Localize o centro de massa ( x - ,   y - ,   z -   ) da conjunto de blocos homogêneo.

Passo 1

O problema quer que a gente encontre o centro de massa, que é dado por:

x - = ∑ x - V ∑ V

y - = ∑ y - V ∑ V

z - = ∑ z - V ∑ V

Passo 2

Então vamos começão calculando o x - :

x - = ∑ ( x - ) V ∑ V

x - = 75 ⋅ 150 ⋅ 150 ⋅ 550 + 225 ⋅ 150 ⋅ 150 ⋅ 200 + 200 1 2   ⋅ 150 ⋅ 150 ⋅ 100 150 ⋅ 150 ⋅ 550 + 150 ⋅ 150 ⋅ 200 + 1 2 150 ⋅ 150 ⋅ 100

x - = 120   m m

Agora o y - :

y - = ∑ ( y - ) V ∑ V

y - = 275 ⋅ 150 ⋅ 150 ⋅ 550 + 450 ⋅ 150 ⋅ 150 ⋅ 200 + 50 1 2   ⋅ 150 ⋅ 150 ⋅ 100 150 ⋅ 150 ⋅ 550 + 150 ⋅ 150 ⋅ 200 + 1 2 150 ⋅ 150 ⋅ 100

y - = 305   m m

E por fim z - :

z - = ∑ ( z - ) V ∑ V

z - = 75 ⋅ 150 ⋅ 150 ⋅ 550 + 75 ⋅ 150 ⋅ 150 ⋅ 200 + 50 1 2   ⋅ 150 ⋅ 150 ⋅ 100 150 ⋅ 150 ⋅ 550 + 150 ⋅ 150 ⋅ 200 + 1 2 150 ⋅ 150 ⋅ 100

z - = 73,4   m m

Passo 3

Então colocando na notação da questão, fica:

C = ( 120 ;   304 ;   73,4 )

Resposta

C = ( 120 ;   304 ;   73,4 )

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