Question

The composite plate of uniform thickness is fabricated from two metals. The metal in volume A has a mass density of 8.00 Mg/m3 and the metal in volume B has a mass density of 9.00 Mg/m? a) Determine the total mass of the composite plate. b) Determine the location of the mass center G referenced from the origin of the coordinate system. 225 mm 150 mm 150 mm 30 mm .x

Answer 1

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Solution. 2 G af SA= 8.00 mg/m3 28 x 10 g/m3 kg/m3 28000 kg/m3 > çolas 1225 mm CK SA B 3 uneesi 20mm = SB²9.oomgim SB: gooo kg/m I somm 3 х (as total mass of the composite plate, m mtmp Total showe SAVAT BBVA [ density : mass volume (scoo x Anxtatqooo Ag to)C: Volumes atzeax thicknes prelu 8000x 0.03 x AA t 9000 x 0.03 AB ( area of trapezoid) Anį ( 150+ 300)*225 -6 = I (450) x 295 X10 que et AA = que gosooo AB x (225) (150)x100 (Area of triande) - AB 0.0168 m2

mtotal ชชา) tmb Mrotal 8000% 0.0 3 x 0.056 + 9000x 0.03% 0.0168 13.44 + 4.536 img 14.976 kg mA = 13.44 kg mo=4.536 kg (6) location of mass Centre a from osign 12 2 A (-4). x the K IB love 0,0,0) centre of mass from origin. 5, 9, z is of A from origin - ła, JA, Z ý centre of mass xos, Ini t for A En let's calculate here dearly hart ja = 30 15 mm (rectangle) =45mm (the y direction) Now; sta and ZA.

lreade V r wwse split trapezium into Section I and seation 2 A 1 nz (0,0,0) lowas! a Ay beetenglea X Azn hiangle. Ix 150x225 225x150 2 33750mm mom² 216845 mm = 150 75 mm | 12 = 150+4 (150) 200 mm sun ats centroid of Section I anda 81 Apsat Azł 11 it AITA 33750* 757 16875* 200 11 33750f 16875 ta 116.66 mm a direction Which is re so that 벨 -116.66 mm

Similarly for A We need ¢ and Z q 228 112.5 mm 2 AS 2+ 225 = 150 non 3 쁘 Ap Zat Az 1 Atih 33750 x 112.5+ 16895150 33750t 16875 IN were sol (nrich is the z direction) brutt am ZB, TB, TB Similarly for ß To i 15 mm 80 2 (rectangles they direction) wine st= 124/3 he clo x 150 + 150 JIL The - 200 mm Xo =-200 mm Are a direction) ŽB ZB 1 x 225 (tre a direction) tere st

bele Esa olla 2 Bo66+ 4.86 13.66 *(125)+ 4.536% (75) Routų the = 2 * he thee leve ste L (that thee) (Phuthue) SH that the (si-ove +(51-) the The thue ht 8h Tret uh tue А ععا عر) bsgetEl- 13044 + 4,536 13.44% (-116.66) + 4.536 (-200 r 'Atm Ixovet xhu =x F of combine block A and B mass centre imon

=) so mass Centre from the origin. is (x, 9 iz) (-134.689, -15, 112.53 ) mm ban answer NOTE: it you give I It may noted that direction other than that take answer is magntude wise same direction that is so but wise different (5 g, i) = (137.689, 15, 112.53) onm