Respuesta :
Answer:
(-1.5,-1.5)m
Explanation:
we know that:
[tex]X_{cm} = \frac{m_1x_1+m_2x_2....m_nX_n}{m_1+m_2...m_n}[/tex]
where [tex]X_{cm}[/tex] is the location of the center of gravity in the axis x, [tex]m_i[/tex] is the mass of the object i and [tex]x_i[/tex] the first coordinate of center of gravity of object i.
so:
[tex]0 = \frac{(5kg)(0)+(3kg)(0)+(4kg)(3)+(8kg)x_4}{5kg+3kg+4kg+8kg}[/tex]
Where [tex]x_4[/tex] is the first coordinate of the center of gravity for the fourth object.
Therefore, solving for [tex]x_4[/tex], we get:
[tex]x_4 = -1.5m[/tex]
At the same way:
[tex]Y_{cm} = \frac{m_1y_1+m_2y_2....m_ny_n}{m_1+m_2...m_n}[/tex]
where [tex]Y_{cm}[/tex] is the location of the center of gravity in the axis y, [tex]m_i[/tex] is the mass of the object i and [tex]y_i[/tex] the second coordinate of center of gravity of object i. replacing values we get:
[tex]Y_{cm} = \frac{(5kg)(0)+(3kg)(4)+(4kg)(0)+(8kg)y_4}{5+3+4+8}[/tex]
Where [tex]y_4[/tex] is the second coordinate of the center of gravity for the fourth object.
solving for [tex]y_4[/tex]:
[tex]y_4 = -1.5m[/tex]
It means that the object of mass 8kg have to be placed in the
coordinates (-1.5,-1.5) m.
