- #1

jisbon

- 476

- 30

- Homework Statement
- Two identical uniform triangular metal played held together by light rods. Caluclate the x coordinate of centre of mass of the two mass object. Give that mass per unit area of plate is 1.4g/cm square and total mass = 25.2g

- Relevant Equations
- -

Not sure what I went wrong here, anyone can help me out on this? Thanks.

EDIT: Reformatted my request.

Diagram:

So as far as I know to calculate the center of mass for x, I have to use the following equation:

COM(x):

##\frac{1}{M}\int x dm##

And I also figured that to find center of mass, I will have to sum the mass of the 2 plates by 'cutting' them into stripes, giving me the following formula:

##dm = \mu * dx * y## where ##\mu## is the mass per unit area.

So subbing in the above equation into the first, I get:

##\frac{1}{M}\int x (\mu * dx *y) ##

##\frac{\mu}{M}\int xy dx##

Since the 2 triangles are identical, I can assume triangle on the left has equation ##y = 1/4x +4##

This is the part where I'm not sure. Do I calculate each of the triangle's center of moment, sum them and divide by 2? Or am I suppose to use another method?

Regardless of what, supposed I am correct:

COM for right triangle:

##\frac{\mu}{M}\int_{4}^{16}x(\frac{1}{4}x+4) dx## = 8 (expected)

COM for left triangle:

##\frac{\mu}{M}\int_{-11}^{1}x(-\frac{1}{4}x+4) dx## = 5.63...

Total COM = ##8+5.63/2## which is wrong :(

Thanks

EDIT: Reformatted my request.

Diagram:

So as far as I know to calculate the center of mass for x, I have to use the following equation:

COM(x):

##\frac{1}{M}\int x dm##

And I also figured that to find center of mass, I will have to sum the mass of the 2 plates by 'cutting' them into stripes, giving me the following formula:

##dm = \mu * dx * y## where ##\mu## is the mass per unit area.

So subbing in the above equation into the first, I get:

##\frac{1}{M}\int x (\mu * dx *y) ##

##\frac{\mu}{M}\int xy dx##

Since the 2 triangles are identical, I can assume triangle on the left has equation ##y = 1/4x +4##

This is the part where I'm not sure. Do I calculate each of the triangle's center of moment, sum them and divide by 2? Or am I suppose to use another method?

Regardless of what, supposed I am correct:

COM for right triangle:

##\frac{\mu}{M}\int_{4}^{16}x(\frac{1}{4}x+4) dx## = 8 (expected)

COM for left triangle:

##\frac{\mu}{M}\int_{-11}^{1}x(-\frac{1}{4}x+4) dx## = 5.63...

Total COM = ##8+5.63/2## which is wrong :(

Thanks

Last edited: