Finding Center of Mass of 800g Steel Plate Triangle

In summary: The mass is found by multiplying the area of the plate by the mass of the material in the plate. The mass of the material in the plate is found by multiplying the width of the material by the mass of the material.
  • #1
Anthonyphy2013
30
0

Homework Statement



An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass?
https://www.physicsforums.com/attachment.php?attachmentid=13559&d=1208292919

Homework Equations



x=1/M ∫ x dm

3. The Attempt at a Solution [/b
I have no idea how to start the question
 
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  • #2
The image gives you a big ole hairy HINT. Did you try following it?
 
  • #3
SteamKing said:
The image gives you a big ole hairy HINT. Did you try following it?

what hint is that ? the triangle is a smmetry and I put xcm=1/M∫xd(ρ/AH)
and the height is y=2/3 x as =mx+C. and should I put h = 2/3 x ?
 
  • #4
Anthonyphy2013 said:
xcm=1/M∫xd(ρ/AH)
and the height is y=2/3 x as =mx+C. and should I put h = 2/3 x ?
That's a pretty confusing mix of variable names. What's AH, C, the m in mx+C? Why switch from y to h?
That said, y (=h) = 2x/3 looks right. What do you get for the integral?
 
  • #5
xcm=1/M∫xd(ρ/AH) , A is the area and H is the height , I need to find h and I use h=mx+c to find the height and the slope is 2/3 . Question is to find the center of mass and only this integration could help me find the answer .
 
  • #6
Anthonyphy2013 said:
xcm=1/M∫xd(ρ/AH) , A is the area and H is the height
ρ/AH is not going to give you mass. And... the area and height of what, exactly?
You want the mass, dm, of an element of width dx and height y = 2x/3. It's a 2-dimensional lamina, so the density is mass/area. So what is dm equal to?
 
  • #7
More importantly, you have a plate with a simple shape composed of a material which has a constant density. Do you really need an integral to determine the location of the centroid?
 

Related to Finding Center of Mass of 800g Steel Plate Triangle

1. What is the center of mass?

The center of mass is a point where the mass of an object is evenly distributed in all directions. It is also known as the center of gravity.

2. How do you find the center of mass of an object?

To find the center of mass of an object, you need to locate the point where the object is perfectly balanced. This can be done by finding the average position of all the individual particles that make up the object.

3. Why is it important to find the center of mass of an object?

Finding the center of mass of an object is important because it helps determine its stability and the way it will behave under different forces. It is also crucial in designing structures and objects that need to be balanced.

4. What is the formula for finding the center of mass of a triangle?

The formula for finding the center of mass of a triangle is (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3. This means that the center of mass is located at the average of the x and y coordinates of the three vertices of the triangle.

5. Can the center of mass of an object be outside of the object?

Yes, the center of mass of an object can be outside of the object if the object is irregularly shaped or has an asymmetrical distribution of mass. This can also occur in objects with holes or hollow spaces.

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