How Do You Calculate the Center of Mass for a Composite Shape?

In summary, the x and y coordinates of the center of mass for the uniform steel plate can be found using the center of mass equation, which is linear and allows the object to be treated as a point mass located at its center of mass. It is easier to consider the object as a square combined with another square of negative mass and to look at each axis separately, choosing convenient ones as reference axes. The mass will cancel out in this equation, so it is not necessary to know the mass of the object.
  • #1
kerbyjonsonjr
34
0

Homework Statement



What is the x and y coordinates of the center of mass for the uniform steel plate shown in the figure ?

Homework Equations



x=1/M [tex]\sum[/tex] x dm

The Attempt at a Solution



I am not really sure how to being this one. Mass isn't given so I am not sure where to start. I feel like this will be really easy to do but I am just not sure how to begin it. I appreciate any help. Thanks!
 

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  • #2
You won't need the mass, it will cancel out.

You didn't attach a figure.

Please show an attempt at a solution using your knowledge of your relevant equation. Look at each axis separately, and choose convenient ones as reference axes.
 
  • #3
Here are two helpful tips:

1. The center of mass equation is linear. This means that once you find the center of mass of an object, you can treat the object as a point mass located at its center of mass.

2. For this question, it's easier to consider the object as a square combined with another square of negative mass.
 

FAQ: How Do You Calculate the Center of Mass for a Composite Shape?

What is the definition of the center of mass?

The center of mass is the point in an object or system where the mass is evenly distributed in all directions. It is also known as the center of gravity.

How do you calculate the coordinates of the center of mass?

The coordinates of the center of mass can be calculated by taking the weighted average of the position of all the individual masses in the object or system. This can be done by using the formula: x_cm = (m1x1 + m2x2 +...+mnxn) / (m1 + m2 +...+mn), where x is the position in the x-axis and m is the mass.

What is the significance of the center of mass in physics?

The center of mass is an important concept in physics as it helps determine the stability, motion, and equilibrium of an object or system. It also allows for the simplification of complex systems by treating them as a single point.

Can the center of mass ever be outside of an object?

Yes, the center of mass can be outside of an object if the mass is unevenly distributed. This can occur in objects with irregular shapes or when external forces are acting on the object.

How does the center of mass change with different objects or systems?

The coordinates of the center of mass can vary depending on the distribution of mass in an object or system. For example, a symmetrical object will have its center of mass at its geometric center, while a non-symmetrical object will have its center of mass shifted towards the heavier side.

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