Respuesta :
ANSWER:
x = 1.8 cm and y = -0.6 cm
STEP-BY-STEP EXPLANATION:
Given:
[tex]\begin{gathered} m_1=3\operatorname{kg}=\mleft\lbrace x_1,y_1=(2\operatorname{cm},0\operatorname{cm}\mright\rbrace \\ m_2=3\operatorname{kg}=\lbrace x_2,y_2=(0\operatorname{cm},2\operatorname{cm}\rbrace \\ m_3=4\operatorname{kg}=\lbrace x_3,y_3=(3\operatorname{cm},-3\operatorname{cm}\rbrace \\ \end{gathered}[/tex]Then x-coordinate of centre of mass is:
[tex]\begin{gathered} x_m=\frac{m_1\cdot x_1+m_2\cdot x_2+m_3\cdot x_3}{m_1+m_2+m_3} \\ \text{ replacing:} \\ x_m=\frac{3\cdot2+3\cdot0+4\cdot3}{3+3+4}=\frac{6+0+12}{10}=1.8\text{ cm} \\ \\ y_m=\frac{m_1\cdot y_1+m_2\cdot y_2+m_3\cdot y_3}{m_1+m_2+m_3} \\ y_m_{}=\frac{3\cdot0+3\cdot2+4\cdot-3}{3+3+4}=\frac{0+6-12}{10}=-0.6\text{ cm} \\ \\ \text{The center mass is (1.8 cm, -0.6 cm)} \end{gathered}[/tex]The location of the center of mass x = 1.8 cm and y = -0.6 cm
