Question

Find the moment \((M)\) of the system about the origin and the center of mass \((\bar x)\).

Short answer

The moment \((M)\) of the system about the origin is 154.

The center of mass \((\bar x)\) is 3.28.

Step-by-step solution

Find the value of M.

\(M\)is the sum of the products of each mass and its\(x\)- coordinate

\(\begin{aligned}{}M = \sum\limits_{i = 1}^n {{m_i}} {x_i}\\M = 12( - 3) + 15(2) + 20(8)\\M = - 36 + 30 + 160\\M = 154\end{aligned}\)

Calculate the mass of \((m)\)the system.

\(m = {m_1} + {m_2} + {m_3}\)

The total mass is

\(\begin{aligned}{}m = 12 + 15 + 20\\m = 47\end{aligned}\)

The center of mass of the system is

\(\bar x = \frac{M}{m} = \frac{{154}}{{47}}\)

Hence, \(M = 154\quad \) center of mass \(\bar x = \frac{{154}}{{47}}\)