Where is the center of mass of a flat triangular plate with given dimensions?

[jsr219]

Find the x and y coordinates of the center of mass of a flat triangular plate of a height H =17.3cm and a base B = 10 Cm

Homework Equations

Area = A = 1/2bh
x = 1/A ∫ x(f(x))
y = 1/A ∫ 1/2((f(x)^2)

The Attempt at a Solution

Area = 1/2(10)(17.3) = 86.5

f(x) = 17.3-1.73x or 17.3-173/100x
... this represents the equation for the line of the hypt. of the triangle, with its y intercept at 17.3 and its x intercept at 10, and a slope of 17.3/10


All interals from 0 to 10

x = 1/86.5 ∫x(17.3-1.73x) = 3.333333cm
y = 1/86.5 ∫1/2((17.3-1.73x)^2) = 5.7666667cm



I've done this problems like these tons of time in calc and on my homework for physics, using this same method... but according to the answers in the book I'm getting this question wrong

their answer says the x,y coordinates are (6.67cm, 11.5cm)

I'm not really sure what I'm doing wrong
Please point out any mistakes I may have made
and the right direction I should be heading in

Thank you !

 

[Villyer]

Is there an accompanying picture? The way the base and height are laid out would effect where the center is.

 

[SteamKing]

Your integral expressions are not properly written. Are you integrating with respect to x or y?

 

[jsr219]

The triangle is a right triangle
The 90 degree angle is situated at the orgin... so the height follows up the y-axis or x= o
and the base follows the x-axis at y=0... more or less the height and base make the x and y axis

I intergrating with repect to x, that's why i created an equation from the line of the hypt. of the triangle. The line/equation will make a triangle with the x and y axis... or the base and height... y intercept = height of 17.3 and x intercept = base of 10


hoped I helped in clearing up questions about my approach

 

[SteamKing]

According to the coordinates of the cg from your book, the base of the triangle is located at y = 17.3 and the other side of the triangle adjacent to the right angle is x = 10. Are you sure of the orientation of your triangle w.r.t. the origin?