The thickness of the triangular plate varies linearly with y

The thickness of the triangular plate varies linearly with y from a value t₀ along its base y = 0 to 1.7 t₀ at y = h. Determine the y-coordinate of the center of mass of the plate.

Solution

CENTROID OF TRAPEZIUM = (h/3)*(t_o+3.4t_o)/(t_o+1.7t_o)

=(h/3)*4.4/2.7

=0.543h

CENTROID OF TRIANGLE=h/3

=0.33h

combined center of mass= (A₁y₁+A₂y₂)/(A₁+A₂)

=[0.5*(2.7t_o)h*0.543h+0.5bh*0.33h]/(0.33h+0.543h)

=(0.733t_oh^2+0.165bh^2)/0.873h

y =(0.733toh+0.165bh)/0.873