Find Center of Mass: Calculate x,y Coordinates with R = sum(m*r)/sum(m)

In summary, the problem involves finding the coordinate (x,y) of the center of mass of an object with two parts, A and B, with densities of p (kg/m^3) and p/2 (kg/m^3) respectively. The object has a length of one meter in the z direction. To solve this problem, it is suggested to break it down into three rectangles, calculate the mass and center of mass of each, and then find the overall center of mass of the object. This is a 2D problem, not a 3D one, and the solution can be found by considering the three masses as point masses at their respective centers of mass.
  • #1
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1. The density of part A (p)(kg/m^3) and in part B (p/2)(kg/m^3). Find the coordinate (x,y) of the center of mass of this object.

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(consider a piece of the object that is one meter in the z direction)

2. R = sum(m*r) / sum(m)...maybe? I am completely stumped on how to start this problem my teacher has done no sample problems that are anything like this, not even anything in 3D, if anyone could at least provide a hint to get me started on this one? Would be greatly appreciated.
 
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  • #2
This isn't a 3d problem, it's a 2d problem and he only wants [itex](\overline x,\overline y)[/itex] Break it up into three rectangles, find the mass and center of mass of each. Then find the center of mass of the three masses as if they were point masses at their centers of mass.
 
  • #3
Awesome, thanks a ton for helping me get started!
 

1. What is the "Find Center of Mass" equation and how does it work?

The "Find Center of Mass" equation is used to calculate the x and y coordinates of the center of mass of a system. It works by taking the sum of the mass of each object in the system multiplied by its distance from a chosen origin point, and then dividing that by the sum of the masses of all the objects.

2. Why is it important to find the center of mass in a system?

Finding the center of mass is important because it can help determine the overall balance and stability of a system. It is also a crucial factor in understanding the motion and interactions of objects within a system.

3. How is the center of mass related to the concept of inertia?

The center of mass is related to inertia because it is the point at which the entire mass of a system can be considered to be concentrated. This means that the center of mass is also the point at which the system's inertia is located, and thus plays a role in determining the system's resistance to changes in motion.

4. Can the "Find Center of Mass" equation be used for any type of system?

Yes, the "Find Center of Mass" equation can be used for any type of system, as long as the mass and distance of each object in the system can be measured or calculated.

5. How can the "Find Center of Mass" equation be applied in real-life situations?

The "Find Center of Mass" equation can be applied in various real-life situations, such as determining the balance of a seesaw or understanding the stability of a building's structure. It is also commonly used in physics and engineering to analyze the motion and interactions of objects in a system.

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