The figure shows a shaded area, bounded by the parabola y = kx² and the x-axis. a. Calculate the value of k. b. Find the x - and y-coordinates of the area's centroid. c. If the area has an area density of = 7xy kg/m², find the x- and y-coordinates of its center of mass. d. Compute the distance between the area's centroid and its center of mass.

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter8: Centroids And Distributed Loads
Section: Chapter Questions
Problem 8.13P: The parametric equations of the plane curve known as a cycloid are x=a(sin) and y=a(1cos). Use...
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The figure shows a shaded area, bounded by the parabola y = kx² and the x-axis.
a. Calculate the value of k.
b. Find the x- and y-coordinates of the area's centroid.
c.
If the area has an area density of a = 7xy kg/m², find the x- and y-coordinates of its
center of mass.
d. Compute the distance between the area's centroid and its center of mass.
y = kx²
4
7
x
Transcribed Image Text:The figure shows a shaded area, bounded by the parabola y = kx² and the x-axis. a. Calculate the value of k. b. Find the x- and y-coordinates of the area's centroid. c. If the area has an area density of a = 7xy kg/m², find the x- and y-coordinates of its center of mass. d. Compute the distance between the area's centroid and its center of mass. y = kx² 4 7 x
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