Question

Chapter 09, Problem 003 The figure shows a composite slab with dimensions d 11.9 cm, d. 3.28 cm, and d. 13.2 cm. Half the slab consists of aluminum (density 2.70 g/cm3) and half consists of iron (density 7.85 g/cm3). What are (a) thex coordinate, (b) the y coordinate, and (c) the z coordinate of the slabs center of mass? Midpoint roll Aluminum (a) Number Units (b) Number Units (c) Number Units

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Answer #1

m1 is iron slab mass = d X V

m1 = 7.85 X 11.9 X 3.28 X 13.2

m1 = 4044.49 g

( x1 , y1 , z1 ) = ( - d3 / 2 , d1 / 2 , d2 / 2 )

= ( - 6.6 , 5.95 , 1.64 )

m2 is alluminium mass = d X V

= 2.7 X 11.9 X 3.28 X 13.2

m2 = 1391.1 g

( x2 , y2 , z2 ) = ( - d3 / 2 , d1 + (d1 / 2) , d2 / 2 )

= ( - 6.6 , 17.85 , 1.64 )

now

Xcm = m1 x1 + m2 x2 / (m1+ m2 )

Xcm = 4044.49 X ( - 6.6 ) + 1391.1 X ( - 6.6 ) / (4044.49 + 1391.1 )

Xcm = - 6.6 cm

Ycm = m1 y1 + m2 y2 / (m1+ m2 )

Ycm = 4044.49 X ( 5.95 ) + 1391.1 X (17.85 ) / (4044.49 + 1391.1 )

Ycm = 8.99 cm

Zcm = m1 z1 + m2 z2 / (m1+ m2 )

Zcm = 4044.49 X ( 1.64 ) + 1391.1 X ( 1.64 ) / (4044.49 + 1391.1 )

Zcm = 1.64 cm

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