A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
Tutorial on finding the Centroid/Center of mass of a complex object. UNISA Students come here.
 one year ago
Tutorial on finding the Centroid/Center of mass of a complex object. UNISA Students come here.

This Question is Closed

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4In this tutorial we will find the Centroid about this complex extruded shape. All cutout pieces shall be taken as negative.dw:1363796078055:dw

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4Split the complex shape into its component shapes.dw:1363796223427:dw

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4Find the area of each of these simple shapes.\[A1 = \frac{ 1 }{ 2 }B \times \tau H\]\[A2 = L \times B\]\[A3 = L x B\]\[A4 = L x B\]

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4\[A1 = 10m ^{2}\]\[A2 = 20m ^{2}\]\[A3 = 7.5m ^{2}\]\[A4 = 2m ^{2}\] The total are of these 4 will be \[AT = 39.5m ^{2}\]

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4Now if we take the origional drawing we see that the shapes are in very definate places, and they are at definate points above and away from the x and y axis.dw:1363796713376:dw

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4To determine the centroid of each shame we must include these distances from the axis as well. So for example the y and x centroid of the cut out square in the center will be. \[y _{Cutout} = \frac{ 3m }{ 2 } + 2m\]\[y_{Cutout} = 3.5m\] \[x_{Cutout} = \frac{ 2.5m }{ 2 } + 0.5m\]\[x_{Cutout} = 1.75m\]

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4yust to make suredw:1363797121334:dw

jores
 one year ago
Best ResponseYou've already chosen the best response.0so we include those formula for the cutout!!!!!

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4The centroid of the triangular shape will thus be.\[y_{Triangle} = \frac{ 5m }{ 2 } + 2m\]\[y_{Triangle} = 4.5m\] \[x_{Triangle} = \frac{ 2m }{ 2 } + 5m\]\[x_{Triangle} = 6m\]The centroid of the large rectangle will be\[y_{LRec} = \frac{ 5m }{ 2 } + 2m\]\[y_{LRec} = 4.5m\] \[x_{LRec} = \frac{ 4m }{ 2 }\]\[x_{LRec} = 2m\] The centroid of the small rectangle is\[y_{sRec} = \frac{ 2m }{ 2 }\]\[y_{sRec} = 1m\] \[x_{sRec} = \frac{ 1m }{ 2 }\]\[x_{sRec} = 0.5m\]

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4yes jores we do, we wer not doing that at UNISA, the textbook did not include that piece of information. You have to find the centroid of the shape and add it to the distance from the x or y axis.

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4So now the final equation to find the centroid of the complex shape will be\[Ay_{Complex}=\frac{ A1y_{Triangle}+A2y_{LRec}−A3y_{Cutout}+A4y_{sRec}}{ AT } \]\[Ax_{Complex}=\frac{ A1x_{Triangle}+A2x_{LRec}−A3x_{Cutout}+A4x_{sRec}}{ AT } \]we minus A3 as it is the cutout shape and therefore is not actually there. The numerical values are as such.\[Ay_{Complex}=\frac{ (10)(4.5)+(20)(4.5)−(7.5)(3.5)+(2)(1) }{ 39.5 }\]\[Ay_{Complex}= 2.80m\] \[Ax_{Complex}=\frac{ (10)(6)+(20)(2)−(7.5)(1.75)+(2)(0.5) }{ 39.5 }\]\[Ax_{Complex}= 2.22m\]

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4To conclude it will be so.dw:1363798358172:dw

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4Questions are free now.

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4Don't forget to drop a medal in the box on your way out if you think this helped you? Also don't be afraid to fan me as well.

jores
 one year ago
Best ResponseYou've already chosen the best response.0where did you get this formula yCutout=3m2+2m

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4I found it while looking on the internet. it is the centroid of the cutout area being 3m over 2 to find the centroid + the distance from the edge of the cutout closest to the y axis to the axis its self. You follow? Should I draw it?

Razzputin
 one year ago
Best ResponseYou've already chosen the best response.4and sorry for my poor spelling i was typing in a rush. It must not be shame it must be shape. I also mistyped just as yust.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.