A cubical box consists of 4 square sides and a square base but has no top. The sides and the base are all made of thin sheet metal of uniform thickness. If the edges of the box are all 200 mm in length, how far above the base is the box’s centre of mass?
1 Answer
From the symmetry we see that the center of mass of the box is on a vertical line directly above the center of the base.
We also know that weight
#w="mass"xxg#
#=>w=("Volume"xx "Density")xxg#
#=>w=(("Area" xx "Thickness")xx "Density")xxg#
It is given that thickness and density is same for base and all four sides of the box. Let edge of each side and base
Area of the base
#= l^2#
Area of each side#=l^2#
As such
Let the box be so placed on its base so that origin coincides with the center of mass of base,
Height of base
Height of CoM is given by
Inserting various values we get
#h_"CoM"=(l^2xx0+l^2xxl/2+l^2xxl/2+l^2xxl/2+l^2xxl/2)/(5l^2)#
#=>h_"CoM"=(2l)/5#
#=>h_"CoM"=(2xx200)/5=80\ mm#