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PrincessIceFall
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<<Mentor note: Thread merged with duplicate from other forum.>>
Half an octagonal prism. A small weight is placed 2 cm from the centreline of the vessel. The rod on which the weight is on is placed at (L/2) i.e at the center of the length of the vessel. The height of center of gravity from the base of the vessel is needed to be found.
In the above figure
A = 0.12 m
B = 0.2 m
H2 = 0.065 m
H1 = 0.095 m
H = 0.16 m
To find the centroid of the above plane surface, the centroid of each individual shapes must be first found.
The centroid of the trapezium on the x and y-axis from the top is given by the following equations
C_x= ( B/2) =0.1 m
C_y= H1/2*[((B+2A)/(B+A))]= 0.095/3*[((0.2+(2*0.12))/(0.2+0.12))]=0.0435 m
The centroid of the rectangle is simply
C_x= B/2= 0.2/2=0.1 m
C_y= H2/2= 0.065/2=0.0325 m
Now to find the centroid of the whole shape, the following tabular method is used
And the centroid of the total area is then given by
C_x= (∑▒〖(A*Cx)〗)/(∑▒A)= (2.82*〖10〗^(-3))/0.0282=0.1 m
C_y= (∑▒〖(A*Cy)〗)/(∑▒A)= (1.0837*〖10〗^(-3))/0.0282=0.03843 m
By taking point O as the origin and taking moments around this point w.r.t the y-axis, the height of centre of gravity from the bottom of the keel (base) can be found
W1 = mass of the small weight attached
W = mass of the whole body
KG= ((W1*y1)+(W*y2))/(W1+W)= ((0.05*0.16)+(1.6*0.12157))/(0.05+1.6)=0.1227 m
Half an octagonal prism. A small weight is placed 2 cm from the centreline of the vessel. The rod on which the weight is on is placed at (L/2) i.e at the center of the length of the vessel. The height of center of gravity from the base of the vessel is needed to be found.
In the above figure
A = 0.12 m
B = 0.2 m
H2 = 0.065 m
H1 = 0.095 m
H = 0.16 m
To find the centroid of the above plane surface, the centroid of each individual shapes must be first found.
The centroid of the trapezium on the x and y-axis from the top is given by the following equations
C_x= ( B/2) =0.1 m
C_y= H1/2*[((B+2A)/(B+A))]= 0.095/3*[((0.2+(2*0.12))/(0.2+0.12))]=0.0435 m
The centroid of the rectangle is simply
C_x= B/2= 0.2/2=0.1 m
C_y= H2/2= 0.065/2=0.0325 m
Now to find the centroid of the whole shape, the following tabular method is used
And the centroid of the total area is then given by
C_x= (∑▒〖(A*Cx)〗)/(∑▒A)= (2.82*〖10〗^(-3))/0.0282=0.1 m
C_y= (∑▒〖(A*Cy)〗)/(∑▒A)= (1.0837*〖10〗^(-3))/0.0282=0.03843 m
By taking point O as the origin and taking moments around this point w.r.t the y-axis, the height of centre of gravity from the bottom of the keel (base) can be found
W1 = mass of the small weight attached
W = mass of the whole body
KG= ((W1*y1)+(W*y2))/(W1+W)= ((0.05*0.16)+(1.6*0.12157))/(0.05+1.6)=0.1227 m
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