Question

c5 - center of mass and moments: problem 1
(4 points)
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2 of the answers are not correct.
the following masses ( m _ { i } ) are located at the given points ( p _ { i } : m _ { 1 } = 6 , quad p _ { 1 } ( 1,5 ) m _ { 2 } = 5 , quad p _ { 2 } ( 3 , - 2 ) m _ { 3 } = 10 , quad p _ { 3 } ( - 2 , - 1 ) ) find the moments ( m _ { x } , m _ { y } ), and the ( x ) and ( y ) coordinates of the center of mass of
the system.
( m _ { x } =)
( m _ { y } =)
( x ) - coordinate of the center of mass ( \bar { x } =)
( y ) - coordinate of the center of mass ( \bar { y } =)
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Explanation:

Step1: Calculate the total mass \(m\)

$$
LATEXBLOCK0
$$

Step2: Calculate the moment \(M_y\)

$$
LATEXBLOCK1
$$

Step3: Calculate the moment \(M_x\)

$$
LATEXBLOCK2
$$

Step4: Calculate the \(x\) - coordinate of the center of mass \(\overline{x}\)

$$ \overline{x}=\frac{M_y}{m}=\frac{1}{21} $$

Step5: Calculate the \(y\) - coordinate of the center of mass \(\overline{y}\)

$$ \overline{y}=\frac{M_x}{m}=\frac{8}{21} $$

Answer:

\(M_x = 8\), \(M_y = 1\), \(x=\frac{1}{21}\), \(y = \frac{8}{21}\)