Finding z component of center of mass of a complex shape

[Ella Tankersley]

Homework Statement

The rigidly connected unit consists of a 2.5-kg circular disk, a 2.8-kg round shaft, and a 4.2-kg square plate. Determine the z-coordinate of the mass center of the unit.

Homework Equations

∑zm/∑m

The Attempt at a Solution

Circular disk:
mass = 2.5 kg
z = 0
zm = 0
Round Shaft:
mass = 2.8 kg
z = 180/2 = 90
zm = 90(2.8) = 252
Square plate:
mass = 4.2 kg
z = 0
zm = 0

Total mass = 2.5+2.8+4.2 = 9.5 kg
Total mz = 252

∑zm/∑m = 252/9.5 = 26.5 mm

 

[gneill]

The rigidly connected unit consists of a 2.5-kg circular disk, a 2.8-kg round shaft, and a 4.2-kg square plate. Determine the z-coordinate of the mass center of the unit.

I think we'll want to see a diagram or better description of the orientations, placement, and dimensions of the objects. We shouldn't have to fish about in your solution equations to find the statement of the problem.

 

[Ella Tankersley]

I think we'll want to see a diagram or better description of the orientations, placement, and dimensions of the objects. We shouldn't have to fish about in your solution equations to find the statement of the problem.

I added a diagram, can you see it?

 

[gneill]

I added a diagram, can you see it?

Ah! Much better! Thanks.

 

[gneill]

Square plate:
mass = 4.2 kg
z = 0
zm = 0

I don't understand this calculation. Why is the plate at z = 0?

 

[Ella Tankersley]

I don't understand this calculation. Why is the plate at z = 0?

I was assuming that the plate is very thin so there is no thickness in the z direction

 

[gneill]

I was assuming that the plate is very thin so there is no thickness in the z direction

What has the plate's thickness have to do with its center of mass position with respect to the xy plane?

Edit: removed spurious thought that I thought I'd removed before posting. Sorry about that.

 

[RPinPA]

I was assuming that the plate is very thin so there is no thickness in the z direction

OK, so assume the mass of the plate is all at the same z value. And that's the z coordinate of the center of mass. What is that z value?

Let me put it a different way. You figure the center of mass of the circular disk is at z = 0. Fine. Now suppose I pick the disk up, raise it 20 meters. Is its center of mass still at z = 0?