Particulae in aequilibrio bidimensionali – applicatio problematum et solutionum legis primae Newtoni

1. Vires tensionales T₁ _, T₂ _, et T₃ _{inveni .} Massam funis neglege.

Solutio

(a) Diagramma corporis liberi pro obiecto (b) Diagramma corporis liberi pro funiculo

Legem primam Newtoni ad rem applica :

ΣFy ₌ 0

T1 – _w = 0

T1 = w = _mg

T₁ = ( 5 kg)(9.8 m/ ^s² ₎

T₁ = ₄₉ kg m/ ^s²

T² = ₄₉ N

Legem primam Newtoni in funiculum applica:

∑ Fx ₌ 0

T _3x – T _2x = 0

T³ _cos³ ° ^– T² _cos³ ° ⁼ 0

0.87 T³ _– 0.77 T² ₌ 0

0.87 T³ ₌ 0.77 _T²

T² = 0.87 T³ _/ 0.77 = 1.1 T³ _———- Aequatio ₁

[irp]

-

∑ F _y = 0

T₂y + _T₂y – _T₁y = ₀

T ₃ sin 30 ^o + T ₂ sin 40 ^o - T ₁ = 0

0.5 T³ ₊ 0.64 T² _– 49 N = 0 ———- Aequatio 2

Substituendo T₂ _in aequatione 2 in aequationem 2:

0.5 T³ ₊ 0.64 (1.1 T³ ₎ – 49 N = 0

0.5 T³ ₊ 0.70 T³ _– 49 = 0

1.2 T ₃ – 49 = 0

1.2 T³ ₌ 49

T³ ₌ 49 / 1.2

T² = ₄₁ N

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T² = _{1.1 T³}

T² = ( _1.1 )(40.8 N)

T² = ₄₅ N

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1. Particulae in aequilibrio unidimensionali
2. Particulae in aequilibrio bidimensionali
3. Aequilibrium corporum funibus et trochleis connexorum
4. Aequilibrium corporum in plano inclinato