What is the solution to the Center of Mass problem?

[Riman643]

Homework Statement

The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 3.30 cm, and d3 = 14.0 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the slab's center of mass?

Relevant Equations

Weighted Average

I was able to find the y and z axis. To find the x-axis I was assuming they would be the same for both of the slab parts and since the center of mass is the middle of the cube it should be halfway between 14.0 cm, which is 7.0cm. I can't think of any other reason why it would not be.

 

[PeroK]

Are you saying that the centre of mass is the geometric centre of the shape?

 

[Riman643]

Are you saying that the centre of mass is the geometric centre of the shape?

No the center of mass is not the center of the shape. I know the z coordinate is the same for both. I found the y value by taking the weighted average of the two components of the slab. I just cannot figure out what the x coordinate is. I can't think why it wouldn't be the same for both.

 

[PeroK]

No the center of mass is not the center of the shape. I know the z coordinate is the same for both. I found the y value by taking the weighted average of the two components of the slab. I just cannot figure out what the x coordinate is. I can't think why it wouldn't be the same for both.

Okay, although I'm not sure why there would be any doubt. You could prove it using symmetry or calculation.

 

[Riman643]

Haha, I figured out my problem. The homework website was showing 7 as wrong because it is on the negative x-axis making it -7 as the right answer.