physics question

Question

Consider the following three masses and the x- and y-components of their displacements (in m):

mass 1: 8.5 kg, (-5.2, -6.5)

mass 2: 6.3 kg, (0.2, -2.3)

mass 3: 6.1 kg, (4.9, 0.9)

mark the location of the center of mass of this system in the accompanying Cartesian coordinate system.

Answer 1

To calculate center of mass, deal with each direction separately.

x-direction:

x_cm = (∑m_ix_i)/m_TOTAL

x_cm = [(8.5)(-5.2) + (6.3)(0.2) + (6.1)(4.9)]/(8.5 + 6.3 + 6.1) = -13.05/20.9 = -0.624

y-direction:

y_cm = (∑m_iy_i)/m_TOTAL

y_cm = [(8.5)(-6.5) + (6.3)(-2.3) + (6.1)(0.9)]/(8.5 + 6.3 + 6.1) = -64.25/20.9 = -3.074

So the center of mass is at (-0.624, -3.074) meters