Y Centroid
For the shown figure, what is the y-coordinate of the centroid in inches? Note the figure is not drawn to scale.
Expand Hint
Split the object into basic shapes (triangles, rectangles, squares, etc.).
Hint 2
The y-component of an area’s centroid is defined as:
$$$y_{ac}=\frac{\sum y_n a_n}{A}$$$
where
$$a_n$$
is the simplified object’s area,
$$y_n$$
is the distance from the origin to the middle of the simplified object, and
$$A$$
is the total area.
The y-component of an area’s centroid is defined as:
$$$y_{ac}=\frac{\sum y_n a_n}{A}$$$
where
$$a_n$$
is the simplified object’s area,
$$y_n$$
is the distance from the origin to the middle of the simplified object, and
$$A$$
is the total area (
$$\Sigma a_n$$
).
First, let’s split the main object into basic shapes (triangles, rectangles, squares, etc.).
To find the y-component of the main object’s centroid, let’s set the ground as the origin:
$$$y_{ac}=\frac{(y_A a_A)+(y_B a_B)}{(a_A+a_B)}=\frac{[(\frac{9in}{2}+4in)(1in\cdot 9in)]+[\frac{4in}{2}\cdot(4in\cdot 5in)]}{[(1in\cdot 9in)+(4in\cdot 5in)]}$$$
$$$=\frac{[(8.5in)(9in^2)]+[(2in)(20in^2)]}{[(9in^2)+(20in^2)]}=\frac{(76.5in^3+40in^3)}{29in^2}$$$
$$$=\frac{116.5in^3}{29in^2}=4.02\:in$$$
4.02 inches
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Centroid of Area
294. Centroid Area
Similar Problems from FE Section: Centroids of Masses, Areas, Lengths, and Volumes
294. Centroid Area