Centroid of a composite area: shape with hole

Error

There was an error loading the page.

Contributors

William Haynes

Feedback

From users who are members of Engineering Statics :

William Haynes

said

Ready to use

4 years, 6 months ago

History

○

William Haynes 4 years, 6 months ago

Gave some feedback: Ready to use

○

William Haynes 4 years, 6 months ago

Gave some feedback: Has some problems

○

William Haynes 4 years, 7 months ago

Gave some feedback: Ready to use

○

William Haynes 4 years, 7 months ago

Gave some feedback: Doesn't work

○

William Haynes 6 years, 5 months ago

Gave some feedback: Ready to use

○

William Haynes 6 years, 5 months ago

Gave some feedback: Needs to be tested

○

William Haynes 6 years, 6 months ago

Gave some feedback: Ready to use

○

William Haynes 6 years, 8 months ago

Published this.

○

William Haynes 6 years, 8 months ago

Gave some feedback: Needs to be tested

○

William Haynes 6 years, 8 months ago

Gave some feedback: Ready to use

○

William Haynes 6 years, 8 months ago

Created this.

There is only one version of this question that you have access to.

There are 5 other versions that do you not have access to.

Question statement

{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius]])}

Complete the table below and detemine the coordinates of the centroid of the composite shape.

Consider the shape to be made up of a {if (m=1,'large','')} rectangle {if (m=0,'and a triangle with a circle','with a triangle and circle')} removed. The circular hole has a {if(random(true,false), 'radius of '+ radius , 'diameter of '+ 2*radius)} {units}, centered at ({(center+A)[0]}, {(center+A)[1]}).

Give any introductory information the student needs.

			Name	Type	Generated Value

A	vector	vector(0,0)
b1	integer	6
h1	integer	4
ht	integer	6
center	vector	vector(5,2)
units	string	in
radius	number	1.5
n	integer	5
m	integer	0

			Name	Type	Generated Value

area_rect	list	[ 24, 48 ]
area_tri	list	[ 12, -12 ]
area_circ	list	List of 2 items
area_total	decimal	dec("28.931416529422965")

			Name	Type	Generated Value

C_rect	list	[ vector(3,2), vector(6,2) ]
C_circ	list	[ vector(5,2), vector(5,2) ]
C_tri	list	[ vector(8,2), vector(10,2) ]

			Name	Type	Generated Value

Q_rect	vector	vector(48,72)
Q_tri	vector	vector(24,96)
Q_circ	vector	Vector with 2 components
Q_total	vector	Vector with 2 components
centroid	vector	vector(4.5852259779,2)

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
-vector(random([0,0],[b1,0],[b1,h1],[0,h1],[b1/2,h1/2],[0,h1/2],[center[0],center[1]]))

JME function reference

Description

This offsets the shape to one of the corners of the rect, the center of the rect, or the center of the circle.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `vector`

vector(0,0)

← Depends on:

b1
center
h1

→ Used by:

C_circ
C_rect
C_tri

Statement
Advice

Parts

Table Gap-fill
Centroid Gap-fill
1. Gap xbar Engineering Accuracy with units
  Add
2. Gap ybar Engineering Accuracy with units
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Part	$A_i$	$\bar{x}_i$	$\bar{y}_i$	$A_i\bar{x}_i$	$A_i\bar{y}_i$
rectangle	Ar	xr	yr	qyr	qxr
triangle	At	xt	yt	qyt	qxt
circle	Ac	xc	yc	qyc	qxr
$\Sigma$	Area			qy	qx

Advice

{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius],['visibility',m]])}

1. Divide the shape into three subshapes as described in the problem statement.

2. You should be able to set up a table to gather the required information like the one provided in this problem.

3. Determine and enter the area and centroidal coordinates for each subshape into the table

$\qquad A_i, \bar{x}_i,\bar{y}_i$

4. Multiply area by the centroidal coordinates to get the moment of areas for the pieces.

$\qquad (Q_x)_i = A_i\bar{y}_i ,\quad(Q_y)_i=A_i\bar{x}_i$.

5. Sum columns 1, 4, and 5 to find the total area and moments of area.

$\qquad A, Q_x, Q_y$

Part	$A_i$ [{units}²]	$\bar{x}_i$ [{units}]	$\bar{y}_i$ [{units}]	$A_i\bar{x}_i$ [{units}³]	$A_i\bar{y}_i$ [{units}³]
rectangle	{area_rect[m]}	{C_rect[m][0]}	{C_rect[m][1]}	{Q_rect[1]}	{Q_rect[0]}
triangle	{area_tri[m]}	{siground(C_tri[m][0],3)}	{siground(C_tri[m][1],3)}	{Q_tri[1]}	{Q_tri[0]}
circle	{siground(area_circ[m],3)}	{C_circ[m][0]}	{C_circ[m][1]}	{siground(Q_circ[1],3)}	{siground(Q_circ[0],3)}
$\Sigma$	{siground(area_total,3)}			{siground(Q_total[1],3)}	{siground(Q_total[0],3)}

6. Find answers with

$\qquad \bar{x} = \dfrac{Q_y}{A} =\dfrac{\Sigma A_i \bar{x}_i}{\Sigma A_i} = \dfrac{\var{siground(Q_total[1],3)}}{\var{siground(area_total,3)}} = \var{siground(centroid[0],3)}\, \var{units}$

$\qquad \bar{y} = \dfrac{Q_x}{A} = \dfrac{\Sigma A_i \bar{y}_i}{\Sigma A_i}= \dfrac{\var{siground(Q_total[0],3)}}{\var{siground(area_total,3)}}= \var{siground(centroid[1],3)}\, \var{units} $

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Centroid of a composite area: shape with hole

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

Loading...

Error

Centroid of a composite area: shape with hole

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`