Answer:
Ycm = 10.769 cm
Xcm = 6.808 cm
Explanation:
Given
B = 15 cm
A = 24 cm
D = 6 cm
C = 8 cm
We can divide the original rectangular plate into two parts and apply the following equations
a) Ycm = ∑Si*Yi / ∑Si
where
S₁ = A₁*B₁ = (9 cm)(24 cm) = 216 cm²
Y₁ = 12 cm
S₂ = A₂*B₂ = (6 cm)(16 cm) = 96 cm²
Y₂ = 8 cm
then
Ycm = (216 cm²*12 cm + 96 cm²*8 cm) / (216 cm² + 96 cm²)
⇒ Ycm = 10.769 cm
b) Xcm = ∑Si*Xi / ∑Si
where
S₁ = 216 cm²
X₁ = 4.5 cm
S₂ = 96 cm²
Y₂ = 12 cm
then
Ycm = (216 cm²*4.5 cm + 96 cm²*12 cm) / (216 cm² + 96 cm²)
⇒ Xcm = 6.808 cm
We have that for the Question, it can be said that
From the question we are told
A uniform rectangular plate of length B = 15 cm and height A = 24 cm has a rectangular corner cut out of it of length D = 6 cm and height C = 8 cm. The plate is made of a material of area mass density σ.
For this problem we set the origin at the lower left corner of the plate with the x-axis horizontal pointing right and the y-axis vertical pointing up.
a. Calculate the value of the y-coordinate, in centimeters, for the center of mass of the plate.
b. Calculate the value of the x-coordinate, in centimeters, for the center of mass of the plate.
Generally the equation for the y and xcm is mathematically given as
[tex]y=\frac{A_1y_2-A_2y_2}{A_1-A_2}\\\\Therefore\\\\y=\frac{(24*28*28/2)-6*9*(A-c/2)}{(24*28)-6*9}\\\\[/tex]
y=13.26cm
b)
[tex]y=\frac{A_1x_2-A_2x_2}{A_1-A_2}\\\\Therefore\\\\X=\frac{24*28*12)-54*21}{24*28-54}\\\\[/tex]
X=11.21cm
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