Concept explainers
Determine the centroid
Prob. F9-1
(a)

The centroid
Answer to Problem 1FP
The centroid
Explanation of Solution
Given:
The length of the shaded area is 1 m.
The height of the shaded area is 1 m.
Show the area of the differential element as in Figure 1.
Using Figure 1,
Express the parabolic value.
Compute the area of the element.
Substitute
Compute the centroid of the differential element along the x-axis using the formula.
Substitute
Determine the location of the centre of gravity of the homogeneous rod along the x-axis
Conclusion:
Apply the limits from 0 to 1 m, substitute
Calculate the numerator part from Equation (III).
Calculate the denominator part from Equation (III).
Substitute
Thus, the centroid
(b)

The centroid
Answer to Problem 1FP
The centroid
Explanation of Solution
Given:
The length of the shaded area is 1 m.
The height of the shaded area is 1 m.
Show the area of the differential element as in Figure 2.
Using Figure 2,
Express the parabolic value.
Compute the area of the element.
Substitute
Compute the centroid of the differential element along the y-axis using the formula.
Determine the location of the centre of gravity of the homogeneous rod along the y-axis
Conclusion:
Apply the limits from 0 to 1 m, substitute
Calculate the numerator part from Equation (V).
Calculate the denominator part from Equation (V).
Substitute
Thus, the centroid
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Chapter 9 Solutions
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