Find the centroid of the area bounded by the function f(x) = 1+ sin(x) and the x-axis and the lines x-1 and x=3. Calculate the center of mass for R (round to 2 decimal places) xbar = ybar Find the centroid (a, g) of the region bounded by: у 3 Зд* + 6л, у — 0, т%3D 0, and I = 3

Find the centroid of the area bounded by the function f(x) = 1+ sin(x) and the x-axis and the lines x-1 and x=3. Calculate the center of mass for R (round to 2 decimal places) xbar = ybar Find the centroid (a, g) of the region bounded by: у 3 Зд* + 6л, у — 0, т%3D 0, and I = 3

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 8.132RP: Find the centroid of the truncated parabolic complement by integration.

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Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

Find the centroid of the area
bounded by the function f(x) = 1+ sin(æ) and the x-axis
and the lines x-1 and x=3.
Calculate the center of mass for R (round to 2 decimal places)
xbar =
ybar
Find the centroid (E, 9) of the region bounded by:
y = 3x2 + 6x, y = 0, = 0, and r = 3

Expert Solution

Step 1

The given function is given by,

$f (x) = y = 1 + \sin x$

At x=1,

$\begin{array}{rcl} y & = & 1 + \sin (1) \\ = & 1 + \sin (1 \times \frac{180}{π}) \\ = & 1.841 m \end{array}$

At x=3,

$\begin{array}{rcl} y & = & 1 + \sin (3) \\ = & 1 + \sin (3 \times \frac{180}{π}) \\ = & 1.139 m \end{array}$

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