Question

A system composed of the following particles: a 0.500 kg particle at the origin; a 1.25 kg particle at x = 0.150 m, y = 0.200 m; and a 0.750 kg particle at x = 0.200 m, y = -0.800 m. Find the x-coordinate of the center of mass of the system.

Answer 1

To solve this problem we will apply the concepts related to the center of mass. This can be defined as the relationship between the sum of the multiplication of the mass and its coordinate on the total sum of the masses. The distances on the x axis have already been given, so assuming that they start from the coordinate center (0,0) we will apply the previous concept to find the distance from the center of mass. So:

$x_{cm} = \frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}$

$x_{cm} = \frac{(0.5*0)+(1.25*0.15)+(0.75*0.20)}{0.5+0.75+1.25}$

$x_{cm} = 0.135m$

Therefore the x-coordinate of the center of mass of the system is 0.135m from the origin.

Now for y,

$y_{cm} = \frac{m_1y_1+m_2y_2+m_3y_3}{m_1+m_2+m_3}$

$y_{cm} = \frac{(0.5*0)+(1.25*0.2)-(0.75*0.80)}{0.5+0.75+1.25}$

$y_{cm} = -0.14 m$

Therefore the y-coordinate of the center of mass of the system is -0.14m below the origin.