Enunciado

Line sources m1 and m2 are near point A, as in Fig. P8.32.

If m1 5 30 m2/2, fi nd the value of m2 for which the resultant

velocity at point A is exactly vertical

Passo 1

Saaaalve, tranquilo? Vamos lá resolver mais uma questão juntos?! 😊

Desenhando o diagrama

Passo 2

Resolva as forças de aceleração horizontalmente.

m 1 c o s ⁡ θ - m 2 c o s ⁡ ϕ = 0

Aqui, m 1 é a aceleração do lado esquerdo, m 2 é a aceleração do lado direito, θ é o ângulo feito pela aceleração do lado esquerdo, e ϕ é o ângulo feito pela aceleração do lado direitoCalcule o valor de θ .

t a n ⁡ θ   = 3   m 4   m θ   = t a n - 1 ⁡ ( 0.75 )   = 36.869 ∘

Passo 3

Calcule o valor de ϕ .

t a n ⁡ ϕ = 4   m 3   m ϕ = t a n - 1 ⁡ ( 1.333 )   = 53.13 ∘

Substituindo valores na equação (1)

m 1 c o s ⁡ θ - m 2 c o s ⁡ ϕ = 0 30   m 2 / s × c o s ⁡ 36.869 ∘ - m 2 × c o s ⁡ 53.13 ∘ = 0 m 2 = 30   m 2 / s × c o s ⁡ 36.869 ∘ c o s ⁡ 53.13 ∘   = 40   m 2 / s

Assim, o valor de m 2 é 40   m 2 / s .

Resposta

m 2 = 40   m 2 / s

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