Question

Find the center of mass of the three-mass system shown in the figure relative to the mass m = 1.03 kg . (Figure 1)
Express your answer to two significant figures and include the appropriate units.

Answer 1

The center of mass of the three-mass system is 0.433m.

A position established in relation to an object or set of objects is the center of mass. It represents the system's average location as weighted by each component's mass. In a collection of unconnected items, the center of mass can also be established.

Given:

Mass of the object, m₁ = 1.03kg

Mass of the object, m₂= 1.50kg

Mass of the object, m₃= 1.10

Taking the location of m as the origin and towards right as positive X-axis.

x₁=0

x₂=0.50m

x₃=0.25+0.50 = 0.75m

The X-coordinate of the center of mass $x_c$ of a system of three masses  m₁, m₂ and m₃ located at the positions x₁, x₂ and x₃ on X-axis is given by,

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

$x_c=\frac{0+1.50*0.50+1.10*0.75}{1.03+1.50+1.10}\\x_c= 0.433 m$

Therefore,  the center of mass of the three-mass system is 0.433m.

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