The figure below shows a composite slab with dimensions d 1 = 13.2 cm, d 2 = 3.0
ID: 2142221 • Letter: T
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
Explanation / Answer
from the figure, by symmetry
Xcom=-d3/s =0.155/2 =0.0775m =7.75cm
negative value is choosing the coordinate system
for finding Ycom
ycom = rhoiViYcomi + rho aVaYcomi/(rhoiVi+rhoaV)
= (13.2*7.85/2) + (3*13.2*2.7/2)/(7.85+2.7)
=10.02 cm
by symmetry, Zcom = 3/2 = 1.5 cm
thus xcm.ycm, zcm = (7.75,10.02,1.5)
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