Center of mass of two metal solids.

[chenying]

Homework Statement

Figure 7-29 shows a composite slab with dimensions 22.0 cm multiplied by 13.0 cm multiplied by 2.8 cm. Half of the slab is made of aluminum (density = 2.70 g/cm3) and half of iron (density = 7.85 g/cm3), as shown. How far from the line joining the two metals is the center of mass of the slab

Homework Equations

Center of mass equations: (\SigmaX*r)/M

M = total mass

The Attempt at a Solution

So, since there are two slabs of metal connected to each other, I first found the center of mass of each metal and then found the center of mass of both together.

Using common sense and the assumption that the density is uniform, the center of masses for each block would be in the exact middle of the metals.

I made my origin for the coordinate system at the bottom left vertex of the the iron part of the slab, where x=0, y=0, and z=0.

For iron, I obtained the (x,y,z) coordinates of (5.5, 6.5, 1.4)

and aluminum (x,y,z) coordinates of (16.5, 6.5, 1.4)

now, I want to find r_{}cm, which i did by squaring all the values, added them together, and the found the square root of that sum:

Iron: r_{}cm: 8.62902
Aluminum: r_{}cm: 17.7893

I found the mass by finding half the volume of the slab, and multiplying each density by half that volume.

so, no i use the center of mass equation, (\SigmaX*r)/M, and get a value of 10.9734 centimeters

Now, to find how far it is from the line, I made a triangle, where 11-10.9734 and 1.4 are my legs, and the hypotenuse is the distance. Using the theorem, i get an answer of:

1.40025 centimeters

Answer does not seem right, so I'm wondering what I might have done wrong?

 

[Delphi51]

The y and z parts are obvious, so just do the x:
sum of (m*r)/(sum of masses)
x = (massOfIron*5.5 + massOfAl*16.5)/(total mass)

 

[chenying]

The y and z parts are obvious, so just do the x:
sum of (m*r)/(sum of masses)
x = (massOfIron*5.5 + massOfAl*16.5)/(total mass)

Why are the y and z parts obvious?

 

[chenying]

Nevermind i got it. Thanks for your help!