Finding z component of center of mass of a complex shape

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Homework Help Overview

The problem involves determining the z-coordinate of the center of mass for a rigidly connected unit consisting of a circular disk, a round shaft, and a square plate, with specified masses for each component.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculations for the z-coordinates of the components and question the assumptions made regarding the placement of the square plate at z = 0. There is a request for a diagram to clarify the orientations and dimensions of the objects involved.

Discussion Status

Some participants have provided clarifications and suggestions regarding the need for a diagram and the assumptions about the thickness of the square plate. There is an ongoing exploration of how the center of mass is affected by the positioning of the components.

Contextual Notes

Participants are considering the implications of the plate's thickness on its center of mass and how changes in position might affect the calculated z-coordinate.

Ella Tankersley
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Homework Statement



453786-5-63IP1.png
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
 

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Ella Tankersley said:
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.
 
gneill said:
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?
 
Ella Tankersley said:
I added a diagram, can you see it?
Ah! Much better! Thanks.
 
Ella Tankersley said:
Square plate:
mass = 4.2 kg
z = 0
zm = 0
I don't understand this calculation. Why is the plate at z = 0?
 
gneill said:
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
 
Ella Tankersley said:
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.
 
Last edited:
Ella Tankersley said:
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?
 

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