The figure below shows a composite slab with dimensions d 1 = 13.2 cm, d 2 = 3.0

Question

The figure below shows a composite slab with dimensions d1 = 13.2 cm, d2 = 3.00 cm, and d3 = 15.5 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are the coordinates of the center of mass of the slab?
(x, y, z) = ( , , ) cm

The figure below shows a composite slab with dimensions d1 = 13.2 cm, d2 = 3.00 cm, and d3 = 15.5 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are the coordinates of the center of mass of the slab?

Explanation / Answer

z _c.m = d2 / 2 = 3/2 = 1.5 cm

x_cm = d3/2 = 15.5 /2 =7.75 cm

both partition have same volume (say A)

y_cm = m1y1 + m2y2 / (m1 +m2)

      = A x 7.85 x (13.2/2)   + A x 2.70 x (13.2 + 13.2/2) / ( 7.85A + 2.70A)

        = 9.98 cm

so c.m ( 7.75 cm , 9.98 cm, 1.5 cm )  

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