What is the solution to the Center of Mass problem?

In summary, the speaker was able to find the y and z axis while trying to find the x-axis by assuming they would be the same for both slab parts. They also mentioned that the center of mass is not the center of the shape and that they know the z coordinate is the same for both. The speaker found the y value by taking the weighted average of the two components of the slab but could not figure out the x coordinate. They mentioned that they cannot think of any other reason why it wouldn't be the same for both and someone suggested proving it using symmetry or calculation. However, the speaker later realized that the homework website was showing the answer as incorrect because it was on the negative x-axis, making -7 the correct answer.
  • #1
Riman643
62
2
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.
 

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  • #2
Are you saying that the centre of mass is the geometric centre of the shape?
 
  • #3
PeroK said:
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.
 
  • #4
Riman643 said:
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.
 
  • #5
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.
 

What is the Center of Mass problem?

The Center of Mass problem, also known as the Centroid problem, is a mathematical and scientific concept that deals with finding the center point of a system or object. This can be used to analyze the distribution of mass and determine the overall balance and stability of the system or object.

Why is the Center of Mass problem important?

The Center of Mass problem is important because it allows scientists and engineers to understand and predict the behavior of systems and objects. Knowing the center of mass can help with designing structures, analyzing the stability of vehicles, and predicting how objects will move under certain conditions.

What is the formula for finding the Center of Mass?

The formula for finding the Center of Mass depends on the shape and distribution of mass in the system or object. For a continuous system, the Center of Mass can be found by using the integral calculus formula: xcm = ∫xρ(x)dx / ∫ρ(x)dx where xcm is the x-coordinate of the Center of Mass, ρ(x) is the mass density at position x, and the integrals are taken over the entire system. For a discrete system, the Center of Mass can be found by taking the sum of the individual mass points weighted by their distance from a chosen reference point.

What factors affect the Center of Mass?

The Center of Mass is affected by the distribution of mass and the geometry of the system or object. As the mass is redistributed or the shape is changed, the Center of Mass will also shift. External forces, such as gravity or external torques, can also affect the Center of Mass.

How is the Center of Mass used in real-world applications?

The Center of Mass is used in a variety of real-world applications, including engineering, physics, and sports. In engineering, it is used to design stable structures and determine the balance of vehicles. In physics, it is used to analyze motion and predict the behavior of objects. In sports, it is used to optimize performance and technique, such as in diving or gymnastics.

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