)

Ukusheshisa kwe-angular kwe-pulley kuyafana, kokubili ngaphambi nangemva kokunamathisela izinto nge-mass M.

Isisindo somthwalo = 1.5 izikhathi zesisindo somthwalo wokuqala.