CoG center

Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all cases, between adjacent material points, the distance is a=1. )

Correct answer:

x =  -0.05
y =  -0.0816
z =  0.7348

Step-by-step explanation:

m1=1 m2=2 m3=3 m4=4  a=1 h33  =3/2   a h=a 6/3=1 6/30.8165 h1=32 h=32 0.81650.5443 h2=hh1=0.81650.54430.2722  A=(0,0,0) B=(0,h1,h)=(0,0.54433105395182,0.81649658092773) C=(a/2,h2,h)=(0.5,0.27216552697591,0.81649658092773) D=(a/2,h2,h)=(0.5,0.27216552697591,0.81649658092773)  m=m1+m2+m3+m4=1+2+3+4=10  x=mm1 Ax+m2 Bx+m3 Cx+m4 Dx=101 0+2 0+3 0.5+4 (0.5)=201=0.05
y=mm1 Ay+m2 By+m3 Cy+m4 Dy=101 0+2 0.5443+3 (0.2722)+4 (0.2722)=0.0816
z=mm1 Az+m2 Bz+m3 Cz+m4 Dz=101 0+2 0.8165+3 0.8165+4 0.8165=0.7348

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